HYPERSPECTRAL IMAGING-BASED SPATIALLY-RESOLVED TECHNIQUE FOR
ACCURATE MEASUREMENT OF THE OPTICAL PROPERTIES OF
HORTICULTRAL PRODUCTS
By
Haiyan Cen

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of
DOCTOR OF PHILOSOPHY
Biosystems Engineering
2011

ABSTRACT
HYPERSPECTRAL IMAGING-BASED SPATIALLY-RESOLVED TECHNIQUE FOR
ACCURATE MEASUREMENT OF THE OPTICAL PROPERTIES OF HORTICULTRAL
PRODUCTS
By
Haiyan Cen
Hyperspectral imaging-based spatially-resolved technique is promising for determining the
optical properties and quality attributes of horticultural and food products. However,
considerable challenges still exist for accurate determination of spectral absorption and scattering
properties from intact horticultural products. The objective of this research was, therefore, to
develop and optimize hyperspectral imaging-based spatially-resolved technique for accurate
measurement of the optical properties of horticultural products. Monte Carlo (MC) simulations
and experiments for model samples of known optical properties were performed to optimize the
inverse algorithm of a single-layer diffusion model and the optical designs, for extracting the
absorption (µa) and reduced scattering (µs') coefficients from spatially-resolved reflectance
profiles. The logarithm and integral data transformation and the relative weighting methods were
found to greatly improve the parameter estimation accuracy with the relative errors of 10.4%,
10.7%, and 11.4% for µa, and 6.6%, 7.0%, and 7.1% for µs', respectively. More accurate
measurements of optical properties were obtained when the light beam was of Gaussian type
with the diameter of less than 1 mm, and the minimum and maximum source-detector distances
were 1.5 mm and 10-20 transport mean free paths, respectively.
An optical property measuring prototype was built based on the optimization results. The
instrument was used to measure the optical properties, and assess quality/maturity, of 500
‘Redstar’ peaches and 1039 ‘Golden Delicious’ (GD) and 1040 ‘Delicious’ (RD) apples. A

separate study was also conducted on confocal laser scanning and scanning electron microscopic
image analysis and compression test of fruit tissue specimens to measure the structural and
mechanical properties of GD and ‘Granny Smith’ (GS) apples under accelerated softening at
high temperature (22 ºC)/high humidity (95%) for up to 30 days. The absorption spectra of peach
and apple fruit were featured with the absorption peaks of major pigments (i.e., chlorophylls and
anthocyanin) and water, while the reduced scattering coefficient generally decreased with the
increase of wavelength. Partial least squares regression resulted in various levels of correlation of
µa and µs' with the firmness, soluble solids content, and skin and flesh color parameters of
peaches (r = 0.204-0.855) and apples (r = 0.460-0.885), and the combination of the two optical
parameters generally gave higher correlations (up to 0.893). The mean value of µa and µs' for
GD and GS apples for each storage date was positively correlated with acoustic/impact firmness,
Young’s modulus, and cell parameters (r = 0.585-0.948 for GD and r = 0.292-0.993 for GS).
A two-layer diffusion model for determining the optical properties of fruit skin and flesh
was further investigated through solid model samples. The average errors of determining two and
four optical parameters were 6.8% and 15.3%, respectively, for MC reflectance data. The errors
of determining the first layer of model samples were approximately 23.0% for µa and 18.4% for
µs', indicating the difficulty and also potential in applying the two-layer diffusion model for fruit.
This research has demonstrated the usefulness of hyperspectral imaging-based spatiallyresolved technique for determining the optical properties and maturity/quality of fruits. However,
further research is needed to reduce measurement variability or error caused by irregular or
rough surface of fruit and the presence of fruit skin, and apply the technique to other foods and
biological materials.

This work is dedicated to my husband Dahai Gao and my son Nicholas Jiatong Gao

iv 
 

ACKNOWLEDGMENTS
I could not have reached the height in my life without tremendous help and support from the
others. I sincerely thank my advisor and major professor, Dr. Renfu Lu, for his guidance,
encouragement, understanding, patience, and friendship throughout my Ph.D. study at Michigan
State University, which was essential to the completion of this research. I would also like to
warmly thank my committee members, Dr. Daniel E. Guyer, co-advisor, for his help on my
course and research work and valuable comments on improvement of my presentation skills, and
Dr. Randolph Beaudry and Dr. Lalita Udpa for their time and enormously helpful advice on my
research project.
My thanks also go to my talented colleagues and friends  Dr. Diwan P. Ariana, Dr.
Fernando Mendoza, Dr. Akira Mizushima, Mr. Benjamin Bailey, Mr. Irwin Donis Gonzalez, and
Mr. Ahmed Rady  for their help, support and advice in my Ph.D. project. In particular, I would
like to acknowledge Dr. Diwan P. Ariana and Mr. Benjamin Bailey for their significant
contributions to the development of the optical property measuring instrument, and Dr. Fernando
Mendoza for his help on image analysis. I am also grateful to Dr. Kirk Dolan and Dr. James V.
Beck for their contributions in solving inverse light transport problems. I especially would like to
thank Dr. Fred W. Bakker-Arkema, Dr. James F. Steffe, and Dr. Ajit K. Srivastava for their help
during my Ph.D. study at Michigan State University. I also thank the Department of Biosystems
and Agricultural Engineering and the College of Agriculture and Natural Resources for
providing me with a fellowship to complete this dissertation.
Last but not least, I would like to thank my husband Dahai Gao for his intellectual help,
moral support, and deep love. My deepest gratitude and love go to my parents, Qingmiao Cen,

v 
 

and Meidi Tu, for their dedication and the many years of support during my study. Thanks also
go to my parents-in-law, Feng Gao and Yang Yang, and my sister, Jie Cen.

vi 
 

TABLE OF CONTENTS
LIST OF TABLES .........................................................................................................................x 
LIST OF FIGURES .................................................................................................................... xii 
KEY TO SYMBOLS OR ABBREVIATIONS ...................................................................... xviii 
CHAPTER 1 

INTRODUCTION ............................................................................................1 

1.1  Background .......................................................................................................................1 
1.2  Objectives ..........................................................................................................................6 
CHAPTER 2 

LITERATURE REVIEW ................................................................................7 

2.1  Principles of Light Interaction with Biological Materials .................................................7 
2.1.1  Absorption Coefficient...............................................................................................7 
2.1.2  Scattering Coefficient ................................................................................................9 
2.1.3  Anisotropy Factor ......................................................................................................9 
2.1.4  Reduced Scattering Coefficient ...............................................................................10 
2.1.5  Refractive Index .......................................................................................................11 
2.2  Modeling of Light Transport in Tissues ..........................................................................12 
2.2.1  Radiation Transport Model ......................................................................................12 
2.2.2  Diffusion Model .......................................................................................................14 
2.2.3  Adding-doubling Model...........................................................................................15 
2.2.4  Monte Carlo Simulation ...........................................................................................17 
2.3  Techniques for Measuring Optical Properties of Biological Materials...........................19 
2.3.1  Time-resolved Technique ........................................................................................19 
2.3.2  Frequency-domain Technique .................................................................................22 
2.3.3  Spatially-resolved Technique...................................................................................25 
2.4  Approaches to Inverse Problems for Determining Optical Parameters ..........................31 
2.4.1  Sensitivity Analysis .................................................................................................31 
2.4.2  Inverse Algorithm ....................................................................................................32 
2.4.3  Data Transformation and Weighting Methods ........................................................33 
2.5  Nondestructive Techniques for Measurement of Maturity and Quality .........................36 
2.5.1  Maturity and Quality of Fruits .................................................................................36 
2.5.2  Mechanical Techniques ...........................................................................................38 
2.5.3  Optical Techniques ..................................................................................................40 
CHAPTER 3  OPTIMIZATION OF INVERSE ALGORITHM FOR ESTIMATING
OPTICAL PROPERTIES OF BIOLOGICAL MATERIALS ................................................46 
3.1  Introduction .....................................................................................................................46 
3.2  Forward Problem .............................................................................................................48 
3.2.1  One-layer Diffusion Model for the Steady-state Case .............................................48 
3.2.2  Monte Carlo Simulation ...........................................................................................49 
3.3  Inverse Problem...............................................................................................................50 
3.3.1  Nonlinear Least Squares Inverse Algorithm ............................................................50 
vii 
 

3.3.2  Data Transformation and Weighting Methods ........................................................51 
3.3.3  Sensitivity Analysis .................................................................................................51 
3.3.4  Statistical Analysis and Model Assessment .............................................................52 
3.4  Simulation Experiments ..................................................................................................53 
3.5  Results and Discussion ....................................................................................................55 
3.5.1  Comparison between the Diffusion Model and Monte Carlo Simulations ..............55 
3.5.2  Sensitivity Coefficients ............................................................................................57 
3.5.3  Estimation of Optical Parameters based on Monte Carlo Simulation Data .............60 
3.5.4  Statistical Analysis ...................................................................................................63 
3.6  Conclusions .....................................................................................................................68 
CHAPTER 4  OPTIMIZATION OF THE HYPERSPECTRAL IMAGING-BASED
SPATIALLY-RESOLVED SYSTEM ........................................................................................70 
4.1  Introduction .....................................................................................................................70 
4.2  Materials and Methods ....................................................................................................72 
4.2.1  Hyperspectral Imaging-based Spatially-resolved Technique ..................................72 
4.2.2  Model Samples Preparation .....................................................................................75 
4.2.3  Reference Methods ..................................................................................................76 
4.2.4  Optimization of the Light Beam and Source-detector Distance ..............................80 
4.2.5  Assessment for Accuracy, Precision/Reproducibility, and Sensitivity ....................82 
4.3  Results and Discussion ....................................................................................................83 
4.3.1  Accuracy of the Reference Methods ........................................................................83 
4.3.2  Light Beam Characteristics ......................................................................................85 
4.3.3  Source-detector Distance .........................................................................................89 
4.3.4  Accuracy, Precision/Reproducibility, and Sensitivity .............................................94 
4.4  Conclusions ...................................................................................................................100 
CHAPTER 5  DEVELOPMENT OF AN OPTICAL PROPERTY MEASUREMENT
PROTOTYPE…………….........................................................................................................101 
5.1  Introduction ...................................................................................................................101 
5.2  System Setup and Software Development ....................................................................102 
5.2.1  Optical Property Analyzer Setup ...........................................................................102 
5.2.2  Optical Property Analyzer Software Development ...............................................105 
5.3  System Calibration and Evaluation ...............................................................................110 
CHAPTER 6  MATURITY/QUALITY ASSESSMENT FOR APPLE AND PEACH
FRUIT USING OPTICAL PROPERTIES..............................................................................114 
6.1  Introduction ...................................................................................................................114 
6.2  Materials and Methods ..................................................................................................115 
6.2.1  Fruit Samples .........................................................................................................115 
6.2.2  Optical Properties Measurement ............................................................................116 
6.2.3  Acoustic Measurement...........................................................................................118 
6.2.4  Destructive Maturity/Quality Measurement ..........................................................119 
6.2.5  Data Analysis .........................................................................................................120 
6.3  Results and Discussion ..................................................................................................121 
viii 
 

6.3.1  Statistical Data of Fruit Maturity/Quality ..............................................................121 
6.3.2  Peach Maturity/Quality Evaluation........................................................................123 
6.3.3  Apple Internal Quality Evaluation .........................................................................131 
6.4  Conclusions ...................................................................................................................135 
CHAPTER 7  RELATIONSHIP
BETWEEN
THE
OPTICAL
AND
MECHANICAL/STRUCTURAL PROPERTIES OF APPLE TISSUE ..............................137 
7.1  Introduction ...................................................................................................................137 
7.2  Materials and Methods ..................................................................................................138 
7.2.1  Apple Samples .......................................................................................................138 
7.2.2  Optical Properties Measurement ............................................................................139 
7.2.3  Acoustic Firmness Measurement and Compression Test for Measuring Mechanical
Properties .........................................................................................................................139 
7.2.4  Confocal Laser Scanning Microscopy and Scanning Electron Microscopy for
Microstructural Analysis ..................................................................................................141 
7.2.5  Data Analysis .........................................................................................................142 
7.3  Results and Discussion ..................................................................................................146 
7.3.1  Changes in the Optical Properties of Apples during Storage ................................146 
7.3.2  Changes in Acoustic Firmness and Mechanical Properties during Storage ..........149 
7.3.3  Microstructural Changes in Apple Tissue during Storage .....................................152 
7.3.4  Correlations between Optical Properties and Mechanical/Structural Properties ...159 
7.4  Conclusions ...................................................................................................................162 
CHAPTER 8  DETERMINATION OF THE OPTICAL PROPERTIES OF TWOLAYER TURBID MATEIRALS ..............................................................................................164 
8.1  Introduction ...................................................................................................................164 
8.2  Materials and Methods ..................................................................................................165 
8.2.1  Two-layer Diffusion Model ...................................................................................165 
8.2.2  Model Samples Preparation and Measurement......................................................167 
8.3  Validation of the Two-layer Diffusion Model and Inverse Algorithm .........................168 
8.4  Results and Discussion ..................................................................................................170 
8.4.1  Monte Carlo Simulations of Spatially-resolved Diffuse Reflectance ....................170 
8.4.2  Sensitivity Coefficient Analysis ............................................................................171 
8.4.3  Extraction of Optical Properties from Monte Carlo Simulation Data ...................174 
8.4.4  Optical Properties of Model Samples Measured with Integrating Sphere .............178 
8.4.5  Optical Properties of Model Samples Determined from Hyperspectral Imaging
Measurements ..................................................................................................................179 
8.5  Conclusions ...................................................................................................................182 
CONCLUSION AND FUTURE RESEARCH ........................................................................184 
BIBLIOGRAPHY ......................................................................................................................189 

ix 
 

LIST OF TABLES
Table 2.1 Summary of the performance of time-resolved, frequency-domain and spatiallyresolved measurements (TS: time-resolved, FD: frequency-domain, SR: spatiallyresolved, POM: polyoxymethylene). .......................................................................... 29 
Table 3.1 Thirty-six combinations of the absorption (µa) and reduced scattering coefficients (µs')
and their corresponding transport mean free path ( mfp' ) used in Monte Carlo
-1

simulations (unit: cm for µa & µs', and mm for mfp'). ............................................ 54 
Table 3.2 Statistical results for estimating the optical parameters using the LTDM method. ..... 67 
Table 5.1 Components of the Optical Property Analyzer control software. ............................... 106 
Table 6.1 Statistics of fruit maturity/quality parameters for 500 ‘Redstar’ peaches measured by
standard methods. ..................................................................................................... 122 
Table 6.2 Statistics of the firmness (i.e., maximum Magness-Taylor force or FM) and soluble
solids content (SSC) of ‘Golden Delicious’ (GD) and ‘Delicious’ (RD) apples for the
freshly harvested, after-storage, and combined groups. ........................................... 123 
Table 6.3 Partial least squares (PLS) prediction results of ‘Redstar’ peach maturity/quality
parameters using absorption coefficient (µa), reduced scattering coefficient (µs') and
their three combinations (µa & µs', µa × µs', and µeff).* .......................................... 129 
Table 6.4 Firmness prediction results for ‘Golden Delicious’ and ‘Delicious’ apples for the
freshly harvested, after-storage and combined groups.* .......................................... 132 
Table 6.5 Prediction results for the soluble solids content of ‘Golden Delicious’ and ‘Delicious’
apples for the freshly harvested, after-storage and combined groups.* .................... 133 
Table 7.1 Mean and standard error of the cell size/shape parameters for ‘Golden Delicious’ and
‘Granny Smith’ apple tissues for different storage days.* ........................................ 154 
Table 7.2 Morphological features extracted from the scanning electron microscopic (SEM)
images acquired at the low resolution for ‘Golden Delicious’ and ‘Granny Smith’
apple tissues.* ........................................................................................................... 158 
Table 7.3 Correlations of selected optical parameters with acoustic and impact firmness and
Young’s modulus for ‘Golden Delicious’ and ‘Granny Smith’ apples.* ................. 160 
Table 7.4 Correlations of optical parameters with the cell size parameters extracted from the
confocal laser scanning microscopic images of ‘Golden Delicious’ and ‘Granny
Smith’ apples. ........................................................................................................... 161 
x 
 

Table 7.5 Correlation of optical parameters with the fractal analysis parameters extracted from
the scanning electron microscopic images of ‘Golden Delicious’ and ‘Granny Smith’
apples. ....................................................................................................................... 161 
Table 8.1 Optical properties of two two-layer model samples at the wavelengths of 535 nm and
700 nm determined by the integrating sphere and the adding-doubling method (Prahl
et al., 1993). .............................................................................................................. 179 

xi 
 

LIST OF FIGURES
Figure 2.1 Light interaction with matter: (a) absorption, (b) scattering, (c) scattering event with
anisotropy factor g, and (d) refraction (For interpretation of the references to color in
this and all other figures, the reader is referred to the electronic version of this
dissertation). .................................................................................................................. 8 
Figure 2.2 Light incident at an angle v that is reflected and transmitted by a slab at an angle v ' in
the adding-doubling method (Welch and van Gemert, 1995)..................................... 17 
Figure 2.3 Measurement principle of (a) time-resolved and (b) frequency-domain techniques. . 20 
Figure 2.4 Measurement principle for spatially-resolved technique. ........................................... 26 
Figure 2.5 Force/deformation (F/D) curves for cylindrical tissue specimens from firm and soft
apples under constant strain-rate (0.42 mm/s) compression (Abbott, 1999). ............. 39 
Figure 2.6 Diagram of the whole electromagnetic spectrum (Mohsenin, 1984). ......................... 41 
Figure 2.7 Three different modes for NIR spectroscopic measurements: a) reflectance, b)
transmittance and c) interactance. ............................................................................... 42 
Figure 3.1 Comparison of the spatially-resolved diffuse reflectance obtained from the diffusion
model (symbols) and Monte Carlo simulation (solid lines): (a) µs'/ µa = 5, and (b) µs'/
µa = 100. ..................................................................................................................... 56 
-1

-

Figure 3.2 Scaled sensitivity coefficients of the optical parameters [µa = 0.06 cm & µs' = 4 cm
1

-1

-1

for the left pane of plots (a1, b1, c1, d1), and µa = 0.57 cm & µs' = 40 cm for the
right pane of plots (a2, b2, c2, d2)] as functions of the source-detector distance for
ODM (a1, a2), LTDM (b1, b2), ITDM (c1, c2), and RWDM (d1, d2). Solid curves
are for R, dash curves for µa and dot curves for µs' (a.u. = arbitrary unit)................. 58 
Figure 3.3 Relative errors of estimating 29 groups of µa (a) and µs' (b) shown in Table 3.1 by the
original model, and the data transformation and relative weighting methods: ODM (·),
LTDM (◦), ITDM (*) and RWDM (∆). ...................................................................... 61 
Figure 3.4 Absolute values of the relative errors of estimating the optical properties (µa = 0.40
-1

-1

cm , µs' = 20 cm ) for different noise levels (each noise level includes 10
replications). Solid circles represent the absorption coefficient, while open circles are
for the reduced scattering coefficient. ......................................................................... 63 
Figure 3.5 Residual plots for the reflectance data versus source-detector distances from (a) ODM,
-1
-1
(b) LTDM, (c) ITDM, and (d) RWDM with µa = 0.06 cm & µs' = 4 cm (dot curve)
-1

-1

and µa = 0.57 cm & µs' = 40 cm (asterisk curve). ................................................. 64 
xii 
 

Figure 3.6 Residual histograms for the reflectance data from ODM (a), LTDM (b), ITDM (c),
-1
-1
and RWDM (d) with 1) µa = 0.06 cm & µs' = 4 cm for the left pane of plots (a1,
-1

-1

b1, c1, d1), and 2) µa = 0.57 cm & µs' = 40 cm for the right pane of plots (a2, b2,
c2, d2). ........................................................................................................................ 65 
Figure 3.7 3-D plot of sum of squares for (a) group 25 and (b) group 30 using the LTDM method.
..................................................................................................................................... 67 
Figure 4.1 Hyperspectral imaging-based spatially-resolved method: (a) schematic showing the
major components of the system; (b) top view of multi-line scanning mode for
acquiring spatially-resolved reflectance profiles. ....................................................... 73 
Figure 4.2 Hyperspectral reflectance image of a liquid model sample: (a) 2-dimensional (2-D)
display with intensities being indicated by pseudo colors, and (b) original spatiallyresolved reflectance profiles at 570 nm and 700 nm. ................................................. 75 
Figure 4.3 Collimated transmittance measurement for absorption using a miniature fiber optic
spectrometer. ............................................................................................................... 77 
Figure 4.4 Single integrating sphere configurations for: (a) total diffuse reflectance measurement,
and (b) total transmittance measurement. ................................................................... 78 
Figure 4.5 Spectra of the absorption coefficient for the three standard solutions measured by the
transmittance method [asterisks () for standard 0.1, triangles () for standard 0.5,
and squares () for standard 0.8] and their true vlaues (solid lines). ........................ 84 
Figure 4.6 Average differences of the reduced scattering coefficient for the model samples at
different concentrations of Intralipid for 500-900 nm obtained from the integrating
sphere measurement and the empirical equation. ....................................................... 85 
Figure 4.7 Comparison of spatially-resolved reflectance produced by an infinitely small beam, a
flat beam with diameter of d = 1 mm, and a Gaussian beam with d = 1 and 2 mm. .. 87 
Figure 4.8 Error analysis for different beam sizes: (a) average errors of estimating six sets of
-1
-1
optical properties with 0.060 ≤ µa ≤ 2.000 cm and 4.0 ≤ µs' ≤40.0 cm , and the
ratios of µs'/µa = 20 and µs'/µa = 70; and (b) and (c) relative errors for three sets of
optical properties with increased µa and µs' from A to C with µa = 0.006, 0.029, 0.057
-1

-1

cm and µs' = 0.4, 2.0, 4.0 cm . ............................................................................... 87 
Figure 4.9 three-dimensional profiles (a and b) and 2-dimensional (c and d) contours of the
incident light beam at wavelengths of 650 nm and 950 nm, where D1 is the direction
along the scan line and D2 is perpendicular to the scan line. ..................................... 89 
Figure 4.10 Relative errors of estimating µa (squares) and µs' (asterisks) from the spatiallyresolved reflectance data generated by Monte Carlo simulations when using different
xiii 
 

-1

minimum and maximum source-detector distances: (a1) and (b1) µa = 0.290 cm
-1

-1

-1

&

µs' = 20.0 cm , and (a2) and (b2) µa = 0.430 cm & µs' = 30.0 cm . .................... 90 
Figure 4.11 Signal-to-noise ratio measurement of the hyperspectral imaging system: (a) average
spatially-resolved reflectance profile of 10 measurements of a model sample at 650
nm, and (b) signal-to-noise ratio of the measurements within 10 mm source-detector
distance. ...................................................................................................................... 92 
-1

-1

Figure 4.12 Errors of estimating µa = 1.00 cm and µs' = 20.0 cm introduced by different
spatial resolutions relative to the optical properties obtained for the resolution of 0.01
mm. ............................................................................................................................. 93 
Figure 4.13 Spectra of absorption and reduced scattering coefficients of three model samples
with (a) blue dye, (b) green dye, and (c) mixed dye as absorbers measured by the
hyperspectral imaging and reference methods............................................................ 95 
Figure 4.14 Confocal laser scanning microscopy images of Intralipid solutions with (a) blue dye,
and (b) green dye. ....................................................................................................... 97 
Figure 4.15 Coefficient of variation versus reordered ascending absorption coefficients of a
model sample at different wavelengths....................................................................... 99 
Figure 5.1 Optical Property Analyzer (or OPA) for measuring optical properties and acquiring
hyperspectral images................................................................................................. 102 
Figure 5.2 Schematic of the Optical Property Analyzer (or OPA) for measuring the optical
properties of biological materials.............................................................................. 103 
Figure 5.3 Main window of the Optical Property Analyzer software......................................... 107 
Figure 5.4 Display window of the Optical Property Analyzer for the image acquisition setup. 108 
Figure 5.5 Display window of the Optical Property Analyzer for optical properties computation.
................................................................................................................................... 109 
Figure 5.6 Display windows of the Optical Property Analyzer for (a) calibration information and
(b) sample size information. ..................................................................................... 110 
Figure 5.7 Reproducibility of the Optical Property Analyzer for measuring absorption and
reduced scattering coefficients of a model sample at 555 nm at each measurement day
with respect to the average value calculated over 5 days. ........................................ 112 
Figure 5.8 Coefficient of variation versus reordered ascending absorption coefficients of a model
sample at different wavelengths................................................................................ 113 
Figure 6.1 Hyperspectral reflectance image and optical property spectra of a peach sample: (a) 2D display of the original reflectance image, (b) a raw spectrum extracted for a
xiv 
 

specific scattering distance, (c) a spatially-resolved reflectance profile extracted for a
selected wavelength, (d) pre-processed or averaged spatially-resolved reflectance
profile at the selected wavelength, (e) the spectrum of absorption coefficient (µa), and
(f) the spectrum of reduced scattering coefficient (µs'). ........................................... 117 
Figure 6.2 Spectra of (a) absorption coefficient for three peaches with different skin colors (light
red, red, dark red), and of (b) reduced scattering coefficient for three peaches at
different firmness levels (hard, medium, soft). ......................................................... 124 
Figure 6.3 Distributions of (a) absorption (µa) and (b) reduced scattering coefficient (µs') for 500
‘Redstar’ peaches at four wavelengths (525 nm for anthocyanin, 620 nm for
chlorophyll-b, 675 nm for chlorophyll-a, and 970 nm for water). ........................... 127 
Figure 6.4 (a) Prediction of Magness-Taylor (MT) firmness (FM) of ‘Redstar’ peaches using
effective attenuation coefficient (µeff) with partial least squares (PLS) and (b)
correlation between acoustic data and MT firmness (FM)....................................... 130 
Figure 6.5 Spectra of (a) absorption and (b) reduced scattering coefficients for four ‘Golden
Delicious’ (GD) apples and four ‘Delicious’ (RD) apples. ...................................... 131 
Figure 6.6 Prediction of fruit firmness (a, c) and soluble solids content or SSC (b, d) using the
best combinations of µa and µs' for the combined group of ‘Golden Delicious’ (GD)
and ‘Delicious’ (RD) apples. .................................................................................... 134 
Figure 7.1 Experimental procedures for compression test of apple tissue specimens: (a)
cylindrical specimen taken from the fruit flesh of the apple; (b) cork borer and
double-blade knife used for cutting tissue specimens; (c) final tissue specimen with
13.9 × 13 mm (D × L); and (d) compression test setup with the Texture Analyzer. 140 
Figure 7.2 Procedures of image processing for extracting cell parameters. ............................... 143 
Figure 7.3 Mean spectra of 10 apple samples each for the five times of storage: (a1) absorption
and (a2) reduced scattering coefficients of ‘Golden Delicious’ (GD) apples; and (b1)
absorption and (b2) reduced scattering coefficients of ‘Granny Smith’ (GS) apples.
................................................................................................................................... 147 
Figure 7.4 Changes in a) acoustic firmness (FI) and impact firmness (IF), and (b) fruit weight,
for the same 10 fruit each of ‘Golden Delicious’ (GD) and ‘Granny Smith’ (GS)
measured at five storage times (the vertical bars denote two standard deviations). . 150 
Figure 7.5 Stress/strain curves obtained from the compression test for the flesh specimens of (a)
five ‘Golden Delicious’ apples and (b) five ‘Granny Smith’ apples, one for each
storage time. .............................................................................................................. 150 
Figure 7.6 Mean values of Young’s modulus for 10 ‘Golden Delicious’ (GD) (columns with
capital letters) and ‘Granny Smith’ (columns with small-cap letters) apples for each of
xv 
 

the five storage times (columns with different letters for the same cultivar are
significantly different with p < 0.05). ....................................................................... 151 
Figure 7.7 Confocal laser scanning microscopic images of a cross-section of apple flesh tissue 10
mm beneath the skin for ‘Golden Delicious’ apple at day 1 (a1) and day 30 (a2), and
for ‘Granny Smith’ apple at day 1 (b1) and day 30 (b2) ( ‘ → ’ denotes the
connection between cells, and ‘×’ denotes the broken cells). ............................ 152 
Figure 7.8 Scanning electron microscopy images of one cross-section of apple flesh tissue 10
mm beneath the skin for ‘Golden Delicious’ at day 1 (a1) and day 30 (a2) acquired at
low resolution for an overview of the cell structures, and at day 1 (b1) and day 30 (b2)
acquired at high resolution for a more detailed view of the cell-to-cell connection [the
red lines in (a1) denotes five cell connections counted manually as examples]. ...... 156 
Figure 7.9 Scanning electron microscopy images of one cross-section of apple flesh tissue 10
mm beneath the skin for ‘Granny Smith’ at day 1 (a1) and day 30 (a2) acquired at low
resolution for an overview of the cell structures, and at day 1 (b1) and day 30 (b2)
acquired at high resolution for a more detailed view of the cell-to-cell connection [the
red lines in (a1) denote five cell connections counted manually as examples]. ....... 157 
Figure 8.1 Comparison of spatially-resolved diffuse reflectance obtained from the two-layer
diffusion model (symbols) and Monte Carlo simulations (solid lines): (a) µa1/µa2 =
0.50 and µs1'/µs2' = 0.86 (0.05, 12, 0.10, 14, 1), (b) µa1/µa2 = 6.50 and µs1'/µs2' =
1.80(2.60, 36, 0.40, 20, 0.5), (c) µa1/µa2 = 0.80 and µs1'/µs2' = 1.58 (0.32, 19, 0.40,
12, 1), and (d) µa1/µa2 = 2 and µs1'/µs2' = 0.75 (1.00, 15, 0.50, 20, 1). Values in the
-1

parentheses are µa1, µs1', µa2, µs2', d with the units of cm for optical properties and
mm for the thickness of the first layer. ..................................................................... 171 
Figure 8.2 Scaled sensitivity coefficients as functions of source-detector distances for four
combinations of optical properties (a) µa1/µa2 = 0.50 and µs1'/µs2' = 0.86 (0.05, 12,
0.10, 14, 1), (b) µa1/µa2 = 6.50 and µs1'/µs2' = 1.80 (2.60, 36, 0.40, 20, 0.5), (c)
µa1/µa2 = 0.80 and µs1'/µs2' = 1.58 (0.32, 19, 0.40, 12, 1), and (d) µa1/µa2 = 2 and
µs1'/µs2' = 0.75 (1.00, 15, 0.50, 20, 1), and the values in the bracket are µa1, µs1', µa2,
-1

µs2', d with the unit cm for optical properties and mm for the thickness of the first
layer (‘-’, ‘·’, ‘+’, ‘ₒ’, and ‘∆’denote reflectance, and scaled sensitivity coefficients of
µa1, µs1', µa2, and µs2', respectively)........................................................................ 172 
Figure 8.3 Scaled sensitivity coefficients as functions of source-detector distances for µa1 = 0.05
-1

-1

-1

-1

cm , µs1' = 12 cm , µa2 = 0.10 cm , µs2' = 14 cm , and the thickness of the first
layer: (a) d = 0.85 mm, (b) d = 2 mm, (c) d = 4 mm, and (d) d = 6 mm (‘-’, ‘·’, ‘+’, ‘ₒ’,
and ‘∆’denote reflectance, and scaled sensitivity coefficients of µa1, µs1', µa2, and
µs2', respectively). ..................................................................................................... 173 
xvi 
 

Figure 8.4 Estimated absorption and reduced scattering coefficients of the first layer from fitting
the diffusion model to the Monte Carlo simulation data: (a) µa1 varies 0.20 - 1.20 cm
1

-1

-1

-1

with µs1' = 12 cm , µa2 = 0.50 cm , µs2' = 11 cm , and d = 2 mm, and (b) µs1'
-1
-1
-1
varies 15-45 cm-1 with µa1= 0.10 cm , µa2 = 0.05 cm , µs2' = 11 cm , and d = 2
mm. ........................................................................................................................... 175 

Figure 8.5 Relative errors of estimating the optical properties of two layers from the Monte Carlo
diffuse reflectance for four combination sets of optical properties: µa1/µa2 = 0.50 and
µs1'/µs2' = 0.86 (0.05, 12, 0.10, 14, 1), µa1/µa2 = 6.50 and µs1'/µs2' = 1.80 (2.60, 36,
0.40, 20, 0.5), µa1/µa2 = 0.80 and µs1'/µs2' = 1.58 (0.32, 19, 0.40, 12, 1), and µa1/µa2
= 2 and µs1'/µs2' = 0.75 (1.00, 15, 0.50, 20, 1). Values in the parentheses are µa1, µs1',
-1

µa2, µs2', d with the units of cm for optical properties and mm for the thickness of
the first layer. ............................................................................................................ 177 
Figure 8.6 Absorption and reduced scattering spectra of the homogenous model disk samples
measured by the integrating sphere........................................................................... 178 
Figure 8.7 Comparison of diffuse reflectance from measurements (symbols) and the two-layer
diffusion model (solid lines) for sample 1 at 535 nm (a) and 700 nm (b), and sample 2
at 535 nm (c) and at 700 nm (d) (See Table 8.1 for the two samples)...................... 180 
Figure 8.8 Relative errors of the estimated optical properties for two model samples (denoted as
S1 and S2) at wavelengths of 535 nm and 700 nm (see Table 8.1 for the optical
property data for the two model samples)................................................................. 181 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

xvii 
 

KEY TO SYMBOLS OR ABBREVIATIONS
CA

Controlled atmosphere

CCD

Charge-coupled device

CI

Confidence interval

CLSM

Confocal laser scanning microscopy

CV

Coefficient of variation

EM

Electromagnetic

EMCCD

Electron multiplying charge-coupled device

FD

Frequency-domain

F/D

Force/deformation

GD

Golden Delicious

GPGPU

General-purpose computing on graphics processing units

GS

Granny Smith

HISR

Hyperspectral imaging-based spatially-resolved

IAD

Inverse adding-doubling

IF

Impact firmness

IMC

Inverse Monte Carlo

xviii 
 

ITDM

Integral-transformed diffusion model

LTDM

Logarithm-transformed diffusion model

MAP

Maximum a posteriori

MC

Monte Carlo

MDI

Multiple document interface

ML

Maximum likelihood

MT

Magness-Taylor

NIRS

Near-infrared spectroscopy

OBF

Order-blocking filter

ODM

Original diffusion model

OLS

Ordinary least squares

OPA

Optical Property Analyzer

PCG

Preconditioned conjugate gradients

PLS

Partial least squares

PRESS

Predicted residual error sum of squares

RD

Delicious

RT

Radiation transport

xix 
 

RWDM

Diffusion model with relative weighting

SDK

Software developer kit

SEM

Scanning electron microscopy

SEP

Standard error of prediction

SNR

Signal-to-noise ratio

SR

Spatially-resolved

SS

Sum of squares

SSC

Soluble solids content

TCSPC

Time-correlated single-photon counting

TR

Time-resolved

A

Internal reflection coefficient, or beam area

a'

Transport albedo

c

Light velocity

C

*

Chroma

D

Diffusion coefficient, or fractal dimension

E

Young’s modulus

xx 
 

f

Frequency

FI

acoustic firmness index

g

Anisotropy factor

h°

Hue angle

I

Light intensity
*

*

L , a , and b

*

CIELAB space

LVs

Latent variables

J0

Zeroth-order Bessel function

M

Modulation

m

Mass

mfp'

Transport mean free path

n

Refractive index

P

Beam perimeter

Q

Source term in radiation transport equation

R

Reflectance

r

Spatial distance, or correlation coefficient

xxi 
 

Rd

Roundness

S

Isotropic source

T

Transmittance

θ

Scattering angle, or phase angle

Ω

Solid angle

Φ

Fluence rate

τ'

Optical thickness

σ

Standard error, or failure stress

λ

Wavelength

ε

Relative error, or failure strain

a

Absorption coefficient

s'

Reduced scattering coefficient

s

Scattering coefficient

µt'

Total attenuation coefficient

µeff

Effective attenuation coefficient

xxii 
 

CHAPTER 1 INTRODUCTION

1.1 Background
Quality of fruits and vegetables is characterized by appearance (color, size and/or shape),
flavor (e.g., sugar content or soluble solids content), texture (e.g., firmness and crispness) and
aroma. The relative importance of each quality index depends on the commodity and its final use.
Many factors such as growing condition, maturity at harvest, and postharvest handling, storage,
and transportation can directly or indirectly affect the quality of fresh produce. With the
increasing demand for all year-round supply of high quality fruits and vegetables in both
domestic and export markets, it is critical that producers supply fresh horticultural products with
desired quality attributes in order to assure consumer satisfaction and confidence. As such, the
horticultural industry is highly interested in adopting new, cost effective objective methods and
techniques for analyzing and monitoring fruit and vegetable quality. Conventional methods for
quality measurement of horticultural products include Magness-Taylor (MT) firmness test and
Brix refractometry for sugar content (or soluble solids content). These techniques are destructive
and only can test a few product pieces, and they are not suitable for sorting and grading each
piece of fruits and vegetables. Over years, many nondestructive methods have been developed
for quality evaluation of food and agricultural products. Among the many types of
nondestructive sensing techniques (i.e., optical, mechanical, and electrical), optical techniques
are particularly useful because they are rapid, nondestructive, cost effective, and generally safe to
use. Abundant literature is available on optical methods and technologies for nondestructive
quality measurement of horticultural products. However, few studies have been reported about

1
 

light propagation in plant materials, and of the determination of optical properties of horticultural
products, which are critical for developing effective optical sensing techniques.
Optical techniques, like imaging and near-infrared spectroscopy (NIRS), are widely used for
nondestructive quality assessment of agricultural and food products (Abbott et al., 1997; Blasco
et al., 2003; McGlone et al., 2003). Imaging or machine vision is mainly used to inspect the
external features of product items. NIRS, on the other hand, has been applied for internal quality
evaluation of agricultural and food products as well as nonfood materials. NIRS measurement
provides approximate quantification of absorption properties of the sample (Dahm and Dahm,
2001), but it does not separate absorption properties from scattering properties, which could limit
its capability in predicting such quality attributes as fruit firmness. Biological materials like fruits
are optically inhomogeneous, and thus light will be attenuated in the fruit through absorption and
scattering, which are affected by the structural and compositional characteristics of the tissue.
Therefore, it would be advantageous and/or desirable to measure both absorption and scattering
properties.
Light propagation in turbid media is characterized by the absorption coefficient (a) and the
reduced scattering coefficient (s') (Tuchin, 2000). Light absorption is mainly related to the
chemical compositions of the medium, while scattering is influenced by the structural properties
(density, particle size, and cellular structures). Changes in the chemical composition and physical
structures are accompanied with the changes in the quality of fruit and vegetables (Lu et al., 2009;
Qin and Lu, 2008). Hence, quantification of the absorption and scattering properties can greatly
expand our understanding of light interaction with biological materials and enable us to assess
the physiological state, properties or characteristics, and thus quality of agricultural and food
products.
2
 

The propagation of light in a medium can be described by radiation transport theory, which
is also known as the Boltzmann equation. When scattering is dominant over absorption (i.e,
s'a), the radiation transport equation may be simplified by diffusion approximation
(Durduran et al., 1997; Ishimaru, 1978). The diffusion equation has been widely used for
modeling light propagation in single-layer or homogeneous and multi-layer turbid media. With
appropriate boundary conditions and known optical parameters, direct solutions to the diffusion
equation, referred to as forward problems, can provide quantitative description of light
propagation in the turbid medium. Conversely, the diffusion equation can be used to estimate the
absorption and reduced scattering coefficients of media for specific boundary conditions, which
is called inverse problems. In solving inverse problems, we often resort to numerical methods
(e.g., Monte Carlo, asymptotic approximation, and finite element) because they are able to deal
with complex boundary conditions (Gonzalez-Rodriguez and Kim, 2008; Schweiger and Arridge,
1997; Seo et al., 2007). However, these methods are computationally intensive. For this reason,
analytical solutions to the diffusion equation, coupled with a proper inverse algorithm, are
preferred in determining the optical properties of turbid materials, which is also referred to as
parameter estimation problems. Inverse light transport problems are much more complicated
than forward problems, and sometimes they are ill-posed, especially for the two-layer diffusion
model, in which four or five parameters (a and s' for each layer plus the thickness of the first
layer) need to be estimated. Therefore, in order to have accurate estimation of optical properties,
it is important to understand the intrinsic properties of the diffusion model, evaluate the
feasibility of estimating all parameters and the uniqueness and stability of the solution, and
consequently develop a reliable inverse algorithm.

3
 

Based on the radiation transport theory or diffusion approximation, several advanced optical
techniques, which mainly include time-resolved (TR), frequency-domain (FD), and spatiallyresolved (SR), have been developed for measuring the optical properties of biological materials.
These techniques have attracted considerable attention in the biomedical field for such
applications as disease diagnosis, photodynamic therapy, and noninvasive monitoring (Bykov et
al., 2006; Welzel et al., 2004; Wilson and Patterson, 2008). However, only limited research has
been reported on measuring the optical properties of agricultural and food products using these
techniques (Anderson et al., 2007; Cubeddu et al., 2001a; Lu et al., 2009; Qin and Lu, 2008).
Time-resolved and frequency-domain techniques require sophisticated instrumentation, and they
currently are still expensive and inconvenient or time consuming in measurement with limited
wavelength range selections. In comparison, the spatially-resolved technique is less expensive,
easier to use, and faster in measurement. It is, thus, more viable for agricultural and food
applications. Spatially-resolved technique is commonly implemented in one of the two sensing
configurations, i.e., multiple fiber arrays connected to spectrometers and non-contact reflectance
imagery (Doornbos et al., 1999; Pilz et al., 2008). The former needs good contact between the
detecting probes and the measured medium, which may not be desirable for food and agricultural
products because of the safety and sanitation requirements. Most research using the non-contact
sensing configuration can only provide optical property information at single or several
wavelengths.
In spite of great progress in instrumentation and theories over the past decade, we still lack a
reliable and convenient method for accurate measurement of the optical properties of biological
materials in general and food and agricultural products in particular. No commercial instruments
based on the spatially-resolved spectroscopic principle are currently available. Over the past

4
 

decade, hyperspectral imaging has emerged as a powerful technique for quality and safety
inspection of food and agricultural products (Lu and Chen, 1998; Lu and Peng, 2006; Nicolai et
al., 2006; Park et al., 2002). Hyperspectral imaging combines conventional imaging and
spectroscopy techniques to acquire spatial and spectral information simultaneously, and it is thus
ideally suited for measuring spatially-resolved diffuse reflectance profiles for a broad spectral
region. In light of those advantages, our laboratory recently developed a hyperspectral imagingbased spatially-resolved technique for measuring the spectra of optical properties of biological
materials. Studies by Qin et al. (2007) showed that the technique is promising for optical
characterization of food and agricultural products. However, limitations in application of this
new technique were observed in our previous studies, and several critical issues need to be
addressed before the technique is suitable for practical applications. These issues include the
development of a robust light propagation model and inverse algorithm, optimization of the
optical design of light beam and source-detector distance in the hyperspectral imaging-based
spatially-resolved system, and the establishment of standard procedures for evaluating the
instrument capability. Moreover, cost and convenience in use of this advanced optical technique
in food and agriculture are also of great concern. Therefore, it is highly desirable to develop an
instrument integrated with robust and user-friendly algorithms, which is capable of automatically
acquiring and processing hyperspectral scattering image data to extract the optical absorption and
scattering properties. In short, optical characterization of the fundamental absorption and
scattering properties will provide opportunities in the development of new sensing technologies
for nondestructive quality evaluation of horticultural and food products.

5
 

1.2 Objectives
This research was aimed at developing a hyperspectral imaging-based spatially-resolved
technique for accurate and reliable measurement of the optical properties of horticultural and
food products and for maturity/quality assessment of peach and apple. The specific objectives
were to:
(1) Develop an improved inverse algorithm, based on a single-layer diffusion model, for
extracting the absorption and reduced scattering coefficients from the hyperspectral reflectance
profiles, and optimize the algorithm using Monte Carlo simulation and statistical analysis;
(2) Evaluate and optimize the design of light beam and source-detector distance so as to
achieve accurate acquisition of spatially-resolved spectral scattering profiles for determination of
the optical properties;
(3) Develop, test and evaluate an optical property measuring prototype, with integration of
image acquisition and processing programs and the optimized inverse algorithm and optical
designs, for automatic measurement of the optical properties of horticultural and food products;
(4) Measure absorption and reduced scattering spectra of peaches and apples for assessing
fruit maturity and/or quality;
(5) Correlate the spectral absorption and scattering properties of apple tissues to the microstructural and mechanical characteristics, as affected by postharvest storage;
(6) Investigate the feasibility of applying a two-layer diffusion model for determining the
optical properties of fruit skin and flesh through solid model samples of known properties.

6
 

CHAPTER 2 LITERATURE REVIEW

2.1 Principles of Light Interaction with Biological Materials
Light interaction with turbid biological materials is characterized by the fundamental optical
properties of absorption, scattering and refraction, which are defined by the absorption
coefficient, reduced scattering coefficient, and refractive index. These optical properties are
present in the radiation transport equation governing light propagation through biological tissues.
The definitions of these optical parameters are presented in the following subsections.
2.1.1

Absorption Coefficient

Absorption coefficient (µa) quantifies the conversion of light energy into other forms of
energy such as heat, electricity, or chemical energy. Absorption or the decrease in the amount of
electromagnetic radiation is proportional to the incident light intensity and the distance over
which the absorption takes place in an absorbing-only medium [Figure 2.1(a)]. According to the
Beer-Lambert law, it can be expressed in the following equation:
I  I 0 exp(   a d )

(2.1)

where I is the intensity of the transmitted light, I0 is the incident light intensity, d is the thickness
-1

-1

of the material in mm or cm, corresponding to the units of µa in mm or cm .
Light absorption is mainly related to the chemical composition of the material. A
relationship between the absorption and the chemical composition may be established, which
could be used to evaluate quality, ripeness, and damage of agricultural and food products.
Chemical bonds of the biological materials absorb light energy at specific wavelengths. The
major absorbers for many horticultural products in the visible wavelength range of 400-770 nm
7
 

are pigments including chlorophylls, carotenoids, anthocyanin, lycopene and other color
compounds, while water, fats, carbohydrates and proteins usually have absorption bands in the
near-infrared wavelength region of 770-2,500 nm. Qin and Lu (2008) showed that as tomato fruit
ripened from the green (unripe) to red (ripe) stage, their chlorophylls content decreased
significantly. As a result, the absorption coefficient at 675 nm also decreased dramatically. An
absorption peak due to water occurs to the µa spectrum of fruit at the wavelength of 975 nm
(Nicolai et al., 2008; Valero et al., 2004).
(a)

Incident
intensity I0

Length d
Absorption
µa

Length d

(b)

Transmitted
intensity I

Incident
intensity I0

(c)

Scattering
µs
Transmitted
intensity I

(d)
Incident light
θ1 
n1 

Incident
photon

Specular
reflection

n2 
θ2  Refraction

Figure 2.1 Light interaction with matter: (a) absorption, (b) scattering, (c) scattering event with
anisotropy factor g, and (d) refraction (For interpretation of the references to color in this and all
other figures, the reader is referred to the electronic version of this dissertation).
8
 

2.1.2

Scattering Coefficient

Scattering (µs) is a physical process that takes place when light interacts with scattering
media, and the travelling path of the photons is no longer direct as shown in Figure 2.1(b). µs
quantifies the probability of photon scattering unit path length, and is the inverse of the average
distance that light travels among scattering events. Similar to absorption, scattering can be
described by the non-scattered transmitted intensity I, incident intensity I0, and the thickness of
the medium with the form identical to equation (2.1).
I  I 0 exp(   s d )

(2.2)

where µs represents a probability per unit length of a photon being scattered, which has the same
-1

units as µa in mm

-1

or cm .

Light scattering in the tissue depends on many variables including the size of scattering
particles, the wavelength of the light, and the variation of the refractive indices of the various
tissue components. In agricultural products, scattering is closely related to the cellular structures
and characteristics, and therefore it could provide useful information about their condition or
quality.
2.1.3

Anisotropy Factor

Anisotropy factor is defined as a measure of the amount of photons retained in the forward
direction after a single scattering event. When a photon is scattered by a particle, its trajectory is
deflected by scattering angle θ as shown in Figure 2.1 (c). It has been proved that the HenyeyGreenstein function can be used to describe the probability density function for scattering, and it
is given by (Tuchin, 2000)
9
 

p( ) 

1 g2
2(1  g 2  2 g cos  )3/2

(2.3)

where g is called anisotropy factor, and it is dimensionless, which is the expected value of cosine
of the scattering angle θ


g  cos    p( ) cos   2 sin  d
0

(2.4)

The scattering phase function p(θ) is usually determined from goniophotometric measurements
in relatively thin tissue samples (Tuchin et al., 1994). The value of g varies in the range from 0 to
1 with g = 0 for isotropic scattering and g = 1 for the total forward scattering. For most biological
tissues, g  0.70  0.99 in the visible and near-infrared region (Vo-Dinh, 2003).

2.1.4

Reduced Scattering Coefficient

The reduced scattering coefficient (µs') is a property incorporating the scattering coefficient
(µs) and anisotropy factor ( g ), which is expressed as follows (Graaff et al., 1993):
 s '   s (1  g )

(2.5)

It is used to describe the diffusion of photons in a random walk with the step size of 1/ µs' (mm
or cm), where each step involves isotropic scattering. In many biological materials, scattering is
dominant during a light transport process, which is known as the diffusion regime. Because the
photons encounter many scattering events in small steps before an absorption event takes place,
the total scattering could be considered as isotropic. Hence the exact value of the anisotropy
factor is no longer needed for the description of light propagation in the tissues. As a result, µa
and µs' are the only optical parameters in the diffusion regime, which is common when visible

10
 

and near-infrared light propagates through biological tissues. Other relevant optical parameters
can be derived from µa and µs', which include total attenuation coefficient (µt'), effective
attenuation coefficient (µeff), transport mean free path ( mfp' ), and transport albedo ( a ' )
t '  a  s '

(2.6)

 eff  3  a (  a   s ') 

1/ 2

(2.7)

mfp '  ( a   s ')1

(2.8)

a '   s '/ (  a   s ')

(2.9)

Values of the reduced scattering coefficient for some biological materials have been
reported in the literature. For instance, the µs' spectrum of fruit tissues in the visible and nearinfrared region is relatively flat compared with the µa spectrum (Cubeddu et al., 2001a; Qin and
Lu, 2008). Empirical equations for determining µs' values of Intralipid, a scattering material
commonly used for creating model samples, in the wavelength range of 400-1,100 nm have been
derived by van Staveren et al. (1991).
2.1.5

Refractive Index

Determination of the optical properties requires knowledge of the refractive index of the
sample and the medium surrounding the sample. The refractive index is a measure of light
refraction at the boundary between two materials [Figure 2.1(d)], and is governed by Snell’s law
n1 sin 1  n2 sin  2

(2.10)

where n1 and n2 are the refractive indices of the media, and θ1 and θ2 are the incident light angle
and refraction angle for the transmitted light.
11
 

Since biological tissues are heterogeneous in composition, the refractive indices are different
for different parts of a biological cell. It is common that only the average value of refractive
index for the tissue is calculated, which is defined by the refractive indices of the scattering
center and ground matter, and their volume fraction of the scatters (Tuchin, 2000). In studying
light propagation in biological tissues, the overall refractive index of 1.35 is often used and it is
considered constant in the visible and near-infrared region (Haskell et al., 1994).
2.2

Modeling of Light Transport in Tissues
Light propagation in tissues can be described by the electromagnetic (EM) theory, i.e.,

Maxwell’s equation. However, it is not feasible to directly use the EM theory for describing light
interaction with biological tissues, because of the complexity of cellular constituents and
physical structures of biological tissues. When light is incident upon the surface of the tissue, it
may be reflected, absorbed, scattered or transmitted, and the relative contribution of each
phenomenon depends on the optical properties of the tissue. For biological materials, several
simple approaches like the Kubelka-Munk model have been employed to describe these
phenomena (Budiastra et al., 1998). However, they are only valid in several particular situations
and cannot be generalized to most cases of practical interest. Mathematical models derived from
the radiation transport equation include diffusion approximation, adding-doubling, and Monte
Carlo simulation, which have been successfully used for modeling light transport in tissues and,
hence, are reviewed in this section.
2.2.1

Radiation Transport Model

The radiation transport (RT) equation is based on the assumption that only the flow of
energy through the medium is considered, and migrating particles do not interact with each other.
12
 

In the case of tissue optics, the particles are photons (i.e., probability electromagnetic wave
packets) interacting with cells structures. The RT equation can be derived by considering the
radiant energy balance in a small volume of tissue. It is a balance equation related to the change
of energy radiance in time and in energy flow, loss due to the absorption and scattering, and gain
due to scattering sources and radiation sources. The time-dependent RT equation is given by
(Ishimaru, 1978)

ˆ
1 L(r, s, t )
ˆ
ˆ ˆ
ˆ
ˆ
ˆ ˆ
   L(r, s, t ) s  ( a   s ) L(r, s, t )  s  L(r, s ', t ) p( s  s ')d  '  Q(r, s, t ) (2.11)
4
t
c
2

ˆ
where L(r , s, t ) is the radiance with the unit of W/(m sr), which represents the energy transfer
ˆ
per unit time per unit solid angle  in direction s through a unit area at position r and time t ,

ˆ ˆ
ˆ
sr is in the unit of solid angle, s is a unit vector pointing in the direction of interest, p(s  s ') is
ˆ
ˆ
the phase function, which equals the probability distribution of the scattering angle from s to s ' ,

ˆ
Q(r, s, t ) is the source term that represents power injected into a unit solid angle centered on the
8

ˆ
direction s in a unit volume at r , and c = (3×10 )/n (m/s) is the velocity of light in the medium,

where n is the refractive index of the medium.
Although the RT equation has been successfully applied in various fields for the light
propagation in absorbing/scattering media, the derivation of direct analytical solutions for
equation (2.11) for many practical problems is difficult. Therefore, further approximations or
numerical methods are needed for specific cases. A number of approximate and stochastic
models of photon transport derived from the RT equation have been developed, of which
diffusion model, adding-doubling, and Monte Carlo simulation are the most widely used.

13
 

2.2.2

Diffusion Model

Diffusion approximation to the RT equation is the most widely used model to describe the
light propagation in biological materials. It assumes that scattering is dominant (i.e., µs' » µa) and
the source-detector distance is greater than the transport mean free path that defines the distance
traveled before the direction of light propagation is randomized (Dogariu and Ellis, 2010). An

ˆ
additional assumption is that the source term Q(r, s, t ) is isotropic with an equal probability of
scattering in all solid angles combined with a net flux. With these conditions, the RT equation is
approximated to the diffusion equation given by (Haskell et al., 1994)

1 (r, t )
 D2(r, t )  a(r, t )  S (r, t )
c t
where (r, t )  

4

(2.12)

ˆ
L(r, s, t )d  is the fluence rate, D  [3( a   s ')]1 is the diffusion

ˆ
coefficient, and S (r, t )   Q(r, s, t )d  represents an isotropic source.
4

It has been confirmed that the diffusion theory is accurate for describing photon migration in
infinite, homogeneous turbid media. For studying biological materials, techniques based on the
diffusion theory have been developed, which include time-resolved (TR), frequency-domain
(FD), and spatial-resolved (SR) techniques. TR method uses a short pulse laser to illuminate the
sample and then collects the time-delayed remitted light at a specific distance from the source,
FD employs a sinusoidally modulated source to measure the phase and modulation, and SR
technique adopts a continuous-wave point light beam incident on the sample surface with the
remitted light collected at different source-detector distances. Different forms of the diffusion
equation for TR, FD, and SR have been derived (Welch and van Gemert, 1995), and details for
these measurement techniques are presented in Section 2.3.

14
 

Several analytical solutions derived from the diffusion equation for the homogenous media
of particular geometries (e.g., semi-infinite, slab, cylindrical, and spherical geometries) are
available (Farrell et al., 1992; Welch and van Gemert, 1995). Solutions for inhomogeneous and
irregular samples are usually obtained using numerical methods (e.g., Monte Carlo, finite
element, and finite difference). Moreover, solutions in analytical form for multilayer media with
certain geometries have also been derived (Kienle et al., 1998b; Swartling et al., 2003b). These
solutions provide an effective means for modeling light propagation in turbid media of specific
geometries under given boundary conditions, and they could be used to extract the optical
properties of biological materials by means of inverse algorithm.
2.2.3

Adding-doubling Model

As a purely numerical method, the adding-doubling method provides another way to solve
the RT equation with high accuracy and flexibility in modeling any medium with mismatched
boundary conditions and anisotropic scattering. The inverse adding-doubling method has
advantages for measuring the optical properties, because the only values needed are the
reflectance and transmittance of the medium. The following assumptions are given for this
modeling approach: no time-dependence of light distribution, homogenous optical properties for
tissue layers, an infinite plane-parallel slab of samples, uniform illumination of collimated or
diffuse light, internal reflection at boundaries governed by Fresnel’s law, and unpolarized light
(Prahl et al., 1993).
In the adding-doubling method, the reflectance function R(v, v ') and transmittance function

T(v, v ') are defined as the radiance reflected or transmitted by the slab in direction v ' for light
incident from the v direction (Figure 2.2). Based on the numerical integration of functions with

15
 

quadrature, the total reflectance and total transmittance for the diffuse irradiance can be
expressed (Welch and van Gemert, 1995)

Rd  

1 1



0 0

R(v, v ')2vdv 2v ' dv '

1 1

Td  

 T (v, v ')2vdv2v ' dv '

0 0

(2.13)
(2.14)

Then, the transport albedo a ' and transport optical thickness  ' may be calculated by
  1  4 R  T 2
d
d
1  

  1 T d


a'  
 4  1  Rd  Td  2
1  

 9  1 T d 


  ln(Td ) ln(0.05)

ln( Rd )
 '
 15( Rd Td )
2

if

if

Rd
 0.1
1  Td

(2.15)

Rd
 0.1
1  Td

if Rd  0.1

(2.16)

if Rd  0.1

where a' = µs'/(µa+µs'), τ' = d(µa+µs'), and d is the physical thickness of the slab. Thus, the two
parameters, i.e., the absorption coefficient µa and the reduced scattering coefficient µs', can be
determined for a combination of Rd and Td using equations (2.13) through (2.16). The
procedures for implementing the adding-doubling method are as follows: 1) guess a set of optical
properties, 2) calculate the reflectance and transmittance using equations (2.13) and (2.14), 3)
compare the calculated values with the measured reflectance and transmittance, and 4) repeat
until the calculated values and measured values are matched.

16
 

v
R(v, v ')

T (v, v ')
Figure 2.2 Light incident at an angle v that is reflected and transmitted by a slab at an angle v ' in
the adding-doubling method (Welch and van Gemert, 1995).
The total reflectance and the total transmittance are usually measured using integrating
spheres. The results obtained from the adding-doubling method are accurate for a wide range of
optical properties but at the cost of increased computational time. Therefore, it is mostly used as
a standard method for measuring the optical properties of biological materials (Lualdi et al., 2001;
Saeys et al., 2008).
2.2.4

Monte Carlo Simulation

Another powerful tool for modeling light transport in tissues is the Monte Carlo (MC)
simulation method. MC simulation is a stochastic numerical method in which the expected value
of a certain random variable is equivalent to the value of a physical quantity to be determined
(Wang et al., 1995a). MC simulation offers a flexible and accurate approach for quantifying the
optical features of light transport that are difficult to measure directly. It can be simply
implemented, and has the ability to handle any complex geometries and multilayer media.
However, the method is statistical in nature and requires computing the propagation of a large
quantity of photons. Therefore, significant computational time is needed to achieve required
precision and resolution.
17
 

The motivation for MC simulations is to predict radiant energy transport in tissues, while
ignoring such features as phase and polarization. In MC simulation of light propagation, a photon
is launched into the turbid medium, and it then propagates in the medium described by the
optical properties (i.e., µa, µs, g, and n) of the investigated material. The photon transported in
the medium is traced step by step, which is expressed as probability distributions to describe the
step size of photon movement between the sites of photon-tissue interaction, and the angles of
deflection in a photon’s trajectory when a scattering event occurs (Wang et al., 1995a). The
simulation of light propagation is then achieved by tracking millions of photons, which can score
multiple physical quantities simultaneously.
Since MC simulation for the light distribution approaches an exact solution of the RT
equation as the number of photons increases, it is also considered a standard method for
describing light propagation in tissues. Forward and inverse MC models have been used to
analyze the diffuse reflectance and extract the optical properties of biological materials. Public
MC simulation programs known as ‘MCML’ and ‘CONV’ developed by Wang et al. (1995a)
have been widely employed in the biomedical field for the study of light transport in tissues.
Several methods to accelerate the MC simulation of photon migration in turbid media were
proposed for slab geometries and inhomogeneous media. Alerstam et al. (2008) found that
general-purpose computing on graphics processing units (GPGPU) can dramatically increase the
speed of MC simulations. Zolek et al. (2008) corrected the calculation of polar deflection angle
to improve the MC simulations of light transport in tissue.
Other numerical approaches, such as finite difference, MC diffusion hybrid model, finite
element, and asymptotic approximation (Alexandrakis et al., 2000; Cui and Ostrander, 1992;
Deulin and L'Huillier, 2006; Seo et al., 2007), have also been used to model light propagation in
18
 

turbid media. Although those numerical methods are generally considered more accurate than the
diffusion approximation model, they suffer the main drawback of computational complexity with
long computational time, especially for solving the inverse problems to obtain the optical
properties of biological materials by iterative fitting methods.
2.3 Techniques for Measuring Optical Properties of Biological Materials
Various techniques have been developed for measuring the absorption and scattering
properties of biological materials. Because of the obvious advantages of noninvasive or
nondestructive measurements, determination of the optical properties of biological materials
based on diffuse reflectance measurements has significant potential in food and agriculture. The
section reviews optical techniques along with their solutions to the diffusion model, and these
techniques may be divided into three main categories: time-resolved (TR) (Patterson et al., 1989),
frequency-domain (FD) (Patterson et al., 1991), and spatially-resolved (SR) (Groenhuis et al.,
1983b). The TR, FD, and SR techniques described in this section are for both single-layer and
two-layer biological materials with a semi-infinite geometry.
2.3.1

Time-resolved Technique

Time-resolved technique is based on measurement of the attenuation, broadening and delay
of a short light pulse, caused by the absorption and scattering events during photon propagation
in highly scattering media. Photon movement in a turbid medium is complicated due to the
strong effect of light scattering at different wavelengths. Photons reflected or transmitted across
the medium may have transported along many different paths within the medium. In a scattering
dominant medium, a photon traveling path can be quite tortuous and may escape from the
medium within several centimeters from the injection point. The photon moves in random
19
 

directions with respect to its trajectory at injection and continues a random walk within the tissue
until it escapes at the tissue surface or is absorbed. Because the pathlength that a photon has
taken within the tissue is proportional to the time, time-resolved technique seeks to use the
pathlength information implied by the time of escape to specify the optical properties of tissue
traveled by the photons [Figure 2.3(a)].
(b)

Light source

Intensity

Detected light

Light source
Detected light

Intensity

(a)

Time

Time

Figure 2.3 Measurement principle of (a) time-resolved and (b) frequency-domain techniques.
Photon propagation measurements in the time domain depend on the ability to extract
photon information encoded in the temporal distribution of the re-emitted light, following the
injection of a short monochromatic pulse in a diffusive medium. Thus, temporal resolution and
high sensitivity become two critical factors in designing a time-resolved system (Cubeddu et al.,
2000). Temporal resolution is mainly affected by the width of the light pulse and by the response
of the detection apparatus, and the power of the injected light pulse should be fixed at
appropriate values to avoid possible damage or injury to the sample when considering the
sensitivity. The safety regulations for the biological tissues give the maximum permissible value
2

of 2 mW/mm for laser pulses in the wavelength range of 600-1,000 nm. For most time-resolved
systems, photons are recorded using the time-correlated single-photon counting (TCSPC)

20
 

technique within a short time period at a specified distance from the beam incident point
(O'Connor and Philip, 1984).
The diffusion model for the time-resolved signals has been developed, which describes light
propagation in its time distribution and allows the quantification of optical coefficients µa and
µs'. Consider a homogenous, semi-infinite turbid medium, the time-resolved reflectance function
is given by (Patterson et al., 1989)

R1layer (r, t )  (4 Dc)

3/2

1 5/2

(s ') t

 r 2  ( ')2 
s
exp 
 exp(act )
4Dct 




(2.17)

where D  [3( a   s ')]1 is the diffusion constant, and c is the velocity of light in the turbid
medium. The term µac represents the absorption of the light, and the other terms are due to the
early spreading of the light in the tissue, such as t

-5/2

dominates the early dynamic of the

reflectance signals.
Kienle et al. (1998a), using the Fourier transform approach, derived an analytical solution
from the diffusion equation using proper boundary conditions for a two-layer medium that has
the first layer of thickness d and the semi-infinite second layer. It is assumed that the thickness of
-1

the first layer is larger than one transport mean free path [d > (µa1+µs1') ]. The time-domain
reflectance R2-layer(r, t) for the two-layer medium can be obtained by calculation of the real and
imaginary parts of the reflectance in the frequency domain R2-layer(r, f), as detailed in the
following section, at many frequencies and by fast Fourier transform of these data.
As a novel nondestructive method, applications of time-resolved technique have been
extensively reported in biomedical research for measuring the optical properties of human tissues
21
 

(Chernomordik et al., 2002; Kacprzak et al., 2007; Svensson et al., 2005). Its applications for
fruits were also reported in several studies. Cubeddu et al. (2001b) developed a time-resolved
spectroscopic measurement system based on the TCSPC technique to measure the optical
properties of peaches, kiwifruit and apples. Nicolai et al. (2008) used the same system to predict
soluble solids content and firmness of pear, although no satisfactory calibration models could be
established between the optical properties from TR measurements and quality attributes.
2.3.2

Frequency-domain Technique

Frequency-domain is another well-recognized technique for quantitatively measuring the
optical properties of biological tissues, which could provide information equivalent to that
obtained in the time domain. In the frequency domain, the propagation and measurement of light
are accomplished through sinusoidally modulated sources. The photon flux at the detector will
also be sinusoidal in time but the oscillation will be delayed in time relative to the source and
reduced in amplitude relative to the average flux [Figure 2.3(b)]. In this case, the measured
quantities are the phase angle between the detected and source signals and the amplitude of the
oscillation relative to the DC level (Welch and van Gemert, 1995). The signal measured at the
frequency-domain and time-domain can be transformed reciprocally by the Fourier transform
(Arridge et al., 1992). However, in practice, there are specific advantages for frequency-domain
technique compared to the time-resolved measurement, such as cheaper and simpler
instrumentation, easier correction for instrument response, real-time measurement of phase and
modulation, and capability for characterizing an entire spectrum from the measurement at a
single frequency.

22
 

The optical parameters (µa & µs') could be obtained from the diffusion model based on the
frequency-domain measurement of the modulation ( M ) and the phase angle. Patterson et al.
(1991) derived the analytical solutions for the modulation and phase by the Fourier transform of
equation (2.17) for a homogenous and semi-infinite medium, which are given as follows
 r 

 1  i 

1layer (r , f )   r  tan 1 

(1   0 2  2 i )1/ 2
exp(   i )
M1 layer ( r , f ) 
1  

(2.18)

(2.19)

where
 0  {3(  a   s ')[ r 2  (  s ') 2 ][(  a c ) 2  (2 f ) 2 ]1/ 2 c 1}1/ 2

1

 2 f
 a c

 r   0 sin  tan 1 
2


1

 2 f
 a c

 i   0 cos  tan 1 
2












   {3 a (  a   s ')[ r 2  (  s ') 2 ]}1/ 2

(2.20)
(2.21)

(2.22)

(2.23)

For the fixed values of distance r and modulation frequency f, optical parameters µa and µs'
can be obtained graphically or using more accurate numerical methods to solve equations (2.18)
and (2.19). The choice of the optimum frequency is very important, which depends on the optical
properties of the measured materials.
A solution to the frequency-domain for a two-layer medium was derived with the phase
angle θ2-layer(r, f) and modulation M2-layer(r, f) calculated based on frequency-domain
reflectance R2-layer(r, f), which is given by (Kienle et al., 1998a)

23
 

2layer (r, f )  tan1

Im  R2layer (r, f )



(2.24)

Re  R2layer (r, f )


1/2

2
2
 
 Im  R2 layer (r , f )   Re  R2 layer (r , f )  



M 2 layer (r , f )  

Re  R2 layer (r , f   2 layer / 2 ) 







(2.25)

where
R2 layer (r , f )  C11  r , z  0, f   C2 D1

i (r, z, f ) 


1  r , z , f 
z
z 0

exp( j 2 ft ) 
0 i ( z, f , s)sJ0 (sr )ds
2

(2.26)

(2.27)

C1 and C2 in equation (2.26) are two constants (see details in Chapter 3). Equation (2.27) is the
fluence rate  i ( r , z , f ) in layer i , J0 is the zeroth-order Bessel function, and i ( z , f , s ) is the
fluence rate of each layer obtained from solving diffusion equations in the frequency domain by
Fourier transformation.
In applications, the frequency-domain technique can be generally classified into ‘multidistance’ and ‘multi-frequency’ categories. The former acquires reflected light signals at several
different tissue locations, and the latter employs a single source-detector position with multiple
source modulation frequencies (Madsen et al., 1994; Tromberg et al., 1997). The light source
such as lamps and lasers used in the frequency-domain is usually modulated by electro-optic and
acousto-optic modulators, and the modulated beam will therefore contain higher harmonics,
which is related to the selection of a detection method. Detectors to be used in frequency-domain
technique require a bandwidth encompassing the desired modulation frequency. In summary,
avalanche photodiodes offer the best frequency response followed by microchannel plate
photomultipliers (MCP-PMTs) and conventional PMTs, which have been widely used in
24
 

biomedical applications (Coquoz et al., 2001; Spichtig et al., 2009; Welch and van Gemert,
1995). The early frequency-domain instrument was developed for measuring the decays of
fluorescence intensity from the flexible molecules in proteins (Lakowicz et al., 1989). It has been
also successfully applied to in vitro spectroscopy studies of turbid media for medical diagnosis
(Banos et al., 2007; Tromberg et al., 2000; Tromberg et al., 1996).
2.3.3

Spatially-resolved Technique

Spatially-resolved technique was first proposed by Reynolds et al. (1976) for understanding
light propagation in the turbid media. Later, Langerholc (1982) and Marquet et al. (1995)
suggested that spatially-resolved measurement could be used to determine the optical properties
of biological tissues. In this method, a small continuous-wave light beam perpendicularly
illuminates the sample’s surface, and the remitted light is measured at different distances from
the light source (Figure 2.4). The optical coefficients µa and µs' of biological materials can then
be extracted from the measured spatially-resolved reflectance profiles using an appropriate
analytical solution of the diffusion equation coupled with an inverse algorithm.

25
 

Spatial profile R(r)
r
Incident
light

Absorption & scattering
Turbid material (µa, µs')

Figure 2.4 Measurement principle for spatially-resolved technique.
For the case of steady-state spatially-resolved reflectance for a homogeneous semi-infinite
turbid medium, Farrell et al. (1992) derived an analytical solution from the diffusion equation
using the extrapolated boundary conditions, at which the fluence is forced to zero by introducing
a negative ‘image source’. The diffuse reflectance from the medium is calculated as the current
across the boundary, and it is originated from a single isotropic point source located at a depth of
one transport mean free path in the medium. The final expression of the reflectance R1-layer at
the surface of the semi-infinite turbid medium is
R1 layer ( r ) 

a'
4

 1
1 exp(   eff r1 )
1
4A
1 exp(   eff r2 ) 
(

(  eff  )
)(  eff  )


r1
t ' 3 t '
r2
r12
r2 2
 t '




(2.28)

where r is the source-detector distance, a '   s '/ (  a   s ') is the transport albedo,

eff  [3a (a  s ')]1/2 is the effective attenuation coefficient, and t '   a   s ' is the total



attenuation coefficient, r1  z02  r 2



1/2

1/2

and r2   z0  2 zb 2  r 2 




26

 

are the distances from the

observation point at the interface to the isotropic source and the image source, z0  (  a   s ') -1 ,

zb  2 AD , and A  0.2190 for n  1.35 is the internal reflection coefficient related to the
relative index of the tissue-air interface n, which can be calculated from an empirical equation
developed by Groenhuis et al. (1983a).
Later, Kienle et al. (1997) proposed an improved analytical solution by expressing the
reflectance as the integral of the radiance over the backward hemisphere based on the study of
Haskell et al. (1994). In this case, the radiance can be expressed as the sum of isotropic fluence
rate and the flux. The details of Kienle’s single-layer model are presented in Chapter 3.
For a two-layer medium in the spatially-resolved condition, Kienle et al. (1998b) solved the
diffusion equation under the same conditions as that for time-resolved and frequency-domain
methods. The Kienle’s two-layer diffusion model is detailed in Chapter 8.
In practice, spatially-resolved measurement employs a point light source or narrow
collimated beam of the constant intensity and multiple detectors at different source-detector
distances. Optical fiber arrays and non-contact reflectance imagery are two commonly used
sensing configurations in spatially-resolved measurement systems (Doornbos et al., 1999;
Fabbri et al., 2003; Jones and Yamada, 1998; Pilz et al., 2008). The former requires multiple
spectrometers or a single imaging spectrometer to measure diffuse reflectance at different
distances from the light incident point. Optical properties at multiple wavelengths or over a
specific spectral region can be obtained using this method. Yet the measurements need good
contact between the detecting probes and the sample, which may not be suitable for agricultural
and food products. The second method usually uses a CCD (charge-coupled device) camera to
acquire diffuse reflectance from the scattering medium generated by a point light beam. The
measurement can be achieved without contacting the investigated medium, which is particularly
27
 

advantageous for food and agricultural products because of the safety and sanitation
requirements. However, most research on non-contact reflectance imagery mode can only
provide optical property information at single or several wavelengths.
Compared with time-resolved and frequency-domain methods, the spatially-resolved
technique has advantages of being relatively easier to use and less expensive in instrumentation
for food and agricultural applications. Moreover, it is faster in measurement in the range of
millisecond for a broad spectral region versus in seconds at single wavelengths with the timeresolved method (Cubeddu et al., 2001a; Qin and Lu, 2006). However, all these techniques still
face considerable challenges in achieving accurate measurement of the optical properties due to
experimental difficulties and complex mathematical modeling. Reported results on the measured
optical properties of biological tissues are still not satisfactory, as shown in Table 2.1. Pifferi et
al. (2007) used time-resolved method to measure the optical properties of Intralipid, and obtained
the maximum error of 27% at 730 nm compared with the result obtained by the standard method.
Spichtig et al. (2009) reported the results of measuring silicone-based model samples with errors
of 10% for µa and 31% for µs' at 690 nm and 830 nm using a frequency-domain method. Pilz et
al.’s (2008) results demonstrated 10% accuracy of µa and 5% of µs' for measuring tissue model
samples using spatially-resolved technique at one single wavelength of 633 nm. Also, Pifferi et
al. (2005) applied a general protocol for assessing several optical methods for determining
optical properties, and they reported significant differences from different instruments in
measuring the same model samples with the maximum discrepancy of 32% for µa and 41% for
µs'. While improved accuracies of determining µa and µs' were reported in several recent studies
(Martelli and Zaccanti, 2007; Xu and Patterson, 2006), large differences are present for the same
28
 

model samples from these studies. Moreover, most reported studies (Table 2.1) only tested a few
model samples with a relatively small range of µa and µs' values for a narrow spectral region.
Table 2.1 Summary of the performance of time-resolved, frequency-domain and spatiallyresolved measurements (TS: time-resolved, FD: frequency-domain, SR: spatially-resolved, POM:
polyoxymethylene).
Method
TS

Reference
AnderssonEngels et al.
(1993)

Wavelength
450-660 nm

Sample
Porcine muscle

Results
Measured optical
properties of tissue over
the visible spectral range

Swartling et
al. (2003a)

660 and 785
nm

Solid tissue model
samples
-1
µa=0.05-0.3 cm

Absolute differences of
less than 0.05 cm-1 for
µa, and 10% difference

µs'=9-20 cm

for µs'

Breast tissue
Average µa of

Variations below 40%
for µa and 20% for µs'

-1

Svensson et
al. (2005)

660, 786,
916 and 974
nm

-1

0.04 cm

-1

and µs'

of 8 cm
Pifferi et al.
(2007)

550-600
nm, and
610-700 nm

Maximum error of 27%
at 730 nm with the
median error of 7% over
the whole range of µa

Intralipid
µa =0.01-0.07
-1

cm

-1

µs'=6-8 cm
FD

Tromberg et
al. (1997)

674, 811,
849, and
957 nm

Detected physiological
changes in breast tissue

Human breast
tissue
µa =0.02-0.16
-1

cm

-1

µs'=7-11 cm
Coquoz et al.
(2001)

674, 811,
and 849 nm

Liquid model
samples
-1
µa =0.04-0.4 cm

Errors of 10-15% for µa,
and 5-10% for µs'

-1

µs'=0.2-0.9 cm
Xu and
Patterson

750 nm

Five IntralipidIndian ink model
29

 

Errors in µa of 1-27%,

Table 2.1 (cont’d)
(2006)

Spichtig et
al. (2009)

samples µs'/µa=110
-1
µs'=20 cm
690 and 830
nm

and µs' of 3-42%

Silicone-based
model samples
µa = 0.10-0.15

Errors in µa of 10% and
µs' of 31%

-1

cm , µs'= 4-11
-1
cm
SR

Bays et al.
(1996)

514 , and
630 nm

POM samples
Human esophagus
-1
µeff = 0-6 cm ,

Errors of 21% and 32%
for µeff and µs'

-1

µs'=0.2-14 cm
Doornbos et
al. (1999)

600-900 nm

Liquid and solid
model samples
in vivo tissue
-1
µa =0-1.5 cm

40% error of µa for the
model sample

-1

µs'=5-20 cm
Qin et al.
(2006)

530-900 nm

Intralipid-dye
model samples
-1
µa =0-0.8 cm

Errors in µa of 16% and
µs' of 11%
-1

µs'=2.2-23.2 cm
Martelli and
Zaccanti
(2007)

750 nm

Intralipid-Indian
ink model samples

µa and µs' with standard
deviation <2% , and no
validation

Pilz et al.
(2008)

633 nm

Tissue model
samples
-1
µa =0.03-1.0 cm

Errors in µa of 10% and

-1

µs'=5-20 cm

30
 

µs' of 5%

2.4 Approaches to Inverse Problems for Determining Optical Parameters
Direct solutions to the diffusion equation, or numerical methods like Monte Carlo simulation
for quantitative description of light propagation in the turbid medium, are referred to as forward
problems. The corresponding inverse problems, also called inverse radiation transport problems,
deal with estimating the optical properties of turbid media using the reflectance data obtained
from the experimental measurement. While forward problems can be solved accurately because
there often exists a unique solution based on complete description of a physical system, inverse
problems are more complicated and may be difficult to solve because it is challenging to find at
least one model system that is consistent with the observed data with unique model parameters.
Therefore, in determining optical properties of biological materials, a suitable inverse algorithm
should be developed, and information involving measurement data uncertainty, model efficiency,
parameter characteristics, and curve fitting errors should be analyzed.
2.4.1

Sensitivity Analysis

Sensitivity analysis determines how a result (or the dependent variable) changes when
parameters that affect the result are changed. It is performed by calculating sensitivity
coefficients, which are the first derivatives of the dependent variable with respect to the
parameters (Beck and Arnold, 1977). Sensitivity coefficients describe the response of the change
of the dependent variable to perturbations in the values of the parameters, and show the
relationship between the dependent variable and the parameters. Sensitivity coefficients can help
us determine if unique solutions for estimating all optical parameters exist, and/or identify those
parameters that can be estimated when it is not possible to uniquely estimate all parameters from
the measurements (Beck and Arnold, 1977; Taktak et al., 1993). They can be calculated by

31
 

X 

R


(2.29)

where β represents optical parameters µa or µs'. Sensitivity coefficients of parameters can be
computed by multiple methods, such as finite different, complex step, differentiation of
analytical solutions, and sampling methods.
In many applications such as design/analysis studies, sensitivity analysis provides important
information for characterization of the changes of a result with parameter variations,
optimization and parameter estimation with gradient-based techniques, optimal experiment
design, and uncertainty analysis (Blackwell, 2009). Thus, it is important and useful to conduct
sensitivity analysis in the study of inverse light transport problems.
2.4.2

Inverse Algorithm

Algorithms for solving inverse problems or parameter estimations have been developed with
the advances of mathematics, statistics and computer technologies. Regression or curve fitting is
the most used inverse method, which can be divided into linear and nonlinear. In the linear
regression, the most commonly used methods are ordinary least squares (OLS), maximum
likelihood (ML), and maximum a posteriori (MAP) (Beck and Arnold, 1977). Estimating optical
properties from the diffusion model is considered a nonlinear regression problem, which can be
solved using nonlinear least squares method by minimizing the general sum of squares (SS)
function when the dependent variable is nonlinear in terms of the parameters. The extreme found
for the sum of squares functions when the model is linear in the parameters can be proved to be
the correct one and the unique minimum point exists. However, it is difficult to assure for the
nonlinear cases since there may be more than one extremum. Therefore, it is recommended that
contours or profiles of sum of squares be plotted in the region in which the solution is expected.
32
 

Another possibility is to start the iteration procedure with different sets of initial parameter
values.
All methods for nonlinear least squares optimization are iterative. From a starting point x0 ,
the method produces a series of vectors x1 , x2 , x3 ,... , which converges to x* , a local minimum
for the given function. Most methods have measures to enforce the descending condition
F ( xk 1 )  F ( xk )

(2.30)

It prevents convergence to a maximizer and also makes it less possible that it converges towards
a saddle point by using descent methods such as the steepest descent, conjugate gradient, line
search, and trust region and damped methods (Tarantola, 2005). The Newton’s, Gauss-Newton
and Levenberg-Marquardt methods are the most used to achieve optimization (Levenberg, 1944;
Marquardt, 1963; Wilkinson, 1961). The Newton’s method provides a general framework for the
least squares problems. However, the convergence is very slow or even fails if the hypothesis of
quadratic convergence is not satisfied. The Gauss-Newton method is a very efficient method
based on the first derivatives of the components of the vector function. It normally only has
linear convergence, and it can give quadratic convergence in special cases. Considerable research
has shown that it gives quite good performance in many applications (Aigner and Juttler, 2009;
Baltagi, 1996; Dastidar, 2006). The Levenberg-Marquardt method is a modification of the
Gauss-Newton method, which is a good choice for small to medium sized nonlinear least squares
problems.
2.4.3

Data Transformation and Weighting Methods

Before an inverse algorithm is implemented, data pre-check or pre-process is usually
developed to analyze nonlinear data. Data transformation is a powerful method for analyzing
33
 

nonlinear regression models by linear approximation or changing data properties to obtain better
estimations. In statistics, data transformation refers to the linear or nonlinear transformation of a
mathematical function that each data point yi is replaced with the transformed value yTi  f ( yi ) .
The linear transformed data (such as dividing, multiplying all Y values by a constant or
subtracting a constant from all Y values) can be analyzed with linear regression, but the nature of
the best-fit curve will not be changed. Nonlinear transformation (such as converting Y values to
their logarithms, square roots, integrals, derivative, or reciprocals) will change the relative
position of data points from the curve and produce a different curve to minimize the sum-ofsquares. It is usually applied when the raw data does not meet the statistical assumptions or the
data range is at several orders of magnitude (Motulsky and Christopoulos, 2004). For the
spatially-resolved diffuse reflectance profile, the reflectance data (dependent variable: Y)
decreases dramatically along the source-detector distance (independent variable: X), and the
statistical assumptions that the Gaussian distribution of errors of the Y-data and constant
variance of errors along the X-axis are violated when nonlinear regression is applied. Therefore,
nonlinear data transformation to the Y-data could be useful to make the scatter more Gaussian.
The logarithm function converts the multiplicative pattern (proportional-variance) to an additive
pattern (constant-variance), and the integral function transforms instantaneous data to
accumulated data, which alters the relationship between the independent variable and the
dependent variable, and could make the experimental data meet the assumptions. The
implementations of the logarithm and integral transformation methods for the experimental data
and Kienle’s model for single-layer turbid media are given below as an example. In the
logarithm transformation, the natural logarithm of diffusion equation (3.4) (see Chapter 3), called
logarithm-transformed diffusion model (LTDM), is given as

34
 

R1layer ,log (r )  log  R1layer (r ) 



(2.31)

The integral of diffusion equation, defined as the integral-transformed diffusion model
(ITDM), is calculated by (Gobin et al., 1999)
r

R1layer ,int (r )   R1layer (  ) d   C1  f (r , z0 )  f (r , z ')  C2  g (r , z0 )  g (r , z ')
0

(2.32)

where
z '  z 0  2 zb

f (r, z) 

g (r , z ) 



(2.33)



1
exp(eff z)  exp eff (r 2  z2 )1/2 


4 Deff



(2.34)



1
exp(eff z )  z (r 2  z 2 )1/2 exp  eff (r 2  z 2 )1/2 


4

(2.35)

If the scatter of Y data is Gaussian and the variance of the scatter is the same at all values of
X, then the correct parameters can be found by least squares estimates without any data
transformation. However, in some cases, the variance of the scatter often increases as Y
increases. With this type of data, the least squares method is inappropriate because it tends to
give undue weight to points with large Y values on the sum-of-squares value and ignores points
with small Y values. To overcome this problem, a proper weighting method can also be applied
in the nonlinear regression. One common method is the relative weighting which is defined as
minimizing the sum-of-squares of the relative distances of the data from the curve
2

(  (Yobs - Y pred ) / Yobs  , where Yobs is the experimental data, and Y pred is the predicted



35
 

reflectance from the diffusion model). Other weighting methods, such as Poisson weighting
(weighting by 1 / Yobs ) and weighting by observed variability, are also used in nonlinear
regression (Motulsky and Christopoulos, 2004).
2.5

Nondestructive Techniques for Measurement of Maturity and Quality
Quality of fruits and vegetables is of primary concern to growers, packers or processors, and

retailers throughout the production, postharvest handling and processing, and marketing steps. It
is a subjective judgment related to the learned criteria for each consumer. With the advent of
instrumentation and computers, a large number of sensing techniques and devices to measure
quality or quality-related attributes have been developed. Traditionally, quality detection of fruits
and vegetables is achieved using destructive techniques based on the chemical and mechanical
properties, like refractometry for soluble solids content (SSC) and mechanical force/deformation
techniques (e.g., Magness-Taylor test) for firmness measurement. Destructive techniques are
confined to testing a small batch of samples. Nondestructive sensing techniques, on the other
hand, have the potential for rapid and nondestructive quality evaluation, sorting and grading of
individual product items. The increasing demands for all-year-round supply of high quality fresh
produce by retailers are driving the development of new sensing technologies for quality
evaluation of horticultural products.
2.5.1

Maturity and Quality of Fruits

It is difficult to establish one single maturity index due to the complexity of physiological
and/or biochemical processes taking place in fruit during growth and ripening as well as further
complication by such factors as variety or cultivar, geographic location, season, and climate
condition. Hence a combination of indices is commonly used to assess the maturity of fruit,
36
 

which include ground color changes, firmness, soluble solids content, titratable acidity, ethylene
production, and starch content. In addition, the maturity stage at which fruits should be harvested
depends, to a great extent, on the final use of the products. For instance, if fruit are to be sold for
fresh eating immediately after harvest, they may be allowed to ripen fully on the tree. However,
if fruit are to be kept in storage for a long time period, they should be picked prior to full
maturity or ripeness in order to prolong the postharvest life and minimize physiological disorders
or quality decay during storage.
Fruit quality is determined by the maturity of the fruit at harvest. It can be characterized by
appearance (color, size and/or shape), flavor, texture and aroma. A definition of quality used in
postharvest quality evaluation was given by Kramer and Twigg (1970): “the composite of those
characteristics that differentiate individual units of a product, and have significance in
determining the degree of acceptability of that unit by the buyer.” The specific quality
requirements for horticultural products also depend on the end use and cultivar. Minimum
quality standards have been established for fruits in many countries, and they can be divided into
external and internal (Wills et al., 2004). The external standards, characterized by appearance
(color, size, shape, and/or surface defect), are one of the key factors for consumers in purchase of
fresh fruit. Many fruits undergo color changes as part of the ripening process. In some cases,
color is a strong indicator of eating quality and shelf life. Internal quality is dependent on the
properties, physical structures, and chemical compositions (e.g., firmness and SSC), which are
directly related to the texture and flavor of fruits. And it is critical in the repeat purchase of a
particular product or cultivar.
Ripening causes changes in the composition and cellular structures of fruit and thus the
eating quality. The sweetness taste development is the result of increased gluconeogenesis,

37
 

hydrolysis of polysaccharides, and decreased acidity. Softness of fruit is due to the loss of
firmness in texture caused by cell wall depolymerization and an increase in solubility of the
middle lamella. Thus, cellular characteristics such as cell wall strength, cell turgor, number of
cells and their shape and size, and intercellular spaces have a significant effect on the texture of
the fruit, which is, in turn, directly related to the mechanical properties of fruit tissue.
Mechanical properties of fruit tissue are influenced by ripening stage and water status, and also
determine the susceptibility of fruit to mechanical damage during harvest, transport, and
postharvest storage and handling. Thus, better understanding of the structural and mechanical
properties of fruit tissue is needed in the development of new or improved techniques for fruit
quality evaluation and monitoring, and better processing operations for the food industry.
2.5.2

Mechanical Techniques

Most nondestructive mechanical techniques measure elastic properties (e.g., modulus of
elasticity or Young’s modulus) at very small deformations, which are related to the texture (e.g.,
firmness) of fruits and vegetables. Modulus of elasticity measures the capacity of the material to
take elastic deformation, and it is the stress/strain ratio, which can be determined from the slope
of the compressive force/deformation curve for cylindrical tissue specimens or whole fruit at
small levels of deformation prior to rupture (Figure 2.5) (Abbott, 1999).

38
 

Figure 2.5 Force/deformation (F/D) curves for cylindrical tissue specimens from firm and soft
apples under constant strain-rate (0.42 mm/s) compression (Abbott, 1999).
Both sonic and ultrasonic vibration techniques have been applied for evaluating fruit
firmness. Ultrasonic waves can be reflected, transmitted, refracted or diffracted as they interact
with the fruit, which are directly related to the mechanical properties and geometry (i.e., size and
shape) of the fruit. Recent advances in ultrasonic technology for monitoring the quality of fruits
and vegetables have been reviewed by Mizrach (2008). The technique has been used for
measuring firmness and mealiness in some fruits, and different ultrasonic sources are needed for
different fruits in order to achieve good penetration (Bechar et al., 2005; Galili et al., 1993; Kim
et al., 2004; Mizrach et al., 2003). Sonic vibration method, on the other hand, measures
vibrational responses of fruit to sonic signals (i.e., impulse or sinusoidal) in the audible
frequency range for up to a few thousand Hz. Sonic firmness is calculated based on the mass of
the fruit and the first or second resonance frequency (Langenakens et al., 1997), depending on
39
 

the measurement configuration. The technique has been used for fruit firmness or stiffness
measurement (Chen and Debaerdemaeker, 1993; De Belie et al., 2000; Diezma-Iglesias et al.,
2004; Wang et al., 2006). Low-mass impact method provides another means for determining
fruit firmness, and the technique currently is commercially available for online sorting and
grading of fruit (De Ketelaere et al., 2006; Diezma-Lglesias et al., 2006).
Although numerous nondestructive mechanical methods have been reported, they are often
slow in measurement and difficult to implement for online applications. Moreover, these
mechanical methods are only limited to firmness evaluation. Therefore, new sensors that are
more reliable and faster and able to measure multiple quality attributes are needed to improve
industry profitability and meet the increasing demands from the consumer for better and more
consistent fresh products.
2.5.3

Optical Techniques
The electromagnetic spectrum from the shortest to longest wavelengths includes Gamma

rays, X-rays, ultraviolet, visible, infrared and radio waves (Figure 2.6). Optical techniques based
on the electromagnetic radiation for a specific spectral range have been developed for
nondestructive quality measurement of fruits and vegetables because of the rich information
obtained from light interaction with materials. For fruits and vegetables, the most useful spectral
regions are visible (400-770 nm) and near-infrared (770-2500 nm), while other spectral regions
such as ultraviolet and X-rays have also been found useful. Visible/near-infrared spectroscopic
and imaging techniques are most popularly used in postharvest quality inspection.

40
 

Figure 2.6 Diagram of the whole electromagnetic spectrum (Mohsenin, 1984).
Color is the basis for sorting many products into commercial grades, which is directly
related to pigments (e.g., chlorophylls, carotenoids, and anthocyanins) in the products, and can
be measured in the visible range. Near-infrared (NIR) spectroscopy is well suitable for the
determination of chemical compositions. The NIR region involves the responses of the molecular
bonds O-H, C-H, C-O and N-H. These bonds are subject to vibrational energy changes when
irradiated by NIR frequencies, and two vibration patterns exist in these bonds including stretch
vibration and bent vibration. The energy absorption of organic molecules in the NIR region
occurs when molecules vibrate or are translated into an absorption spectrum (Cen and He, 2007;
Williams and Norris, 2001). Chemical constituents, such as ethanol, water, sugars (glucose and
fructose), organic acids (citric, lactic, tartaric and malic acids), phenolic compounds and
oxidation in fruits and vegetables, either in combination or alone, have strong influences on the

41
 

quality evaluation of fruits and vegetables. In practice, NIR measurement can be classified into
three different modes: reflectance, transmittance and interactance (Figure 2.7). Transmittance
measurement is often applied for liquid samples, such as fruit juice, using glass or quartz
chamber with different sizes, while diffuse reflectance or interactance measurement is popular
for solid samples such as fruits (Abbott et al., 1997; Lu et al., 2000; McGlone et al., 2003). Over
the past two decades, considerable research has been reported on NIR technique for
nondestructive determination of firmness, soluble solids content, acidity, maturity, dry matter,
moisture and other characteristics of fruits and vegetables, including apple, pear, cherry, melon,
tomato, cucumber, potato, etc. (Carlomagno et al., 2004; Lammertyn et al., 1998; Pedro and
Ferreira, 2005; Sirisomboon et al., 2007).
(a)

(b)

Figure 2.7 Three different modes for NIR spectroscopic measurements: a) reflectance, b)
transmittance and c) interactance.

 
 

42
 

Figure 2.7 (cont’d)
(c)

Imaging techniques are widely used for classification or sorting of agricultural products
based on the recognition of shape, size, surface defect, and color (Brosnan and Sun, 2004; Chao
et al., 1999; Chinchuluun et al., 2009; Singh and Delwiche, 1994). Conventional imaging (e.g.,
monochrome and color camera) is based on the analysis of spatial information, acquired by a
digital imaging device, from the object, which is effective when quality attributes of a product
are related to its extrinsic characteristics. Recently, multispectral and hyperspectral imaging
techniques have been used for quality evaluation of horticultural and food products.
Multispectral imaging usually generates a set of images at fewer than 10 discrete wavelengths,
which can be obtained either by positioning a bandpass filter in front of a monochrome camera
(Park et al., 2004), or by capturing a series of spectral image using an acousto-optic tunable filter
or a liquid crystal tunable filter (Peng and Lu, 2006; Tran, 2000). Hyperspectral imaging
combines conventional spectroscopy and imaging techniques to acquire both spectral and spatial
information from an object simultaneously, enabling us to analyze product properties or
characteristics more reliably and completely than existing imaging and spectroscopic techniques.
The technique may be implemented by acquiring a sequence of narrow-band spectral images or
43
 

capturing scan line images with a full spectral range to create 3-D spatial-spectral data or
hypercubes (Bernhardt, 1995; Park et al., 2002). Many studies on multispectral imaging (Blasco
et al., 2009; Lu and Peng, 2007; Park and Chen, 1994) and hyperspectral imaging (ElMasry et al.,
2007; Lawrence et al., 2003; Lu, 2003) have been reported on quality and safety inspection of
food and agricultural products.
Besides spectroscopic and imaging techniques for the visible and NIR region, other optical
techniques have also been developed for quality inspection of agricultural and food products,
such as X-ray (Brecht et al., 1991; Haff et al., 2006; Schatzki et al., 1997), fluorescence and
delayed light emission (Abbott and Massie, 1985; Gunasekaran, 1990; Kolb et al., 2006; Noh
and Lu, 2007; Seiden et al., 1996), magnetic resonance and magnetic resonance imaging
(Barreiro et al., 2000; Kim et al., 1999; Koizumi et al., 2009). Techniques based on
electrochemistry, such as electronic nose and electronic tongue (Buratti et al., 2006; Infante et al.,
2008; Rudnitskaya et al., 2006; Zoltan et al., 2008), are used for measuring the concentration of
volatiles of fruits or vegetables to evaluate the ripeness.
Optical techniques are advantageous for nondestructive maturity and quality measurement
of horticultural products since they are generally nondestructive or noninvasive, fast, and more
easy to implement for offline and online applications. However, spectroscopic techniques such as
NIR mostly rely on statistical methods to establish empirical relationships between experimental
data and chemical compositions, while most imaging techniques are mainly restricted to
quantifying the physical or surface characteristics of the samples. Due to inadequate
understanding of, and technical challenges in measuring, light transfer in biological materials,
many optical techniques still are of empirical nature in measurement, and thus cannot provide
accurate, complete information about the optical characteristics or properties of food products.

44
 

Consequently, they have not been able to accurately measure fruit quality or establish reliable,
robust relationships or models for predicting the quality of fruit.

45
 

CHAPTER 3 OPTIMIZATION OF INVERSE ALGORITHM FOR ESTIMATING

OPTICAL PROPERTIES OF BIOLOGICAL MATERIALS
3.1 Introduction
When light scattering is dominant, the radiation transport equation can be simplified to a
diffusion approximation equation (Ishimaru, 1978). Direct solutions to the diffusion equation
coupled with appropriate boundary conditions, referred to as forward problems, provide a
quantitative description of light transport in the medium. The corresponding inverse problems,
also called inverse radiation transport problems, deal with estimating the optical properties of
turbid media.
Different approaches and methods have been developed for determining or measuring the
optical properties of turbid media. They may be divided into three groups: direct, empirical and
inverse (Cheong et al., 1990). Direct methods, such as the Beer-Lambert law for measuring
collimated light transmission, are based on some fundamental concepts and rules without using
any models to obtain optical parameters from measurements. The methods are conceptually
simple, but they can be used only for samples of simple geometry (e.g., thin slabs). Empirical
methods, on the other hand, obtain optical properties from the measured transmittance and
reflectance using mathematical models that are based on simplifications and restrictive boundary
conditions [e.g., Kubelka-Munk theory (Edstrom, 2004)]. As a result, empirical methods lack
accuracy and generality, and they are only suitable for samples of specific geometry. Unlike
direct and empirical methods, inverse methods determine optical properties by solving the
radiation transport equation coupled with appropriate boundary conditions and an inverse
algorithm. Inverse methods are of great interest to researchers because they are applicable to a
wide range of intact turbid materials with minimal or no sample preparation. Inverse methods
46
 

may be implemented using diffusion theory, inverse Monte Carlo (IMC) simulation, and inverse
adding-doubling (IAD). Being purely numerical, IMC and IAD achieve relatively high accuracy
by describing the light propagation more rigorously using the radiation transport equation
(Palmer and Ramanujam, 2007; Prahl et al., 1993). But they suffer the main drawback of
computational complexity with long computational time. In this work, a diffusion model was
chosen because it is more efficient and accurate for describing the radiation transport in turbid
media, needs less computational time, and is particularly useful for nondestructive measurement.
For the case of steady-state spatially-resolved reflectance for a homogeneous semi-infinite turbid
medium, Kienle’s model was used in this study (Kienle et al., 1996).
Because of the complexity of the analytical solution and potential experimental
difficulties/errors in measuring diffuse reflectance profiles from the medium, there exist
considerable difficulties in accurate estimation of the optical parameters from spatially-resolved
diffuse reflectance. In this work, the optical parameter estimation is formulated as a nonlinear
least squares optimization problem, which is based on several important assumptions (i.e.,
constant variance errors, uncorrelated errors, and the Gaussian distribution of errors). The results
will not be valid if these assumptions are violated and the data are not presented in appropriate
format. Proper data transformation and weighting methods should be considered when some of
the assumptions are violated. Moreover, to improve the accuracy of the parameter estimation, the
inverse algorithm and the experimental design need to be optimized and the information
involving measurement uncertainty, model efficiency, curve fitting errors, and parameter
characteristics should be acquired and analyzed.
Therefore, the overall objective of this part of the research was to optimize the inverse
diffusion theory algorithm and instrumental measurement for accurate estimation of the

47
 

absorption and reduced scattering coefficients from spatially-resolved diffuse reflectance data.
The specific objectives of this research were to: a) examine different data transformation and
weighting methods for nonlinear least squares estimates; b) perform sensitivity analysis to
determine an appropriate data transformation and/or weighting method to improve the inverse
algorithm for estimating the optical properties of turbid media; and c) assess the robustness of
the diffusion model and the inverse algorithm using statistical analysis.
3.2 Forward Problem
3.2.1

One-layer Diffusion Model for the Steady-state Case

Consider a semi-infinite turbid medium which is impinged upon perpendicularly by an
infinitely small light beam. Under steady-state condition, the diffusion equation (2.12) can be
rewritten as
D2(r)  a(r)  S (r)

(3.1)

where r  ( x, y, z) , D  1 / [3(  a   s ')] is the diffusion constant, and S (r) is the isotropic
scattering source. The solution of the fluence rate at the surface (z = 0) using the extrapolated
boundary in which the fluence rate is forced to be zero is given by (Farrell et al., 1992)
 ( r , z  0) 

1  exp(   eff r1 ) exp(   eff r2 ) 



4 D 
r1
r2


(3.2)

where eff  [3 a (  a   s ')]1/ 2 is the effective attenuation coefficient, r1  ( z02  r 2 )1/2 ,
r2  [( z0  2 zb )2  r 2 ]1/2 , r  ( x2  y 2 )1/2 is the source-detector distance, z0  ( a   s ')1 , and

zb  2 D

1  R e ff
1  R e ff

for the extrapolated boundary condition. Reff is the effective reflection

48
 

coefficient, which is equal to 0.4498 for the refractive index n = 1.35 (Haskell et al., 1994). The
diffuse reflectance calculated as the flux across the boundary is expressed by

R flux ( r ) 

1
4


1 exp(  eff r1 )
1 exp( eff r2 ) 
 ( z0  2 zb )( eff  )
 z0 ( eff  )

r1
r2
r12
r22





(3.3)

The final solution for the steady-state spatially-resolved diffuse reflectance for a single-layer
material derived by Kienle and Patterson (1997) is given below

R1layer (r )  C1(r , z  0)  C2 R flux (r )

where C1 

(3.4)

1
3
2
2 [1  R fres ( )]cos d  and C2  4 2 [1  R fres ( )]cos  d  are constants
4

determined by the relative refractive index mismatch at the tissue-air interface, in which R fres ( )
is the Fresnel reflection coefficient for a photon with an incident angle  relative to the normal
to the boundary, and  is the solid angle. Details on these parameters can be found in the
literature (Haskell et al., 1994). For a refractive index n = 1.35, a typical value for many
biological materials (Mourant et al., 1997), C1 and C2 are equal to 0.1277 and 0.3269,
respectively. Hence, the diffuse reflectance R(r) at the surface of the turbid medium is a function
of the source-detector distance (r) as well as two unknown optical parameters of the medium.
3.2.2

Monte Carlo Simulation

For accurate estimation of the optical parameters of turbid media, the diffusion model and
inverse algorithm were validated by MC simulations. The MC simulation assumes that an
infinitely narrow photon beam is normally incident on the surface of the medium, which is
considered infinitely wide compared to the spatial extent of photon distribution. For a
49
 

homogenous medium, the light transport is determined by its refractive index (n), absorption
coefficient (µa), and reduced scattering coefficient (µs').
A publicly available MC simulation program for light propagation in biological materials
was used (Wang et al., 1995b). The low-noise reflectance generated by MC simulation provided
an ideal measurement without introducing experimental uncertainties. Several groups of
absorption and reduced scattering coefficients that are similar to the optical properties of fruits
were selected.
3.3 Inverse Problem
3.3.1

Nonlinear Least Squares Inverse Algorithm

To extract the optical properties from the spatially-resolved diffuse reflectance for a turbid
medium, a suitable inverse algorithm should be selected. Equation (3.4) shows that the two
optical parameters may be estimated based on the measured reflectance when no a priori
information related to these parameters is given.
Nonlinear least squares method was used to find the minimum of the sum-of-squares of the
difference between the true reflectance and predicted reflectance values with estimated
parameters. A large-scale algorithm such as a subspace trust-region method based on the interiorreflective Newton approach was selected to achieve the algorithm optimization (Thomas and Li,
1994). It is defined by minimizing a quadratic function subject only to an ellipsoidal constraint,
and is globally and locally quadratically convergent. The interior-reflective Newton approach
can generate iterates in the strictly feasible region by using a new affine scaling transformation,
and the speed of convergence is accelerated by following a reflective line search technique. A
preconditioned conjugate gradients (PCG) method was used to produce an approximate solution
50
 

to a large linear system in each iteration (Thomas and Li, 1994). The upper bandwidth of
preconditioner for PCG was 2, which was determined by the preliminary implementation of the
algorithm to achieve a better quality step towards the solution and also by consideration of the
number of PCG iterations to reduce the computational time. The inverse algorithm for parameter
estimations was implemented using the Toolbox function ‘lsqcurvefit’ in Matlab 7.5 (The
MathWorks, Inc., Natick, MA).
3.3.2

Data Transformation and Weighting Methods

In this study, two data transformation methods including logarithm and integral
transformation for the experimental data and the diffusion model were used before the curve
fitting process. In addition, the diffusion model with relative weighting (RWDM) was also used
for the nonlinear least squares curve fitting to extract the optical properties, and the results were
compared with those obtained from the data transformation methods with absolute weighting



[  Robs  R pred

3.3.3



2

] . The details of LTDM, ITDM, and RWDM are presented in Section 2.4.3.

Sensitivity Analysis

To better understand how the changes in the reflectance profiles of the diffusion model are
attributed to the changes in the optical parameters, sensitivity analysis was performed before the
inverse algorithm was implemented. The sensitivity coefficients for the original diffusion model
(ODM), LTDM, ITDM, and RWDM were calculated by equations (3.5)-(3.8), which were
derived from equation (2.29).

X ori _   

R


51
 

(3.5)

 log( R)


(3.6)

X int_   

Rint


(3.7)

X RW _   

R
R

(3.8)

X log_   

The sensitivity coefficients defined in equations (3.5)-(3.8) have the same unit as the dependent
variable and can be readily compared for different parameters. In these equations, the sensitivity
coefficients are expressed in absolute values in order to facilitate the comparison of different
parameters. In this study, sensitivity coefficients were first calculated for the absorption and
reduced scattering coefficients using the finite difference method. They were examined against
the Monte Carlo simulation data to determine if it is possible to estimate individual optical
parameters before an inverse algorithm was developed.
3.3.4

Statistical Analysis and Model Assessment

Statistical analysis was conducted to interpret the results of parameter estimation. It
systematically considers the characteristics of the model and algorithm. Several statistical
parameters used for assessing the mathematical model and analyzing the curve-fitting results are
listed in this section. The equations given below are based on the ODM. Corresponding
equations for the transformed models can be derived easily from these given equations. To
compare the estimated optical parameters by fitting the MC simulation data to the diffusion
model with the true values, the relative errors are calculated by
ˆ
  t
 100%
t

52
 

(3.9)

ˆ
ˆ
ˆ
where  is the estimated value for optical parameter  a or s ' , and βt is the true value of µa or

µs'.
The residual for reflectance is given by
resi  Robs,i  R pred ,i

(3.10)

The sum-of-squares for the n data points are minimized by the nonlinear least squares
regression to obtain the estimated values of µa and µs'.
n

SS   resi 2

(3.11)

i 1

The variance-covariance matrix gives the information about the standard error   of the
parameters. The vector of   is the square root of the corresponding diagonal of the symmetric
parameter

   diag ([ J T J ]1 s2 )

(3.12)

where    [ a ,  s ' ] , in which   a and   s ' are the standard errors of µa and µs',
J   R pred is the estimated Jacobian, and s 2 

1
SS is the mean squared residual with p
n p

parameters.
To compute the confidence intervals (CIs) for the two parameters, the ‘NLPARCI’ (beta,
residuals, Jacobian) function in Matlab was used.
3.4 Simulation Experiments
To validate the diffusion model and the inverse algorithm by using MC simulations, the
medium was considered to be turbid and semi-infinite. Absorption and reduced scattering
53
 

coefficients are two input parameters for the MC simulation model, and their values determine
the simulation results. Thirty-six different combinations of µa and µs' and their transport mean
-1

free path [1mfp' = (µa+µs') ] were selected (Table 3.1), which span a large range of values:
-1

-1

0.04  µa  8 cm , 4  µs'  40 cm

and 5  µs'/ µa  100 . These values were chosen based on

the published data for the optical properties of fruit and other food products (Budiastra et al.,
1998; Cubeddu et al., 2001b; Qin and Lu, 2008). For groups 5, 6 and 12, MC simulations gave
zero reflectance at large source-detector distances due to large values for µa and µs'. Therefore,
these three groups are not included in the following discussion. The refractive index of the
medium was assumed to be 1.35, similar to that of fruit (Mourant et al., 1997), and the refractive
6

index for the medium above was 1.0, equal to that for the air. A total of 3×10 photons and 0.1
mm spatial resolution of both radial distance and depth were used to produce the reflectance for
the spatial distance of 0.1- 10 mm. The MC generated diffuse reflectance profiles were then
fitted by the inverse algorithm for the diffusion model to deduce the optical properties of the
media. MC simulations introduced small stochastic variability in the calculated reflectance for
any given set of optical properties; in this study the average variability was 0.8-3.1%, generated
from five simulations for each set of optical properties.
Table 3.1 Thirty-six combinations of the absorption (µa) and reduced scattering coefficients (µs')
and their corresponding transport mean free path ( mfp' ) used in Monte Carlo simulations (unit:
-1

cm

for µa & µs', and mm for mfp').

Group no.
1
2

µa
µs'/ µa = 5
0.80
1.40

µs'
4
7

mfp'

Group no.

2.08
1.19

19
20
54

 

µa
µs'/ µa = 50
0.08
0.14

µs'

mfp'

4
7

2.45
1.40

Table 3.1 (cont’d)
3
4
*5
*6

2.00
4.00
6.00
8.00

7
8
9
10
11
*12

µs'/ µa = 10
0.40
0.70
1.00
2.00
3.00
4.00

10
20
30
40
4
7
10
20
30
40

0.83
0.42
0.28
0.21

21
22
23
24

2.27
1.30
0.91
0.45
0.30
0.23

25
26
27
28
29
30

µs'/ µa = 20
13
0.20
4
2.38
31
14
0.35
7
1.36
32
15
0.50
10
0.95
33
16
1.00
20
0.48
34
17
1.50
30
0.32
35
18
2.00
40
0.24
36
* These groups were excluded in the data analysis.

0.20
0.40
0.60
0.80

10
20
30
40

0.98
0.49
0.33
0.25

µs'/ µa = 70
0.06
0.10
0.14
0.29
0.43
0.57

4
7
10
20
30
40

2.46
1.41
0.99
0.49
0.33
0.25

µs'/ µa = 100
0.04
0.07
0.10
0.20
0.30
0.40

4
7
10
20
30
40

2.48
1.41
0.99
0.50
0.33
0.25

3.5 Results and Discussion
3.5.1

Comparison between the Diffusion Model and Monte Carlo Simulations

Figure 3.1 shows the spatially-resolved diffuse reflectance calculated from the diffusion
model and MC simulations for the two sets of optical properties with µs'/ µa = 5 and µs'/ µa =
100. Overall, the reflectance profiles calculated from the diffusion model well match those from
MC simulations, except for small distances close to the light source, where relatively large
differences are observed. However, the differences of reflectance are affected by the ratio of µs'/
µa. The average differences for groups 1-4 with µs'/ µa = 5, groups 7-11 with µs'/ µa = 10, and
groups 13-36 with 20  µs'/ µa  100 are 18.1%, 10.8%, and 4.3%, respectively, for the source55
 

detector distances of greater than 1.5 mm. With relatively large values for µs'/ µa (i.e., ≥10) the
differences between the diffusion model and MC simulations become smaller, which can be
explained by the scattering dominated condition for the diffusion model. Hence the optical
properties with 10  µs'/ µa  100 (a total of 29 groups in Table 3.1) were used in the parameter
estimation. Larger deviations for reflectance are observed in Figure 3.1 when the detector is
close to the light source (less than one transport mean free path), because the diffusion
approximation is not valid in this situation. These results indicate that overall the diffusion model
accurately quantifies light propagation in the turbid media.
(a)
0

Reflectance (mm-2)

10

-2

10

-4

10

0

2

4
6
Distance (mm)
(b)

8

10

0

2

4
6
Distance (mm)

8

10

0

Reflectance (mm-2)

10

-5

10

Figure 3.1 Comparison of the spatially-resolved diffuse reflectance obtained from the diffusion
model (symbols) and Monte Carlo simulation (solid lines): (a) µs'/ µa = 5, and (b) µs'/ µa = 100.
56
 

3.5.2

Sensitivity Coefficients

The sensitivity coefficients for the absorption and reduced scattering coefficients for the
ODM, LTDM, ITDM, and RWDM were calculated as functions of the source-detector distance
(ranging between 1 mfp' and 10 mm) for the corresponding transformed diffuse reflectance
profiles [equations (3.5)-(3.8)]. Figure 3.2 shows the sensitivity coefficients as well as the diffuse
-1

-1

-

reflectance for two sets of optical properties with µa = 0.06 cm , µs' = 4 cm , and µa = 0.57 cm
1

-1

, µs' = 40 cm . In all of the four models, the magnitudes of the reduced scattering sensitivity

coefficients are generally closer to those of the corresponding values of R. Moreover, the shapes
of the two sensitivity coefficients are quite different. These observations show that values for the
sensitivity coefficient of µs' are ‘large’ (i.e. on the order of R) and uncorrelated to those for the
sensitivity coefficient of µa (different shapes), which are desirable conditions for estimating µs'
in all four models with the exception of the sensitivity coefficients of µs' at the distance larger
than 3 mm in Figure 3.2(a2). Furthermore, in general, the sensitivity coefficients for µs' are
closer to the values of reflectance R at small source-detector distances than those at far sourcedetector distances, while the situation is different for the sensitivity coefficient of µa. This is
because under the scattering dominant condition (µs'  µa), diffuse reflectance close to and far
from the incident point of the light source does not have equal sensitivity to the optical properties
of the medium. Overall, signals close to the source depend strongly on the reduced scattering
property, whereas those far from the source exhibit large dependence on the absorption effect.
This information is useful for determination of the minimum and maximum source-detector

57
 

distances for the curve fitting, and also provides a guide for the selection of appropriate data
transformation and weighting methods.
(a2)
-2

4

x 10

Sensitivity coefficient (mm )

-2

Sensitivity coefficient (mm )

(a1)
-3

3
2
1
0

4

6
8
Distance (mm)

10

0.3
0.2
0.1
0

2

Sensitivity coefficient (mm )

-2

-2

Sensitivity coefficient (mm )

6
4
2
6
8
Distance (mm)

4
6
8
Distance (mm)

10

(b2)

8

4

)

0.4

(b1)

0

(

10

20
15
10
5
0

2

4
6
8
Distance (mm)
-1

10
-

Figure 3.2 Scaled sensitivity coefficients of the optical parameters [µa = 0.06 cm & µs' = 4 cm
1
-1
-1
for the left pane of plots (a1, b1, c1, d1), and µa = 0.57 cm & µs' = 40 cm for the right pane
of plots (a2, b2, c2, d2)] as functions of the source-detector distance for ODM (a1, a2), LTDM
(b1, b2), ITDM (c1, c2), and RWDM (d1, d2). Solid curves are for R, dash curves for µa and dot
curves for µs' (a.u. = arbitrary unit).

58
 

Figure 3.2 (cont’d)
(c2)

0.08
0.06
0.04
0.02
0

4

6
8
Distance (mm)

10

Sensitivity coefficient (a.u.)

Sensitivity coefficient (a.u.)

(c1)

0.15
0.1
0.05
0

2

1.5
1
0.5
0

4

6
8
Distance (mm)

10

(d2)

Sensitivity coefficient (a.u.)

Sensitivity coefficient (a.u.)

(d1)

4
6
8
Distance (mm)

10

6
4
2
0

2

4
6
8
Distance (mm)

10

Values of the sensitivity coefficient for µa are relatively smaller compared with those for µs'
due to much smaller values of µa than those of µs', especially for the ODM Figure 3.2a. However,
with the use of the data transformation or relative weighting methods, values for the sensitivity
coefficient of absorption have increased, as shown in Figure 3.2b, 3.2c, and 3.2d. This means
that better estimations of µa can be achieved with the data transformation or relative weighting
methods. Since in most cases, values of the reduced scattering sensitivity coefficient are still
59
 

larger in magnitude than those of the absorption sensitivity coefficient, µs', on average, would be
estimated more accurately than µa for the diffusion model.

3.5.3

Estimation of Optical Parameters based on Monte Carlo Simulation Data

Figure 3.3 shows the relative errors of estimating the absorption and reduced scattering
coefficients of the turbid media by fitting ODM, LTDM, ITDM, and RWDM to the MC
simulation data with the true values of optical properties shown in Table 3.1. The same fitting
range with 1.5 mm minimum source-detector distance and 10 mm maximum source-detector
distance for each group was used, which covered 86 detector positions with the resolution of 0.1
mm. The average relative errors for the 29 sets of optical properties extracted from ODM,
LTDM, ITDM, and RWDM are 16.8%, 10.4%, 10.7%, and 11.4% for µa, respectively, and 8.1%,
6.6%, 7.0%, and 7.1% for µs', respectively. Better estimations of µs' were obtained, which are in
agreement with the sensitivity analysis. The patterns of the relative errors in estimating µa and
µs' obtained from these models are similar for the 29 simulation groups. Larger errors of µa for
ODM appear in the groups with the largest and smallest mfp' for the same ratios of µs'/ µa, with
the exception of µs'/ µa = 5. This is probably because the preselected 1.5 mm minimum sourcedetector distance is too small for those groups with large mfp' compared with the optimal
position of 1-2 mfp' , and because the diffusion theory is unable to account for the nondiffuse
component of the reflectance that is encountered for these small source-detector separations.
Relatively large errors of estimating µs' with ODM were also obtained for those groups with the
small value of mfp' [Figure 3.3(b)], due to the removal of the reflectance data close to the light
60
 

source. Therefore, it is important to select an optimal source-detector distance range in the
experimental design and curve fitting process. It is also observed in Figure 3.3 that the error
curves of µa and µs' are strikingly symmetric, which indicates that they are highly correlated.
Hence when one of the parameters is overestimated, the other is likely to be underestimated in
the nonlinear least squares.
(a)

a

Relative error of  (%)

60
40
20
0
-20
-40

10

15

20
Group no.
( )

25

30

35

25

30

35

Relative error of   (%)
s

(b)
20
10
0
-10
-20
-30

10

15

20
Group no.

Figure 3.3 Relative errors of estimating 29 groups of µa (a) and µs' (b) shown in Table 3.1 by the
original model, and the data transformation and relative weighting methods: ODM (·), LTDM (◦),
ITDM (*) and RWDM (∆).
The errors of estimating µa and µs' dramatically decrease when the data transformation and
weighting methods are applied to most of the data groups. The logarithm transformation of the
61
 

raw data gives the best results with the smallest average errors of estimating the two optical
parameters. However, the data transformation and weighting methods do not yield smaller errors
-1

-1

-1

-1

for group 11 (µa = 3.00 cm , µs' = 30 cm ) and group 18 (µa = 2.00 cm , µs' = 40 cm ), when
compared with those obtained using the original model. For these two cases, large values for the
absorption and reduced scattering coefficients do not allow photons to travel farther away from
the incident beam, resulting in extremely small reflectance at large source-detector distances.
With small reflectance, the variability from MC simulations rapidly increases at large distances,
which is further magnified when the data transformation and weighting methods are
implemented. This suggests that it is also important to consider the signal-to-noise ratio (SNR) of
the measured data used for the parameter estimation.
To investigate the effect of the SNR of the experimental data on the parameters estimation,
we examined the optical parameters extracted from the LTDM-generated diffuse reflectance data
added with different levels of noise. Figure 3.4 shows absolute values of the relative errors of
-1

estimating µa = 0.40 cm

-1

and µs' = 20 cm

under different noise levels. The error of estimating

the optical parameters increases linearly with the noise level. If the maximum acceptable error is
5% in the parameters estimation, the noise level should be controlled to less than 5%. The errors
of estimating µa are consistently higher than those of estimating µs' at different noise levels,
which is consistent with the sensitivity analysis that µs' can be estimated more accurately. As the
noise level increases, uncertainties in the MC simulation results also increase, which is clearly
manifested by an unusually high estimation error at the noise level of 14% (Figure 3.4). Similar
results and patterns were also obtained for the other groups of optical properties shown in Table
3.1.
62
 

Absolute values of relative error (%)

25

20

15

10

5

0

0

5

10

15

Noise level (%)

Figure 3.4 Absolute values of the relative errors of estimating the optical properties (µa = 0.40
-1

-1

cm , µs' = 20 cm ) for different noise levels (each noise level includes 10 replications). Solid
circles represent the absorption coefficient, while open circles are for the reduced scattering
coefficient.
3.5.4

Statistical Analysis

Nonlinear least squares estimates are based on a set of statistical assumptions. The above
results were further tested by examining the validity of these assumptions. In this study,
independent variable (source-detector distance r) is known precisely and nonstochastically, and
all the “error” comes from the dependent variable (reflectance R). For different data
transformation/weighting methods, the runs test (change of sign plus 1) of groups 25 and 30 was
conducted based on the plots of the residual versus source-detector distance shown in Figure 3.5.
The average numbers of runs of these two groups for the ODM, LTDM, ITDM, and RWDM are
4.5, 42, 3, and 41, respectively. The expected number of runs for the independent disturbances
along the source-detector distance is about half of the measurements. There are 86 observations
63
 

for each group, and the numbers of runs from ODM and ITDM are considerably smaller than
86 / 2  43 , while the numbers of runs from LTDM and RWDM are close to the expected

numbers of runs. Similar numbers of runs were obtained for other cases. It indicates that the
residuals in ODM and ITDM are highly correlated, which violates the assumption of
uncorrelated errors. Hence it is not appropriate to select the original model or integral
transformation for the parameters estimation. The frequencies of residuals for groups 25 and 30
from ODM, LTDM, ITDM, and RWDM are shown in Figure 3.6. The distributions of the
residuals approximately follow a normal distribution except for the one shown in Figure 3.6(c2).
Further examination of the distributions of residuals was conducted for other groups of optical
parameters; they follow similar patterns as shown in Figure 3.6: normal distributions are always
observed for LTDM and RWDM, while this normal distribution assumption is violated by using
ODM and ITDM in several cases. Hence, it can be concluded that the logarithm transformation
and relative weighting methods are more suitable and reliable for accurate estimation of the
absorption and reduced scattering coefficients of turbid media.

x 10

(a)

(b)

1
0
-1
-2
-3

0.2

-2

Residual (mm )

-2

Residual (mm )

2

-4

0

2

4
6
8
Distance (mm)

0.1
0
-0.1
-0.2

10

0

2

4
6
8
Distance (mm)

10

Figure 3.5 Residual plots for the reflectance data versus source-detector distances from (a) ODM,
-1
-1
(b) LTDM, (c) ITDM, and (d) RWDM with µa = 0.06 cm & µs' = 4 cm (dot curve) and µa =
-1

-1

0.57 cm & µs' = 40 cm (asterisk curve).
64
 

Figure 3.5 (cont’d)

x 10

(d)

0.2
-2

Residual (mm )

-2

Residual (mm )

2

(c)

-4

1
0
-1
-2

0.1
0
-0.1
-0.2

0

 

2

4
6
8
Distance (mm)

10

Frequency

Frequency

20

10

10

30
20
10
0
-1

-2
0
2
-2
-4
Residual (mm ) x 10
(b1)

-0.5
0
0.5
1
-2
-4
Residual (mm ) x 10
(b2)

15

15
Frequency

Frequency

4
6
8
Distance (mm)

40

30

10
5
0
-0.1

2

(a2)

(a1)

0
-4

0

-0.05
0
0.05
-2
Residual (mm )

10
5
0
-0.2

0.1

-0.1
0
0.1
-2
Residual (mm )

0.2

Figure 3.6 Residual histograms for the reflectance data from ODM (a), LTDM (b), ITDM (c),
-1
-1
and RWDM (d) with 1) µa = 0.06 cm & µs' = 4 cm for the left pane of plots (a1, b1, c1, d1),
-1

-1

and 2) µa = 0.57 cm & µs' = 40 cm for the right pane of plots (a2, b2, c2, d2).
65
 

Figure 3.6 (cont’d)

10

30
Frequency

Frequency

(c2)

(c1)

5

0
-2

20
10
0
-15

-1
0
1
2
-4
Residual (a.u.) x 10
(d1)

(d2)

15
Frequency

Frequency

10

5

0
-0.1

-10
-5
0
5
Residual (a.u.) x 10-5

-0.05

0

0.05

10
5
0
-0.2

0.1

-2

Residual (mm )

-0.1
0
0.1
-2
Residual (mm )

0.2

As examples, the estimated optical parameters for groups 25 and 30 (Table 3.1) extracted
using the nonlinear least squares for the LTDM method are shown in Table 3.2. Figure 3.7 shows
the corresponding 3D plots of sum-of-squares, which provide information about the
characteristics of the standard error, confidence intervals and relative ease of convergence of the
nonlinear regression routine (Mishra et al., 2008). It is observed that the sum-of-squares surface
in Figure 3.7(a) is much shallower along both µa-axis and µs'-axis than in Figure 3.7(b), causing
the difficult convergence of group 25 to find the lowest point on that surface, while it is easy to
visualize the optimization of µa and µs' in Figure 3.7(b) for group 30. For the two groups, the

66
 

surfaces of both plots are shallower along the µa-axis than along the µs'-axis, resulting in the
standard errors and confidence intervals for µa to be larger than those for µs', which are
consistent with the results shown in Table 3.2. Better convergence can be obtained if the curve
shows steeper changes along both µa-axis and µs'-axis.
Table 3.2 Statistical results for estimating the optical parameters using the LTDM method.
Group parameter
no.
25
30

True value
-1
(cm )
0.06

µa

Estimated
-1
value (cm )
0.07

Standard
-1
Error (cm )
0.015

Relative
Error (%)

95% asymptotic
confidence interval

16.7

[0.069, 0.072]
[3.77, 3.81]

4.0

µs'

0.23

- 5.0

0.59

0.129

3.5

[0.560, 0.616]

40.0

µa

3.8

0.57

µs'

38.8

6.60

- 3.0

[37.34, 40.02]

Sum of Squares (mm -4)

(a)

-7

x 10
4

7.4

3
7.2

2
0.382

-3

x 10
7  (mm -1)
a

0.38
-1
s  (mm ) 0.378

0.376

6.8

Figure 3.7 3-D plot of sum of squares for (a) group 25 and (b) group 30 using the LTDM method.
 

67
 

Figure 3.7 (cont’d)

Sum of Squares (mm-4)

(b)

-6

x 10
2

1

0
3.7

0.055

0.06
3.8

3.9
-1
s  (mm )

-1
a (mm )

4

4.1

0.065

 

3.6 Conclusions

In this research, an inverse algorithm combined with data transformation and weighting
methods was applied in solving the inverse radiation transport problem for estimating the optical
properties of biological materials. The results for the estimation of µa and µs' from the Monte
Carlo generated reflectance data show that the minimum and maximum source-detector distances
and signal-to-noise ratio should be considered in order to obtain sufficient and accurate
information to uniquely determine µa and µs'. Sensitivity analysis demonstrates that the reduced
scattering coefficient can be estimated more accurately than the absorption coefficient, which is
also validated by the simulation results. The logarithm and integral transformation of the original
data and the relative weighting method greatly improve the estimations of the two optical
parameters with the relative errors of 10.4%, 10.7%, and 11.4% for µa, and 6.6%, 7.0% and 7.1%

68
 

for µs', which are much smaller than those obtained from the original diffusion model. Further
statistical analysis shows that the logarithm transformation and relative weighting methods can
improve the inverse algorithm to obtain more reliable estimations of the two optical parameters.
The present work on parameter estimation, combined with statistical analysis, provides an
appropriate means and guide in quantifying estimation errors for the optical properties. It
suggests that attention should be paid on studying the characteristics and complexity of a
mathematical model when it is used in an inverse algorithm for estimating their parameters. The
methods proposed in this work should help us better interpret light propagation in biological
materials and more accurately determine the relevant optical properties.

69
 

CHAPTER 4

OPTIMIZATION OF THE HYPERSPECTRAL IMAGING-BASED
SPATIALLY-RESOLVED SYSTEM

4.1 Introduction

Measurement of the optical properties of biological materials can be achieved using either
direct or indirect methods. Direct methods (e.g., total transmittance and reflectance) are easy to
carry out, but they are destructive or invasive. In contrast, indirect methods can be performed on
intact samples nondestructively but need sophisticated instrumentation and complex
mathematical models. Therefore, recent research has been focused on indirect methods,
including time-resolved (TR), frequency-domain (FD), and spatially-resolved (SR). Based on
radiation transfer theory, these indirect methods allow noninvasive or nondestructive
measurement of the optical properties from intact biological samples. While TR and FD
techniques have been extensively researched in the biomedical area, they may not be most
suitable for food and agriculture because of expensive instrumentation, slow speed in
measurement, and the requirement of good contact between the sample and detector. In
comparison, spatially-resolved technique is less expensive in instrumentation, and it is easier to
use and faster in measurement. The technique is, thus, potentially more viable for food and
agriculture applications.
A hyperspectral imaging-based spatially-resolved technique was recently developed in our
lab to measure the optical properties of biological materials for a broad spectral range (i.e., 5001,000 nm) simultaneously (Cen and Lu, 2009; Qin and Lu, 2007). While the technique is
promising for optical characterization of food and agricultural products, several critical issues
need to be resolved. First, a reference method is needed to provide true values of the optical
properties of samples, against which the hyperspectral imaging system can be evaluated and
70
 

validated. This would require model samples with known optical properties for a specific range
of values. Several reference methods including transmittance, integrating sphere and empirical
equation have been reported (Prahl et al., 1993; van Staveren et al., 1991); however, they have
not been accepted as ‘standard’. Therefore, it is necessary to test and cross-validate these
methods in order to provide accurate and reliable references for the optical system. Second, the
hyperspectral imaging system needs to be such designed that it fully meets the requirements of
the diffusion theory that governs light transfer in turbid biological materials. The hyperspectral
imaging-based spatially-resolved system uses a continuous-wave point light beam to illuminate
the sample. The shape and size of the beam can directly affect measurement accuracies. It is
therefore important to examine and optimize the light beam. Third, an appropriate sourcedetector distance is critical for accurate estimate of the optical properties. Additionally,
optimization of the inverse algorithm for the diffusion theory model is equally important in
extracting the optical parameters from the reflectance profiles, which has been described in
Chapter 3.
This research was therefore aimed at addressing key technical issues in the development of
the hyperspectral imaging-based spatially-resolved technique, so that it can provide accurate and
reliable measurement of the optical properties of food and agricultural products. The specific
objectives were to: a) evaluate and cross-validate three reference methods (i.e., transmittance,
integrating sphere, and empirical equation) for determining the true values of optical properties
of model samples, so as to establish a standard procedure of evaluating the hyperspectral
imaging system; b) optimize the design of the light beam and source-detector distance in the
hyperspectral imaging system, using Monte Carlo (MC) simulation and experiments for model
samples, to improve the measurement of the absorption and reduced scattering coefficients; and c)

71
 

assess the performance of the hyperspectral imaging system in terms of accuracy,
precision/reproducibility, and sensitivity.
4.2 Materials and Methods
4.2.1

Hyperspectral Imaging-based Spatially-resolved Technique

In the spatially-resolved method, a small continuous-wave light beam perpendicularly
illuminates the sample’s surface, and the remitted light is measured at different distances from
the light source to obtain a spatially-resolved reflectance profile (see Figure 2.4).
A laboratory hyperspectral imaging system in line scan mode used for acquiring spatiallyresolved diffuse reflectance profiles from a sample is schematically shown in Figure 4.1(a). The
system mainly consisted of a high performance 512×512 pixel camera with a back-thinned
illuminated CCD detector (Model C4880-21-24A, Hamamatsu Photonics Systems, Bridgewater,
NJ, USA) covering the wavelengths of 200-1,100 nm, an imaging spectrograph (ImSpector V10,
Spectral Imaging Ltd., Oulu, Finland) covering the wavelength region of 400-1,000 nm, a zoom
lens with the focal length of 11-110 (10×) mm (Zoom 7000, Navitar Inc., Rochester, NY, USA),
a quartz tungsten halogen light source (Oriel Instruments, Stratford, CT, USA) with a feedback
controller, an optical fiber coupled with a focusing lens for delivering a small beam to the sample,
and a computer installed with a frame grabber board for controlling the camera and acquiring
images. The hyperspectral imaging technique, combining imaging and spectroscopy methods,
acquires both spectral and spatial information simultaneously, and it is, therefore, ideally suitable
for measuring spatially-resolved diffuse reflectance profiles for a broad wavelength region. To
improve the repeatability of measurements, 10 line scans were taken from each sample for every
1 mm horizontal displacement over a range of 9 mm as the sample was moving at the

72
 

predetermined velocity during the image acquisition [Figure 4.1(b)]. The sample movement and
positioning were controlled by the two motorized stages, and the distance between the sample
and the lens was 243 mm. Spectral and spatial calibrations and nonuniform instrument response
corrections for the hyperspectral imaging system were performed by following the procedure
described in the literature (Lu and Chen, 1998; Qin and Lu, 2007).
(a)

Figure 4.1 Hyperspectral imaging-based spatially-resolved method: (a) schematic showing the
major components of the system; (b) top view of multi-line scanning mode for acquiring
spatially-resolved reflectance profiles.
 
 
 
 
 

73
 

Figure 4.1 (cont’d)
(b)
Scan line

Point light source
Sample moving direction

Figure 4.2(a) shows a typical hyperspectral reflectance image for a liquid model sample
made up of Intralipid fat emulsion as scatterers and blue dye as absorbers (see more details in
Section 4.2.2). Each horizontal line taken from the image represents one spatially-resolved
reflectance profile at a specific wavelength, as shown in Figure 4.2(b). Hence the reflectance
image which had a calculated spectral resolution of 4.55 nm by the spectral calibration, in effect,
consisted of more than 100 spatially-resolved reflectance profiles for the wavelengths of 5001,000 nm. Since the spatially-resolved reflectance profiles were symmetric to the light incident
point, the two sides were averaged in the extraction of optical properties. Each spatially-resolved
reflectance profile was then fitted by the diffusion model with the inverse algorithm, from which
the spectra of absorption and reduced scattering coefficients for 500-1,000 nm were obtained.

74
 

(a)

(b)
12000
Intensity(CCD count)

Wavelength (nm)

400

600

800

-5
0
5
10
Distance (mm)

700 nm

8000
6000
4000

570 nm

2000
0
-10

1000
-10

10000

-5

0
5
Distance(mm)

10

Figure 4.2 Hyperspectral reflectance image of a liquid model sample: (a) 2-dimensional (2-D)
display with intensities being indicated by pseudo colors, and (b) original spatially-resolved
reflectance profiles at 570 nm and 700 nm.
4.2.2

Model Samples Preparation

To optimize and evaluate the hyperspectral imaging system, 12 liquid model samples were
created with two different dyes (Direct Blue 71 and Naphthol Green B, Sigma-Aldrich Inc., St.
Louis, MO, USA) and their mixture as absorbers and fat emulsion (Intralipid-20%, SigmaAldrich Inc., St. Louis, MO, USA) as scatters for different concentration levels. The three dye
absorbers were used in the model samples to allow fine adjustment of the absorption coefficient
and comprehensive investigation of the accuracy for estimating µa over the entire spectral region
of 500-1,000 nm because each dye had high absorption for a specific wavelength range. For each
absorber, aqueous absorbing stock solution with the concentration of 1 mg/mL was first prepared,
and it was then added to 250 mL distilled water followed by adding different volumes of
Intralipid (10-50 mL) into the absorbing solutions to form the model samples with specified
values of µa and µs'. The ranges of µa and µs' values for these model samples were 0.0-0.934
-1

-1

cm and 7.0-39.9 cm , respectively, at the wavelength range of 500-1,000 nm.
75
 

The model samples were first measured using the hyperspectral imaging system [Figure
4.1(a)]. Each sample was scanned in a 600 mL cylindrical beaker with 80 mm diameter and the
solution height of approximately 50 mm, which can be considered semi-infinite. Prior to imaging
acquisition, the liquid model samples were gently stirred by a magnetic stirrer until the absorbers
and scatters were distributed homogenously. The beaker containing the liquid model sample was
placed on a flat platform fixed on the motorized stage, and the images were then acquired after
the solution was stable. After the imaging, confocal laser scanning microscopy (CLSM) images
of these model samples were acquired for gaining an insight of the distribution and interaction of
the dye and Intralipid particles in the solution. This is because when the dye and Intralipid were
mixed, the two components could interact with each other, which might in turn affect the
stability of its mixture and thus of the optical properties (Ren et al., 2007). Finally, the true
optical properties of these model samples were measured using the reference methods discussed
below.
4.2.3

Reference Methods

The true values of µa and µs' of the model samples were needed to validate the hyperspectral
imaging system. However, in the real situation, it is impossible to obtain true µa and µs' of the
model samples. Therefore, nominal true values (or reference values) were derived as reliable
estimates of the true values by using three commonly used methods, and evaluation and crossvalidation of these methods were performed.
A collimated transmittance method was first employed for the standard absorption
measurement using a miniature fiber optic spectrometer (USB4000-VIS-NIR, Ocean Optics,
Dunedin, FL, USA) with a 10-mm pathlength quartz cuvette sitting in a cuvette holder (Figure
76
 

4.3). The true values of µa at the wavelengths of 500-1,000 nm were calculated by the BeerLambert law

 a   ln

Is  Id
Ir  Id

(4.1)

where Is is the sample intensity, Id is the dark intensity, and Ir is the reference intensity (empty
cuvette). The accuracy of the transmittance measurement was experimentally quantified by
testing In-Spec® certified UV and visible standards (Standard 0.10, 0.5, 0.8, and Background
solution, GFS Chemicals, Inc., Columbus, OH, USA) with known µa at selected wavelengths
provided by the manufacturer.

Spectrometer

Light source

Cuvette holder with
sample

Computer

Figure 4.3 Collimated transmittance measurement for absorption using a miniature fiber optic
spectrometer. 
For each absorber, eight concentration levels of pure absorbing solutions with the absorption
-1

coefficient varied from 0.0 to 1.800 cm

for the wavelength range of 500-1,000 nm were made

for transmittance measurements, which covered the range of µa for the model samples. The
linear relationship between the absorption coefficient and the concentration of each absorber was

77
 

established at each wavelength, and the absorption coefficient was then derived based on the
concentration of the absorber in the model samples.
A 152.4 mm diameter integrating sphere (RT-060-SF, Labsphere, Inc., North Sutton, NH,
USA) with a 12.7 mm diameter detector port and a 25.4 mm sample port was used for collecting
the total transmittance and reflectance to estimate true values of the absorption and reduced
scattering coefficients of the model samples (Figure 4.4). The sphere was coated with
®

Spectraflect

diffuse reflectance materials with 98% reflectance at 500-1,000 nm. A quartz

tungsten halogen light source was used and the light received from the sample port of the
integrating sphere by a 400 µm diameter fiber was delivered to the miniature fiber optic
spectrometer, the same one used in the collimated transmittance measurement (Figure 4.3). Each
model sample held in a 2 mm pathlength cuvette was placed in the sample holder. For measuring
total diffuse reflectance [Figure 4.4(a)], the sample was placed at the sample port and the light
beam was arranged at the beam entrance port. For total transmittance measurements [Figure
4.4(b)], the sample was placed at the sample port with other ports covered by the standard masks,
and all light transmitted through the sample was collected by the detector. The same beam size
was used for both reflectance and transmittance measurements to ensure measurement accuracy.
(b)
Detector

(a)
Detector

Rsample
Sample

Specular
exclusion
Tsample
Light
beam

Light
beam
Sample

Figure 4.4 Single integrating sphere configurations for: (a) total diffuse reflectance measurement,
and (b) total transmittance measurement.
78
 

After completion of the total transmittance and reflectance measurements, an inverse
adding-doubling algorithm developed by Prahl et al. (1993) was used to calculate µa and µs'
values of the model samples based on the total reflectance and transmittance. Prahl et al. (1993)
reported that the accuracy of the integrating sphere with the adding-doubling algorithm for
determining the optical properties (µa & µs') was 2-3% for most reflectance and transmittance
values. However, a 1% variation in the reflectance and transmittance values would result in
errors of 0.4% for µs' and 17% for µa. This suggests that the integrating sphere method could be
problematic in estimating µa.
For estimating the µs' of Intralipid scatterers, an empirical equation derived by van Staveren
et al. (van Staveren et al., 1991) is widely used, which has been experimentally proved to have
accuracies better than 6% in the wavelength range of 400-1,100 nm. Therefore, µs' values
obtained from the integrating sphere were also compared with those from the empirical equation
given below

s '  (928 1.4  160 2.4 )C %

(4.2)

-1

where µs' is in cm ,  is the wavelength in µm, and C% is the percent Intralipid concentration.
For easy comparison of the results obtained from the hyperspectral imaging system and the three
∆

reference methods, the absorption and reduced scattering coefficients are denoted as µa & µs'
*

*

o

∆

for the hyperspectral imaging system, µa & µs' for the integrating sphere, µa for the
o

transmittance measurement, and µs' for the empirical equation.

79
 

4.2.4

Optimization of the Light Beam and Source-detector Distance

To achieve accurate measurement of the optical properties, optimization of the hyperspectral
imaging system was performed for two key factors, i.e., light beam and source-detector distance.
In the experimental setup, a finite size beam was used to illuminate the sample, which deviates
from the solution of the diffusion model that was derived for an infinitely small beam. Therefore,
the effect of the incident beam on the determination of the optical properties was investigated
based on MC simulation, which offers a flexible and accurate approach for quantifying the
optical features of light transport that are difficult to measure experimentally.
In the simulation experiment, a semi-infinite medium was described by its refractive index
(n), absorption coefficient (µa) and reduced scattering coefficient (µs'). The spatially-resolved
reflectance generated by MC simulation for an infinitely small photon beam was first convolved
for the finite size beam using the programs ‘MCML’ and ‘CONV’ developed by Wang et al.
(1997, 1995b). Two specific beams, i.e., Gaussian and circularly flat, were investigated.
Meanwhile, the error of estimating µa and µs' caused by the finite size Gaussian beam with the
diameter of 0.1 ≤ d ≤ 2 mm was quantified. Six sets of µa and µs' with the ranges of 0.060 ≤ µa ≤
-1

2.000 cm

-1

and 4.0 ≤ µs' ≤ 40.0 cm

and with the ratios of µs'/µa = 20 and µs'/µa = 70 were

investigated.
In conjunction with the MC simulations, actual beam profiles for the hyperspectral imaging
system were measured and characterized. This was accomplished by moving and imaging the
beam for every 0.12 mm distance (determined by the width of scan line) in the direction
perpendicular to the scan line. Twelve 512×512 pixel images were acquired with the resolution
of 0.1 mm along the scan line direction, and the 3-D beam profiles were then reconstructed from
80
 

these images at each wavelength, from which the beam profile type (i.e., Gaussian and flat) and
beam circularity were determined. The circularity of the beam was calculated based on the
roundness (Rd), which is given by
Rd  4 A / P 2

(4.3)

where A and P are the beam area and perimeter, respectively, and Rd = 1 for circle.
Accurate information on the source-detector distance, including minimum source-detector
distance (rmin), maximum source-detector distance (rmax) and spatial resolution, is required for
determining the range of the spatially-resolved reflectance profile. MC simulation experiments
were first conducted to investigate the effects of the minimum and maximum source-detector
-1

distances on estimating 29 sets of µa and µs' with 0.040 ≤ µa ≤ 3.000 cm and 4.0 ≤ µs' ≤ 40.0
-1

cm . In experimental measurements, signal-to-noise ratio (SNR) should be considered when
determining the optimal maximum source-detector distance since SNR varies at different
radiation locations and decreases with the decreasing signal. Ten images from a model sample
were acquired at the same location. The mean profile divided by the standard deviation of the
CCD count at each wavelength was considered as an estimate of SNR.
Sufficient data points for the spatially-resolved reflectance profile are needed to obtain good
estimates of µa and µs'. Hence the effect of spatial resolution on calculating the optical
coefficients was also examined. The reflectance profile with the resolution of 0.01 mm for µa =
-1

1.000 cm

-1

and µs' = 20.0 cm

was firstly obtained from the diffusion model. Seven new

reflectance profiles with the spatial resolution ranging from 0.07 mm to 0.25 mm were then
derived from the original profile by integration of the light intensity over the area covered

81
 

between the two adjacent data points divided by the corresponding spatial resolution. These
seven profiles were fitted by the diffusion model to obtain the estimated µa and µs', and they
were then compared with the true values of µa and µs' obtained from the reflectance profile with
the resolution of 0.01 mm.
4.2.5

Assessment for Accuracy, Precision/Reproducibility, and Sensitivity

Assessment of the performance of the system is an important step to determine its validity,
reliability, and robustness. The hyperspectral imaging system was evaluated for accuracy,
precision/reproducibility, and sensitivity. The accuracy of a measurement is defined as the
closeness of agreement between the measured values and the nominal true values of parameter 
(αmeas & αtrue) such as µa and µs' obtained from the reference methods under optimal
experimental conditions. Accuracy can be quantified by the relative error of the measurement,
given in equation (4.4)



 meas   true
 100%
 true

(4.4)

Accuracy is important for the absolute measurement, i.e., for simulating light transport and
deriving the physiological information about the biological tissue.
Precision/reproducibility is a term frequently used to characterize the random error and
describe the system consistency of measurement over a long time period. It quantifies how the
system is self-consistent over different times, and it is particularly important for a long time
experiment like fruit quality monitoring during postharvest. Repetition of the measurement on
the same model samples under the same experiment conditions over a period of four days was

82
 

performed. The precision of the system was evaluated by calculating the coefficient of variation
(CV) with respect to the average values calculated over the entire experiment.
Sensitivity is described by the minimum detectable value under an acceptable noise level,
and it determines the detection limit. Clearly, the noise level is affected by the signal intensities
and detection efficiencies, and thus the sensitivity of the system depends on the amount of signal
acquired at each measurement point. Sensitivity analysis is especially important in measuring
biological materials with small values of absorption coefficient. The analysis was performed on a
blue dye model sample which had minimal levels of the absorption coefficient for the
wavelengths of 500-1,000 nm.
4.3 Results and Discussion
4.3.1

Accuracy of the Reference Methods

Figure 4.5 shows the measured absorption spectra of the three standard solutions by
transmittance as well as the true absorption values provided by the manufacturer. The average
error of µa by the transmittance measurement was 3% at 500-850 nm, and less than 5% at 850-1

900 nm with the minimum detectable value of 0.050 cm . The performance of the method for
measuring µa above 900 nm was not evaluated because the true absorption values of these
standard solutions were not available. However, it was found that the water absorption at 970 nm
-1

measured by the transmittance method was 0.414 cm , which is within 1.4% of the reported data
(Hale and Querry, 1973). Hence, it was concluded that the transmittance method gave accurate
measurement of the absorption coefficient with errors less than 5%, and it was therefore
appropriate for determining µa of the model samples.
83
 

2.5

µa (cm-1)

2
1.5
1
0.5
0
500

600

700
800
Wavelength (nm)

900

Figure 4.5 Spectra of the absorption coefficient for the three standard solutions measured by the
transmittance method [asterisks () for standard 0.1, triangles () for standard 0.5, and squares
() for standard 0.8] and their true vlaues (solid lines).
Integrating sphere measurements of µs' for the 12 model samples were compared with the
calculated values from the empirical equation. It was found that the empirical equation, on
average, overestimated µs' measured with the integrating sphere method by 9% for the
wavelengths of 500-900 nm when the Intralipid concentration ranged between 0.8% and 3.2%.
However, at low Intralipid concentrations (i.e., <1.2%), the measured values of µs' from the
integrating sphere matched well the calculated values from the empirical equation with the
differences being less than 4.5% (Figure 4.6). As the concentration of the Intralipid increased,
the measured value deviated more from the calculated value. This may be because the
relationship between the reduced scattering coefficient and the particle concentration at high
density Intralipid solutions was no longer linear, as reported by Giusto et al. (2003) and Zaccanti
et al. (2003). The empirical equation was derived based on the linear relationship between µs'
and the particle concentration. In addition, variation in batches of Intralipid might have also
84
 

existed, which, in turn, could have introduced errors in calculating µs' values. In view of these
results, it was concluded that the integrating sphere method would give more accurate
measurement of µs' than the empirical equation for a wider range of µs', and it was therefore used

Average difference of µs' (%)

to determine the true µs' of the model samples.

20
16
12
8
4
0
0.5

1

1.5

2

2.5

3

3.5

Concentration of Intralipid (%)
Figure 4.6 Average differences of the reduced scattering coefficient for the model samples at
different concentrations of Intralipid for 500-900 nm obtained from the integrating sphere
measurement and the empirical equation.
4.3.2

Light Beam Characteristics

Since a Gaussian beam, like most optical beams, does not have sharp physical edges, the
beam size is usually determined between the two points that contain a selected percentage of the
2

‘useful’ energy. In this study, the size of Gaussian beam was defined by the 1/e diameter, where
the beam’s power is at 13.5% of the maximum height. Figure 4.7 shows the spatially-resolved
reflectance profiles obtained for an infinitely small beam and flat and Gaussian beams of
different sizes through Monte Carlo simulations. The Gaussian beam and the flat beam nearly
85
 

gave the same results for the same beam diameter of d = 1 mm. Finite circular beams with
different sizes generated reflectance similar to that produced by the infinitely small beam when
the source-detector distance was larger than the beam size (r > d). The average errors of
estimating six sets of µa and µs' from the reflectance generated by the Gaussian beam of different
sizes are presented in Figure 4.8(a). The error produced by the finite beams relative to the
infinitely small beam was less than 1% for the beam size of less than 0.5 mm; it increased
linearly with the beam size larger than 0.5 mm. Generally, a 1-mm light beam introduces around
5% error of estimating µa and µs' compared to the infinitely small beam. These results suggest
that the beam in the system should be less than 1 mm in size in order to control the error to
within 5%. The error introduced by a finite beam was also influenced by the value of the optical
properties, as shown in Figure 4.8(b) and (c). The error curves are relatively flat for small values
of µa and µs', which indicates that beam size had less effect on the smaller µa and µs' than on
large µa and µs'.

86
 

0

10

Infinitely small beam
Flat beam with d=1mm
Gaussian beam with d=1mm
Gaussian beam with d=2mm

Reflectance (mm-2)

-1

10

-2

10

-3

10

-4

10

0

2

4
6
Distance (mm)

8

10

Figure 4.7 Comparison of spatially-resolved reflectance produced by an infinitely small beam, a
flat beam with diameter of d = 1 mm, and a Gaussian beam with d = 1 and 2 mm.
(a)

Relative error (%)

15

a
s 

10
5
0
-5

0

0.5

1
1.5
Beam size (mm)

2

Figure 4.8 Error analysis for different beam sizes: (a) average errors of estimating six sets of
-1
-1
optical properties with 0.060 ≤ µa ≤ 2.000 cm and 4.0 ≤ µs' ≤40.0 cm , and the ratios of µs'/µa
= 20 and µs'/µa = 70; and (b) and (c) relative errors for three sets of optical properties with
-1
-1
increased µa and µs' from A to C with µa = 0.006, 0.029, 0.057 cm and µs' = 0.4, 2.0, 4.0 cm .

87
 

Figure 4.8 (cont’d)
(c)

(b)
30
A
B
C

30

Relative error of  s  (% )

Relative error of  a (%)

40

20
10
0

0

0.5
1
1.5
Beam size (mm)

2

A
B
C

20

10

0

0

0.5
1
1.5
Beam size (mm)

2

Simulation results for the light beam showed that it is necessary to understand beam
characteristics (i.e., beam profile, shape, and size) in the experimental measurements. Figure 4.9
gives an example of the measured 3-D beam profiles and 2-D contours at the wavelengths of 650
nm and 950 nm. The beam at the visible and short near-infrared region had a good Gaussian
distribution and its shape was circular with the roundness Rd = 0.986 (  1 ). Based on the
commonly accepted method for defining the size of Gaussian beam, the beam size in the current
setup was 0.83 mm, which would have contributed to less than 4% error in estimating µa and µs'
based on the simulation experiments. Although a smaller beam is preferred, other factors such as
light intensity or throughput and measurement repeatability also need to be considered in the
optical design.

88
 

(b)
Intensity (CCD count)

Intensity (CCD count)

(a)
650nm

10000
5000
0
1

0.5
0
D2 (mm) -0.5

-1

0

-1

0.5

1

950nm

3000
2000
1000
0
1

0.5
0
D2 (mm) -0.5

-0.5
D1 (mm)

(c)

-1

-1

0.5

1

-0.5
D1 (mm)

(d)

1

1

650nm

950nm

0.5

0.5
D2 (mm)

D2 (mm)

0

0

-0.5

0
-0.5

-1
-1

-0.5

0
D1 (mm)

0.5

-1
-1

1

-0.5

0
D1 (mm)

0.5

1

Figure 4.9 three-dimensional profiles (a and b) and 2-dimensional (c and d) contours of the
incident light beam at wavelengths of 650 nm and 950 nm, where D1 is the direction along the
scan line and D2 is perpendicular to the scan line.
4.3.3

Source-detector Distance

Two examples of the relative errors between the true (values selected for Monte Carlo
-1

simulations) and estimated values of µa = 0.290 cm
-1

µs' = 30.0 cm

-1

-1

& µs' = 20.0 cm , and µa = 0.430 cm &

at different ranges of the source-detector distance are shown in Figure 4.10. For

each set, 23 fittings were performed with 0.2 ≤ rmin ≤ 4 mm & rmax = 10 mm, and 4 ≤ rmax ≤ 10
mm & rmin = 1.5 mm. The estimated parameters from the reflectance data containing the
smallest minimum source-detector distance (rmin = 0.2 mm) resulted in the largest errors for

89
 

both µa and µs' [Figure 4.10(a1) and (a2)]. Values of the absorption coefficient were
systematically underestimated, while those of the reduced scattering coefficient were
overestimated. These results may indicate the failure of the diffusion model which does not
account for the nondiffusive component of the reflectance at these small source-detector
distances. As the minimum source-detector distance was increased, the errors decreased,
reaching minimum for rmin  0.5 mm (1 mfp', i.e., transport mean free path) to 2 mm (4 mfp') [1
-1

mfp' = (µa+µs') ], depending on the values of µa and µs'. For the minimum source-detector
distance from 2 to 4 mm, the errors were relative stable. Also, the symmetrical curves of the
relative errors of µa and µs' indicated that these errors were highly correlated. Patterns similar to
Figure 4.10 were obtained for a wide range of the optical parameters.

8

Relative error (%)

Relative error (%)

10

(a1)

12
4
0
-4

0

1

2

3

4

-8
-12

Minimum source-detector distance
(mm)
 

(a2)

6
2
-2 0

1

2

3

4

-6
-10

Minimum source-detector distance
(mm)
 

Figure 4.10 Relative errors of estimating µa (squares) and µs' (asterisks) from the spatiallyresolved reflectance data generated by Monte Carlo simulations when using different minimum
-1
-1
and maximum source-detector distances: (a1) and (b1) µa = 0.290 cm & µs' = 20.0 cm , and
-1

-1

(a2) and (b2) µa = 0.430 cm & µs' = 30.0 cm .

 

90
 

Figure 4.10 (cont’d)
20

(b1)
Relative error (%)

Relative error (%)

8
4
0
4

5

6

7

8

9

10

-4
-8

Maximum source-detector distance
(mm)

10
0
4

5

6

7

8

9

10

-10
-20

 

(b2)

Maximum source-detector distance
(mm)
 

The optimal minimum source-detector distance of rmin

 1-4 mfp' found in this study is

different from the study of Nichols et al. (1997) (0.75-1 mfp') but is consistent with the finding
of Farrell et al. (1992) that the minimum source-detector distance should be larger than 1 mfp'.
However, in practice, there is no a priori information about the exact values of µa and µs' over a
specified wavelength range, and thus it is difficult to determine the optimal minimum sourcedetector distance based on these loose criteria. But considering the average errors of 29 sets of
µa and µs' that were investigated in the simulation experiments, the smallest average estimated
errors of µa and µs' were obtained when rmin = 1.5 mm. Experimentally, the minimum sourcedetector distance should also be larger than the incident beam size (rmin > 0.83 mm). Hence, the
1.5 mm minimum source-detector distance selected in the system was considered optimal.
Similar error patterns were found for the maximum source-detector distance, as shown in
Figure 4.10(b1) and (b2). With rmax changing from 4 mm to 10 mm, the error varies between
0.03%-19% for µa, and 0.09%-13% for µs'. The optimal maximum source-detector distance

91
 

varied with the values of µa and µs', approximately between 10-20 mfp', which is also in
agreement with Nichols et al. (1997) and Pham et al. (2000). Hence, the maximum sourcedetector distance should be optimized to obtain accurate estimates of µa and µs'. In practice, the
optimal maximum source-detector distance may be largely determined by the SNR. As shown in
Figure 4.11, to control the minimum SNR of 20 (corresponding to 5% of the variation
coefficient), the signal level should be greater than 150 CCD counts at 650 nm with the
maximum source-detector distance around 7.7 mm. A similar threshold of the signal level was
obtained at other wavelengths with 150±12 CCD counts, while the maximum source-detector
distance varied at different wavelengths for this signal level. Therefore, the threshold of 150
CCD counts (SNR = 20) was used in the curve fitting to determine the maximum source-detector
distance at each wavelength.
(a)

Reflectance (CCD count)

5

10

4

10

3

10

2

10

1

10

2

3

4

5
6
7
Distance (mm)

8

9

10

Figure 4.11 Signal-to-noise ratio measurement of the hyperspectral imaging system: (a) average
spatially-resolved reflectance profile of 10 measurements of a model sample at 650 nm, and (b)
signal-to-noise ratio of the measurements within 10 mm source-detector distance.

92
 

Figure 4.11 (cont’d)
(b)
Signal-to-noise ratio

500
400
300
200
100
0

2

3

4

5
6
7
Distance (mm)

8

9

10

Further, the change of spatial resolution from 0.07 mm to 0.25 mm introduced an
insignificant error of 0.53% for µa and 0.36% for µs' relative to the optical properties obtained
for the resolution of 0.01 mm, as shown in Figure 4.12. In the system setup, the highest spatial
resolution that the imaging sensor can achieve was 0.1 mm without binning. To reduce
measurement time and also enhance the signal-to-noise ratio, the 0.2 mm spatial resolution with
2×2 binning was selected in our measurements since high resolution is not critical in this case.

Relative error (%)

0.6
0.4

µa
µs'

0.2
0.0
0.05
-0.2

0.10

0.15

0.20

0.25

-0.4
-0.6

Spatial resolution (mm)

-1

-1

Figure 4.12 Errors of estimating µa = 1.00 cm and µs' = 20.0 cm introduced by different
spatial resolutions relative to the optical properties obtained for the resolution of 0.01 mm.
93
 

4.3.4

Accuracy, Precision/Reproducibility, and Sensitivity

Figure 4.13 shows the measured absorption and reduced scattering spectra for three model
samples over 500-1,000 nm, determined by the hyperspectral imaging system and the reference
methods. As can be seen from the plots on the left pane of Figure 4.13 (i.e., a1, b1 and c1), the
shape of the absorption spectra for the three dyes obtained by transmittance, integrating sphere
and hyperspectral imaging system was similar. They all showed a blue dye absorption peak at
585 nm [Figure 4.13(a1)], green dye absorption peak at 714 nm [Figure 4.13(b1)], mixed dye
absorption peak around 600 nm [Figure 4.13(c1)], and water absorption at 970 nm in all three
*

plots. However, the µa values measured by the integrating sphere (µa ) were far off compared
∆

with those from transmittance (µa°) and hyperspectral imaging (µa ). Similar results were
reported by Saeys et al. (2008) when they compared the integrating sphere measurement with the
time-resolved method. It could be due to the fact that light losses at the sample edge are not
accounted for in the integrating sphere measurement, and also, µa is very sensitive to the
measured reflectance and transmittance according to Prahl et al. (1993) and Chen et al. (2006).
Hence, the accuracy of hyperspectral imaging measurements for µa was evaluated against the
transmittance method. The average errors of µa were calculated at 530-700 nm for the blue dye,
600-850 nm for the green dye, and 530-800 nm for the mixed dye, because the transmittance
method was unable to measure µa at very small levels for some wavelengths. Overall, the
average error of estimating µa for all model samples was 23% at 530-850 nm, and 16%, 26% and
26% for samples with blue, green, and mixed dyes, respectively. For the three model samples
with small amount of blue dye, the absorption caused by the blue dye was almost zero at 750 nm,
94
 

and thus the absorption at 750 nm for these samples was mainly attributed to the water. The
-1

reported results show that water absorption at 750 nm is between 0.0247 to 0.0286 cm

(Prahl,

-1

1998), and our result of µa = 0.0275 ± 0.0006 cm falls in this range and is only 1% different
-1

compared with the recent report from Martelli et al. (2007) with µa = 0.0278 cm .
(a1)

(a2)

µa (cm-1)

µs' (cm-1)

1.4
Transmittance
1.2
Hyperspectral imaging
1.0
Integrating sphere
0.8
0.6
0.4
0.2
0.0
-0.2 500 600 700 800 900 1000
Wavelength (nm)

20
18
16
14
12
10
8
6

Empirical equation
Hyperspectral Imaging
Integrating sphere

500

1.4
1.2
1
0.8
0.6
0.4
0.2
0

(b2)
20
18
16
14
12
10
8
6

Transmittance
Hyperspectral imaging
Integrating sphere

Empirical equation
Hyperspectral imaging
Integrating sphere

µs' (cm-1)

µa (cm-1)

(b1)

600 700 800 900 1000
Wavelength (nm)

500

500

600 700 800 900 1000
Wavelength (nm)

600 700 800 900 1000
Wavelength (nm)

Figure 4.13 Spectra of absorption and reduced scattering coefficients of three model samples
with (a) blue dye, (b) green dye, and (c) mixed dye as absorbers measured by the hyperspectral
imaging and reference methods.

95
 

Figure 4.13 (cont’d)

1.4
1.2
1
0.8
0.6
0.4
0.2
0

(c2)
20
18
16
14
12
10
8
6

Transmittance
Hyperspectral imaging
Integrating sphere

500

Empirical equation
Hyperspectral imaging
Integrating sphere

µs' (cm-1)

µa (cm-1)

(c1)

500

600 700 800 900 1000
Wavelength (nm)

600 700 800 900 1000
Wavelength (nm)

For most samples, µa from the hyperspectral imaging measurement, on average, was
underestimated. A possible explanation for the discrepancies is that the dye might have interfered
with the Intralipid particles. The confocal laser scanning microscopy (CLSM) images of the
Intralipid solutions with blue and green dyes in Figure 4.14 showed that some dye particles,
which were much smaller than Intralipid particles, went into the lipid vesicles in the Intralipid,
resulting in a low dye concentration in the solution. It was also observed during the CLSM
experiment that the Intralipid particles were relatively stable in the blue dye sample, while they
were actively moving in the green dye sample. Since unstable scattering particles in the model
samples could have an effect on the measurement, this may explain why better estimations of µa
were obtained from the blue dye samples compared with those from the green and mixed dye
model samples. It was also found that the hyperspectral imaging-estimated absorption above 900
nm was consistently lower for all the samples, particularly at the water absorption band of 970
nm. This might have been caused by the beam position change due to the different diffraction of

96
 

the focusing lens in the near-infrared region, which needs to be confirmed in further research.
Therefore, the absorption above 900 nm was not used in calculating the accuracy.
(a)

(b)

 

 

Figure 4.14 Confocal laser scanning microscopy images of Intralipid solutions with (a) blue dye,
and (b) green dye.
The spectra of µs' presented in Figure 4.13(a2), (b2) and (c2) show that the measured values
∆

*

(µs' ) matched well with those obtained from the integrating sphere measurement (µs' ) at 500900 nm, and lower than those calculated from the empirical equation (µs'°). The average error of
estimating µs' was 7% at 500-900 nm compared with the integrating sphere measurement. The
divergence of µs' above 900 nm appeared between the integrating sphere method and the
wavelength-dependent exponential decay function of µs'. It is difficult to know which method is
more accurate for determining µs' at the wavelength above 900 nm because no published paper
reported the µs' values of Intralipid in these wavelengths. However, this wavelength-dependent

97
 

exponential decay function of µs' could be violated with the variation of the refractive index at
long wavelengths according to the study of Mourant et al. (1997).
When comparing our measurement accuracy with other techniques or other spatiallyresolved methods, one should notice the differences of experimental conditions, model samples
and wavelength ranges. Bays et al. (1996) reported 32% accuracy of µs' at 633 nm for
polyoxymethlene model samples by using a spatially-resolved reflectometry. Pifferi et al. (2005)
applied a general protocol for assessing several optical methods for determining optical
properties, and they reported large differences from different instruments in measuring the same
model samples with the maximum discrepancies of 32% for µa at 970 nm and 41% for µs' at 820
nm. Spichtig et al. (2009) used the frequency-domain technique to measure the optical properties
of Intralipid model samples with accuracies being less than 10% for µa and 31% for µs' at eight
wavelengths. While covering a wider wavelength range of optical properties, the hyperspectral
imaging-based spatially-resolved method has achieved superior results for measuring µa and µs',
compared with these reported studies that were only conducted at single or several wavelengths.
The system precision or reproducibility was calculated by repeated measurements of a blue
dye model sample at four different days under the same experimental conditions with a 30 min
warm-up time and the same level of source power and acquisition time. The coefficient of
variation (or CV) in the absorption peak at 585 nm was 2.4% for µa and 3.8% for µs' with the
maximum discrepancies of 4.9% and 6.3%, respectively. However, the model sample could have
undergone some small changes over the four days, thus inducing some variations in the optical

98
 

properties of the tested sample. Hence the system has demonstrated good reproducibility and
consistency over a prolonged time period.
Ten measurements were performed on a model sample made up with the blue dye as the
absorber because its minimum absorption coefficient was almost zero for the wavelengths of
700-900 nm. The result of the sensitivity test on µa is presented in Figure 4.15, with the CV of µa
for the 10 measurements being plotted as a function of µa for different wavelengths. The
-1

minimum detectable value of µa was around 0.0082 cm

for a noise level of 10%. The

sensitivity of measuring µs', as determined by the CV values, was always less than 4% because
-1

µs' was much larger than µa for the investigated range of 7.0 ≤ µs' ≤ 40.0 cm .
3

Coefficient of variation of a (%)

10

2

10

1

10

0

10

0

0.02

0.04

0.06

0.08

0.1

0.12

-1

a (cm )

Figure 4.15 Coefficient of variation versus reordered ascending absorption coefficients of a
model sample at different wavelengths.

99
 

4.4 Conclusions

This research examined critical factors in the development of a hyperspectral imaging-based
spatially-resolved technique (i.e., methods for providing reference measures of the optical
properties, light beam and source-detector distance, etc.) for determining the absorption and
reduced scattering coefficients of biological materials over the wavelengths of 500-1,000 nm.
Monte Carlo simulations, coupled with experiments for model samples, demonstrated that to
achieve the best performance for the hyperspectral imaging system, the light beam should be of
circular shape and Gaussian type with the diameter of less than 1 mm, the optimal minimum
source-detector distance should be about 1.5 mm, and the optimal maximum source-detector
distance should be equivalent to 10-20 mfp' or determined by the minimum signal-to-noise ratio
of 20 (or 150 CCD counts for the system). Under these optimal conditions, the hyperspectral
imaging system achieved average accuracies of 23% for the absorption coefficient at 530-850
nm and 7% for the reduced scattering coefficient at 500-900 nm, when it was evaluated using the
model samples against the transmittance and integrating sphere methods. These results are better
than, or similar to, those obtained with other spatially-resolved sensing configurations, and
frequency-domain and time-resolved techniques for single or several wavelengths. The system
also had good reproducibility and sensitivity with the minimum detectable µa value of 0.0082
-1

cm . The research provided a systematic guide for optimizing and evaluating the optical system
and offered solutions to improve accuracy in measuring the absorption and reduced scattering
coefficients, which will be valuable for nondestructive quality evaluation of food and agricultural
products.

100
 

CHAPTER 5

DEVELOPMENT OF AN OPTICAL PROPERTY MEASUREMENT
PROTOTYPE

5.1 Introduction

A general-purpose bench-top optical property measurement prototype, which is named
‘Optical Property Analyzer’ (or OPA, as shown in Figure 5.1), was designed and built for optical
property measurement and hyperspectral image acquisition. The OPA was developed based on
the concept of hyperspectral imaging-based spatially-resolved technology and the optimization
studies on the inverse algorithm and optical designs presented in Chapters 3 and 4.
Several important factors were considered in designing and assembling the OPA. First, it
should be a stand-alone portable instrument incorporating the optimal optical designs, which is
easy to use and relatively low in cost. Second, it should be able to measure the optical properties
of turbid foods and biological materials for the visible and short-wave near-infrared region of
500-1,000 nm since rich information related to the quality attributes of food and agricultural
products can be obtained from this wavelength window. Third, the prototype should be such
designed that it can accommodate different sizes of samples whose effect on measurement of the
optical absorption and scattering properties would be minimized or eliminated. Fourth, the OPA
should also have full functions for acquiring and preprocessing hyperspectral images, which
would expand the scope of use for the instrument and thus reduce overall costs for the user.
Finally, it is important to develop integrated software for the OPA to control the hardware
including camera, light source and linear stage, and also be able to perform real-time data
processing and analysis for optical properties computation. Based on these considerations, the
first version of the OPA was designed and built.

101
 

Figure 5.1 Optical Property Analyzer (or OPA) for measuring optical properties and acquiring
hyperspectral images.
5.2 System Setup and Software Development
5.2.1

Optical Property Analyzer Setup

The hardware of the OPA includes three main parts: imaging, illumination, and sample
positioning as shown in Figure 5.2. The software for hardware control, imaging acquisition, and
data processing and analysis was developed using Microsoft Visual C#. Details of the hardware
and software in the OPA prototype are discussed in this section.

102
 

Figure 5.2 Schematic of the Optical Property Analyzer (or OPA) for measuring the optical
properties of biological materials.
The imaging unit consists of a high performance 14-bit electron-multiplying CCD (EMCCD)
camera (Luca

EM

R604, ANDOR

TM

Technology, South Windsor, Connecticut, USA), an

enhanced imaging spectrograph attached to the camera (ImSpector V10E, Spectral Imaging Ltd.,
Oulu, Finland) and a prime lens. Two different prime lenses are used alternatively to meet the
different field of view requirements for two types of measurement; one is for optical properties
measurement (Xenoplan 1.9/35, Schneider Optics, Hauppauge, NY, USA), and the other for
hyperspectral image acquisition (Cinegon 1.4/12, Schneider Optics, Hauppauge, NY, USA). The
EMCCD camera covers the wavelength range from 400 nm to 1,000 nm with the peak quantum
efficiency of 65% at 600 nm. It can operate with the EM gain off for conventional CCD
operation under strong illumination conditions, and with the EM gain on when the illumination
intensity is low. It utilizes a monochrome megapixel frame transfer EMCCD sensor with
1,004×1,002 pixels of 8×8 µm, and is thermoelectrically cooled down to -20 °C. The sensor has
103
 

-

an active pixel well depth of 30,000 electrons, a gain register pixel well depth of 80,000 e , a
-

-

system readout noise of 18 e and less than 1 e for typical use and electron multiplication,
respectively. The imaging spectrograph attached to the camera covers the wavelength range of
400-1,000 nm. The ImSpector Enhanced imaging spectrograph V10E is based on the principle of
transmission diffraction grating in a prism-grating-prism configuration which provides high
diffraction efficiency and good spectral linearity. The imaging spectrograph has a greater spatial
image width, high resolution (small spot size), low smile and keystone distortions at subpixel
level (smile <1.5 µm, keystone <1 µm), and high throughput with telecentric input. The imaging
spectrograph has the slit width of 30 µm and slit length of 14.2 mm with the optical resolution of
2.8 nm. Based on the grating equation, different wavelengths can be diffracted to the same place
on the detector surface. Therefore, an order-blocking filter (OBF) is installed between the
imaging spectrograph and the camera close to the detector sensor to prevent the second-order
below 500 nm from overlapping with the long wavelength range of 800-1,000 nm.
Two illumination systems including a point light source and a line light source are used in
the OPA for optical properties measurement and hyperspectral image acquisition, respectively.
Only the point light source is shown in Figure 5.2 since this study was focused on optical
properties measurement. A tungsten halogen light bulb with the output of 20 watts and the
variation of 0.5% (HL-2000-HP, Ocean Optics, Dunedin, FL, USA) is connected to a DC
regulated controller chips (PT6204N, 12V, Texas Instruments Inc., Dallas, Texas, USA), to
provide point light, which covers a broad wavelength range of 360-2,000 nm with a cooling fan
installed to keep the light source from overheating, thus maintaining its stability. A specially
designed optical fiber coupled with a focusing lens is used to deliver a circular beam with the
diameter of 1 mm at the focal point. The incident beam is arranged 1.5 mm away from the
104
 

scanning line with the angle of 15° with respect to the vertical axis, and it is parallel to the
scanning line, which allows to maintain the constant source-scanning line distance, thus
eliminating or minimizing errors in acquiring spatially-resolved reflectance that would be caused
by the sample position’s variation.
The sample positioning unit is composed of a motorized linear horizontal stage (Twintrac,
TSZ8020, US23T22104-8LS, US Automation, Laguna Hills, CA, USA) with the maximum
linear speed of 203 mm/sec, the maximum dynamic loading of 91 kg and a positioning accuracy
of 0.0006 mm/mm, a manually adjustable vertical stage and a sample holder for positioning
samples to the predetermined position. The stage motor (US23T22104-8LS, US Automation,
Laguna Hills, CA, USA) is connected to the bi-polar stepper motor driver (SideStep, Probotix,
Peoria, IL, USA).
The light source controller and the motor controller are connected to a microcontroller board
based on the ATmega168 (Arduino Duemilanove, Arduino, open-source electronics prototyping
platform), which is, in turn, connected to a Windows-based computer with a USB cable. A
specially developed software program in Arduino programming code is uploaded to the
microcontroller to accept serial commands from the host application software installed in the
computer to control stage movement and the light sources. The EMCCD camera is connected to
the computer through another USB cable. The application software controls the camera operation
by using Software Developer Kit (SDK) provided by the camera's manufacture.
5.2.2

Optical Property Analyzer Software Development

The OPA software contains three components, including main program, optical property
computation program, and microcontroller program, which were developed in three different
environments, as shown in Table 5.1. The main program was developed using Microsoft Visual
105
 

Studio and written in C#.NET language. The graphical user interface uses Multiple Document
Interface (MDI) style. It uses a third party external library to plot chart (PlotLab, a freeware
downloaded from http://www.mitov.com/html/plotlab.html) and also an SDK library
(Atmcd32cs.dll, library for C#) provided by Andor Corporation, the camera manufacturer.
Table 5.1 Components of the Optical Property Analyzer control software.
Component
Main program

Development Environment
Microsoft Visual Studio
(C# language)

Function
Multiple-Document Interface
(MDI) container to call dialogs
and functions;
interact with other components
to perform tasks (image
acquisition, motor control,
illumination control, and optical
property computations)

Optical property
computation program

MATLAB

Perform optical property
computation

Microcontroller
program

Arduino (C language)

Control linear stage;
control light sources

The OPA control software is designed for the system control (light source, camera and
stage), image acquisition, and optical property computation. The main window of the optical
property analyzer software is shown in Figure 5.3, which consists of File, Edit, View,
Acquisition, Tool, Windows, and Help menu, and each menu contains submenu related to a
particular task. File, Edit, and View menus are used to open, save, view and simply edit existing
images (images with .bil extension).

106
 

Figure 5.3 Main window of the Optical Property Analyzer software.
Figure 5.4 shows the window for setting parameters related to the camera, stage, illumination
and image saving functions for the optical properties measurement. This display window is
obtained by Control menu in Acquisition menu. Before images are acquired from samples, the
camera dark current images are collected first by clicking ‘Background’, ‘Back Sub’ in
Acquisition will be enabled, and the background image is then subtracted from the sample
images. Auto Increment mode can be used in the experiment, which saves images in multiband
format (ENVI format) with the given File Name and automatically adds sample number.

107
 

Figure 5.4 Display window of the Optical Property Analyzer for the image acquisition setup.
A user-friendly interface for calculating the spectra of absorption and reduced scattering
coefficients was also developed in the software, which includes two diffusion models and
corresponding inverse algorithms, preselected parameters, and data pre-processing methods
(Figure 5.5). After all parameters in the left column of ‘Optical Properties Computation Dialog’
are set up, image files, output directory and output file name are defined in the right column of
108
 

the dialog, and optical properties computations can be triggered with a processing message
window by clicking ‘Compute OP’. In addition, the software has Calibration and Diameter
menus as shown in Figure 5.6 for storing the spectral and spatial calibration information, and
sample size information, which can be recalled during the optical properties computation.

Figure 5.5 Display window of the Optical Property Analyzer for optical properties computation.
 
 

109
 

(a)

(b)

Figure 5.6 Display windows of the Optical Property Analyzer for (a) calibration information and
(b) sample size information.
5.3 System Calibration and Evaluation

To accurately measure spatially-resolved diffuse reflectance profiles from a sample, the
Optical Property Analyzer was calibrated spectrally and spatially by following the procedure
described in Lu and Chen (1998). Spectral calibrations were performed using a xenon lamp
(model 6033, Newport, Irvine, CA, USA), a mercury-argon lamp (model 6035, Newport, Irvine,
CA, USA) and a laser at 905 nm (model PM15/4586, Power Technology Inc., Little Rock, AR,
USA). Spatial calibrations were achieved using a telecentricity target with a series of parallel
lines (model 58404, Edmund Optics Inc., Barrington, NJ, USA). Finally, the OPA acquired twodimensional (2-D) spatially-resolved reflectance images with a spectral resolution of 3.1
nm/pixel in the vertical direction and a spatial resolution of 0.2 mm/pixel in the horizontal
direction.

110
 

The performance of the OPA was also evaluated for accuracy, stability, precision/
reproducibility, and sensitivity by using the homogenous liquid model samples described in
Section 4.2.2 and following the same procedures presented in Section 4.2.5 of Chapter 4. The
average estimated error for all model samples was 24% for µa and 7% for µs'. Figure 5.7 shows
the system reproducibility (or precision), and the coefficient of variation (or CV) in the
absorption peak at 555 nm was less than 10% for µa, and less than 4% for µs'. It has to be
mentioned that the absolute values of µa were very small, thus causing the relatively large error
of estimating µa compared with that of µs'. The main error sources for estimating µa and µs'
could have come from the light beam, source-detector distance, and inverse algorithm, according
to the optimization studies of the inverse algorithm and optical designs described in Chapters 3
and 4. Additionally, the result of the sensitivity measurement on µa is presented in Figure 5.8.
-1

The minimum detectable value of µa was 0.0117 cm . The sensitivity of µs', as determined by
the CV values, was always less than 3% because µs' was much larger than µa for the investigated
-1

range of 7.0 ≤ µs' ≤ 39.9 cm . These results showed that the Optical Property Analyzer has
achieved acceptable accuracies for measuring the absorption and reduced scattering coefficients,
which are either comparable to or superior to other reported studies using time-resolved,
frequency-domain, or other types of spatially-resolved instruments based on the discussion in
Section 4.3.4 of Chapter 4.

111
 

a

Relative variations of  (%)

(a)
15
10
5
0
-5
-10

1

2

3
day

4

5

4

5

Relative variations of   (%)
s

(b)
4
2
0
-2
-4
-6

1

2

3
day

Figure 5.7 Reproducibility of the Optical Property Analyzer for measuring absorption and
reduced scattering coefficients of a model sample at 555 nm at each measurement day with
respect to the average value calculated over 5 days.

112
 

3

Coefficient of variation of a (% )

10

2

10

1

10

0

10

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

-1

a (cm )
Figure 5.8 Coefficient of variation versus reordered ascending absorption coefficients of a model
sample at different wavelengths.

113
 

CHAPTER 6

MATURITY/QUALITY ASSESSMENT FOR APPLE AND PEACH
FRUIT USING OPTICAL PROPERTIES

6.1 Introduction

Fruit quality represents a combination of the attributes and properties that give them value in
terms of consumer’s satisfaction. Maturity determines the final quality of harvested fruit and how
fruit should be handled and marketed after harvest. The maturity/quality of fresh fruit is
determined by multiple indices including firmness, sugar (or soluble solids content), starch level,
and titratable acidity, as well as external appearance characteristics such as skin and flesh color
(Crisosto, 1994). Firmness directly influences the texture, shelf life and consumer acceptance.
Soluble solids content (SSC) and acidity determine the flavor of the fruit, while changes in the
skin/flesh color during fruit ripening are mainly related to the breakdown of chlorophylls and the
increase of other pigments. Methods commonly used for maturity/quality measurement include
Magness-Taylor (MT) firmness tester, Brix refractometry for SSC, and titratable methods for
acidity. These methods are destructive, time consuming and prone to operational error, and only
can test a small percentage of products. Therefore, nondestructive sensing techniques are needed
for analyzing and monitoring fruit maturity/quality.
Nondestructive assessment of maturity/quality of fresh products like apple is challenging
because their properties and characteristics can vary greatly within each fruit and between
cultivars and are also affected by environmental factors, postharvest storage condition, etc. A
number of nondestructive techniques based on measurement of the optical, mechanical, and
electrical properties have been developed to evaluate fruit maturity/quality. In this study, an
advanced optical technique for measuring absorption and scattering properties was used for
assessing the quality of apple and peach fruit. Absorption is mainly related to the chemical
114
 

compositions of the sample, while scattering is influenced by the structural properties. Therefore,
separate quantification of absorption and scattering properties could provide a new means for
assessing fruit internal quality.
The objective of this research was therefore to determine the absorption and reduced
scattering coefficient spectra of peach and apple fruit using hyperspectral imaging-based
spatially-resolved (HISR) technique, and to assess the maturity/quality of the fruit with the
measured optical properties.
6.2 Materials and Methods
6.2.1

Fruit Samples

To determine fruit maturity/quality using the optical properties, peaches and apples
harvested from the experimental orchard of Michigan State University’s Clarksville Horticultural
Experiment Station in Clarksville, Michigan were used. Samples were selected such that they
had large variations in the maturity/quality parameters to be measured.
Five hundred ‘Redstar’ peaches were hand harvested at three different dates within one
week in 2010. Tests for these fruit were conducted in the same harvest day. ‘Golden Delicious’
(GD) and ‘Delicious’ (RD) apples were harvested once a week during six consecutive weeks for
the harvest season of 2010. Eighty apples for each cultivar were tested one day after each harvest,
and the remaining apples were kept in refrigerated air storage at 0°C. Tests for the stored apples
were begun one week after the last harvest for up to six weeks. A total of 1,039 GD and 1,040
RD apples were used in the experiment. Optical properties and maturity/quality indices were
measured from the fruit samples using the OPA and standard destructive methods respectively.

115
 

All laboratory measurements for peaches and apples were performed after the samples had
reached room temperature (~ 24°C).

6.2.2

Optical Properties Measurement

The OPA was used to measure the optical properties of peaches and apples (Figure 5.1).
Binning operations of 4×4 were carried out during the image acquisitions to reduce the exposure
time of 500 ms for each scan, which resulted in hyperspectral scattering images of 251×250
pixels from the 1004×1002 EMCCD camera. Each sample was first moved to the pre-determined
height via the vertical stage, and it then began to move horizontally by the horizontal stage in
synchronization with image acquisitions by the imaging system. To improve the repeatability of
measurements, 10 scans were taken from each peach sample for every 1 mm horizontal
displacement increment for a total of 9 mm distance during the image acquisition at the
predetermined speed. The motorized stage was operated in the ‘go-stop’ mode, so that the fruit
sample remained stationary during the image acquisition. From the peach study, large variation
among the scans for individual samples was observed. Therefore, for the apple experiment, 19
scans were acquired from each apple sample for every 0.5 mm horizontal displacement over a 9
mm distance in order to further reduce the variation.
Figure 6.1 shows a typical hyperspectral reflectance image for a peach fruit sample. A raw
reflectance spectrum obtained by taking a vertical line at the center spatial position is presented
in Figure 6.1(b), which had an absorption valley around 675 nm due to the presence of
chlorophyll-a in the fruit. Other absorption valleys were primarily caused by the spectral
response of the optical system, which would be eliminated through the normalization and
nonlinear curve-fitting process. Each horizontal line taken from the image represents one

116
 

spatially-resolved reflectance profile at a specific wavelength [Figure 6.1(c)], and hence the
entire image, in effect, consisted of ninety-eight spatially-resolved reflectance profiles for the
wavelengths of 515-1,000 nm with the interval of 5 nm. Similar images were obtained for the
apple fruit; there were 101 reflectance profiles for GD apples extracted from the scattering
images for 500-1,000 nm and 98 for RD apples for 515-1,000 nm.
(a)

(b)

(c)

(d)

Figure 6.1 Hyperspectral reflectance image and optical property spectra of a peach sample: (a) 2D display of the original reflectance image, (b) a raw spectrum extracted for a specific scattering
distance, (c) a spatially-resolved reflectance profile extracted for a selected wavelength, (d) preprocessed or averaged spatially-resolved reflectance profile at the selected wavelength, (e) the
spectrum of absorption coefficient (µa), and (f) the spectrum of reduced scattering coefficient
(µs').

117
 

Figure 6.1 (cont’d)
(e)

(f)

The acquired hyperspectral reflectance images were then analyzed to obtain µa and µs'
spectra. Since the spatially-resolved reflectance profiles were symmetric to the light incident
point, the two sides were averaged in the extraction of optical properties [Figure 6.1(d)].
Smoothing and normalization using the peak value for each profile were also applied to the
averaged profiles to reduce the noise and avoid the need for absolute reflectance measurement.
Each pre-processed spatially-resolved reflectance profile for every wavelength was then fitted by
the Kienle diffusion model [equation (3.4)] using the least squares inverse algorithm presented in
Chapter 3, from which the spectra of absorption and reduced scattering coefficients were
obtained. The final µa and µs' spectra were determined by averaging the spectra of optical
parameters from 10 or 19 images for each peach (or apple) sample, which are shown in Figure
6.1(e) and (f).
6.2.3

Acoustic Measurement

Since it was the first time that the OPA was used to assess peach maturity/quality, acoustic
firmness measurements were also performed after the optical measurement and before the
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destructive measurements for each peach sample to compare with the measurements from the
OPA. A commercial desktop acoustic firmness sensor (AFS, AWETA, Nootdorp, Netherlands)
was used in this study. The acoustic firmness sensor detects the vibration pattern of the acoustic
wave travelling across the fruit generated by gently tapping the fruit by a plastic probe, which is
2 2/3

related to the overall firmness of the fruit. The acoustic firmness index (FI = f m

6

/10 , where f

is the first resonance frequency and m is the mass of the fruit) was obtained from each
measurement. For each sample, three replicated measurements were performed at the same
imaging area. Only average values were recorded for further analysis.
6.2.4

Destructive Maturity/Quality Measurement

Peach maturity/quality measurements included firmness, SSC and skin and fresh color,
whereas only firmness and SSC were measured for the apple fruit, by using standard destructive
methods. The firmness of peaches and apples was measured from the same imaging area after
removal of the fruit skin, using a Texture Analyzer (Model TA.XT2i, Stable Micro Systems, Inc.,
Surrey, UK) equipped with an 11-mm Magness-Taylor (MT) probe at a loading speed of 2 mm/s.
Force/displacement curves were recorded for a penetration depth of 9 mm, and the following
parameters were then determined from the curves: maximum force (FM in N), the area under the
2

force/displacement curve corresponding to maximum force (AM in mm ), and slope
(force/deformation, SM in N/mm) measured between the point of initial contact and the point
corresponding to maximum force. Soluble solids content (SSC in °Brix) was determined from
the juice of the fruit samples using a hand-held digital refractometer (Model PR-101, ATAGO
CO, Tokyo, Japan). A chroma meter (CR-400, Konica Minolta Sensing, Inc., Japan) was used

119
 

*

*

*

*

for color readings of the peach skin and flesh with the CIELAB color space (L , a , and b ). L
*

is a measure of lightness on a scale from 0 to 100, and can be easily explained. However, a and
*

b are merely coordinates and difficult to interpret separately (McGuire, 1992). Therefore, they
* *

*

were converted to hue angle [h°, arc tan (b /a )] and chroma (C ,

a*2  b*2 ). Hue angle is a

more appropriate measure of color. The color goes from red to bluish/green with the hue angle
from 0° to 180°. Chroma is the degree of departure from gray to white towards the pure hue
color or pure chromatic color (McGuire, 1992).
6.2.5

Data Analysis

Statistical methods were applied for assessment of the peach and apple maturity/quality
using the optical data. For the peach study, simple linear regression analyses were first
performed on the relationship among the fruit maturity/quality parameters (firmness, SSC, and
skin and flesh color). Prediction models for peach firmness, SSC and color parameters based on
spectra of the absorption and reduced scattering coefficients and their three combinations (i.e., µa,
1/2

µs', µa&µs', µa×µs', µeff = [3µa(µa+µs')]

, where µa&µs' refers to the combination of the two

coefficient spectra in sequence, µa×µs' is the multiplication of the two coefficients, and µeff is
the effective attenuation coefficient which defines the ability of light to penetrate the tissue) were
developed using partial least squares (PLS). Simple regressions were performed between the MT
firmness and acoustic/impact data. The 500 peach samples were first sorted in ascending order
*

*

for firmness (FM, AM, and SM), SSC, and skin and flesh color (L , h°, and C ), respectively, and
they were then divided into two groups with 75% for the calibration set and 25% for the
120
 

validation set. A four-fold cross-validation strategy by repeating the above subsampling
procedure for four times was used to ensure all the samples in the dataset were eventually used
for both calibration and validation. With this sampling technique and large data size for
modeling, the effect caused by the sample selection on the calibration and validation results
could be reduced or eliminated. The same modeling method and sampling technique were also
used for the prediction of apple firmness and SSC.
Partial least squares (PLS) regression is a bilinear modeling method where the original
independent information is projected onto a small number of latent variables (LVs) to simplify
the relationship between independent and dependent variables for prediction with the smallest
number of LVs. A leave-one-out cross-validation method was applied on the calibration set to
determine the optimal number of LVs based on the predicted residual error sum of squares
(PRESS) value, which could avoid the overfitting problem. The calibration models were then
evaluated for the validation set of samples using the statistical parameters, including standard
error of prediction (SEP) calculated as the standard deviation of the prediction residuals, and
correlation coefficient (r) between the predicted and the measured values of fruit maturity/quality
parameters.
6.3 Results and Discussion
6.3.1

Statistical Data of Fruit Maturity/Quality

The statistical data of peach firmness, SSC, and skin and flesh color for all tested samples
are summarized in Table 6.1. The MT firmness distribution of the tested peaches, as measured by
each of the three extracted parameters, was relatively uniform. While the SSC of the samples had
a narrow range from 6.7 to 13.0 °Brix, with the mean of 10.0 °Brix and the standard deviation of

121
 

1.1 °Brix. Skin color variations in terms of lightness, hue angle, and chroma for the samples
were greater than those for the fruit flesh.
Table 6.1 Statistics of fruit maturity/quality parameters for 500 ‘Redstar’ peaches measured by
standard methods.
Maturity/quality
parameter
Magness- Maximum
Taylor
force, FM (N)
firmness
Area, AM
(mm2)
Slope, SM
(N/mm)

Mean
42.4

Standard
deviation
26.2

Maximum

Minimum

109.9

3.7

146.8

70.8

355.4

11.4

9.2

4.2

20.7

0.8

Sugar
content

Soluble
solids
content, SSC
(°Brix)

10.0

1.1

13.0

6.7

Skin color

Lightness, L*
Hue angle,
h°
Chroma, C*

24.4

7.8

45.1

7.9

25.1

2.9

41.4

18.0

19.7

7.8

45.5

7.5

Lightness, L*
Hue angle,
h°
Chroma, C*

49.4

5.5

57.4

16.2

24.4

2.2

32.5

17.0

55.2

6.2

66.3

16.6

Flesh
color

Table 6.2 shows the statistical data of fruit firmness and SSC for the two apple cultivars for
three test groups (freshly harvested, after storage, and combined). The firmness of GD and RD
apples decreased with storage time, whose mean values changed from 78.6 N and 79.7 N for the
freshly harvested group to 48.4 N and 57.0 N for the after-storage group, respectively. The mean
values of SSC, however, only changed slightly with storage time.

122
 

Table 6.2 Statistics of the firmness (i.e., maximum Magness-Taylor force or FM) and soluble
solids content (SSC) of ‘Golden Delicious’ (GD) and ‘Delicious’ (RD) apples for the freshly
harvested, after-storage, and combined groups.

GD

Mean
Standard deviation
Maximum
Minimum
Total samples

Freshly harvested
Firmness SSC
(N)
(°Brix)
78.6
12.9
8.3
1.1
105.1
16.9
50.2
10.1
479

RD

Mean
Standard deviation
Maximum
Minimum
Total samples

79.7
13.4
114.2
32.2
480

6.3.2

11.4
1.3
15.2
8.6

After-storage
Firmness SSC
(N)
(°Brix)
48.4
13.6
8.8
1.3
76.4
17.9
29.4
9.7
560

Combined
Firmness
(N)
62.3
17.3
105.1
29.4
1039

57.0
13.9
92.8
16.8
560

67.5
17.7
114.2
16.8
1040

13.3
1.0
17.0
9.7

SSC
(°Brix)
13.3
1.3
17.9
9.7

12.4
1.5
17.0
8.6

Peach Maturity/Quality Evaluation

6.3.2.1 Absorption and Scattering Spectra of Peach Fruit

Figure 6.2 shows the absorption and reduced scattering coefficients spectra of peach fruit
with different skin colors (h° = 23.7, 21.9, and 20.4) and firmness levels (FM = 72, 47, and 21 N)
for the spectral region of 515-1,000 nm. The µa spectra of the three peaches with different skin
colors had two prominent peaks around 675 nm and 970 nm, which were caused by the
absorption of chlorophyll-a and water in the fruit tissue, respectively [Figure 6.2(a)]. Values of
the absorption coefficient for 720-850 nm were relatively small and consistent, compared with
the rest of the spectral region. Since the color of peaches at different maturity stages varies
greatly due to the changes of major pigments (i.e., chlorophyll and anthocyanin), the absorption
spectrum for the dark red peach presented another peak around 525 nm due to the large amount
of anthocyanin. For the peaches with light red and red colors, smaller absorption peaks from
123
 

chlorophyll-b were also observed around 620 nm. In addition, it was found that the absorption
peak around 675 nm decreased with the increase of absorption at 525 nm, as the value of hue
angle decreased with the fruit color that changed from light red to dark red (Figure 6.2). This is
because during the fruit ripening, the chlorophyll content of peaches is expected to decrease,
while anthocyanin is produced and then becomes the dominant pigment. Large changes in the
pattern of the absorption spectra demonstrate that the absorption properties can be useful for
evaluating the maturity/quality of peach fruit.
(a)
0.5
Peach (light red, ho =23.7)

0.4
-1

0.3

 a (cm

)

Peach (red, ho =21.9)

0.2

Peach (dark red, ho =20.4)

0.1
0

550

600

650

900

950

1000

Peach (hard, 72N)
Peach (medium, 47N)
Peach (soft, 21N)

15

10

)
-1

850

(b)

20

s  (cm

700
750
800
Wavelength (nm)

5

550

600

650

700
750
800
Wavelength (nm)

850

900

950

1000

Figure 6.2 Spectra of (a) absorption coefficient for three peaches with different skin colors (light
red, red, dark red), and of (b) reduced scattering coefficient for three peaches at different
firmness levels (hard, medium, soft).
124
 

Compared to the absorption spectra, the reduced scattering coefficient spectra were
relatively flat, with few features, for the spectral region of 515-1,000 nm [Figure 6.2(b)]. For
most of the tested samples, their µs' values decreased steadily with the increasing wavelength.
This pattern of changes is consistent with Mie scattering theory and other reported studies that
scattering is wavelength-dependent (Keener et al., 2007; Michels et al., 2008). Considerable
variations in the µs' spectra exist for different firmness levels. Hard peaches had consistently
higher µs' values than the softer ones throughout the entire wavelength range. The softening of
fruit is primarily due to the loss of firmness in texture caused by cell wall depolymerization and
an increase in solubility of the middle lamella, leading to cell separations. Eventually, the
scattering particles’ density in the fruit tissue would decrease during the softening process.
Moreover, the particle size can also change due to the solubilization of pectic substances. These
physical properties are related to the ability of the scattering particles in the fruit tissue to scatter
-b

light, according to the empirical equation (µs' = aλ ) for describing the relationship between µs'
and wavelength λ, in which a is proportional to the density of the scattering particles, and b
depends on the particle size (Mourant et al., 1997). For a few very soft peaches (with MT
firmness below 16 N), an opposite trend was observed for the scattering spectra that the µs' value
increased with the increasing wavelength. Dramatic drops of the µs' value for soft fruit could
have invalidated the scattering-dominant assumption and, thus, the diffusion model, which could,
in turn, have resulted in erroneous µs' and µa spectra. This issue warrants further investigation.
The optical properties of fruits measured using different techniques have been reported;
however the reported values of µa and µs' are quite different even for fruit of the same variety or
125
 

cultivar. When comparing the results from different studies, one should notice different
experimental setups, fruit conditions (i.e., maturity level, postharvest storage, etc.), and other
factors such as measurement techniques, each of which could affect the optical properties
measurement. To roughly compare the results of this study with other studies, the distributions of
µa and µs' values for all tested samples at four wavelengths (525 nm for anthocyanin, 620 nm for
chlorophyll-b, 675 nm for chlorophyll-a, and 970 nm for water) are plotted in Figure 6.3. The µa
-1

values for most of the samples at 525 nm, 620 nm, 675 nm, and 970 nm were 0.030 cm

with

-1
-1
-1
-1
the range of 0.002-0.550 cm , 0.090 cm with the range of 0.005-0.464 cm , 0.090 cm with
-1

-1

the range of 0.0003-0.375 cm , and 0.450 cm

-1

with the range of 0.108-1.144 cm ,

respectively. Large variations of µa values existed due to different maturity levels of the tested
fruit. However, the µa values for most of the tested peach fruit at the four wavelengths obtained
from this study are comparable with those of stone fruit from other reported studies. Cubeddu et
-1

al. (2001a) showed µa values of one peach fruit ranging approximately from 0.020 to 0.450 cm
-1

at 650-1,000 nm, with 0.085 cm

-1

at 675 nm and 0.45 cm

at 970 nm. Tijskens et al. (2007)

reported µa values of several groups of nectarines at the commercial harvest stage for 670 nm
-1

with the range from 0.05 to 0.35 cm . The variations of µs' values for all tested samples were
-1

relatively consistent at the four wavelengths ranging approximately from 3 cm
-1

-1

to 23 cm , and

the µs' values for most of the samples were around 11 cm , which are different from the µs' of
-1

~20-24 cm

at 700 nm for a peach fruit reported by Cubeddu et al. (2001a).
126

 

(a)

Sample number

120
100
80

120

525 nm
620 nm
675 nm
970 nm

Sample number

140

60
40

(b)

100
80
60

525 nm
620 nm
675 nm
970 nm

40

20

20

0

0
0

0.25
0.5
0.75
1
µa at four wavelengths (cm-1)

0

5
10
15
20
25
-1)
µs' at four wavelengths (cm

Figure 6.3 Distributions of (a) absorption (µa) and (b) reduced scattering coefficient (µs') for 500
‘Redstar’ peaches at four wavelengths (525 nm for anthocyanin, 620 nm for chlorophyll-b, 675
nm for chlorophyll-a, and 970 nm for water).
6.3.2.2 Prediction of Peach Maturity/Quality

The PLS prediction results of ‘Redstar’ peach firmness, SSC, and skin and flesh color using
µa, µs' and their combinations (µa & µs', µa × µs' and µeff) are shown in Table 6.3. Individual µa
and µs' spectra showed correlations with various maturity/quality parameters with values of the
correlation coefficient (r) varying from 0.420 to 0.855 for µa and from 0.204 to 0.840 for µs'. In
most cases, prediction results obtained from µa spectra were better than those from µs' spectra,
which is similar to that for apples reported by Qin et al. (2009). However, the PLS prediction
models developed for µs' are simpler with fewer factors and faster computation, compared to
those for µa. The physiological process of fruit ripening is accompanied with simultaneous
changes in the chemical compositions, which are related to µa, and the cellulosic structures,
which influence µs'. Hence the combinations of µa and µs' (µa&µs', µa×µs', and µeff) could yield

127
 

better predictions of peach maturity/quality attributes. As shown in Table 6.3, using the
combined data of µa and µs' generally improved prediction results with r = 0.724 (SEP = 18.13 N)
for firmness parameter FM, r = 0.458 (SEP = 0.96 °Brix) for SSC, r = 0.893 (SEP = 3.54) for the
*

*

skin color parameter L , and r = 0.722 (SEP = 3.32) for the flesh color L . It was observed that
most of the improved results were obtained using the effective attenuation coefficient (µeff),
which is reciprocal of light penetration depth, and describes how easily a medium can be
penetrated by the light. Hence, it seems reasonable to have obtained better predictions for the
peach maturity/quality parameters using the µeff values (except for AM and SSC). The PLS
results for prediction of peach firmness, SSC, skin and flesh color demonstrated that the optical
properties are useful for assessing multiple peach maturity/quality attributes simultaneously.

128
 

Table 6.3 Partial least squares (PLS) prediction results of ‘Redstar’ peach maturity/quality parameters using absorption coefficient
(µa), reduced scattering coefficient (µs') and their three combinations (µa & µs', µa × µs', and µeff).*
Maturity/
quality
Fact.
Firmness
10
FM

r

µa

µs'

µa & µs'
SEP Fact. r
SEP

µa × µs'
Fact. r
SEP

Fact.

r

µeff

SEP

Fact.

r

SEP

0.713

18.47

6

0.494

10

12

0.720

18.38

11

0.722

18.43

10

0.724

18.13

AM

10

0.547

59.90

5

0.383

9

11

0.582

58.51

8

0.570

59.07

9

0.553

59.92

SM

14

0.665

3.23

6

0.559

14

11

0.711

3.05

12

0.685

3.13

14

0.712

3.01

Soluble solids content
SSC
15
0.420

0.99

5

0.315

13

12

0.458

0.96

14

0.451

0.96

13

0.419

0.99

Skin color
*
13
L
h°
16
*
14
C

0.855
0.717
0.847

4.07
2.82
4.19

6
6
6

0.837
0.795
0.840

13
13
13

15
16

0.884
0.765

3.65
2.58

13

0.883

3.66

14
16
13

0.881
0.738
0.882

3.70
2.70
3.69

13
13
13

0.893
0.778
0.886

3.54
2.50
3.63

Flesh color
*
16
L
h°
8
*
25
C

0.660
0.457
0.580

3.62
1.99
5.33

6
4
6

0.630
0.204
0.575

21
6
20

15
10

0.674
0.433

3.63
2.03

10

0.640

4.87

18
7
19

0.711
0.447
0.640

3.40
1.99
4.86

21
6
20

0.722
0.462
0.645

3.32
1.98
4.84

* See Table 6.1 for the explanation of individual maturity/quality parameters and SEP = standard error of prediction.

129 
 

Further analysis showed that firmness predictions (r = 0.724 and SEP = 18.13 N) by µeff
based on the PLS model were better than those obtained using the acoustic method with r =
0.639 (Figure 6.4). These results suggest that there is good potential of using HISR technique for
peach firmness assessment. Further research for other peach cultivars is needed to determine the
accuracy and reliability of the new technique for firmness measurement.
The prediction results for the three flesh color parameters were poorer than those for the skin
*

*

color (r = 0.722, 0.462, and 0.645 for L , h°, and C , with the corresponding SEP = 3.32, 1.98,
and 4.84, respectively). The presence of fruit skin and smaller variations in flesh lightness, hue
angle and chroma compared with the fruit skin for the test samples (Table 6.1) could be the
possible reasons for lower correlations for flesh color prediction. For SSC, the prediction results
were not as good as those for firmness and color. Previous studies for apple quality assessment
using optical properties also showed poorer SSC predictions than firmness predictions (Qin et al.,
2009).

100

r=0.724
SEP=18.13N

80
60
40
20
0
0

20 40 60 80 100 120
Actual MT firmness, FM (N)

(b)
Acoustic firmness, FI (Hz2 g2/3)

Optical prediction, FM (N)

(a)
30

y = 0.0941x + 9.8821
r = 0.639

25
20
15
10
5
0
0

20 40 60 80 100 120
Actual MT firmness, FM (N)

Figure 6.4 (a) Prediction of Magness-Taylor (MT) firmness (FM) of ‘Redstar’ peaches using
effective attenuation coefficient (µeff) with partial least squares (PLS) and (b) correlation
between acoustic data and MT firmness (FM).
130 
 

6.3.3

Apple Internal Quality Evaluation

6.3.3.1 Absorption and Scattering Spectra of Apple Fruit

Typical absorption and reduced scattering coefficient spectra for the two apple cultivars for
the spectral region of 500-1,000 nm for GD and 515-1,000 nm for RD are shown in Figure 6.5.
The absorption spectra of apples showed a pattern similar to that of peach fruit in Figure 6.2. The
µa spectra had two prominent peaks around 675 nm and 970 nm, which were caused by the
absorption of chlorophyll-a and water in the fruit tissue, respectively [Figure 6.5(a)]. Since
chlorophyll in the apple tissue decreased during the fruit ripening, the values of µa at 675 nm for
-1

all samples ranged from 0.028 cm

-1

-1

-1

to 0.841 cm for GD and from 0.041 cm to 0.762 cm for

RD. Similar to those of peaches, the µs' spectra of apples were also relatively flat with fewer
features [Figure 6.5(b)]. For most of the tested samples, their µs' values decreased steadily with
-1

the increasing wavelength. The µs' values ranged between 7-20 cm

-1

for GD and 4-26 cm

for

RD, which are at least one order in magnitude greater than the µa values.
20

(a)

(b)

GD
RD

-1

-1

a (cm

0.4
0.2
0
500

600

700
800
900
Wavelength (nm)

GD
RD

15

s  (cm

)

0.6

)

0.8

10

1000

5
500

600
700 800
900
Wavelength (nm)

1000

Figure 6.5 Spectra of (a) absorption and (b) reduced scattering coefficients for four ‘Golden
Delicious’ (GD) apples and four ‘Delicious’ (RD) apples.

131 
 

6.3.3.2 Prediction of Apple Firmness and Soluble Solids Content

Table 6.4 presents prediction results for the firmness of GD and RD apples using µa and µs',
and their combinations (µa&µs', µa×µs', and µeff) for the freshly harvested, after-storage and
combined groups. Likewise, the SSC prediction results using the optical properties for each
group are summarized in Table 6.5. Both µa and µs' for each cultivar were correlated with the
apple firmness and SSC. Firmness prediction results obtained from the µa spectra (r = 0.6870.885 for GD, and r = 0.744-0.844 for RD) were better than those from the µs' spectra (r = 0.6300.793 for GD, and r = 0.702-0.768 for RD) for each of the three sample groups. This was also
true for the SSC evaluation. Fewer factors were used in the PLS prediction models with µs',
because its spectra had fewer features. Using the three combinations of µa and µs' generally
improved the prediction of apple firmness and SSC. With the best combination of µa and µs', the
correlations for the firmness of RD and GD apples for the three test groups were 0.692-0.892 and
0.788-0.863, respectively, and they were 0.741-0.791 and 0.536-0.842 for SSC, respectively.
Table 6.4 Firmness prediction results for ‘Golden Delicious’ and ‘Delicious’ apples for the
freshly harvested, after-storage and combined groups.*
Optical parameter
Freshly
harvested

µa

Golden Delicious
Factors
r
16
0.687

SEP
6.10

Delicious
Factors r
20
0.785

SEP
8.43

0.630

6.49

7

0.764

8.68

µa&µs'

12

0.651

6.37

18

0.809

7.91

µa×µs'

17

0.692

6.06

19

0.813

7.83

µeff
Afterstorage

6

16

0.687

6.10

22

0.822

7.67

µa

17

0.726

6.11

25

0.744

9.36

µs'

7

0.689

6.44

7

0.702

9.90

µs'

132 
 

Table 6.4 (cont’d)
µa&µs'

14

0.712

6.24

17

0.788

8.57

µa×µs'

17

0.734

6.02

20

0.765

9.00

µeff

18

0.730

6.07

29

0.762

9.10

µa

34

0.885

8.14

34

0.844

9.56

µs'

9

0.793

10.60

9

0.768

11.35

µa&µs'

38

0.881

8.29

19

0.852

9.31

µa×µs'

39

0.892

7.89

35

0.857

9.12

33
0.884
µeff
* SEP = standard error of prediction.

8.16

38

0.863

8.94

Combined

Table 6.5 Prediction results for the soluble solids content of ‘Golden Delicious’ and ‘Delicious’
apples for the freshly harvested, after-storage and combined groups.*
Optical parameter
Freshly
harvest

µa

Golden Delicious
Factors r
16
0.787

SEP
0.70

Delicious
Factors r
17
0.823

SEP
0.76

6

0.489

0.99

7

0.784

0.84

12

0.781

0.70

17

0.842

0.73

17

0.791

0.69

20

0.816

0.78

µeff

16

0.777

0.72

22

0.821

0.77

µa

18

0.713

0.95

14

0.533

0.88

7

0.561

1.12

6

0.460

0.92

14

0.741

0.92

13

0.518

0.89

18

0.732

0.93

11

0.502

0.90

µeff

19

0.726

0.94

18

0.536

0.87

µa

20

0.760

0.84

23

0.812

0.88

8

0.544

1.09

8

0.750

0.99

16

0.768

0.83

19

0.825

0.85

23

0.778

0.82

21

0.804

0.89

0.773

0.83

27

0.805

0.89

µs'
µa&µs'
µa×µs'

Afterstorage

µs'
µa&µs'
µa×µs'

Combined

µs'
µa&µs'
µa×µs'

22
µeff
*SEP = standard error of prediction.

For the freshly harvested and after-storage groups, the correlations were relatively low
because of smaller firmness variations for each group (Table 6.2). However, when the data from
133 
 

these two groups were pooled, improved correlations for the firmness prediction of both cultivars
were obtained, although the SEP values increased slightly due to larger firmness variations in the
combined group. For SSC, the best predictions were achieved for the freshly harvested group
with r = 0.791 (SEP = 0.69 °Brix) for GD and r = 0.842 (SEP = 0.73 °Brix) for RD. Comparable
results were obtained for the combined group because the SSC in the apple fruit did not change
significantly during storage. Figure 6.6 shows the firmness and SSC predictions for GD and RD
apples obtained with the best combination of µa and µs' for the combined group. Better
predictions of firmness for GD and RD apples with the correlation of 0.892 and 0.863,
respectively, were obtained than for SSC predictions with r = 0.778 and 0.825. These results are
better than, or comparable with, other reported studies using hyperspectral scattering technique

100

R = 0.892
SEP = 7.89 N

80

(a)

Predicted SSC (°Brix)

Predicted firmness (N)

(Mendoza et al., 2010; Qin et al., 2009).

GD

60
40

16

R = 0.778
SEP = 0.82 °Brix

14

(b)
GD

12
10
8

20
20

40
60
80
Actual firmness (N)

100

8

10
12
14
Actual SSC (°Brix)

16

Figure 6.6 Prediction of fruit firmness (a, c) and soluble solids content or SSC (b, d) using the
best combinations of µa and µs' for the combined group of ‘Golden Delicious’ (GD) and
‘Delicious’ (RD) apples.

 

134 
 

100
80

R = 0.863
SEP = 8.94 N

(c)

Predicted SSC (°Brix)

Predicted firmness (N)

Figure 6.6 (cont’d)

RD

60
40
20
20

40
60
80
Actual firmness (N)

100

16

R = 0.825
SEP = 0.85 °Brix

14

(d)
RD

12
10
8
8

10
12
14
Actual SSC (°Brix)

16

6.4 Conclusions

The spectra of absorption and reduced scattering coefficients for ‘Redstar’ peaches for the
spectral region of 515-1,000 nm, ‘Golden Delicious’ apples for 500-1,000 nm, and ‘Delicious’
apples for 515-1,000 nm were measured using the Optical Property Analyzer. Significant
changes in the absorption and reduced scattering spectra were observed for peaches with
different levels of maturity. The absorption spectra were shaped by major pigments (i.e.,
chlorophyll and anthocyanin) and water in the fruit, while the reduced scattering spectra
decreased in value during the fruit softening. Similar absorption and scattering features were also
found for the apple samples.
Both µa and µs' were correlated with the peach firmness, SSC, and skin and flesh color and
with the apple firmness and SSC; however, better correlations were obtained using the
absorption spectra than using the scattering spectra. The combinations of µa and µs' (i.e., µa&µs',
µa×µs', and µeff) based on PLS models gave better predictions of firmness (FM), SSC, and skin
*

and flesh color parameter L for peach fruit, with values of the correlation coefficient (r) being
135 
 

0.724 (SEP = 18.13 N), 0.458 (SEP = 0.96 °Brix), 0.893 (SEP = 3.54), and 0.722 (SEP = 3.32),
respectively. For the apple study, the best firmness prediction was obtained with r = 0.892 (SEP
= 7.89 N) for GD and r = 0.863 (SEP = 8.94 N) for RD. For SSC evaluation, better results were
achieved for the freshly harvested group with r = 0.791 (SEP = 0.69 °Brix) for GD and r = 0.842
(SEP = 0.73 °Brix) for RD. These two studies demonstrated that the hyperspectral imaging-based
spatially-resolved technique is useful for measuring the optical properties of fruit, and it provides
a new means of assessing fruit maturity/quality.
 

136 
 

CHAPTER 7

RELATIONSHIP BETWEEN THE OPTICAL AND

MECHANICAL/STRUCTURAL PROPERTIES OF APPLE TISSUE
7.1 Introduction

The texture of fresh fruit depends on variety, maturity, climate condition during growth, and
postharvest storage condition, and it is largely determined by the structural and mechanical
properties of fruit tissue. The softening and its resultant change in the texture of apples during
the ripening mainly results from cell wall depolymerization and the dissolving of the middle
lamella (Wood et al., 2009). Accompanied with the tissue softening and the weakened adhesion
between cells are changes in the cell wall strength, cell turgor and the number, size, and shape of
intercellular spaces, which, in turn, affect the fruit firmness or rigidity. It is thus critical to
understand how the structural and/or mechanical properties of cells and their changes affect the
textural properties and ultimately the quality of fruit in storage.
Considerable studies have been reported on the relationship between fruit quality and
physiological changes. Both destructive and nondestructive techniques that are based on quasistatic, impact, vibration, and acoustic principles have been used for measuring the mechanical
and/or textural properties (e.g., firmness and strength or elasticity) of fruit. Electron microscopy
was also utilized to evaluate the structural changes of fruit during ripening and storage, and to
examine or quantify the physiological activities in the fruit. While it is well known that the
optical absorption and scattering properties are related to the composition and cellular structure
of fruit tissue, no research has been attempted to elucidate and quantify their interrelationships.
Better understanding of these relationships can help us develop better techniques for fruit quality
inspection, monitoring and control.

137 
 

The research reported in this chapter was therefore aimed at gaining a fundamental,
quantitative understanding of the relationships between the optical and mechanical/structural
properties of apple fruit. The specific objectives of the research were to: 1) measure the
absorption and reduced scattering coefficient spectra and the mechanical and structural
properties of apple tissues for ‘Golden Delicious’ and ‘Granny Smith’ cultivars over time during
high temperature/high humidity storage, and 2) relate the optical measurements to the elastic
modulus (Young’s modulus) of flesh tissues and cell structures, including cell size/shape and
morphological characteristics.
7.2

Materials and Methods

7.2.1

Apple Samples

Two apple cultivars, ‘Golden Delicious’ (GD) and ‘Granny Smith’ (GS), were chosen in this
study. The apples were harvested at the commercial maturity stage in 2010 from the
experimental orchards of Michigan State University’s Horticultural Teaching and Research
Center in Holt, MI and Clarksville Horticultural Experiment Station in Clarksville, MI. GD
apples were harvested three weeks earlier, and they were kept in a controlled atmosphere (CA)
environment (2% O2 and 3% CO2 at 0 °C), until after GS apples were received. The test apples
were visually inspected to ensure they were absent of damage or blemishes, and they were of
relatively uniform in size with the equatorial diameter of 73-78 mm for GD and 77-85 mm for
GS. The apples were randomly grouped into five groups of 10 fruit each for each cultivar. They
were kept at ~ 22 °C and ~ 95% relative humidity for 1, 8, 15, 22, and 30 days, respectively, to
accelerate the changes in fruit quality and condition.

138 
 

For each storage time, one group of apples was taken out from the storage. Measurements
were first performed of the optical properties of all apple fruit. Thereafter, compression tests (see
the following subsection for details) were conducted for each apple sample. Finally, microscopic
image analyses of fruit tissue specimens were performed. Because of the extensive time needed,
and the difficulty, in preparing tissue specimens for micro-structural analysis, only three
specimens for each group of 10 apple samples were prepared for confocal laser scanning
microscopy (CLSM) and two specimens for scanning electron microscopy (SEM).
To monitor the apple firmness and weight change with storage time, another subset of 10
intact fruit samples for each cultivar were kept in the same storage condition for up to 30 days.
Acoustic firmness and optical properties measurements were taken for these samples at each of
the five test dates.
7.2.2

Optical Properties Measurement

The Optical Property Analyzer (OPA) (see Chapter 5) was used to measure the spectral
absorption and reduced scattering coefficients of GD and GS apples for the spectral region of
500-1,000 nm, following the procedure described in Section 6.2.2 of Chapter 6. Mean spectra of
absorption and reduced scattering coefficients were calculated for the 10 fruit of each group for
each storage time.
7.2.3

Acoustic Firmness Measurement and Compression Test for Measuring Mechanical

Properties

The commercial desktop firmness sensing system (AFS, AWETA, Nootdorp, Netherlands),
described in Chapter 6, was used to monitor the apple firmness and weight change during storage.
The fruit was gently tapped by a plastic rod in the instrument. Four parameters, including the

139 
 

2 2/3

mass of the fruit (m), first resonance frequency (f), the acoustic firmness index (FI=f m

6

/10 ),

and impact firmness (IF), were obtained from each measurement. For each sample, three
replicate measurements were performed at the same equatorial location where the optical
property measurements had been performed earlier. Only the average values were recorded for
further analysis.
Compression tests were conducted following the optical properties and acoustic
measurements. The test apples were first cut into two halves parallel to the longitudinal axis as
shown in Figure 7.1(a). Cylindrical specimens of 13.9 mm in diameter and 13 mm in length were
then taken from the fruit flesh of one apple half 5 mm beneath the skin, using a cork borer and a
double-blade knife [Figure 7.1(b) and (c)]. The specimen size was determined based on the
literature (Abbott and Lu, 1996) and preliminary study of the effect of specimen size on the
mechanical properties measurement. Each flesh specimen was compressed between two parallel
plates using a Texture Analyzer (Model TA.XT2i, Stable Micro Systems, Inc., Surrey, UK) at a
loading speed of 0.42 mm/s [Figure 7.1(d)]. Force/displacement curves were recorded for up to 4
mm of displacement; and failure stress (σ), failure strain (ε), and Young’s modulus (or apparent
modulus of elasticity, E) were then calculated from these curves.
(a)

(b)

13.9 mm
13 mm 5 mm
Figure 7.1 Experimental procedures for compression test of apple tissue specimens: (a)
cylindrical specimen taken from the fruit flesh of the apple; (b) cork borer and double-blade
knife used for cutting tissue specimens; (c) final tissue specimen with 13.9 × 13 mm (D × L); and
(d) compression test setup with the Texture Analyzer.
140 
 

Figure 7.1 (cont’d)
(d)

(c)

7.2.4

Confocal Laser Scanning Microscopy and Scanning Electron Microscopy for

Microstructural Analysis
Confocal laser scanning microscopy (CLSM, Olympus FluoView 1000 LSM, Olympus
America Inc., Center Valley, PA, USA) and scanning electron microscopy (SEM, JEOL 6400V,
Japan Electron Optics Laboratories, Tokyo, Japan) were conducted on the apple tissue specimens
to quantify their microstructural changes for different storage times ranging from 1 to 30 days.
CLSM enables us to view a single layer of cells from the tissue and reduces noise from adjacent
layers of cells, and it was used for quantitative analysis of apple tissues for cell information (e.g.
cell size and shape parameters). SEM allows surface examination to obtain cellular
characteristics at higher resolutions.
For CLSM, tissue specimens from the outer cortex of apples about 10 mm away from the
skin were cut by a cork borer with a diameter of 13.9 mm, using the same sampling procedure as
shown in Figure 7.1(a) for the compression test except for the sampling location or depth. A
razor blade was then used to obtain cylindrical specimens of 1 mm thickness. Thereafter, the
specimens were soaked with 0.1% Cango Red (Sigma-Aldrich Co. LLC, St. Louis, MO) for 10
min and then were washed by water several times prior to CLSM imaging.

141 
 

For SEM, tissue specimens with the same dimensions as those for CLSM were cut from the
fruit. The specimen preparation procedure was according to that described by Kim et al. (1990).
The specimens were first fixed for 2 h in 2% glutaraldehyde/0.1M phosphate buffer at 0°C. The
fixed specimens were then washed with 0.1M phosphate buffer for at least 30 min at 0°C, and
post-fixed in 1% phosphate buffered osmium tetroxide (OsO4) solution for 1 h at 0°C. After
another wash with phosphate buffer, they were dehydrated with a series of ethanol
concentrations for various time periods as follows: 40% (5 min), 50% (5 min), 60% (5 min), 70%
(15 min), 80% (10 min), 90% (15 min), and 100% (three times for 10 min each). The fixed and
dehydrated specimens were quench-cooled in nitrogen slush under vacuum within the
preparation chamber of the SEM (< 210°C). Each specimen was fractured using a movable
blade, sublimated for 15 min at -90°C, and coated by gold/palladium. The specimens were then
viewed by the SEM with 10 kV accelerating voltage at < 130°C. In order to obtain more
comprehensive information on the cellular structure change during storage, SEM images were
acquired at two different resolutions (magnifications of 50× and 1500×).
7.2.5

Data Analysis

To quantify the optical property changes of apple tissue with storage time and their
relationship with the mechanical/structural properties, image analysis and statistical analysis
were carried out using Matlab programs. Analysis of variance with the storage time was first
applied to the mean values of optical properties, acoustic firmness data, and compression test
data for each storage time. Young’s modulus calculated as the gradient of the initial linear slope
between 5.8% and 9.8% strain from the stress/strain curves obtained by the compression test was

142 
 

used for characterizing the mechanical properties of fruit tissues and for understanding the
structural changes in apples during storage.
Cell morphological parameters including area, equivalent diameter, major and minor length,
2

perimeter, elongation (major length/minor length) and roundness (4 × π × area/perimeter ) were
extracted from the CLSM images of apple tissues. Six images acquired from three specimens
(two images for two locations from each specimen) for each cultivar were quantified using image
segmentations to obtain average cell parameters for each storage time. Analysis of variance
(ANOVA) and least significant difference (LSD) test were conducted to evaluate the cell
changes among the storage days. The procedures of image processing are shown in Figure 7.2.
First, the original images were preprocessed by converting the RGB images into binary images.
Second, morphological operations on the binary images were implemented using the function
‘bwmorph’ in Matlab Imaging Processing Toolbox by bridging unconnected pixels, removing
spur pixels, and performing dilation using the structuring element ‘ones (3)’. Third, the
watershed transformation was performed on the images after the morphological operations, and
morphological structuring elements were created. Finally, the segmented cells were labeled, and
their morphological parameters were calculated using Matlab function ‘regionprops’.
Original

Preprocessed

Clean-bridge

Figure 7.2 Procedures of image processing for extracting cell parameters.

143 
 

Figure 7.2 (cont’d)
Clean-spur

Clean-dilate

Watershed

Dilate-disk

Overlay

Label

The SEM images of apple tissues acquired at the low resolution were analyzed to further
quantify their microstructure using histogram probability and fractal analysis methods. The
histogram of an image is a graphic description of the distribution of the gray levels, which are the
gray level values versus the number of pixels at that value. It provides information related to the
nature and characteristics of the image. Statistical-based histogram features including energy and
entropy were extracted from the SEM images, where the histogram is used as a model of the
probability distribution of the gray levels. The energy describes the distribution of the gray levels
of an image and is defined as (Umbaugh, 2005).

energy 

n 1

2

  p( g )

(7.1)

g 0

where p( g ) 

N (g)
is the first-order histogram probability, in which M is the pixel number in
M

the image, N(g) is the pixel number at gray level g, and n is the total number of gray levels. The
entropy tells us how many bits we need to code the image data, and is given by
144 
 

entropy 

L 1



g 0

p( g ) log 2  p( g )

(7.2)

The value of entropy increases when the pixel values in the image are distributed among more
number of different gray levels. A complex image has higher entropy than a simple image, and
the energy tends to vary inversely.
Fractal analysis was used for description and quantification of surface topographies,
providing texture information of the SEM image. Three parameters were extracted from the
fractal analysis, which are fractal dimension at low scale (D) related to the surface roughness, the
minimum elemental cell (dmin) related to the cell size, and the periodical region (dper) at high
scale related to the distance between cells. The procedure to compute the fractal dimension (D)
and parameters dper and dmin are based on the variogram of the intensity pixels in grayscale
images and the method was proposed and successfully used in scanning electron microscopy
images by Bonetto and Ladaga (1998), Bianchi and Bonetto (2001) and Quevedo et al. (2002).
The variogram method has been detailed by Bianchi and Bonetto (2001) as follows. It calculates
the fractal dimension from the V variance of the grey level distribution of the image
corresponding to the studied surface sample
V  z  s 2H

(7.3)

where the angle brackets <> denote the expectation value, Δzi is the difference of the gray level
between two different positions in the image for a step i of length s measured in pixels. H value
can be obtained by means of the graph slope in logarithmic scale from V versus s, which is
related to the fractal dimension D by
D  3 H

145 
 

(7.4)

The variogram presents a fractal behavior at a certain scale and simultaneously it produces
minimums at other scales. Such minimums result from the presence of a periodical structure in
the gray levels. This periodic region is described as a spectrum of space frequencies represented
by “k wave vectors”. kxi and kyi can be obtained by projecting the “ki wave vector” on the pair of
orthogonal coordinate axes, and therefore
2
2
 k 2  k x    k y 

(7.5)

The periodic region parameter is then defined as
d per 

2
2
2
 kx    k y 

(7.6)

The parameter dper is a measurement of the average diameter between the nearest elementary
cells of enough statistic weight so as to produce periods. The parameter dmin is the intersection
between the fractal and periodic zones that explains the highest value of the smallest cell size of
enough statistic weight. These three parameters (D, dmin, and dper) extracted from fractal
analysis have provided good characterization of image texture (Bonetto and Ladaga, 1998).
Finally, general linear regression analysis was performed on correlating acoustic firmness,
Young’s modulus and cell structural parameters to the optical properties of apple fruit.
7.3 Results and Discussion
7.3.1

Changes in the Optical Properties of Apples during Storage

Figure 7.3 shows the mean absorption (µa) and reduced scattering coefficients (µs') spectra
over 500-1,000 nm for 10 apples each of GD and GS for each test date. While the general

146 
 

patterns of µa and µs' spectra for GD and GS apples were similar, their absolute values were
different.
(a1)

µa (cm-1)

0.6
0.4

15

Day 1
Day 8
Day 15
Day 22
Day 30

0.2

13
12
11
10
9

0

0.8

(b1)

0.6
0.4

500

600 700 800 900 1000
Wavelength (nm)
Day 1
Day 8
Day 15
Day 22
Day 30

µs' (cm-1)

500

µa (cm-1)

(a2)

14
µs' (cm-1)

0.8

0.2
0
500

600 700 800 900 1000
Wavelength (nm)

15
14
13
12
11
10
9

600 700 800 900 1000
Wavelength (nm)
(b2)

500

600 700 800 900 1000
Wavelength (nm)

Figure 7.3 Mean spectra of 10 apple samples each for the five times of storage: (a1) absorption
and (a2) reduced scattering coefficients of ‘Golden Delicious’ (GD) apples; and (b1) absorption
and (b2) reduced scattering coefficients of ‘Granny Smith’ (GS) apples.
There were two prominent peaks around 675 nm and 970 nm for the µa spectra of both GD
and GS apples, which were caused by the absorption of chlorophyll-a and water in the fruit
tissue, respectively. There were also small chlorophyll-b absorption peaks around 620 nm and
water absorption peaks around 750 nm. Other absorption peaks were also observed in the µa
spectra of GD and GS apples around 525 nm due to the presence of anthocyanin in the apple
147 
 

skin. Moreover, the absorption peak around 675 nm for GD apples decreased consistently with
-1

storage time; the average value of µa changed from 0.324 cm

-1

to 0.103 cm

over 30 days of

storage, and dramatic decreases of µa values took place after eight days of storage. On the other
hand, absorption around 525 nm increased slightly over time, with the mean values of µa
-1

changing from 0.179 cm

-1

to 0.207 cm

during the 30 days of storage. This is because during

storage, the chlorophyll content of GD apples was expected to decrease as the apple skin color
changed from green to yellow and more anthocyanin was produced, which then became the
dominant pigment. Similar changes also happened to the absorption spectra for GS apples.
-1

However, the decrease of µa values around 675 nm from 0.248 cm

-1

to 0.235 cm for GS apples

was much smaller than that for GD apples, whereas the increase of µa values around 525 nm
-1

-1

from 0.150 cm to 0.306 cm was much greater than that for GD apples. Overall, the change in
absorption for the spectral region of 750-1,000 nm was much smaller during the entire storage
period, compared to that for the visible spectral region of 500-750 nm.
Compared to the absorption spectra, the reduced scattering coefficient spectra exhibited a
different pattern for the spectral region of 500-1,000 nm [Figure 7.3(a2) and (b2)]. The µs'
spectra were relatively flat, with few features. For most of the tested fruit samples of both
cultivars, their µs' values decreased steadily with the increasing wavelength throughout the
spectral region of 500-1,000 nm. Like the absorption coefficient, the reduced scattering
coefficient also exhibited a consistent pattern of change during storage and its values for the
fresh apples (i.e., day 1) were considerably higher than those for the stored apples for all other

148 
 

test dates, except for GS for the region of 900 nm or higher due to the large variation of GS
apples with small change of their µs' values. The maximum value for the mean reduced
scattering coefficient for the entire wavelength range decreased with storage time consistently
-1

from 13.4 cm

-1

-1

to 11.4 cm for GD and from 12.4 cm

-1

to 10.0 cm

for GS over 30 days of

storage.
7.3.2

Changes in Acoustic Firmness and Mechanical Properties during Storage

Acoustic and impact firmness (e.g., FI and IF) for both cultivars decreased steadily with
storage time [Figure 7.4(a)]. FI and IF decreased by 42.3% and 21.2% for GD, and 16.9% and
6.7% for GS, respectively, over the storage period of 30 days. GS apples had a lower rate of loss
in firmness during the storage. The weight change of apples due to water loss can affect the
mechanical and microstructural properties of the fruit. Figure 7.4(b) shows that there were 3.1%
and 1.9% decreases in the average weight of GD and GS apples, respectively, but the decreases
were not statistically significant.

149 
 

45

105
90

35

75

25

60

15

45

5

350
Weight (g)

GD_FI
GS_FI
GD_IF
GS_IF

(a)

Impact firmness, IF

Acoustic firmness, FI (Hz2 kg2/3)

55

GD
GS

(b)

300
250

30

200
150
100
50

1
8
15
22
30
15
22
30
Storage days
Storage days
Figure 7.4 Changes in a) acoustic firmness (FI) and impact firmness (IF), and (b) fruit weight,
for the same 10 fruit each of ‘Golden Delicious’ (GD) and ‘Granny Smith’ (GS) measured at five
storage times (the vertical bars denote two standard deviations).
1

8

The stress/strain curves for a GD apple and a GS apple measured for each of the five storage
times are shown in Figure 7.5. For both cultivars, the stress/strain curve at day 1 had a sharp
peak at the yield point with a sudden drop in the failure stress because the flesh tissue was still
crispy or crunchy. As the storage time increased, the stress/strain curve became smoother, and it
did not show a prominent yield point at days 8-30 for GD and at days 15-30 for GS.
Day 1
Day 8
Day 15
Day 22
Day 30

(a)

0.5
0.4

0.6
Stress, σ (MPa)

Stress, σ (MPa)

0.6

0.3
0.2
0.1

(b)

0.5
0.4
0.3
0.2
0.1

0
0

5

10 15 20
Strain, ε (%)

25

0

30

0

5

10

15 20 25
Strain, ε (%)

30

Figure 7.5 Stress/strain curves obtained from the compression test for the flesh specimens of (a)
five ‘Golden Delicious’ apples and (b) five ‘Granny Smith’ apples, one for each storage time.
150 
 

Figure 7.6 shows the mean values and statistical differences of Young’s modulus for GD
and GS apples at five storage times. GS apples had significantly higher values of Young’s
modulus compared with GD apples, which was in agreement with the relative values of acoustic
firmness measurements for the two cultivars (Figure 7.4). The mean value of Young’s modulus
decreased by 45.6% for GD and 34.2% for GS within 30 days of storage. This indicated that the
rigidity of the cellular structures had decreased significantly over 30 days of storage time, and
thus the fruit became soft at the end of storage. A dramatic decrease (significant at the 0.05 level)
in Young’s modulus for GD apples occurred between day 1 and day 8, while a significant
decrease in Young’s modulus for GS apples was only observed for day 22 and 30.
6

a

a

GD
GS

Young's modulus (MPa)

a
5
4

b
A

b

3
BC

B
C

2

D

1
Day1

Day8

Day15
Stroage days

Day22

Day30
 

Figure 7.6 Mean values of Young’s modulus for 10 ‘Golden Delicious’ (GD) (columns with
capital letters) and ‘Granny Smith’ (columns with small-cap letters) apples for each of the five
storage times (columns with different letters for the same cultivar are significantly different with
p < 0.05).

151 
 

7.3.3

Microstructural Changes in Apple Tissue during Storage

‘Golden Delicious’ apples are crispy, whereas GS fruit are firm, crunchy and juicy. These
textural differences are related to the different cellular structures of the two cultivars. The CLSM
images showed that the cells of GS tissues [Figure 7.7(b1)] were more rounded compared with
those of GD tissues [Figure 7.7(a1)]. Closer contact between the cells of GS tissues was
observed, while there was more space between the cells of GD tissues. Weaknesses at the cell
conjunction may indicate less firmness or mealiness of the texture. During the storage, the cellto-cell adhesion was reduced and cell separation along the middle lamella increased. More
broken cells were observed for both cultivars at day 30, as shown in Figure 7.7 (a2) and (b2).
(a1)

(a2)

100 µm 

Figure 7.7 Confocal laser scanning microscopic images of a cross-section of apple flesh tissue 10
mm beneath the skin for ‘Golden Delicious’ apple at day 1 (a1) and day 30 (a2), and for ‘Granny
Smith’ apple at day 1 (b1) and day 30 (b2) (‘→’ denotes the connection between cells, and ‘×’
denotes the broken cells).

 
 
152 
 

Figure 7.7 (cont’d)
(b2)

(b1)

100 µm 

Table 7.1 summarizes the cell morphological parameters for GD and GS apple tissue
specimens, extracted from the CLSM images. The average cell area of GD apples (19.0-15.7
3

2

3

2

×10 µm for day 1-30) was smaller than the average cell area of GS (28.3-22.2 ×10 µm for
day 1-30). The same trend was observed for the equivalent diameter, major and minor length,
and perimeter. The cell size of both cultivars decreased with storage time from day 1 to day 30.
While significant differences in each of the cell size parameters for the two cultivars were found
between day 1 and day 30, differences between two adjacent test days were not always
significant. For the shape-related parameters (i.e., elongation and roundness), no consistent trend
with the storage time was found for the two cultivars. During the storage, the breakdown of
pectin in the weak intercellular lamella and the water redistribution in the cells and cellular space
would have caused changes in the cell size and shape. But the cell shape change was difficult to
quantify based on the two-dimensional CLSM images, since the cell deformation could have
happened in all directions.
153 
 

Table 7.1 Mean and standard error of the cell size/shape parameters for ‘Golden Delicious’ and ‘Granny Smith’ apple tissues for
different storage days.*
Storage day

Cell size parameters
Equiv. diameter Major length Minor length Perimeter
(µm)
(µm)
(µm)
(µm)

Area
(µm2)
Golden Delicious
a
Day 1
18990±698

150.2±2.9

Day 8

17677±658

143.7±2.9

Day 15

16939±550

Day 22

16478±613

ac
bc
bc

141.9±2.5
139.2±2.7

a
ac
bc
bc

b
b
Day 30
15670±527 135.5±2.6
Granny Smith
a
a
Day 1
28332±1120 184.3±3.8
b
b
Day 8
24292±1098 167.8±4.1

Day 15

21648±930

Day 22

23645±991

b
b

158.2±3.6
166.0±3.8

b
b

181.7±3.5
175.6±3.6
173.4±3.2
174.4±3.6
161.6±3.0
223.0±4.7
200.9±5.0
192.7±4.6
197.6±4.5

a
a
a
a
b
a
b
b
b

129.8±2.8
123.3±2.6
121.0±2.3
116.5±2.5
117.8±2.4
157.6±3.6
144.9±3.8
134.7±3.2
144.8±3.7

a
ac
bc
bc
bc
a
b
c
bc

Cell shape parameters
RSE of Elongation
Roundness
area (%)

545.2±10.4
524.3±10.5
515.2±9.2

1.60

ac

1.426±0.032

bce

1.527±0.044

de

705.0±15.5
603.7±14.7
570.0±13.0
595.1±13.5

a
b
b
b

1.438±0.037
1.486±0.035

bc

510.9±10.1
485.1±9.1

a

1.420±0.028
1.92

1.408±0.033
1.396±0.023
1.470±0.036
1.429±0.054

ab
ab
ab
a
b
a
a
a
a

0.766±0.0061
0.754±0.0060
0.763±0.0053
0.757±0.0060
0.773±0.0054
0.765±0.0064
0.774±0.0059
0.777±0.0062
0.778±0.0087

ab
ab
a
b
ab
a
a
a
a

b
b
b
bc
b
b
a
Day 30
22181±910 161.9±3.6
188.0±4.2
143.4±3.4
576.0±12.7
1.346±0.020 0.789±0.0040
Values in the same column with different letters are significantly different at the 95% confidence interval (p<0.05);

Standard error = standard deviation / cell number ;
RSE (relative standard error) = standard error/mean  100%.

154 

To further quantify the changes of tissue cells during the storage, the cell connections,
denoted by the red lines in Figure 7.8(a1), were manually counted and measured for each
scanning electron microscopic (SEM) image acquired at the low resolution for day 1 and day 30.
The average connection length and standard error (standard deviation divided by the number of
the cell connection) had decreased approximately from 87.80 ± 1.02 µm to 62.39 ± 0.52 µm for
GD apples, and from 99.03 ± 0.71 µm to 78.29 ± 1.11 µm for GS apples for 30 days of storage.
The high-resolution SEM images of GD and GS apples for 1 and 30 days of storage have
presented significant differences in the cellular structures, as shown in Figure 7.8(b1)-(b2) and
Figure 7.9(b1)-(b2). For both cultivars, cell separation in the middle lamella was observed after
30 days of storage, which was associated with pectin solubilization and the subsequent reduction
in the connection between cells. This was also consistent with the changes observed from the
CLSM images. At day 1, the cells of GD had a smoother external surface with some exudates
[Figure 7.8(b1)], which indicated that the cell structure degradation might have begun. For day
30, more exudates were observed on the surface of cell walls [Figure 7.8(b2)]. Similar changes
were also found in the cells of GS specimens. The cellular materials had appeared to be pulled
away in the cells of GS even at day 1 [Figure 7.9(b1)]. Although attention was paid to the initial
selection of fruit with the same level of maturity for both cultivars, it was still difficult to achieve
this by visual inspection of the external appearance of each fruit. Therefore, image textural
analysis was performed on the low-resolution SEM images to obtain quantitative information for
the cellular structures.

155 

a1

a2
500 µm

500 µm

(b1)

(b2)

20 µm

20 µm

Figure 7.8 Scanning electron microscopy images of one cross-section of apple flesh tissue 10
mm beneath the skin for ‘Golden Delicious’ at day 1 (a1) and day 30 (a2) acquired at low
resolution for an overview of the cell structures, and at day 1 (b1) and day 30 (b2) acquired at
high resolution for a more detailed view of the cell-to-cell connection [the red lines in (a1)
denotes five cell connections counted manually as examples].
 
 
 
 

156 

(a1)

(a2)
500 µm

500 µm

(b2)

(b1)
20 µm

20 µm

Figure 7.9 Scanning electron microscopy images of one cross-section of apple flesh tissue 10
mm beneath the skin for ‘Granny Smith’ at day 1 (a1) and day 30 (a2) acquired at low resolution
for an overview of the cell structures, and at day 1 (b1) and day 30 (b2) acquired at high
resolution for a more detailed view of the cell-to-cell connection [the red lines in (a1) denote five
cell connections counted manually as examples].
Table 7.2 shows the morphological features obtained from the SEM images of apple tissues.
The energy and entropy changes for the two cultivars were not consistent over the storage time,
and so was the change in fractal dimension D. There were differences in the microstructural
characteristics, cell topology and physiological activity during storage as well as the level of
maturity at harvest for GD and GS apples. These differences have thus resulted in different

157 

morphological features, as described by their kinetic changes. A general tendency of decrease in
dmin and increase in dper during storage was observed. A greater value of dmin or dper
corresponds to a larger cell size or a longer distance between cells. Since only two specimens
were used for each cultivar for each storage time in SEM imaging, no statistical test could be
done for the five storage times. Compared with the cell size parameters obtained from the CLSM
images, the change pattern for the morphological features extracted from the SEM images for
different storage times was not apparent. It has to mention that only the intact cells in the CLSM
images were segmented for extracting the cell size parameters; whereas for the analysis of SEM
images, the entire images including both intact cells and void structures (i.e., pores or broken
cells) were considered, which would have posed more difficulty for the differentiation and
characterization of morphological features from the SEM images. Further, large variations in the
SEM images were observed because of the small imaging area. It is, therefore, suggested that
more specimens for the same apple fruit should be considered in future experiment in order to
better assess the biological changes of apple fruit during storage.
Table 7.2 Morphological features extracted from the scanning electron microscopic (SEM)
images acquired at the low resolution for ‘Golden Delicious’ and ‘Granny Smith’ apple tissues.*
Storage day

First order histogram probability

Fractal analysis parameters

Energy

Entropy

D

dmin (pixel)

dper (pixel)

4.942
5.188
5.300
4.974
5.276

2.589
2.579
2.571
2.546
2.561

40.68
35.44
29.77
31.38
33.51

159.4
162.2
164.8
161.4
173.7

5.084
5.239
5.216
5.283

2.577
2.622
2.581
2.608

40.00
42.09
38.73
42.60

169.5
182.3
173.7
168.4

Golden Delicious
Day 1
20352
Day 8
17048
Day 15
18098
Day 22
17415
Day 30
16800
Granny Smith
Day 1
15607
Day 8
15936
Day 15
13975
Day 22
16998

158 

Table 7.2 (cont’d)
Day 30

18832

5.310

2.578

39.50

189.1

*D is the fractal dimension at low scale, dmin is the parameter of the minimum elemental cell,

and dper is the parameter of the periodical region at high scale.
7.3.4

Correlations between Optical Properties and Mechanical/Structural Properties

Table 7.3 shows correlation coefficients for the four optical parameters (µa, 675 nm, µs', 675
nm, aµs' and bµs') with the acoustic and impact firmness (FI and IF) and Young’s modulus (E) for

GD and GS apples, where µa, 675 nm and µs', 675 nm represent the absorption and reduced
scattering coefficients at the wavelength of 675 nm, which is related to the chlorophyll
absorption, and aµs' and bµs' are the parameters related to the µs' spectra (i.e., µs' = aµs'λ

-bµs'

,

where λ is the wavelength in nm). Optical parameter µa, 675 nm was highly correlated with the
acoustic and impact firmness (r=0.870 and 0.918, respectively) for GD; however, the correlations
for GS were much lower (r=0.334 and 0.421 respectively). Scattering parameter µs', 675 nm
generally had better correlation with acoustic and impact firmness for both cultivars (r=0.9030.993). Both µa, 675 nm and µs', 675 nm had much lower correlations with Young’s modulus for
the two cultivars, although better correlations were obtained for GD than for GS (Table 7.3),
which could have been due to the relatively small change of chlorophyll in GS apples during the
storage. It should also be noted that the measurement of Young’s modulus was subject to error
due to variations in the dimension and shape, and sampling position of tissue specimens, whereas
acoustic measurements were taken for the entire fruit and, thus, were more consistent.

159 

Table 7.3 Correlations of selected optical parameters with acoustic and impact firmness and
Young’s modulus for ‘Golden Delicious’ and ‘Granny Smith’ apples.*
Optical
parameters
µa, 675 nm
µs', 675 nm
aµs'
bµs'

Golden Delicious
FI
IF
E
0.870
0.918
0.585

Granny Smith
FI
IF
0.334
0.421

E
0.292

0.903

0.932

0.766

0.993

0.992

0.694

0.948

0.939

0.947

0.902

0.941

0.584

0.924

0.938

0.804

0.974

0.974

0.620

*µa, 675 nm and µs', 675 nm are absorption and reduced scattering coefficients at 675 nm, and aµs'
- bµs'
, where λ is the wavelength
and bµs' are the parameters related to the µs' spectra (µs' = aµs'λ
in nm); FI and IF are the acoustic firmness index and impact firmness index, respectively, and E
is Young’s modulus.
Since aµs' and bµs' are the two parameters in the wavelength-dependent exponential function
for quantifying the entire µs' spectra, they should be more useful to characterize the main
features of µs' spectra, compared with using single wavelengths. As expected, higher correlations
between these two optical parameters and acoustic/impact firmness (r=0.902-0.974) were
obtained. Likewise, better correlations of aµs' and bµs' with the Young’s modulus were also
obtained, compared with µa, 675 nm and µs', 675 nm for GD, and compared with µa, 675 nm for
GS.
Correlations between the optical properties including transport mean free path (mfp) and
tissue structural parameters (i.e., cell size parameters from CLSM images and fractal analysis
parameters from SEM images) are shown in Table 7.4 and Table 7.5. The transport mean free
path [or mfp = 1/(µa+µs')] represents the average path distance by moving photons between
successive interactions with the fruit tissue. There were positive correlations between the optical
parameters (i.e., µa, 675 nm, µs', 675 nm, aµs' and bµs', mfp) and cell size parameters (i.e., area,

160 

equivalent diameter, major length, minor length and perimeter) for both cultivars. Values of the
five optical parameters decreased with storage time, as the cell size decreased due to the
disintegration and/or separation of cells. Better correlations (r = 0.843-0.955) were obtained
between µa, 675 nm and cell size parameters for GD apples, which could have been attributed to
the larger change in the absorption coefficient at 675 nm from day 1 to day 30, compared with
GS apples. For GS apples, aµs' had better correlation (r = 0.876-0.906) with cell size parameters
among the five optical parameters.
Table 7.4 Correlations of optical parameters with the cell size parameters extracted from the
confocal laser scanning microscopic images of ‘Golden Delicious’ and ‘Granny Smith’ apples.
Area
Optical
parameter
Golden Delicious
0.934
µa, 675 nm

Equivalent
diameter

Major length Minor length

Perimeter

0.941

0.912

0.843

0.955

µs', 675 nm

0.777

0.657

0.845

0.686

0.842

aµs'

0.767

0.774

0.670

0.754

0.730

bµs'

0.660

0.657

0.627

0.600

0.646

mfp'675nm

0.830

0.872

0.890

0.728

0.891

Granny Smith
µa, 675 nm

0.630

0.607

0.593

0.613

0.547

µs', 675 nm

0.581

0.572

0.716

0.372

0.681

aµs'

0.903

0.906

0.891

0.876

0.902

bµs'

0.850

0.845

0.796

0.861

0.796

mfp'675nm

0.704

0.690

0.826

0.499

0.779

Table 7.5 Correlation of optical parameters with the fractal analysis parameters extracted from
the scanning electron microscopic images of ‘Golden Delicious’ and ‘Granny Smith’ apples.
Optical parameter
µa, 675 nm

Golden Delicious

Granny Smith

dmin
0.512

dmin
0.740

dper
-0.820

161 

dper
-0.706

Table 7.5 (cont’d)
µs', 675 nm

0.276

-0.755

0.517

-0.556

aµs'

0.821

-0.572

0.244

-0.689

bµs'

0.770

-0.582

0.549

-0.612

 

The four optical parameters (not including mfp) were positively correlated with dmin,but
were negatively correlated with dper (Table 7.5). dmin decreased with storage time due to the
change of the cell size, while dper increased as a result of the rupture and clustering of cells,
causing separation between the cell structures. These microstructural changes were primarily
responsible for changes in the optical properties. However, correlations between the optical
parameters and fractal analysis parameters from the SEM images were relatively low due to the
high variability in the SEM images and fewer specimens used for each test date. Hence in further
research, more specimens with greater physiological variations should be considered in order to
more accurately quantify the relationship between the optical and microstrucultural parameters.
7.4 Conclusions

This research, for the first time, provided quantitative information on how the optical
absorption and scattering properties were related to the elastic properties and the cellular
structure of apples stored in a high temperature (~22 C)/high humidity (95%) environment. The
µa value at 675 nm for both ‘Golden Delicious’ and ‘Granny Smith’ cultivars decreased
consistently over 30 days of storage due to the decrease in chlorophyll-a, while the µa value
increased around 525 nm, likely resulting from the increase in anthocyanin during the fruit
storage. The reduced scattering coefficient of apple fruit also exhibited a consistent pattern of

162 

change during storage; its value for the fresh apples was considerably higher than that for the
stored apples for all test dates. The changes or decreases in the optical properties were
accompanied with decreases in the acoustic/impact firmness, Young’s modulus, and cell size
parameters with storage time. These changes were directly related to changes in the cellular
structures/properties, primarily caused by the degradation of pectin and decrease in the molecular
weight distribution of hemicelluloses (Harker et al., 1997). The optical parameters (i.e., µa, 675
nm, µs', 675 nm, aµs', bµs', and mfp) had various degrees of correlation  with acoustic/impact

firmness, Young’s modulus, and cell morphological parameters for both cultivars. These findings
suggest the potential of using optical properties to study or monitor the mechanical properties
and microstructural changes of apples during storage and/or in the softening or ripening process.

163 

CHAPTER 8 DETERMINATION OF THE OPTICAL PROPERTIES OF TWO-LAYER

TURBID MATEIRALS
8.1 Introduction

Previous studies have shown that hyperspectral imaging-based spatially-resolved technique
is useful for determining the optical properties of fruits and food products that are approximately
homogeneous. It is, however, desirable to consider fruit to be composed of two homogenous
layers of skin and flesh in order to better quantify light propagation in the fruit and more
accurately assess fruit quality attributes.
Light transfer in two-layer media is more complex than in homogeneous media. Hence,
determination of the optical properties of two-layer media entails great challenges both
mathematically and experimentally. A two-layer diffusion model has four (or five) property
parameters (i.e., µa and µs' of each layer, plus the unknown thickness of the first layer).
Parameter estimation accuracy, computational time, and model efficiency must be considered in
the development of an inverse algorithm for layered media. Several studies have provided
analytical solutions to the diffusion equations for layered media (Alexandrakis et al., 2001;
Hollmann and Wang, 2007; Kienle et al., 1998b; Schmitt et al., 1990). Numerical methods (e.g.,
Monte Carlo, asymptotic approximation, and finite element) have also been used to extract
optical properties from the diffusion models (Gonzalez-Rodriguez and Kim, 2008; Schweiger
and Arridge, 1997; Seo et al., 2007). Kienle et al. (1998b) derived an analytical form of the twolayer diffusion model, which enables fast forward computation and inverse algorithm
implementation to estimate the optical properties. The increased number of free parameters in the
two-layer model can dramatically increase computational time, exacerbate the process of

164 

estimating the optical parameters, and/or cause convergence problems for the inverse algorithm.
It is thus important to understand the intrinsic properties of the diffusion model and evaluate the
feasibility of estimating all parameters simultaneously prior to implementing an inverse
algorithm.
Therefore, the overall objective of this research was to explore the feasibility of determining
the optical properties of the surface layer (skin) and subsurface layer (flesh) for those fruits and
food products that can be modeled as two-layer homogeneous media. The specific objectives
were to: 1) perform sensitivity coefficient analysis and develop an inverse algorithm for a twolayer diffusion model to estimate the optical properties of each homogeneous layer; 2) create
solid model samples and measure their optical properties using an integrating sphere method;
and 3) validate the diffusion model and the inverse algorithm using Monte Carlo simulations and
experimental data acquired from the model samples using hyperspectral imaging-based spatiallyresolved technique.
8.2 Materials and Methods
8.2.1

Two-layer Diffusion Model

Consider a two-layer turbid medium which is impinged upon perpendicularly by an
infinitely small light beam. The thickness of the first layer (d) is assumed to be larger than one
transport mean free path of the first layer [ z0  1/ (a1  s1 ') , in which µa1 and µs1' are
absorption and reduced scattering coefficients of the first layer]. Under steady-state condition,
the fluence rate, defined as the irradiance that is incident from all solid angles onto a small
sphere in a two-layer turbid medium, is given by (Kienle et al., 1998b)

D121(r )  a11(r )    x, y, z  z0 
165 

0 zd

(8.1)

D2 2 2 (r )  a 2 2 (r )  0

dz

(8.2)

where  i is the fluence rate of layer i , and Di  1 / [3(  ai   si ')] is the diffusion constant.
Equations (8.1) and (8.2) can be converted to ordinary differential equations using a twodimensional Fourier transform (1998b). The following boundary conditions are applied for
obtaining solutions for the fluence rates [ i ( z , s ) ] of each layer on the frequency domain
(Haskell et al., 1994; Kienle et al., 1998b): the same refractive index for the first layer and
second layer, the zero fluence rate at the extrapolated boundary, a finite photon fluence rate as
z   , and the continuity of fluence rate at the boundary between the first and second layer.

After the differential equations in the frequency domain are solved, the two-dimensional
inverse Fourier transform is implemented to obtain the following fluence solution on the
Cartesian coordinate system:
 i (r , z ) 

1

 2 

 
1 
 ( z , s ) exp  i  s1 x  s2 y  ds1ds2 
i ( z , s ) sJ 0 ( sr ) ds


2   i
2 0

 



(8.3)

where r  ( x2  y 2 )1/2 , and J 0 is the zeroth-order Bessel function. This inverse transform is
achieved by numerically evaluating the integral using an adaptive Gauss-Kronrod quadrature
(Shampine, 2008). Spatially-resolved diffuse reflectance R(r) is obtained from the integration of
radiance over the solid angle accepted by the fiber. Then, the final solution of the two-layer
diffusion model is given as (Kienle et al., 1998b)

R2layer (r )  C11  r , z  0   C2 D1


1  r , z 
z
z 0

(8.4)

The details related to the parameters C1 and C2 can be found in Chapter 3. Based on equation
(8.4), the diffuse reflectance R(r) at the surface of the two-layer turbid medium is a function of
the source-detector distance (r) as well as five unknown optical parameters of the two layers and
166 

the thickness of the first layer (µa1, µs1', µa2, µs2', and d, where µa2 and µs2' are absorption and
reduced scattering coefficients of the second layer). Researchers have used the two-layer model
[equation (8.4)] to model photon propagation in turbid media under steady-state conditions
(Hollmann and Wang, 2007; Kienle et al., 1998b; Tseng et al., 2008).
8.2.2

Model Samples Preparation and Measurement

To investigate the feasibility of the two-layer diffusion model and test the performance of
the hyperspectral imaging system for measuring the optical properties of two-layer materials, the
two-layer model samples were created, which were made up of two-component roomtemperature-vulcanizing silicone (part A + part B, ELASTOSIL®RT 604, Wacker Chemie AG,
Munich, Germany) as the host, aluminum oxide particles (Al2O3, Duke Scientific, Fremont,
California, USA) as scattering materials, and blue dye (Direct Blue 71, Sigma-Aldrich, St. Louis,
MO, USA) as absorbers. The stock solution of blue dye was prepared in ethanol with the
concentration of 0.6 mg/L. The solution of the absorber was mixed with 360 g part A of silicone
with a stirrer and heated gently for several hours to remove the ethanol. The scattering materials
were dispersed in 40 g part B of silicone and put in the sonicator for several minutes to break up
large particles. Then, these components were mixed together and the bubbles produced in the
process of mixing were removed in the vacuum chamber. Two silicone mixtures were made by
adding different absorbing stock solutions (34 mL and 27 mL) and scattering materials (8 g and 5
g). Two cylindrical model samples with a diameter (D) of 81 mm and a height (h) of 57 mm and
two disk samples of 81 mm diameter and a height of 2.64 mm and 3.29 mm respectively were
created by pouring the mixtures into the plastic cylindrical and disk modes. One disk sample
corresponded to one cylindrical sample with the same optical properties. Finally, the two-layer

167 

model samples were obtained by attaching a disk sample with different optical properties onto a
cylindrical sample. These two model samples would satisfy the assumption for the two-layer
diffusion model with a limited thickness of the first layer and semi-infinite second layer.
An integrating sphere system, which has been used as a standard method for measuring the
optical properties of solid turbid samples in many reported studies (Prahl et al., 1993; Saeys et al.,
2008), was used to obtain reference values of the absorption and reduced scattering coefficients
for each layer of the two model samples. Total diffuse reflectance and transmittance
measurements were performed on the two model disk samples of 3.29 mm and 2.64 mm thick,
respectively, using the same configurations shown in Figure 4.4 in Chapter 4. An inverse addingdoubling algorithm was used to calculate the scattering and absorption coefficients of the model
samples based on the total reflectance and transmittance. A detailed description of the method
can be found in Prahl et al. (1993).
8.3 Validation of the Two-layer Diffusion Model and Inverse Algorithm

Like the single-layer diffusion model described in Chapter 3, the sensitivity analysis was
also performed, and sensitivity coefficients were first calculated for each of the four optical
parameters (i.e., the absorption and reduced scattering coefficients for each layer) by the
following equations, which were derived from equation (2.29):
R ai  ai

R
ai

R si '   si '

R
 si '

where µai and µsi' are the absorption and reduced scattering coefficients of layer i.

168 

(8.5)

(8.6)

For accurate determination of the optical properties of fruit and food samples, the diffusion
model and the inverse algorithm were then validated by Monte Carlo simulations. A publicly
available MC simulation program for multi-layered media was used (Wang et al., 1995b). The
low-noise reflectance generated by MC simulation provided an ideal measurement without
6

experimental uncertainties. A total of 3×10 photons were used to produce the reflectance for a
spatial distance of 0.1-10 mm at 0.1 mm spatial resolution for both radial distance and depth.
Four different combinations of µa1, µs1', µa2, and µs2' were selected, which span a large range of
-1

values: 0.05 ≤ µa ≤ 2.60 cm

-1

and 12 ≤ µs' ≤ 36 cm . These values were selected based on the

published data for fruit skin and flesh (Budiastra et al., 1998; Saeys et al., 2008). The diffusion
model was first compared with MC simulation for generating spatially-resolved reflectance
profiles for a two-layer medium with the selected values for the four optical parameters. Then,
the MC generated reflectance profiles were fitted by the inverse algorithm of the two-layer
diffusion model, from which the optical properties for each layer were determined. MC
simulations of light propagation in a two-layer turbid medium introduced small stochastic
variability in the calculated reflectance for any given set of optical properties. The resulting
variability was less than 1.7% in 20 simulations for each set of optical properties.
The diffusion model and inverse algorithm were further validated with experimental data
obtained from the two-layer model samples using the laboratory hyperspectral imaging system
(Figure 4.1), following the same procedures for liquid model samples described in Section 4.2.1.
The time required for each scan of the two-layer mode sample was 100-200 ms. Two cases were
considered: 1) only two unknown optical parameters for one of the two layers with known
optical properties for the other layer, and 2) four unknown optical properties for both layers.

169 

Finally, the optical properties of the model samples estimated by the inverse algorithm were
compared with those measured using the integrating sphere method.
8.4 Results and Discussion
8.4.1

Monte Carlo Simulations of Spatially-resolved Diffuse Reflectance

Figure 8.1 compared diffuse reflectance from the two-layer diffusion model and MC
simulations for the four sets of optical properties (µa1/µa2 = 0.50 and µs1'/µs2' = 0.86, µa1/µa2 =
6.50 and µs1'/µs2' = 1.80, µa1/µa2 = 0.80 and µs1'/µs2' = 1.58, µa1/µa2 = 2 and µs1'/µs2' = 0.75).
The reflectance profiles calculated from the diffusion equation matched those from the MC
simulations. The differences for the given values of optical properties used in Figure 8.1(a), (c)
and (d) were less than 6% for source-detector distances greater than 1.5 mm. For case 2 with
µa1/µa2 = 6.50 and µs1'/µs2' = 1.80 [Figure 8.1(b)], the average difference was 12%, greater than
those for the other three cases. This was likely due to low levels of diffuse reflectance resulting
from high absorption of both layers. Larger deviations of reflectance were observed when the
detector was close to the light source (less than one transport mean free path), because the
diffusion approximation is not valid in this situation. These results indicate that overall the
diffusion model accurately quantifies light propagation in two-layer turbid media.

170 

(a)

10

10

-2

-4

-6

0

2

0

4
6
8
Distance (mm)
(c)

10
10
10

10

10

(b)

0

-2

-4

-6

0

2

4
6
8
Distance (mm)
(d)

10

0

2

4
6
8
Distance (mm)

10

0

-2

-2

Reflectance (mm )

10

10

Reflectance (mm )

10

-2

Reflectance (mm )

0

-2

Reflectance (mm )

10

10
10
10

-2

-4

-6

0

2

4
6
8
Distance (mm)

10

10
10

-2

-4

Figure 8.1 Comparison of spatially-resolved diffuse reflectance obtained from the two-layer
diffusion model (symbols) and Monte Carlo simulations (solid lines): (a) µa1/µa2 = 0.50 and
µs1'/µs2' = 0.86 (0.05, 12, 0.10, 14, 1), (b) µa1/µa2 = 6.50 and µs1'/µs2' = 1.80(2.60, 36, 0.40, 20,
0.5), (c) µa1/µa2 = 0.80 and µs1'/µs2' = 1.58 (0.32, 19, 0.40, 12, 1), and (d) µa1/µa2 = 2 and
µs1'/µs2' = 0.75 (1.00, 15, 0.50, 20, 1). Values in the parentheses are µa1, µs1', µa2, µs2', d with
-1

the units of cm
8.4.2

for optical properties and mm for the thickness of the first layer.

Sensitivity Coefficient Analysis

The scaled sensitivity coefficients for the absorption and reduced scattering coefficients of
the two layers were calculated as functions of the source-detector distance for the corresponding
diffuse reflectance profiles (Figure 8.2). For the four combinations of optical properties
discussed in this study, the magnitudes of the reduced scattering sensitivity coefficients are

171 

almost equal to those of R, while the sensitivity coefficients of absorption are relatively smaller,
especially in Figure 8.2(a) because of the small values of the selected absorption coefficients in
this case. For the other three combinations, the sensitivity coefficients of absorption are still on
the same order of R at the large source-detector distances. Also it is noted that the shapes of the
four sensitivity coefficients are quite different. These observations show that the four sensitivity
coefficients of µa1, µs1', µa2, and µs2' are ‘large’ (i.e., on the order of R) and uncorrelated
(different shapes), which are desirable conditions for estimating these parameters. Since the
reduced scattering sensitivity coefficients are larger in magnitude than the absorption sensitivity
coefficients in Figure 8.2, on average µsi' should be estimated more accurately than µai for such

10
10
10

(a)

0

-2

10

Scaled Sensitivity(mm )

-2

Scaled Sensitivity(mm )

model.

-2

-4

-6

0

2

4
6
8
Distance (mm)

10
 

10
10
10
10

(b)

0

-2

-4

-6

0

2

4
6
8
Distance (mm)

10

Figure 8.2 Scaled sensitivity coefficients as functions of source-detector distances for four
combinations of optical properties (a) µa1/µa2 = 0.50 and µs1'/µs2' = 0.86 (0.05, 12, 0.10, 14, 1),
(b) µa1/µa2 = 6.50 and µs1'/µs2' = 1.80 (2.60, 36, 0.40, 20, 0.5), (c) µa1/µa2 = 0.80 and µs1'/µs2' =
1.58 (0.32, 19, 0.40, 12, 1), and (d) µa1/µa2 = 2 and µs1'/µs2' = 0.75 (1.00, 15, 0.50, 20, 1), and
-1

the values in the bracket are µa1, µs1', µa2, µs2', d with the unit cm for optical properties and
mm for the thickness of the first layer (‘-’, ‘·’, ‘+’, ‘ₒ’, and ‘∆’denote reflectance, and scaled
sensitivity coefficients of µa1, µs1', µa2, and µs2', respectively).
 

172 

10
10
10

(c)

0

-2

10

Scaled Sensitivity(mm )

-2

Scaled Sensitivity(mm )

Figure 8.2 (cont’d)

-2

-4

-6

0

2

4
6
8
Distance (mm)

10

10
10
10
10

(d)

0

-2

-4

-6

0

2

 

4
6
8
Distance (mm)

10
 

The effect of the thickness of the first layer on the sensitivity coefficients of optical
properties is presented in Figure 8.3 for four different thicknesses of the first layer with the same
optical properties. Values for the four sensitivity coefficients vary with the thickness (d) that
changes from 0.85 mm to 6 mm. For the thin thickness of the first layer, it is easy to estimate
optical properties of the second layer. While for the larger d, it is more difficult to obtain
accurate estimations of optical properties of the second layer due to small sensitivity coefficients
for µa2 and µs2'. This may be explained by the fact that only a small number of photons

10
10
10

(a)

0

-2

10

Scaled Sensitivity(mm )

-2

Scaled Sensitivity(mm )

propagating through the second layer are remitted when the first layer is relatively thick.

-2

-4

-6

0

2

4
6
8
Distance (mm)

10

10
10
10
10

(b)

0

-2

-4

-6

0

2

4
6
8
Distance (mm)

10

Figure 8.3 Scaled sensitivity coefficients as functions of source-detector distances for µa1 = 0.05
-1

-1

-1

-1

cm , µs1' = 12 cm , µa2 = 0.10 cm , µs2' = 14 cm , and the thickness of the first layer: (a) d =
173 

0.85 mm, (b) d = 2 mm, (c) d = 4 mm, and (d) d = 6 mm (‘-’, ‘·’, ‘+’, ‘ₒ’, and ‘∆’denote
reflectance, and scaled sensitivity coefficients of µa1, µs1', µa2, and µs2', respectively).

8.4.3

10
10
10

(c)

0

-2

10

Scaled Sensitivity(mm )

-2

Scaled Sensitivity(mm )

Figure 8.3 (cont’d)

-2

-4

-6

0

2

4
6
8
Distance (mm)

10

10
10
10
10

(d)

0

-2

-4

-6

0

2

4
6
8
Distance (mm)

10

Extraction of Optical Properties from Monte Carlo Simulation Data

When the optical properties of the second layer and the thickness of the first layer are treated
as known, the inverse algorithm gives almost zero errors in estimating absorption and reduced
scattering coefficients for the first layer from the noiseless reflectance data produced by the
diffusion model. These results indicate that it is possible to accurately estimate two optical
parameters in the diffusion model using nonlinear least squares method.
Figure 8.4 shows the estimated absorption and reduced scattering coefficients of the first
layer from the two-layer diffusion model fitted to the MC data that has a noise level of 2%. For
-1

case 1 [Figure 8.4(a)], the actual value of µa1 varies between 0.20 to 1.20 cm
-1

-1

with µs1' = 12

-1

cm , µa2 = 0.50 cm , µs2' = 11 cm , and d = 2 mm. The average errors of estimating µa1 and
µs1' are 4.2% and 4.1% compared with the true values. While for case 2 [Figure 8.4(b)], µs1'
-1

changes in the range of 15-45 cm

with the fixed values of µa1, µa2, µs2' and L. The average

174 

errors are 12.7% for µa1 and 5.8% for µs1'. The optical parameters of the second layer were also
estimated with the optical parameters and the thickness of the first layer being treated as known.
For the same combination of the optical parameters as in case 1, the average errors are 10.0% for
µa2, and 9.3% for µs2', higher than those for case 1. The statistic uncertainty of MC simulations
reduces the accuracy of the inverse algorithm for parameter estimations compared with the
fitting results using the noiseless diffusion model-generated data.
(a)
0.14

Estimated 

a1

(mm -1)

0.12
0.1
0.08
0.06
0.04
0.02
0
0.02

0.04

0.06

0.08

True a1 (mm

0.1

0.12

-1

)

Figure 8.4 Estimated absorption and reduced scattering coefficients of the first layer from fitting
-1
the diffusion model to the Monte Carlo simulation data: (a) µa1 varies 0.20 - 1.20 cm with µs1'
-1

-1

-1

-1

= 12 cm , µa2 = 0.50 cm , µs2' = 11 cm , and d = 2 mm, and (b) µs1' varies 15-45 cm
-1
-1
-1
µa1= 0.10 cm , µa2 = 0.05 cm , µs2' = 11 cm , and d = 2 mm.

175 

with

Figure 8.4 (cont’d)
(b)
4.5

Estimated s1 (mm -1)

4
3.5
3
2.5
2
1.5
1.5

2

2.5

3

True s1 (mm

3.5

4

4.5

-1

)

The four optical parameters of µa1, µs1', µa2, µs2'  were also estimated simultaneously with
the known d, and the same four sets of optical properties (µa1/µa2 = 0.50 and µs1'/µs2' = 0.86,
µa1/µa2 = 6.50 and µs1'/µs2' = 1.80, µa1/µa2 = 0.80 and µs1'/µs2' = 1.58, µa1/µa2 = 2 and
µs1'/µs2' = 0.75) shown in Figure 8.1 were used. The average errors of estimating µa1, µs1', µa2,
and µs2' from the reflectance generated by the diffusion model are 1.4%, 0.01%, 0.4% and 0.1%,
respectively, which shows that the inverse algorithm can accurately estimate four parameters
based on the noiseless data. Mean and maximum errors in the estimated absorption and reduced
scattering coefficients of both layers from the MC generated reflectance are presented in Figure
8.5. The mean errors for estimating the first layer’s optical properties are 14.5% and 8.1% for the
absorption and reduced scattering coefficients, respectively. For the second layer, the mean

176 

errors are 29.3% and 9.1% for the absorption and reduced scattering coefficients, respectively.
The relatively smaller errors are obtained for the optical parameters of the first layer compared
with those in the second layer, and the errors of estimating the reduced scattering coefficients are
smaller than those for the absorption coefficients. The maximum error for µa2 reaches 40%, two
to four times greater than that for the other three parameters. The relative scales of the estimation
errors for the four optical parameters are in agreement with the findings from the sensitivity
analysis. Comparison of the results for estimation of two and four parameters demonstrates that
the errors increased with the number of parameters to be estimated in the two-layer model. Also,
to obtain a good estimation, the signal-to-noise ratio must be considered in the measurement of
the reflectance.

45
mean
max

40

Relative error (%)

35
30
25
20
15
10
5
0

a1

a2

s1

s2

Optical properties

 

Figure 8.5 Relative errors of estimating the optical properties of two layers from the Monte Carlo
diffuse reflectance for four combination sets of optical properties: µa1/µa2 = 0.50 and µs1'/µs2' =

177 

0.86 (0.05, 12, 0.10, 14, 1), µa1/µa2 = 6.50 and µs1'/µs2' = 1.80 (2.60, 36, 0.40, 20, 0.5), µa1/µa2
= 0.80 and µs1'/µs2' = 1.58 (0.32, 19, 0.40, 12, 1), and µa1/µa2 = 2 and µs1'/µs2' = 0.75 (1.00, 15,
-1

0.50, 20, 1). Values in the parentheses are µa1, µs1', µa2, µs2', d with the units of cm
properties and mm for the thickness of the first layer.
8.4.4

for optical

Optical Properties of Model Samples Measured with Integrating Sphere

Values of the absorption and reduced scattering coefficients for the two model disk samples
measured using the integrating sphere at wavelengths of 500-1,000 nm are shown in Figure 8.6.
Light absorption by the blue dye absorber is observed at 535 nm for both samples. The
absorption peak around 910 nm was caused by the silicone. The reduced scattering spectra are
relatively flat compared with the absorption spectra of the model samples. The standard method
has good repeatability of measuring the model samples, whose variation coefficients for the
absorption and reduced scattering coefficients from four replicated measurements are 2.4% and
2.3%, respectively. The optical properties of the two-layer model samples at 535 nm and 700 nm
are listed in Table 8.1; they were used as the true optical values when compared with those
obtained from the spatially-resolved technique with the inverse algorithm.
(a)
0.6

-1
a (cm )

Disk sample 1
Disk sample 2
0.4

0.2

0
500

600

700
800
Wavelength (nm)

900

1000

Figure 8.6 Absorption and reduced scattering spectra of the homogenous model disk samples
measured by the integrating sphere.

178 

Figure 8.6 (cont’d)
(b)
14

-1
s (cm )

12
10

Disk sample 1
Disk sample 2

8
6
500

600

700
800
Wavelength (nm)

900

1000

 

Table 8.1 Optical properties of two two-layer model samples at the wavelengths of 535 nm and
700 nm determined by the integrating sphere and the adding-doubling method (Prahl et al., 1993).
Model
sample

Wavelength
(nm)

Sample 1

µa1

-1)

µs1'

-1)

µa2

-1)

µs2'

-1)

535
700

(cm
0.51
0.18

(cm
12.97
11.72

(cm
0.45
0.13

(cm
8.08
7.29

535
700

0.45
0.13

8.08
7.29

0.51
0.18

12.97
11.72

d
(mm)
2.64

Table 8.1 (cont’d)
Sample 2

3.29

 

8.4.5

Optical Properties of Model Samples Determined from Hyperspectral Imaging

Measurements

Figure 8.7 shows the measured reflectance profiles of the two two-layer model samples at
wavelengths of 535 nm and 700 nm, and also the theoretical profiles calculated from the twolayer diffusion model using the optical parameters given in Table 8.1. These two particular
wavelengths were selected in this study because they represented the lower and upper range of
values for the absorption and scattering coefficients for the model samples over the spectral
range of 500-1,000 nm (Figure 8.6). Hence the estimation errors for the two wavelengths should

179 

be representative for the other wavelengths. Because the diffuse reflectance profiles from the
experiment and the diffusion model were not on the same scale, the profiles were normalized at a
distance of 1.5 mm. As shown in Figure 8.7, the experimental measurements covering the
source-detector distance from 1.5 mm to 10 mm are in good agreement with the theoretical
predictions. However, differences between the measurements and predictions become larger at
distances close to the source due to the violation of diffusion theory assumptions.
(a)

(b)

4

4

10
Reflectance (a.u.)

Reflectance (a.u.)

10

2

10

0

10

-2

10

4
6
8
Distance (mm)

10

10

(c)

4

2

4
6
8
Distance (mm)

10

(d)

4

10
Reflectance (a.u.)

10
Reflectance (a.u.)

0

10

-2

2

2

10

0

10

2

10

0

10

-2

-2

10

2

10

10
2

4
6
8
Distance (mm)

10

2

4
6
8
Distance (mm)
(d)

10

Figure 8.7 Comparison of diffuse reflectance from measurements (symbols) and the two-layer
diffusion model (solid lines) for sample 1 at 535 nm (a) and 700 nm (b), and sample 2 at 535 nm
(c) and at 700 nm (d) (See Table 8.1 for the two samples).
Figure 8.8 shows estimated values for the absorption and reduced scattering coefficients of
the first layer when the optical properties of the second layer and the thickness of the first layer

180 

are considered as known parameters. The errors of estimating µa1 and µs1' of the model samples
are 11.3-23.0% and 3.8-18.4%, respectively. Overall, relatively small values of the optical
coefficients produce larger errors in the estimation of the optical properties (values of µa1 and
µs1' at 700 nm are less than those at 500 nm). While the results are worse than those obtained
from the MC simulations, they are better than those reported by Kienel et al. (1998b) for twolayer turbid media with the errors in µa of 6-24% and in µs' of 0-88%.
25
535 nm
700 nm

Relative error (%)

20

15

10

5

0
S1-a1

S1-s1

S2-a1

Optical properties

S2-s1

 

Figure 8.8 Relative errors of the estimated optical properties for two model samples (denoted as
S1 and S2) at wavelengths of 535 nm and 700 nm (see Table 8.1 for the optical property data for
the two model samples).
When the optical properties of the second layer are considered as only unknown and those
of the first or upper layer are treated as known, the inverse algorithm does not give reasonable
estimates. This may have been attributed to the effect of the relatively thick first layer (2.64 mm

181 

and 3.29 mm). These results suggest that the two-layer model coupled with the hyperspectral
imaging technique can be used to obtain the optical properties of fruit skin with the thickness
similar to those studied in this research. However, further study is needed to determine if the
method is also suitable for thin-skin fruit like apple. Unsatisfactory results for estimating the
optical properties of the lower or second layer for the model samples suggest that further
improvements in the method are needed in order to measure the optical properties of both fruit
skin and flesh simultaneously.
8.5 Conclusions

This research has demonstrated a methodology for determining the optical properties of twolayer turbid materials, using a steady-state diffusion model for spatially-resolved reflectance
acquired by a hyperspectral imaging system. The diffusion model accurately described light
propagation in two-layer turbid media. Accurate estimations for two and four parameters were
achieved based on the noiseless data from the diffusion model. The inverse algorithm also gave
good estimates of two unknown optical parameters of the first layer or the second layer for MC
generated reflectance data, with errors of 8.5% for µa1 and 5.0% for µs1', 10.0% for µa2 and 9.3%
for µs2'. The errors, however, were greater in estimating four optical parameters. Experimental
validation with the model samples showed larger errors (11.3-23.0% for µa1 and 3.8-18.4% for
µs1') in estimating the optical properties of the first layer.
Satisfactory results can be achieved when two unknown parameters for the first or upper
layer are to be determined. While the results for determining the two optical parameters of the
second or lower layer of the model samples are still unsatisfactory, Monte Carlo simulations for

182 

ideal samples suggest that it is possible to accurately estimate the optical properties of both
layers simultaneously. Hence further study should be focused on improving the reflectance
measurement by the hyperspectral imaging system and the inverse algorithm. To accurately
evaluate the diffusion model for determining the optical properties of two-layer samples, it is
important that standard model samples with known optical properties be made available for
calibrating or validating the inverse algorithm. Efforts should also be made to reduce the
computational complexity and time for estimating the four optical parameters plus the thickness
of the first layer simultaneously.

183 

CONCLUSION AND FUTURE RESEARCH

This dissertation research has made significant progress in the development of new methods
and techniques for optical characterization and nondestructive quality evaluation of horticultural
products. A hyperspectral imaging-based spatially-resolved technique, along with a bench-top
optical property measuring prototype, was developed, through optimization of the inverse
algorithm and optical designs, to accurately and reliably measure the optical absorption and
scattering properties of horticultural and food products. The instrument was used for measuring
the optical properties of apple and peach and for assessing their maturity/quality attributes.
Moreover, research was conducted in quantification of the relationships of the optical properties
with the mechanical properties and microstructural characteristics of apples that were subject to
accelerated softening in a high temperature (~22 ºC)/high humidity (95%) environment. Further
study was also carried out to evaluate the feasibility of determining the optical properties of twolayer media representing fruit skin and flesh. The following major conclusions were drawn from
the research:
(1) An inverse algorithm for estimating the absorption and reduced scattering coefficients from
spatially-resolved reflectance profiles based on a single-layer diffusion model was developed
and optimized by using data transformation and weighting methods. The logarithm and
integral transformation of the original data and the relative weighting method greatly
improved the estimations of the two optical parameters with the relative errors of 10.4%,
10.7%, and 11.4% for µa, and 6.6%, 7.0% and 7.1% for µs' for liquid model samples made
up of dye and intralipid, which were much smaller than those obtained from the original
diffusion model. Further statistical analysis showed that the logarithm transformation and

184 

relative weighting methods improved the inverse algorithm for more reliable estimation of
the two optical parameters.
(2) Main optical design factors, including light beam and source-detector distance, in the
development of hyperspectral imaging-based spatially-resolved technique were examined
and optimized through Monte Carlo (MC) simulation and experimental studies. To achieve
the best performance of the system, the light beam should be of circular shape and Gaussian
type with the diameter of less than 1 mm, the optimal minimum source-detector distance
should be about 1.5 mm, and the optimal maximum source-detector distance should be
equivalent to 10-20 mfp' or determined by the minimum signal-to-noise ratio of 20 (or 150
CCD counts for the system used in this research).
(3) A new multi-purpose Optical Property Analyzer (OPA) prototype was designed and
constructed, based on the optimization studies, for optical characterization and hyperspectral
imaging of biological materials for the spectral region of 500-1,000 nm. Software
incorporating two popular diffusion models (Farrell et al., 1992; Kienle and Patterson, 1997)
with the corresponding inverse algorithms was developed for the system control and
automatic imaging acquisition and optical properties computation. The OPA was extensively
tested and evaluated for measurement accuracy, precision/reproducibility, and sensitivity
using liquid model samples with known optical properties. The test results showed that the
OPA has achieved acceptable accuracies for the absorption and reduced scattering
coefficients, which are either comparable or superior to other reported studies using more
sophisticated time-resolved, frequency-domain, or other types of spatially-resolved
instruments.

185 

(4) Spectra of the absorption and reduced scattering coefficients for one cultivar of peach and
two cultivars of apple were determined for the spectral region of 500-1,000 nm using the
Optical Property Analyzer. The absorption spectra of fruit were shaped by major pigments
(i.e., chlorophyll and anthocyamin) and water in the fruit tissue, while the reduced scattering
spectra decreased steadily with the increasing wavelength for most of the fruit samples. The
best prediction results for peach fruit were obtained with the combinations of absorption and
scattering spectra, with values of the correlation coefficient (r) for Magness-Talyor firmness,
*

*

soluble solids content (SSC), the skin color parameter (L ) and the flesh color parameter (L )
being 0.724 (SEP = 18.13 N), 0.458 (SEP = 0.96 °Brix), 0.893 (SEP = 3.54), and 0.722 (SEP
= 3.32), respectively. For the apple study, the best firmness prediction was obtained with r =
0.892 (SEP = 7.89 N) for ‘Golden Delicious’ (GD) and r = 0.863 (SEP = 8.94 N) for
‘Delicious’ (RD). The best result for SSC was achieved for the freshly harvested group with r
= 0.791 (SEP = 0.69 °Brix) for GD and r = 0.842 (SEP = 0.73 °Brix) for RD. It demonstrated
that measurement of optical properties provides a new means for quantifying the quality of
fruit.
(5) The absorption and reduced scattering coefficients, acoustic/impact firmness, Young’s
modulus, and cell size for GD and ‘Granny Smith’ apples all decreased with time when they
were subject to accelerated softening at high temperature(~22 C)/high humidity (95%). The
decreases were caused by changes in the cellular structure and properties, primarily resulting
from the degradation of pectin and decrease on the molecular weight distribution of
hemicelluloses (Harker et al., 1997). Various correlations for the optical parameters with
acoustic/impact firmness, Young’s modulus, and cell size and morphological parameters
were found. These findings suggest the potential of using optical properties to study or

186 

monitor changes in the mechanical properties and physiological condition of apple fruit
during storage or in the softening process.
(6) The inverse algorithm of the two-layer diffusion model gave good estimates of two unknown
optical parameters of the first layer or the second layer for MC generated reflectance data,
with errors of 8.5% for µa1 and 5.0% for µs1' for the first or top layer, and 10.0% for µa2 and
9.3% for µs2' for the second or substrate layer. The errors, however, were considerably
greater in estimating the four optical parameters. Experimental validation with the solid
model samples showed larger errors (11.3-23.0% for µa1 and 3.8-18.4% for µs1') in
estimating the optical properties of the first layer.
The results and findings from this research provide a fundamental understanding of optical
characterization of biological materials, and a systematic guide in designing spatially-resolved
optical systems for nondestructive quality measurement of horticultural and food products. The
new optical property measuring instrument developed in this research can have applications for a
wide range of food and biological materials. The following are recommendations for future work:
(1) It is much more difficult to tackle inverse light transport problems than forward problems.
Therefore, attention should be paid to studying the characteristics and complexity of the
diffusion model when it is used in an inverse algorithm for estimating optical parameters.
This research was based on the diffusion model with several assumptions (i.e., scatteringdominant, isotropic source, and source-detector distance greater than one transport mean free
path). Further work is needed to extend the diffusion model to different biological materials
and expand its scope of application.

187 

(2) Although the optical system and algorithm of the OPA has been carefully evaluated and
optimized using the model samples, other factors such as roughness and possible geometric
irregularities on the surface of fruit should be studied for their effect on the optical properties
measurement and on maturity/quality assessment of fruit.
(3) This research has shown that the optical properties were correlated with the cell size and
cellular structures of fruit tissue. To better quantify the interaction of light with plant tissue, it
would be useful to consider a multi-scale approach (Kienle et al., 2007) for describing the
light propagation in different volumes of biological tissue at macroscopic and microscopic
scales, respectively.
(4) Based on the preliminary study of the two-layer diffusion model for determining optical
properties of fruit skin and flesh, further efforts should be made to develop light propagation
models and optical techniques for measuring the optical properties of heterogeneous or multilayer biological materials, as well as to reduce the computational complexity and time for
estimating the absorption and reduced scattering coefficients.
(5) The OPA is a general-purpose optical instrument designed for measuring a wide range of
biological materials. To expand its application to other areas and other agricultural and food
products, the OPA should be further evaluated for its stability, accuracy, and measurement
limit.

188 

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