OPTICAL TRANSMISSION SCANNING AND HYBRID ACOUSTO-OPTICAL

TECHNIQUES FOR NDE AND SHM OF STRUCTURAL COMPOSITES

By

Oleksii Karpenko

A DISSERTATION

Michigan State University

in partial fulfillment of the requirements

Submitted to

for the degree of

Electrical Engineering – Doctor of Philosophy

2018

ABSTRACT

OPTICAL TRANSMISSION SCANNING AND HYBRID ACOUSTO-OPTICAL

TECHNIQUES FOR NDE AND SHM OF STRUCTURAL COMPOSITES

By

Oleksii Karpenko

Fiber reinforced polymer (FRP) composites have been extensively used in aerospace, marine
and defense industries due to the many advantages they offer including light-weight, corrosion
resistance and excellent thermo-mechanical properties.
Increasing fuel-efficiency demands and
reducing green-house emissions has also propelled the use of FRP composites in the automotive
industry. However, despite excellent mechanical properties of FRPs, their anisotropy, brittle
nature and the vulnerability to flaws during fabrication and service has propelled the need of non-
destructive evaluation (NDE) and structural health monitoring (SHM) techniques. This dissertation
presents three major contributions to the fields of NDE and SHM of structural composites:

• optical transmission scanning (OTS) for rapid, non-contact and quantitative NDE of glass

and aramid FRPs;

• optical frequency-domain reflectometry (OFDR) for distributed monitoring of strains in FRPs

using single-mode (SM) optical fibers and Rayleigh back-scattering;

• hybrid acousto-optic health monitoring of FRPs using guided waves (GW) and Fabry-Perot

interferometric sensors based on chirped fiber Bragg-gratings (CFBG-FPI).

Chapter I presents an OTS system for quantitative NDE of GFRP samples. The technique
provides high-resolution, rapid, and non-contact optical transmittance scans. Experimental im-
plementation of the technique and advanced data analysis protocol developed for impact damage
evaluation are presented. Obtained experimental results show that other defects and certain mi-
crostructural variations in GFRP composites can be easily identified by OTS, because the technique
is sensitive to localized changes of optical properties such as radiation absorption and scattering.

The applications of OTS are extended to GFRP plates with improperly mixed resin, inclusions, and
delaminations. Finally, the capabilities of the technique to evaluate the distribution of adhesive and
detect fatigue damage in adhesively bonded GFRP joints are demonstrated.

Chapter II describes the development of advanced signal processing algorithms for strain sensing
in optical fibers using Rayleigh back-scattering and the OFDR technique. Distributed displacement
and strain sensing along the fiber length is implemented using the OFDR-1000 system from General
Photonics Corporation (Chino, CA). Performance of the system is validated by measuring strains
introduced in the optical fiber by the piezoelectric fiber stretcher.

Chapter III lays out the approach for diagnostic imaging of plate-like structures using hybrid
acousto-optic technique. Guided waves are excited with surface-bonded piezoelectric wafers and are
sensed with pairs of chirped fiber Bragg-gratings that form Fabry-Perot interferometers inside the
surface-bonded optical fiber. Initial experimental results obtained on aluminum plates demonstrate
that CFBG-FPIs are sensitive to both symmetric and antisymmetric fundamental GW modes.
Structural damage is successfully located using Delay-and-Sum (DAS) imaging.

Copyright by
OLEKSII KARPENKO
2018

ACKNOWLEDGEMENTS

I would like to express all my gratitude and respect to my research advisors Dr. Lalita Udpa and
Dr. Mahmood Haq. I am thankful that Dr. Udpa and Dr. Haq introduced me to a fascinating world
of advanced materials and nondestructive evaluation. Their vast knowledge and skill in many areas
inspired me to grow as a graduate student and a researcher. Apart from their professional guidance
and supervision, Dr. Udpa and Dr. Haq have been my excellent teachers and mentors in all issues
that I ever had during the time I worked on this dissertation. I am really glad that fortune has given
me the chance to work with these outstanding people. I would like to give special thanks to other
members of my committee, Dr. Satish Udpa and Dr. Selin Aviyente, for their fruitful discussions
and valuable comments on my dissertation.

I would like to express my gratitude to Dr. Anton Khomenko, Dr. Ermias Koricho and Dr. Gary
Cloud, whose expertise and support added considerably to my graduate experience at Composite
Vehicle Research Center. I would also like to thank my colleagues from my internship at General
Photonics Corporation, Dr. Steve Yao and Dr. James Chen, for giving me the opportunity to work
with advanced optical measurement systems. I am also grateful to Dr. Ming Han and his research
group for helping me with experiments required for this dissertation.

Furthermore, I thank my fellow lab-mates for providing a friendly atmosphere in the lab that
has made me feel welcome and comfortable. I must thank my friends Pavel Polunin and Roshan
Angoshtari for their support that made my life and work more enjoyable. Finally, I owe a debt of
gratitude to my parents. Thank you for encouraging me in all of my pursuits and inspiring me to
follow my dreams!

v

TABLE OF CONTENTS

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
LIST OF TABLES .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
LIST OF FIGURES .
CHAPTER 1 OPTICAL TRANSMISSION SCANNING . . . . . . . . . . . . . . . . . .

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1.1 Theory and validation of OTS for quantitative NDE of impact damage in GFRP

ix

x

1

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. .

. .
.
.

. .
Introduction .

composites .
.
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.1
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2.1 OTS set-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1.2.2 Manufacturing of GFRP samples
. . . . . . . . . . . . . . . . .
1.1.2.3 Material properties of GFRP samples . . . . . . . . . . . . . . .
1.1.2.4 Drop-weight impact tests . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1
1
4
4
4
6
7
8
1.1.3.1 Determination of a “standard” transmission coefficient T . . . . . 11
1.1.3.2 Robustness of OTS . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.1.4 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.1.3 Theory of OTS .

1.1.4.1 Advanced signal processing for quantitative evaluation of im-

pact damage . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 14
1.1.4.2
Post-processed OT-scans of GFRP samples . . . . . . . . . . . . 16
1.1.4.3 OTS validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
. . . . . . . 21

1.2 Quantitative Comparison of OTS with Conventional NDE Techniques

1.1.5 Conclusions .

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. .

1.2.1

Impact Testing and Standard NDE Techniques used for Comparison with
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
OTS .
1.2.1.1 Drop-weight impact tests . . . . . . . . . . . . . . . . . . . . . . 21
1.2.1.2
Pulse-echo UT Testing . . . . . . . . . . . . . . . . . . . . . . . 21
1.2.1.3 Ultraviolet Dye Penetrant Testing . . . . . . . . . . . . . . . . . 22
1.2.2 Experimental Results and Discussion . . . . . . . . . . . . . . . . . . . . 22

1.2.2.1 Mechanical response of the GFRP composite laminates to low

velocity impacts

. . . . . . . . . . . . . . . . . . . . . . . . . . 22
1.2.2.2 OT-scans of impacted GFRP samples . . . . . . . . . . . . . . . 24
1.2.2.3 UT C-scans of GFRP samples . . . . . . . . . . . . . . . . . . . 25
. . . . . . 30
. . . . . . . . . . . . . . . 37

1.2.3.1 UV DPT of impacted GFRP samples
1.2.3.2 Quantitative comparison of OTS and other NDE methods in

1.2.3 Comparative analysis of pulse-echo UT and OTS measurements

1.2.4 Conclusions .

estimation of the total damage area

. . . . . . . . . . . . . . . . 39
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
1.3 Feasibility of OTS for Quality Control and NDE of GFRP Composite Structures . . 43
1.3.1 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

. .

vi

1.3.1.1 Manufacturing of GFRP samples with improper cured resin

component proportions . . . . . . . . . . . . . . . . . . . . . . . 43
. 44

1.3.1.2 Manufacturing of GFRP samples with inclusions . . . . . . . .
1.3.1.3 Manufacturing of double cantilever beam samples and mode I

fracture tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
1.3.1.4 Manufacturing of adhesively bonded GFRP joints and fatigue tests 45
. 46
. . . . . . 46

1.3.2 Experimental Results and Discussion . . . . . . . . . . . . . . . . . . .

1.3.2.1 Detection of foreign object inclusions in GFRP plates
1.3.2.2

Evaluation of GFRP plates having improper proportions of
matrix components . . . . . . . . . . . . . . . . . . . . . . . . . 48
1.3.2.3 Monitoring of crack propagation in DCB samples . . . . . . . . . 49
1.3.2.4 Detection of non-uniform adhesive distribution and fatigue

.

.

.

1.3.3 Conclusions .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

damage in adhesively bonded lap-shear joints . . . . . . . . . . . 50
. 52
1.4 Robust Implementation of OTS and Advanced NDE Features . . . . . . . . . . . . 53
. . . . . . . . . . . . . . 53
1.4.1 OTS system with advanced scanning capabilities
. . . . . . . . . . . . . . 55
1.4.2 Multi-wavelength evaluation of GFRP structures
State of polarization measurements . . . . . . . . . . . . . . . . . . . . . . 58
1.4.3
Separation of ballistic and scattered photons . . . . . . . . . . . . . . . . . 61
1.4.4
. 62
1.4.5
Feasibility of 3D imaging . . . . . . . . . . . . . . . . . . . . . . . . . .
. 65
1.4.6 Detection of fiber breakage, lack of infusion, air voids and fiber waviness
1.4.7 Conclusions .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. 66

.

.

.

CHAPTER 2 OPTICAL FREQUENCY DOMAIN REFLECTOMETRY FOR SHM OF

.

.

.

STRUCTURAL COMPOSITES . . . . . . . . . . . . . . . . . . . . . . . . 69
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
2.1 Fiber-optic sensing .
. 71
2.2 Scattering of radiation in optical fibers . . . . . . . . . . . . . . . . . . . . . . .
2.3 OFDR operating principle .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
2.4 Theory of polarization diverse OFDR . . . . . . . . . . . . . . . . . . . . . . . . 74
2.5 Strain sensing approach based on detection of physical shifts of point-like reflectors
79
2.6 Validation of signal processing technique for strain sensing using OFDR . . . . . . 82
2.7 Conclusions .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

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CHAPTER 3 HYBRID ACOUSTO-OPTIC HEALTH MONITORING OF STRUC-
TURAL COMPOSITES USING GUIDED WAVES AND CFBG-FPI SEN-
SORS .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.1 Proposed approach for hybrid acousto-optic SHM . . . . . . . . . . . . . . . . . . 89
3.2 Guided wave theory .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Symmetric solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
3.2.1
3.2.2 Antisymmetric solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
3.2.3
Phase velocity and group velocity dispersion curves . . . . . . . . . . . . . 96
3.3 Detection of guided waves with FBG and CFBG-FPI sensors . . . . . . . . . . . . 98
3.4 Delay-and-Sum diagnostic imaging . . . . . . . . . . . . . . . . . . . . . . . . .
. 104
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
3.5 Conclusions .

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vii

BIBLIOGRAPHY .

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viii

LIST OF TABLES

Table 1.1: Elastic properties of GFRP material. Young’s and shear moduli are measured

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6

in GPa.

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Table 1.2: Absolute percent difference in estimation of the total damage area between the

OTS and other NDE techniques.

. . . . . . . . . . . . . . . . . . . . . . . . . . 40

ix

LIST OF FIGURES

Figure 1.1: Schematic overview of common defects in composites.

. . . . . . . . . . . . .

2

Figure 1.2: Optical transmission scanning: a) experimental setup; (b) test of the “stan-
dard” specimen which has a delamination crack (mode I) created by loading
it as a double cantilever beam according to ASTM D5528; (c) impacted spec-
imen under test; (d) adhesively bonded lap-joint under test. For interpretation
of the references to color in this and all other figures, the reader is referred to
the electronic version of this dissertation. . . . . . . . . . . . . . . . . . . . . .

Figure 1.3: Experimental setup for drop-weight impact testing. . . . . . . . . . . . . . . .

.

5

8

Figure 1.4:

(a) Healthy GFRP sample (no impact); (b) GFRP sample after E = 20 J impact.

13

Figure 1.5:

Figure 1.6:

(a) OT-scan of healthy GFRP sample; (b) OT-scan of the GFRP sample after
E = 20 J impact. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

.

(a) Gradual change of transmitted radiation power across delamination bound-
ary due to partial beam scattering through the transition regions; (b) OT-scan
of the double cantilever beam (DCB) sample with a crack that served as the
“standard”; (c) OT-scan of the metal-to-composite interface in the support re-
gion; (d) determination of contour levels corresponding to different numbers
of delaminations.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

.

Figure 1.7:

(a) Post-processed OT-scan of the healthy sample; (b) post-processed OT-scan
of the sample after E = 20 J impact.

. . . . . . . . . . . . . . . . . . . . . . . 17

Figure 1.8: Estimated damage area corresponding to different numbers of delaminations N.

18

Figure 1.9:

(a) Cross-section of the GFRP sample (thickness H = 4.8 mm, impact energy
E = 20 J); (b) delaminations identified using edge detection and filtering of
the image data; (c) corresponding OT-linescan; (d) the number of delamina-
tions, N registered by the OTS; (e) the number of delaminations, N along the
cross-section length obtained from post-processed digital camera images; (f)
comparison of results obtained with OTS and digital camera imaging wherein
the regions in which the numbers of detected delaminations match are high-
lighted in purple. For interpretation of the references to color in this figure
legend, the reader is referred to the web version of this report. . . . . . . . . . . 19

Figure 1.10: Pulse-echo UT inspection with ULTRAPAC II system. . . . . . . . . . . . . . . 22

Figure 1.11: (a) Force-time curves; (b) energy-time curves.

. . . . . . . . . . . . . . . . . . 23

x

Figure 1.12: Damage degree corresponding to different impact energies.

. . . . . . . . . . . 24

Figure 1.13: Top surface images of tested GFRP samples: (a) healthy GFRP sample; (b)
GFRP sample subjected to 20 J impact; (c) GFRP sample subjected to 40 J
impact; (d) GFRP sample subjected to 80 J impact.

. . . . . . . . . . . . . . . 25

Figure 1.14: OT-scans:

(a) healthy GFRP sample; (b) GFRP sample subjected to 20
J impact; (c) GFRP sample subjected to 40 J impact; (d) GFRP sample
subjected to 80 J impact.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

Figure 1.15: Delamination profiles identified using enhanced signal processing of OT
scans: (a) healthy GFRP sample; (b) GFRP sample subjected to 20 J impact;
(c) GFRP sample subjected to 40 J impact; (d) GFRP sample subjected to 80
J impact. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

. .

. .

.

. 27

Figure 1.16: Estimated damage area corresponding to different numbers of delaminations

as obtained from OT scans.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

Figure 1.17: UT A-scans of the GFRP sample subjected to E = 20 J impact ( f = 1 MHz).

. 28

Figure 1.18: UT C-scans of GFRP samples showing the AUT

(a) healthy
GFRP sample; (b) damage from 20 J impact; (c) damage from 40 J impact;
(d) damage from 80 J impact. . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

1 /AUT
2

ratio:

Figure 1.19: Damage contours identified from UT scans using AUT

2 UT ratio: (a)
healthy GFRP sample; (b) damage from 20 J impact; (c) damage from 40 J
impact; (d) damage from 80 J impact.

. . . . . . . . . . . . . . . . . . . . . . 30

1 /AUT

Figure 1.20: UT C-scans of GFRP samples showing the ToF difference between AUT
1

and
AUT
2 : (a) healthy GFRP sample; (b) damage from 20 J impact; (c) damage
from 40 J impact; (d) damage from 80 J impact. . . . . . . . . . . . . . . . . . 31

Figure 1.21: Damage contours identified using the UT ToF difference: (a) healthy GFRP
sample; (b) damage from 20 J impact; (c) damage from 40 J impact; (d)
damage from 80 J impact. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

Figure 1.22: Binary union of damage contours estimated from the amplitude and ToF UT
measurements: (a) healthy GFRP sample; (b) damage from 20 J impact; (c)
damage from 40 J impact; (d) damage from 80 J impact.

. . . . . . . . . . . . 33

Figure 1.23: (a) Ultrasonic reflections from the top surface of the sample and from in-
terlaminar delaminations in case of immersion UT inspection in pulse-echo
mode; (b) transmission of electromagnetic radiation through healthy and de-
laminated regions of the test sample in case of OTS inspection.

. . . . . . . . . 33

xi

(cid:16)
(cid:16)
˜αOTS(cid:17)2· ln

ln

(cid:16)

(cid:17)
(cid:17)

1−RUT
D
1−ROTS

D

Figure 1.24: Normalized UT C-scans showing ˜αUT for: (a) healthy GFRP sample; (b)
GFRP sample subjected to 20 J impact; (c) GFRP sample subjected to 40 J
impact; (d) GFRP sample subjected to 80 J impact.

. . . . . . . . . . . . . . . 38

Figure 1.25: Normalized OT-scans adjusted according to Eq. (1.35) that show

for: (a) healthy GFRP sample; (b) GFRP sample subjected to 20 J impact; (c)
GFRP sample subjected to 40 J impact; (d) GFRP sample subjected to 80 J
impact. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

.

.

.

.

.

.

.

.

. 39

Figure 1.26: Images of damaged GFRP samples soaked in UV dye and illuminated with
UV light: (a) top surface, E = 20 J; (b) top surface, E = 40 J; (c) top surface,
E = 80 J; (d) bottom surface, E = 20 J; (e) bottom surface, E = 40 J; (f)
bottom surface, E = 80 J.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

Figure 1.27: UV DPT images of damaged GFRP samples after normalization of image
intensity: (a) top surface, E = 20 J; (b) top surface, E = 40 J; (c) top surface,
E = 80 J; (d) bottom surface, E = 20 J; (e) bottom surface, E = 40 J; (f)
bottom surface, E = 80 J.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Figure 1.28: Damage contours identified from normalized UV DPT images of GFRP sam-
ples: (a) top surface, E = 20 J; (b) top surface, E = 40 J; (c) top surface,
E = 80 J; (d) bottom surface, E = 20 J; (e) bottom surface, E = 40 J; (f)
bottom surface, E = 80 J.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

Figure 1.29: Total damage area evaluated as a union of UV DPT images taken from top
and bottom sides of GFRP samples: (a) E = 20 J; (b) E = 40 J; (c) E = 80 J.

. 42

Figure 1.30: Comparison of damage areas obtained by the OTS, UT, and UV DPT for

different impact energy levels. . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

Figure 1.31: Side view of the manufactured GFRP lap-joint. . . . . . . . . . . . . . . . . .

. 45

Figure 1.32: (a) GFRP sample with red inclusions (small pieces of resin transfer medium);
(b) OT-scan of the same sample. Inclusions are highlighted by circles in both
images. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

.

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.

Figure 1.33: (a) 8-layer GFRP sample with black fiber inclusions and impact damage; (b)

OT-scan of the same sample.

. . . . . . . . . . . . . . . . . . . . . . . . . . . 47

xii

Figure 1.34: Evaluation of 8-layer GFRP samples and QC detection of faulty resin com-
ponent ratios using OTS: (a) Photo of GFRP sample having proper resin
proportions; (b) Photo of GFRP sample having moderate error in resin pro-
portions; (c) Photo of GFRP sample having extreme error in resin proportions;
(d) OT-scan GFRP sample having proper resin proportions; (e) OT-scan of
GFRP sample having moderate error in resin proportion; (f) OT-scan of GFRP
sample having extreme error in resin proportions.

. . . . . . . . . . . . . . . . 48

Figure 1.35: (a) GFRP DCB mode I test sample); (b) OT-scan of the DCB sample before
cyclic load test; (c) OT-scan of the DCB sample after crack growth caused by
cyclic load. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

.

. .

. .

Figure 1.36: OT-scans of composite lap-joints: (a) properly cured adhesive bond, quasi-
uniform pressure applied to adherends, P = 150 mW; (b) lap-joint before
fatigue tests, manufactured using a single C-clamp, non-uniform pressure
applied to the adherends when curing, P = 150 mW; (c) adherends of a lap-
joint (output radiation power, P = 3 mW); (d) lap-joint pictured in (b) after
20000 fatigue cycles, manufactured using a single C-clamp, non-uniform
pressure applied to the adherends during curing, P = 150 mW.

. . . . . . . . . 51

Figure 1.37: Block-diagram of OTS-1000 system for NDE of GFRP composites. . . . . . . . 53

Figure 1.38: OTS-1000 system for NDE of GFRP composites.

. . . . . . . . . . . . . . .

. 54

Figure 1.39: Geometry of adhesively bonded lap-joint.

. . . . . . . . . . . . . . . . . . . . 56

Figure 1.40: Polarization state generator based on 4 magneto-optic rotators.

. . . . . . . .

. 58

Figure 1.41: Polarization state analyzer based on 6 magneto-optic rotators.

. . . . . . . . . . 58

Figure 1.42: Spatial and temporal discrimination of ballistic and scattered photons.

. . . . . 61

Figure 1.43: 3D scanning concept using variable focus lens. . . . . . . . . . . . . . . . . . . 62

Figure 1.44: 3D scanning concept using scattering pattern correlation.

. . . . . . . . . . .

. 63

Figure 1.45: Schematic of the experimental setup for measuring the power of transmitted

radiation as a function of focal distance along Z-axis.

. . . . . . . . . . . . . . 64

Figure 1.46: Measured signal as a function of focal distance along Z-axis.

. . . . . . . . . . 64

Figure 1.47: OT-scan of GFRP sample with lack of infusion (dry spots) and cracks.

. . . . . 65

Figure 1.48: GFRP sample with irregular distribution of chopped glass fibers. Region with

air bubbles is highlighted with red ellipse.

. . . . . . . . . . . . . . . . . . . . 65

xiii

Figure 1.49: OT-scan of GFRP sample with chopped glass fibers (640 nm wavelength).

. . . 67

Figure 1.50: OT-scan of GFRP sample with chopped glass fibers (1310 nm wavelength). . . . 67

Figure 1.51: Zoomed region of the OT-scan shown in Fig. 1.47. Individual fiber tows are

visible and fibers are well aligned.

. . . . . . . . . . . . . . . . . . . . . . . . 68

Figure 1.52: Zoomed region of the OT-scan shown in Fig. 1.47. Wavy fibers are detected.

.

. 68

Figure 2.1: Categories of fiber-optic sensors and main interrogation techniques. . . . . . . . 69

Figure 2.2: Typical spectrum of scattered radiation in solid state medium. . . . . . . . . . . 71

Figure 2.3: Weak FBG model describing Rayleigh scattering as superposition of point-

like reflectors along the fiber.

. . . . . . . . . . . . . . . . . . . . . . . . . . . 72

Figure 2.4: Schematics of the OFDR system for measuring Rayleigh back-scattered radi-

ation in single-mode optical fibers.

. . . . . . . . . . . . . . . . . . . . . . . . 73

Figure 2.5: Perfect linear TLS tuning (ω is instantaneous optical frequency, ω0 is initial

optical frequency, and γ is tuning rate). . . . . . . . . . . . . . . . . . . . . . . 74

Figure 2.6: Conventional approach for strain measurement using OFDR.

. . . . . . . . . . 80

Figure 2.7: Alternative approach for strain measurement using OFDR. . . . . . . . . . . . . 81

Figure 2.8: OFDR experimental setup at General Photonics Corporation.

. . . . . . . . . . 83

Figure 2.9: Radiation intensity sensed by photodetector PD1 (ˆs-polarized component).

. . . 83

Figure 2.10: Typical OFDR measurement showing reflectance of FUT: single mode fiber,

PZT fiber stretcher and optical fiber with CBFGs.

. . . . . . . . . . . . . . . . 84

Figure 2.11: Fresnel reflection at APC connector.

. . . . . . . . . . . . . . . . . . . . . . . 84

Figure 2.12: Reflections from continuously written Bragg-gratings. . . . . . . . . . . . . . . 85

Figure 2.13: Shift of reflection from APC connector at different strain states.

. . . . . . . . . 85

Figure 2.14: Cross-correlation of segments of back-scattering profile at the end of the fiber
stretcher. Baseline reflectance measurement is compared to a measurement
after applying 190 V to the input of FST-005. . . . . . . . . . . . . . . . . . . . 86

Figure 2.15: Displacement profiles along the 35-m long optical fiber section inside the

FST-005 fiber stretcher.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

xiv

Figure 2.16: Strain profiles along the 35-m long optical fiber section inside the FST-005

fiber stretcher.

.

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

Figure 3.1: Overall approach for hybrid acousto-optic SHM of structural composites. . . . . 89

Figure 3.2: Unique features of the proposed hybrid acousto-optic SHM.

. . . . . . . . . . . 91

Figure 3.3: Shear vertical and pressure waves in solids. . . . . . . . . . . . . . . . . . . . . 93

Figure 3.4:

Isotropic plate of infinite length and thickness 2d. Wave propagates in x-direction. 94

Figure 3.5: Phase velocity dispersion curves of 3-mm thick aluminum plate.

. . . . . . . . 97

Figure 3.6: Group velocity dispersion curves of 3-mm thick aluminum plate.

. . . . . . . . 97

Figure 3.7: Operation principle of the fiber Bragg-grating sensor.

. . . . . . . . . . . . . . 98

Figure 3.8: Principle of FBG wave division multiplexing.

. . . . . . . . . . . . . . . . . . 99

Figure 3.9: Design of the Fabry-Perot interferometer based on a pair of chirped fiber

Bragg-grating sensors (CFBG-FPI). . . . . . . . . . . . . . . . . . . . . . . . . 99

Figure 3.10: (a) Spectrum of radiation reflected from a CFBG-FPI sensor; (b) approach
for high-resolution strain sensing by modulating the intensity of radiation
back-reflected from CFBG-FPI. . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Figure 3.11: Block diagram of the setup for GW detection using surface-mounted CFBG-

FPI sensors.

.

.

.

.

.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

Figure 3.12: Experimental setup for GW detection using the CFBG-FPI sensors. . . . . . . . 102

Figure 3.13: Aluminum plate with CFBG-FPI sensors, piezoelectric transducer and surface-
bonded reflector: (a) drawing with exact dimensions; (b) photo of the test
setup. .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

.

.

.

.

.

.

.

.

Figure 3.14: Guided waves registered with the CFBG-FPI sensor 3. . . . . . . . . . . . . . . 104

Figure 3.15: DAS image of aluminum plate with the surface-bonded reflector. Location
of PZT actuator is marked as a black dot, CFBG-FPI sensors are marked as
black squares, and location of damage is marked by a white circle with a cross. . 106

xv

CHAPTER 1

OPTICAL TRANSMISSION SCANNING

1.1 Theory and validation of OTS for quantitative NDE of impact damage

in GFRP composites

1.1.1

Introduction

Glass fiber reinforced polymer (GFRP) composites are a superior design choice for many
applications due to the multitude of benefits they offer, such as light weight, high specific stiffness,
high specific strength, and good resistance to chemical agents. Combined with design flexibility
and strategic tailoring of mechanical properties, these key advantages have propelled the wide
acceptance of GFRP composites in marine, automotive, aerospace, sporting, and construction
industries [1]. GFRPs are commonly used in wind turbine blades, boat hulls, tanks, pipes, structural
panels, and adhesively bonded joints. However, the increasing demand for such advanced multi-
component materials brings along major challenges.

The elastic behavior and fracture of GFRP composites largely depend on the mechanical
properties of the fibers and the matrix, the strategic stacking sequence of layers, and the selection of
weave patterns. Anisotropy and mismatch of material properties at the interlaminar interfaces are
roots for many flaws. These include fiber breakage, matrix cracking, inclusions of foreign objects,
and air voids as summarized in Fig. 1.1. Fiber waviness, misoriented plies, and fiber/volume
fraction are other important properties of GFRPs to be monitored. A laminated structure subjected
to a low velocity impact, such as a tool drop, may develop delaminations between the inner layers
that are not visible on the surface. The major concerns for bonded joints are fatigue degradation of
the adhesive layer and disbond between adherends, which reduce the load carrying capacity of the
joint leading to its premature failure. Hence, non-destructive evaluation (NDE) techniques that can
measure both surface and subsurface defects are of critical importance in evaluating the integrity
of GFRP composite structures both at manufacturing stage and during their service lives.

1

Figure 1.1: Schematic overview of common defects in composites.

Current industrial practice involves the implementation of well-established NDE techniques
including ultrasonic testing (UT), X-ray, infrared (IR) or visible range radiation to inspect GFRP
structures. Depending on the particular application, each of these methods has its own advantages
and limitations. For instance, phased array UT may furnish precise information about the location of
damage and its spatial distribution inside the GFRP laminate [2,3]. However, phased arrays require
coupling with the test specimen, and they can be rather complex and costly because sophisticated
electronics are needed to adjust the time delays between the piezoelectric transducers for proper
focusing of the wave energy at the defect site. Hence, relatively simpler systems for immersed
and air coupled UT with a single transducer have been routinely used for NDE of composite
structures [4–8].

X-ray computed tomography (CT) can provide detailed images of delaminations and other
defects in composites [8–12]. However, X-ray CT uses relatively high levels of ionizing radiation,
which can be dangerous for inspectors. Moreover, chamber volume for X-ray CT severely limits
the size of the sample which can be evaluated. IR thermography is suitable for rapid screening of
large components, but it provides little information about the volumetric distribution of damage
[10,13–15].

2

Optical methods are generally non-invasive, safe, non-contacting, sensitive, whole-field, and
inexpensive. Hence, they are often used in biomedical applications to evaluate the properties of
biological tissues [16, 17]. Some optical techniques initially designed for medical imaging can
be adapted for NDE of GFRP composites. Conventional techniques for optical NDE of GFRP
laminates include electronic shearography, digital speckle pattern interferometry (DSPI), digital
image correlation (DIC) [10, 18], digital holography (DH), and optical coherence tomography
(OCT) [12,19–22]. These approaches can be used for locating defects and studying the mechanical
behavior of GFRP composites. However, a limitation of shearography, DSPI, DH, and DIC
techniques is that thermal or mechanical loading of the test specimen is required to create a
displacement field and locate structural damage. Both time domain (TD) and Fourier domain (FD)
OCT are based upon registering back-scattered and back-reflected radiation; and have been used
to study internal structure, defects, and stress in GFRP structures [12, 19–22]. Although TD OCT
and FD OCT have their own advantages, they suffer from common major limitation [23, 24]. The
penetration depth inside the GFRP specimens is limited to only a few millimeters due to very strong
scattering inside GFRP composite. In contrast to OCT, ballistic scanners rely on detecting ballistic
photons transmitted through the tissue [25]. Since glass fibers and many epoxy resins have good
transmission properties in the visible range, a similar principle was employed in this dissertation
for NDE of GFRP composites.

Chapter I presents an optical transmission scanning (OTS) system for quantitative NDE of GFRP
samples. The technique provides high-resolution, rapid, and non-contact OT (optical transmittance)
scans. Section 1 describes experimental implementation of the technique and advanced data
analysis protocol developed for impact damage evaluation. In Section 1, the OTS system is used for
inspection of pristine GFRP samples and those damaged by low velocity impact. The number of
delaminations across the thickness of the impacted samples as provided by the OTS with advanced
data analysis is validated by observing the damage in a cross-section of the impacted GFRP samples
after cutting them with a diamond saw. Section 2 provides quantitative comparisons of obtained
OT-scans with well-established NDE techniques, such as pulse-echo ultrasound and ultraviolet

3

dye penetrant testing. Potential applications of OTS for quality control (QC) and NDE of various
composite structures are summarized in Section 3. Finally, Section 4 presents the rugged OTS
system that provides high-resolution OT-scans (up to 100 µm) of GFRP samples with micro-
structural defects and variations. Section 4 also provides some insight into further refinement of
OTS by adding 3D imaging capability.

1.1.2 Materials and methods

1.1.2.1 OTS set-up

The experimental setup for acquiring non-contact OT-scans consists of a translation stage that
moves the sample, a laser source that illuminates the sample, and a downstream photodetector, as
shown in Fig. 1.2a. Fig. 1.2b shows the test setup for a cantilever beam with a mid-plane crack that
was used as the “standard” specimen as described below. Fig. 1.2c illustrates how the healthy and
impacted plates were examined.

In the present setup, the light source is an iBeam-smart-640s laser diode with 640 nm funda-
mental wavelength, 1.5 mm beam diameter, and up to 150 mW output power. The transmitted
radiation is registered using a DET36A Si detector with 350-1100 nm wavelength range, 14 ns rise
time and 13 mm2 active area. The voltage at the output of the photodetector is directly proportional
to registered radiation power. The XY-coordinate stage with stepper motors allows for rapid raster
scanning of the GFRP samples with a lateral resolution of 0.25 mm. The lateral resolution of OTS
system was mainly determined by the beam diameter and was kept at 0.5 mm in all the experiments
described in Section 1.

1.1.2.2 Manufacturing of GFRP samples

GFRP composite samples were manufactured using a vacuum-assisted liquid molding pro-
cess. The reinforcement was S2-glass plain weave fabric with areal weight of 818 g/m2, namely
ShieldStrand S®, provided by Owens Corning. The GFRP samples comprised eight layers of such

4

Figure 1.2: Optical transmission scanning: a) experimental setup; (b) test of the “standard”
specimen which has a delamination crack (mode I) created by loading it as a double cantilever
beam according to ASTM D5528; (c) impacted specimen under test; (d) adhesively bonded lap-
joint under test. For interpretation of the references to color in this and all other figures, the reader
is referred to the electronic version of this dissertation.

fabric stacked at the same angle. The distribution medium was Resinflow 60 LDPE/HDPE blend
fabric from Airtech Advanced Materials Group. The resin was SC-15, a two part toughened epoxy
obtained from Applied Poleramic. The GFRP plate (508.0 × 609.6 mm) was manufactured in a
609.6 × 914.4 mm aluminum mold with point injection and point venting. After the materials were
placed, the mold was sealed using a vacuum bag and sealant tape, and it was then infused under
vacuum at 29 in Hg. The resin-infused panel was cured in a convection oven at 60◦C for two hours
and post-cured at 94◦C for four hours. Finally, impact samples with dimensions of 100 × 100 ×
4.7 mm were cut from the manufactured GFRP plate using a diamond saw.

5

1.1.2.3 Material properties of GFRP samples

Elastic properties of the orthotropic GFRP samples used in experimental study were determined

from tensile tests, and are presented in Table 1.1 [26].

E11
23.1

E22
23.1

E33 G12 G13 G23
6.9
2.54

2.54

3.2

ν12
0.36

ν13
0.28

ν23
0.28

ρ, kg/m3
1907

Table 1.1: Elastic properties of GFRP material. Young’s and shear moduli are measured in GPa.

The refractive index of manufactured GFRP sample can be calculated using the rule of mixtures

for the resin and the fiber volumes [19] as:

nc = nr · Vr + n f · Vf ,

(1.1)

where nr and n f are the refractive indices of resin and fiber, respectively; and Vr and Vf are the
volume fractions of resin and fiber, respectively. SC-15 is a combination of bisphenol A diglycidyl
ether resin and cycloaliphatic amine curing agent with weight fractions of ≈ 0.77 (100/130) and
≈ 0.23 (30/130), respectively [27]. Weight fractions can be converted to volume fractions using
the following relation:

(1.2)

(cid:16)
(cid:16)

(cid:17)
(cid:17) ,

Ve
Vh

=

me·ρh
mh·ρe

me·ρh+mh·ρe
me·ρh+mh·ρe

where me and mh are the weight fractions of epoxy and hardener, and ρe and ρh are the densities
of epoxy and hardener, respectively. Using Eq. (1.2), the Ve and Vh for SC-15 can be calculated as
≈ 0.75 (105/141) and ≈ 0.25 (36/141), respectively. Also, density of SC-15 can be calculated as

ρr = ρh · Vh
mh

= ρe · Ve
me

= 1160 kg/m3

(1.3)
The refractive index of bisphenol A diglycidyl ether resin is ne ≈ 1.574 [28], and average refractive
index of cycloaliphatic amine hardener is nh ≈ 1.5 [29]. Hence, according to Eq. (1.1), refractive
index of uncured SC-15 can be estimated as nr ≈ 1.556. Density and refractive index of S-glass
fiber is 2480-2490 kg/m3 and 1.523, respectively [30]. The weight fraction of resin in manufactured

6

GFRP composite is 0.365 [31]. Using Eq. (1.2), volume fractions of resin and glass fibers can be
found as Vr ≈ 0.55 and Vf ≈ 0.45, respectively. According to Eq. (1.1), the refractive index of
resulting GFRP composite can be estimated as nc ≈ 1.541. However, it has to be noted that the
refractive index of resulting composite depends on many factors, such as the inspection wavelength,
curing conditions, working environment, to name a few.

The linear attenuation of GFRP composite material was measured with 1.7 mW incident radi-
ation power for 4-, 8-, and 16-layer laminates with the average thickness of 2.6, 4.6, and 9.2 mm,
respectively. In general, for collimated monochromatic radiation in homogeneous media, the power
−(cid:80)M
of the transmitted radiation can be calculated using the Beer-Lambert law [32]:
i=1 µi·li,

(cid:17)·li = P0 · e

Pas = P0 · Tas = P0 · e

µi
a+µi
s

(cid:16)

−(cid:80)M

i=1

(1.4)

where Pas is the transmitted radiation power that is attenuated by the local material in its pristine
state; P0 is incident radiation power; Tas is the transmission coefficient, which accounts only for
absorption and scattering in the test specimen in the absence of reflections from its interlaminar
interfaces; M is the number of attenuating species of the material sample; µi
s, and µi are the
absorption coefficient, scattering coefficient, and attenuation coefficient, respectively; and li is the
thickness of ith specie.

a, µi

The transmitted radiation power for 4-, 8-, and 16-layer GFRP laminates corresponded to 8.99,
5.22, and 1.52 V output from the receiving photodetector. Thus, from the ratios of the photodetector
outputs corresponding to GFRP samples with different thickness, a linear attenuation coefficient
µ was found to be approximately 2.7 cm−1. Generally, at a given power and signal to noise ratio
(SNR), this value determines the maximum thickness of GFRP composite which can be evaluated
using the OTS system.

1.1.2.4 Drop-weight impact tests

The drop-weight tests were performed according to the ASTM D7136 standard using an Instron
9250 HV Dynatup machine that was equipped with an 88.96 kN load cell impactor, a velocity

7

detector, and a pneumatic brake to prevent multiple impacts (see Fig. 1.3). The edges of the GFRP
specimen were clamped by pneumatically assisted grips. The exposed diameter of the composite
plate for impact loading was 76.2 mm, as per ASTM D7136. A 12.7-mm diameter hemispherical
head impactor was used for the impact testing. Three GFRP specimens were impacted with 20 J
energy for subsequent NDE by the developed OTS system.

Figure 1.3: Experimental setup for drop-weight impact testing.

1.1.3 Theory of OTS

Since the operating principle of OTS is based upon measuring the optical transmittance of GFRP
samples, it is necessary to establish a relationship between the severity of damage and the level of
transmitted radiation power measured with the photodetector. When the radiation interacts with
the material, such effects as transmission, absorption, chromatic dispersion, diffraction, scattering,
reflection, refraction, and conversion can mainly take place [33]. Conversion of radiation occurs
when the dielectric polarization of the medium responds nonlinearly to the applied electric field,
and can be neglected if the medium is fairly linear. Refraction affects the direction of radiation

8

propagation, and can be neglected if the incident radiation is normal to the interface. Diffraction is
mostly prominent at the edges and is hardly manifested in the bulk of a material. Dispersion effects
will be insignificant if the radiation is quasi-monochromatic. Note that these latter three effects
influence the direction of radiation propagation rather than the energy or the power of radiation.
Power losses partially occur due to reflection, which happens whenever there is a mismatch between
the refractive indexes of two materials (e.g., an interface such as a delamination).
In order to
calculate the reflection coefficients for s-polarized (Rs) and p-polarized (Rp) light at the interface
between dielectric materials, the Fresnel equations are used [33]:

n1 · cos Θi + n2 ·

(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)n1 · cos Θi − n2 ·
(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)n1 ·
(cid:114)
1 −(cid:16) n1
(cid:114)
1 −(cid:16) n1

n1 ·

n2

n2

n2

· sin Θi
· sin Θi

(cid:114)
1 −(cid:16) n1
(cid:17)2
(cid:114)
1 −(cid:16) n1
(cid:17)2
(cid:17)2 − n2 · cos Θi
(cid:17)2

+ n2 · cos Θi

n2

· sin Θi
· sin Θi

2

2

(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)
(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)

Rs =

Rp =

,

,

(1.5)

(1.6)

(cid:12)(cid:12)(cid:12)(cid:12)n1 − n2

n1 + n2

(cid:12)(cid:12)(cid:12)(cid:12)2

where Θi is the angle of incidence, n1 is the refractive index of the material through which the light
is reflected; n2 is the refractive index of the material through which light is further transmitted.

Eq. (1.5) and Eq. (1.6) hold for specular reflection from ideal mirror-like surfaces, and in the

case of normal incidence (Θi = 0) they reduce to the following formula:

Rsp = Rs = Rp =

(1.7)

For instance, at normal incidence angle, the specular reflection coefficient Rsp for an air (n1 = 1)
/ glass (n2 ≈ 1.5 [30, 34]) interface is around 0.04, meaning that approximately 4% of incident
radiation is reflected. However, if the surface is optically rough, such as an interface of interlaminar
delamination, diffuse reflection can take place. For example, an analytical model for reflection by
roughened plastic surfaces has been proposed and experimentally validated by Torrance et al [35].
The model pictured a studied surface as consisting of small randomly disposed mirror-like facets.

9

The reflection coefficient Rd predicted by the model depended on specular reflection from these
facets plus a diffuse component caused by multiple reflections and internal scattering:

Rd (ψ; Θ, φ) =

δNr,s (ψ; Θ, φ) + δNr,d (ψ)

Ni · cos ψ · δω
b · f · Ni (ψ) · δω

4 · F (ψ(cid:48), ˆn) G(cid:0)ψp,Θp(cid:1)

=

cos Θ · e−c2α2 + a · Ni (ψ) · cos ψ

,

(1.8)

Ni (ψ) · cos ψ · δω

where ψ is the zenith angle of incident radiation; Θ and φ are the zenith and the azimuthal angles of
reflected flux, respectively; δNr,s is the specular component of reflected flux; δNr,d is the diffuse
component of reflected flux; Ni is the radiance of the small source; δω is the solid angle of the
source; F is the Fresnel reflectance; ψ(cid:48) is the angle of flux reflected from an elementary facet with a
surface normal n(cid:48); G is a masking and shadowing factor; ψp and Θp are the projections of ψ and Θ
onto the plane determined by the facet normal and the surface normal; α is the angle at which facet
normals are inclined with respect to the normal of the mean surface; f is the area of an elementary
facet; a, b and c are scalar constants that depend on surface preparation.

Eq. (1.8) shows that the interaction of the radiation with the material is complex; and the
reflection coefficient can change drastically depending on incident angle of radiation, observation
angle, surface roughness, and refractive index [35,36]. Since GFRP composite refractive index itself
depends on many factors, modeling of light propagation in composite material is quite challenging
and cumbersome task.

The analysis provided below offers guidance to the development of a simple and straightforward
way to quantify the interior impact damage in materials, particularly laminated composites that
have been subjected to impacts. If normally incident monochromatic and collimated laser radiation
is passed along a local transect of a fairly linear and homogeneous medium without considering
interfaces such as delaminations, it seems reasonable to use modified Eq. (1.4) and approximate
the radiation transmitted to a downstream detector as follows:

Pas = P0 · (1 − Rac) · Tas · (1 − Rca) ,

(1.9)

10

where Rac and Rca are the reflection coefficients of air-to-composite and composite-to-air inter-
faces, respectively.

Any possible changes in registered power Pas defined by Eq. (1.9) can be explained by local
variations of fiber/matrix content and thickness over the extent of a composite test specimen in its
pristine condition. This conclusion follows from Eq. (1.4), assuming that the reflection coefficients
at the top and bottom surfaces, Rac and Rca remain constant.

Logic suggests an extension of Eq. (1.9) to determine the power of the transmitted radiation Pt
in the presence of defects such as delaminations by including reflections at interlaminar interfaces:

(1.10)

Pt = Pas ·(cid:0)1 − R1

(cid:1) ·(cid:0)1 − R2

(cid:1) · . . . ·(cid:0)1 − RN

(cid:1) = Pas · T1 · T2 · . . . · TN,

where R1, R2,. . . ,RN and TR1, TR2,. . . ,TRN are the local reflection and transmission coefficients
for each of the N interfaces in the transect of the sample, respectively.

Actual calculation of Pt using Eq. (1.10) is problematical because a map of delaminations
with their respective transmission coefficients, TR1, TR2,. . . ,TRN, is not known a priori, and the
determining of it would be forbiddingly counterproductive. Offered here is a practical solution that
replaces the set of unknown transmission coefficients by a single “standard” value T:

Pt ≈ Pas · T N

(1.11)

The transmission coefficient T is determined by scanning a representative sample containing a single
interior delamination. Hence, if delamination is considered to be the main damage mechanism, then
Eq. (1.11) can be used to relate the registered transmitted power and the number of delaminations.

1.1.3.1 Determination of a “standard” transmission coefficient T

The value of T was obtained from the OT-scan of a double cantilever beam (DCB) sample after
the mode I interlaminar fracture toughness test (as per the ASTM D5528 standard) as shown in
Fig. 1.2b. The DCB sample was comprised of eight layers of plain-weave S2 glass with a single
fracture-induced delamination between the four upper and four lower laminates. The OT-scan was

11

acquired with a laser output power of 5.2 mW and a lateral resolution of 0.5 mm. The transmission
coefficient was calculated as the ratio of the transmitted radiation powers Pt and Pas averaged over
two separate 2 cm2 regions of the sample, one region containing the crack and the other without a
crack as shown in Fig. 1.6b. The sample was clamped with a few miniature C-clamps prior to OTS
to ensure that the crack was closed as tightly as possible. The value of T was found to be 0.61,
apparently owing to the diffuse surface of the crack interface.

1.1.3.2 Robustness of OTS

It should be noted that Eq. (1.4) and Eq. (1.10) strictly hold for only ballistic photons, which
travel from the point-like radiation source down to the photo-detector in a straight line. However,
if a collimated beam with a large diameter propagates through a scattering medium such as a
GFRP, the transmitted radiation can be scattered, taking on some sort of angular distribution. In
such a case, the size of the delamination/air gap inside the sample, variation of sample thickness,
and the distance between the detector and the output interface might affect the measurement of
the transmitted radiation.
In addition, propagation of a wide laser beam through the edges of
delaminations will introduce partial attenuation and, possibly, edge diffraction effects. These
issues can be addressed by using a laser with a small beam diameter, or by installing a diaphragm
with a pin hole in front of the detector. In the first version of OTS setup, the effect of a relatively
large beam footprint (d ≈ 1.5 mm) was compensated for in signal processing, which allowed for
more accurate detection of delamination boundaries. It was also noticed that the uncertainties in
the determinations of the delamination contours were mainly governed by the size of the footprint
of the laser beam and the associated transition region rather than by uncertainties in the estimation
of T, as will be seen in the next section. Another important consideration is that Eq. (1.11) provides
a self-referencing capability for the developed system. That is to say, the thickness of the composite
sample and the delamination depth do not affect the transmission coefficient for a single interface
(delamination) T, because it is defined as the ratio of the radiation Pt transmitted through the region
with the delamination to the radiation Pas transmitted through the healthy region of the sample.

12

1.1.4 Results and discussion

The previously described experimental setup for OTS was used for inspection of the GFRP
samples shown in Fig. 1.4. The first sample was healthy (no impact), and the second one was
subjected to low velocity impact of 20 J. OT-scans were acquired with a laser output power of
5.2 mW and a spatial resolution of 0.5 mm. The distance between the bottom side of the sample
and the receiver was 5 mm. The raw results before post-processing are demonstrated in Fig. 1.5.
As seen from Fig. 1.5a, some areas of the plain weave GFRP plate with no damage had higher
transmittance than other areas, which was apparently caused by thickness variations of the sample
and glass fiber irregularities as follows from Eq. (1.9). The transmitted power Pas was minimal
when radiation propagated via clusters of fibers.
In contrast, the highest Pas corresponded to
propagation of radiation via resin-rich areas. Hence, in the case of the pristine GFRP composite,

the amplitude values in the output of the photodetector fell in a region Γ0 =(cid:2)Amax, Amin

(cid:3) which

was directly proportional to the range of transmitted powers

Pmax
as

, Pmin
as

.

(cid:104)

(cid:105)

Figure 1.4: (a) Healthy GFRP sample (no impact); (b) GFRP sample after E = 20 J impact.

The incident power from the laser source, P0 was adjusted before each scan such that the
maximum amplitude registered by the photodetector Amax was as close as possible to its saturation
limit of 10 V in order to provide the widest measurement range and the highest SNR.

13

Figure 1.5: (a) OT-scan of healthy GFRP sample; (b) OT-scan of the GFRP sample after E = 20 J
impact.

1.1.4.1 Advanced signal processing for quantitative evaluation of impact damage

Owing to the mismatch of material properties at the interfaces within the GFRP composite
plate, the low velocity impact with E = 20 J resulted in multiple interlaminar delaminations whose
areas increased with depth. In order to quantify the extent and severity of impact damage from the
OT-scans, an advanced signal processing procedure was developed to determine the delamination
contours as a function of depth. The concept is illustrated in Fig. 1.6. Assuming that delamination
is the main damage mechanism, the registered power of radiation transmitted through the sample
Pt can be divided into discrete amplitude levels depending on the number of interfaces below the
scan point that affect the beam power. If the transmission coefficient T of a similar GFRP sample
with one delamination in its mid-plane is known and only diffuse reflection is assumed, meaning

no increase in scattering or absorption is taken into account, the range(cid:2)Amax, Amin

(cid:3) associated

with the pristine composite can be simply scaled down to plot damage contours representing N
delaminations. The scaling factor can be established through the use of Eq. (1.12) as [37]:

ΓN = Γ0 · T N =(cid:2)Amax, Amin

(cid:3) N

(1.12)

As suggested above, the governing assumption here is that each delamination encountered has a
transmission coefficient T that is reasonably near the value found for the single delamination in

14

the “standard” specimen. However, one might encounter intensity values that may not fall in any
of these discrete intervals. This happens because the incident laser beam is not focused and has
a footprint of d ≈ 1.5 mm.
It was observed that at the boundaries between each delamination
and the sample there were smooth transition regions that were caused by partial attenuation of the
incident beam. Fig. 1.6a through Fig. 1.6c illustrate this behavior conceptually for regions near the
delamination in the “standard” specimen (Fig. 1.6b) and near the specimen supporting structure
(Fig. 1.6c). The widths of the transition regions were estimated to be 2 · d ≈ 3 mm. So, the
intermediate values were arbitrarily split equally between the adjacent levels, and the new contour
margins were computed as illustrated in Fig. 1.6d to be [37]:

(cid:0)Amax · T + Amin
(cid:0)Amax · T + Amin

(cid:1) · T N−1
(cid:1) · T N

2

2

Cmax
N

=

Cmin
N =

,

(1.13)

(1.14)

,

N

N

and Cmin

are the upper and lower levels of contours corresponding to the Nth
where Cmax
delamination, Amax and Amin are the maximal and minimal amplitudes of registered radiation
transmitted through a healthy composite, taken as the amplitudes of the corresponding detector
output voltages, and T is the transmission coefficient of the “standard” sample with a single
delamination in its mid-plane.

The values of Amax and Amin were computed for healthy and impacted GFRP samples by
considering the histograms of their healthy regions only (see Fig. 1.6a). The voltage outputs of the
photodetector were split into 512 bins, whose mean values were sorted in ascending order. The
Amin was selected as the average of the first bin containing more than 25 elements. Similarly,
the Amax was assigned the average of the last bin, whose number of elements exceeded the same
threshold. This procedure was applied to remove measurement variations potentially caused by the
circuit noise, tilt of the sample, surface roughness or contamination, and vibration of the fixture
during the acquisition of the OT-scans.

15

Figure 1.6: (a) Gradual change of transmitted radiation power across delamination boundary due
to partial beam scattering through the transition regions; (b) OT-scan of the double cantilever beam
(DCB) sample with a crack that served as the “standard”; (c) OT-scan of the metal-to-composite
interface in the support region; (d) determination of contour levels corresponding to different
numbers of delaminations.

1.1.4.2 Post-processed OT-scans of GFRP samples

Post-processed OT-scans of healthy and impacted GFRP samples are shown in Fig. 1.7a and
Fig. 1.7b. The color bar of contour plots was partitioned as per Eq. (1.13) and Eq. (1.14) to highlight
the healthy regions of each composite plate and the regions with given numbers of delaminations.
As seen from Fig. 1.7b, the total delamination count was the largest in the middle region of the

16

impacted sample, and it decreased radially from the point of impact.
In addition, the extents
of delaminations were slightly larger along the principle directions of the glass fibers, [0/90]4.
The results demonstrated that it was difficult to determine the differences between contours for

Figure 1.7: (a) Post-processed OT-scan of the healthy sample; (b) post-processed OT-scan of the
sample after E = 20 J impact.

a large number of interlaminar defects, in particular, for N > 4, because the margins became
too closely spaced and the overall level of radiation intensity at the photodetector approached the
noise limit. Hence, whenever the voltage output of the photodetector fell below Cmin
= 1.58 V,
this indicated that N exceeded four, which is simply denoted as “4+” in the subsequent figures.
Fig. 1.8 provides comparisons of the damage extent as a function of the number of delaminations.
The results demonstrate that regions of the GFRP sample where the impact created only one or
two delaminations were significantly larger than the regions where three and more delaminations
appeared.

4

1.1.4.3 OTS validation

The impacted sample (E= 20 J) shown in Fig. 1.4b was cut with a diamond saw at location
x = 37.8 mm along its y-axis (see the corresponding OT-scan in Fig. 1.5b). The left half of the
sample was arbitrarily chosen for determining the delamination contours.
Its new face created

17

Figure 1.8: Estimated damage area corresponding to different numbers of delaminations N.

after cutting was saturated with a UV dye penetrant, and it was left to soak for 30 minutes. After
absorption of the UV dye by the interlaminar defects, the sample was illuminated with a UV
lamp in a dark ambience in order to enhance the contrast between the delaminations and the
pristine GFRP material in the transect. The image of the cross-section was taken with a digital
camera, and it was later converted into a gray-scale format for post-processing in MatLab with
the result shown in Fig. 1.9a. Delaminations were identified using the two-stage Canny edge
detection algorithm followed by Wiener filtering to smooth the image and remove the residual
artifacts [38]. Applying a hard threshold to the resulting image effectively converted it into a binary
representation, whose high-value pixels determined the delamination boundaries, and whose zero-
value pixels corresponded to the pristine GFRP material. Fig. 1.9b shows the obtained binary
image merged with the original digital picture of the cross-section area. The delaminations were
highlighted as red curves, and the total number of delaminations at a given scanning position was
easily determined by automatically counting the number of curves through the height of the image.
Fig. 1.9c illustrates the OT-linescan of the corresponding cross section of the GFRP sample. In
this figure, the curve is partitioned based on the voltage levels determined from Eq. (1.13) and
Eq. (1.14). Thereby, if the total number of delaminations N in the cross-section changes, this is
highlighted with a different color in accordance with the discrete color map on the right hand side.

18

Figure 1.9: (a) Cross-section of the GFRP sample (thickness H = 4.8 mm, impact energy E = 20 J);
(b) delaminations identified using edge detection and filtering of the image data; (c) corresponding
OT-linescan; (d) the number of delaminations, N registered by the OTS; (e) the number of delami-
nations, N along the cross-section length obtained from post-processed digital camera images; (f)
comparison of results obtained with OTS and digital camera imaging wherein the regions in which
the numbers of detected delaminations match are highlighted in purple. For interpretation of the
references to color in this figure legend, the reader is referred to the web version of this report.

19

The total number of delaminations along the cross-section of the GFRP sample, determined
from the OT-linescan and the post-processed digital image, are shown in Fig. 1.9d and Fig. 1.9e,
respectively. Both plots are well aligned along the x-axis, which indicates that the OTS technique
accurately determines the outer margins of the impact damage. In addition, one of the characteristic
features of the scanned sample is that only two delaminations appear in the middle of the cross-
section, as seen from the Fig. 1.9b. This trend is very well captured by the OTS system. In Fig. 1.9f
both results are plotted on top of each other, and the regions in which the numbers of delaminations
detected by the two methods match are highlighted in purple. As seen, the results obtained with
OTS and the digital camera match well, differing at most by one delamination. This difference can
be explained by the fairly large transition region of the laser beam (2· d ≈ 3 mm) and light scattering
previously discussed. At the same time, the digital image of the cross section shows the distribution
of the impact damage only in two dimensions. However, the damage is three-dimensional, and if the
number of delaminations in the plane parallel to the transect of the sample is not constant within the
footprint of the laser beam, the amount of the received radiation at the downstream photodetector
would be affected. A simple way to improve the agreement and to enhance the resolution would be
to reduce the beam diameter.

1.1.5 Conclusions

Section 1 presented optical transmission scanning (OTS) as a valuable technique for quantitative
NDE of GFRP composites. In OTS, structural damage is detected and evaluated by measuring
the amount of radiation transmitted through the test samples. OT-scans are rapidly acquired
without any couplants and do not require extensive processing. Moreover, OTS can be readily
applied for inspection of thick GFRP structures. A special post-processing technique for raw OT-
scans was developed for evaluation of the damage introduced in GFRP composite by low velocity
impacts. A basic prototype of the OTS system was able to accurately identify the total number
of delaminations, up to a maximum of four, in the cross-section of the GFRP sample at each scan
point. If more than four delaminations were encountered along a transect, the exact number could

20

not be ascertained with basic OTS system. Additional useful information about the severity of
impact damage was obtained by measuring the extent of each detected delamination. The OTS and
advanced image processing algorithm were experimentally validated by comparing OT-linescans
with the observed distribution of delaminations in the cross-section of GFRP samples after cutting
them with a diamond saw. The presented OTS setup is a promising tool, which lays groundwork
for cost-effective, non-contact, rapid, and quantitative NDE of GFRP composite structures.

1.2 Quantitative Comparison of OTS with Conventional NDE Techniques

In this Section, the extent of the damage obtained from OT-scans is compared with that identified
by other NDE techniques such as UV DPT and conventional water-immersion pulse-echo UT C-
scans. In addition, quantitative comparison of OT-scans with UT C-scans is provided by converting
the images to a normalized damage scale.

1.2.1

Impact Testing and Standard NDE Techniques used for Comparison with OTS

1.2.1.1 Drop-weight impact tests

Drop-weight impact tests were performed similar to approach described in Section 1.1, but with
addition of two extra impact energy levels: E = 40 J, and E = 80 J. After each impact the GFRP
samples were evaluated using visual inspection, pulse-echo UT, UV DPT, and OTS.

1.2.1.2 Pulse-echo UT Testing

Water-immersion UT in the pulse-echo mode was utilized for evaluating damage extent in the
impacted GFRP samples (see Fig. 1.10). An ULTRAPAC II system with a 1 MHz, 25.4 mm
transducer was used for data acquisition, and UTwin software was used for imaging and analysis.
ToF and amplitude of back-surface reflection was determined by setting the electronic gate on each
A-scan.

21

Figure 1.10: Pulse-echo UT inspection with ULTRAPAC II system.

1.2.1.3 Ultraviolet Dye Penetrant Testing

UV DPT was performed to evaluate the extent of surface and interlaminar damage in the GFRP
specimens after the low-velocity impacts at different energies. Fluorescent dye penetrant Zyglo
ZL-27A was sprayed onto the front and rear sides of each specimen. After 30 minutes of soaking,
excess penetrant was removed using acetone. Each side of the sample was illuminated with a UV
lamp, and the fluorescence was captured using a digital camera.

1.2.2 Experimental Results and Discussion

1.2.2.1 Mechanical response of the GFRP composite laminates to low velocity impacts

Impact energies of 20, 40, and 80 J were selected for the drop weight experiments, and a
minimum of three tests were performed for each material configuration and impact energy value.
The reaction force due to the interaction between the laminate and the impactor was measured
by a strain gauge transducer located on the shank of the impactor. Fig. 1.11a demonstrates the
representative force-time curves for each impact energy level. The first load drop observed at
t ≈ 1 ms primarily corresponds to the occurrence of initial damage in the form of localized matrix

22

Figure 1.11: (a) Force-time curves; (b) energy-time curves.

cracking and delamination at the contact point of the impactor, whereas the second load drop that
follows the peak of the curve is associated with extensive matrix cracking, fiber breakage and
delamination in the wider area surrounding the impactor [22, 39]. The point of the first damage
onset was nearly insensitive to strain rate, since the initial damage occurred around 3.75 kN in
all test configurations. On the other hand, the influence of strain rate on the peak reaction force
of GFRP was more evident as the energy level was increased from 20 to 80 J. In the absence of
penetration and perforation by the impactor, the damage extent can be estimated using the damage
degree parameter, µ, as introduced in Eq. (1.15):

(cid:0)tmp(cid:1) + Lwi

Lwi

µ =

(S)
e

E

(1.15)

is the elastic energy in the
where Lwi is the dissipated energy due to internal mechanisms, E
specimen, and tmp is the time of the maximal penetration at which the impactor reaches null
velocity.

(S)
e

Generally, the damage degree is defined as the ratio between the dissipated energy and the
impact energy. Because the impact energy applied on the laminate was not high enough to develop
either penetration or perforation, the difference between the impact, rebound (elastic), and absorbed
energies for each impact level could be easily observed, as illustrated in Fig. 1.11b. As shown in

23

Fig. 1.12, the damage degree demonstrated a monotonically growing trend as the impact energy
increased. These results imply that the internal dissipated energy (Lwi) due to delamination, matrix
cracking, and fiber breakage was more significant at the higher impact energy level of 80 J than at
20 J.

Figure 1.12: Damage degree corresponding to different impact energies.

1.2.2.2 OT-scans of impacted GFRP samples

Top surface images of four of the GFRP samples used in experimental studies are shown in
Figure Fig. 1.13. OT-scans were acquired using the previously described setup with a laser output
power of 5.2 mW. The results are demonstrated in Fig. 1.14.
Post-processed OT-scans of the
GFRP samples are shown in Fig. 1.15. The color bar of the image was partitioned using the
procedure described in Section 1. As seen from Fig. 1.15, the total number of delaminations was
the largest in the middle of the tested samples, and decreased radially from the point of impact. In
addition, the extent of the delaminations was slightly larger along the principle directions of the
glass fibers, [0/90]4. For the 80 J impact, the introduced damage reached the boundaries of the
clamping fixture. Fig. 1.16 provides comparisons of damage extents for different impact energies
and calculated numbers of delaminations. According to the results, the area covered by one and

24

Figure 1.13: Top surface images of tested GFRP samples: (a) healthy GFRP sample; (b) GFRP
sample subjected to 20 J impact; (c) GFRP sample subjected to 40 J impact; (d) GFRP sample
subjected to 80 J impact.

two delamination layers was significantly higher for the 80 J impact energy than that for the 40 J
impact, while the damage areas corresponding to three and four delaminated layers were relatively
similar. That is, the areal extent of damage reduced with increasing number of delaminations.

1.2.2.3 UT C-scans of GFRP samples

GFRP samples were placed in a water tank for the UT inspection. C-scans were obtained in
the pulse-echo mode using the ULTRAPAC II system. A piston source transducer was kept 15
cm above the surface of the test samples to produce a more uniform ultrasonic beam and avoid
operation in the near field. The transducer was driven at 900 V, which is the peak voltage of
the pulser-receiver module. The actuation frequency of 1 MHz provided an acceptable amplitude
of a back-wall reflection. Longitudinal waves excited at higher frequencies (e.g., up to 20 MHz)

25

Figure 1.14: OT-scans: (a) healthy GFRP sample; (b) GFRP sample subjected to 20 J impact; (c)
GFRP sample subjected to 40 J impact; (d) GFRP sample subjected to 80 J impact.

(cid:16)

(cid:17)

(cid:16)

(cid:17)

would have shorter wavelengths and better sensitivity to defects. However, the manufactured GFRP
samples had 5-6 volume fraction of air voids with average size of 0.3 mm, which increased wave
scattering dramatically above 1 MHz. Figure 7 shows typical A-scans acquired on the pristine and
damaged regions of the GFRP sample after the 20 J impact.

AUT
2

D

AUT
2

H

In Fig. 1.17, AUT
1

is the reflection from the top surface, and

is the reflection from
denotes the amplitude of the wave packet, which
the rear surface of the test sample.
is received when a delamination is present in the layer above the bottom side of the test sample.
As seen from the image, the interlaminar defect affects both amplitude and ToF of the second
wave packet, while the shape of the first wave packet remains nearly the same. The results of the
UT inspections also demonstrated that it was quite difficult to resolve reflections from multiple
interfaces in the A-scans. If two delaminations occur in subsequent layers, the UT system used
in the experiments cannot resolve them accurately, because the time support of the wave packets

26

Figure 1.15: Delamination profiles identified using enhanced signal processing of OT scans: (a)
healthy GFRP sample; (b) GFRP sample subjected to 20 J impact; (c) GFRP sample subjected to
40 J impact; (d) GFRP sample subjected to 80 J impact.

Figure 1.16: Estimated damage area corresponding to different numbers of delaminations as
obtained from OT scans.

27

Figure 1.17: UT A-scans of the GFRP sample subjected to E = 20 J impact ( f = 1 MHz).

would be comparable to the time delay between their arrivals. That is, the wave packets would
merge together. This issue could not be eliminated by reducing the count or the duration of the
excitation pulses owing to high scattering in the bulk GFRP material. The composite samples
soaked in the tank for some period of time, so the subsurface defects apparently became filled with
water.

1 /AUT
2

Fig. 1.18 demonstrates the amplitude ratio AUT

that approximately characterizes wave
scattering across the delaminations in the test specimen. As seen from the UT C-scans, the ratio
increases in the vicinity of the impact location, indicating more severe damage. The overall damage
extent is measured by setting a hard threshold on the obtained image data. The thresholding level
is determined for each sample individually by considering the maximal amplitude ratio outside the
damage area. The overall procedure is similar to post-processing of the OT-scans in Section 1. If
the amplitude ratio is lower than the smallest value in the healthy region after histogram filtering,
the pixel of the image is treated as a damage. Damage contours identified from the previously
described UT C-scans are shown in Fig. 1.19. The results demonstrated that the overall damage
extent grows with increasing impact energy. The ToFs of the reflections from the outer surfaces of
the GFRP samples and the delaminations were automatically extracted from the A-scans by setting
gates in the ULTRAPAC II software and detecting the positions of the peaks. The relative difference
between the respective times of arrival are plotted in the UT C-scans that are shown in Fig. 1.20.

28

Figure 1.18: UT C-scans of GFRP samples showing the AUT
(b) damage from 20 J impact; (c) damage from 40 J impact; (d) damage from 80 J impact.

ratio: (a) healthy GFRP sample;

1 /AUT
2

The best qualitative result was obtained for the GFRP sample with the largest damage introduced by
the 80 J impact. As seen from the Fig. 1.20d, the ToF difference lies in the range of 3.2-3.6 µs for
the pristine regions of the sample. The respective ToFs in the regions with delaminations reduced to
approximately 2.5 and 2.0 µs depending on the depth at which the interlaminar defects were located
in the cross-section. Clearly, the delaminations that occurred closer to the top surface resulted in
a smaller ToF difference. In the case of 20 or 40 J impacts the damage was more concentrated in
the center of the samples. In some of these regions, only the reflections from the top surface were
present in the A-scans, and the amplitude of reflections from defects diminished to the noise level.
As a result, the ToF difference could not be automatically identified, and the respective pixels of
the UT C-scans were highlighted with a white color (see Fig. 1.20b and Fig. 1.20c). Nevertheless,
these image segments were treated as structural damage in the contour plots after thresholding as
shown in Fig. 1.21.

29

Figure 1.19: Damage contours identified from UT scans using AUT
2 UT ratio: (a) healthy
GFRP sample; (b) damage from 20 J impact; (c) damage from 40 J impact; (d) damage from 80 J
impact.

1 /AUT

The amplitude and ToF measurements were combined together in order to provide the most
accurate estimation of the total extent of the impact damage. Since the UT C-scans in Fig. 1.18
and Fig. 1.20 shared the same coordinate grid, the binary union of damage contours could be
easily computed. The final results are demonstrated in Fig. 1.22, and were used as a reference for
comparison with other NDE techniques. As seen from the same figure, most of the information
about the damage was obtained from the amplitude data for E = 20 J and E = 40 J impacts, while
the ToF revealed a larger damage extent for E = 80 J impact.

1.2.3 Comparative analysis of pulse-echo UT and OTS measurements

Even though the natures of ultrasonic and optical NDE techniques seem quite different at the
first glance, they share many similarities, and it is of a great interest to compare the obtained

30

Figure 1.20: UT C-scans of GFRP samples showing the ToF difference between AUT
and AUT
2 :
1
(a) healthy GFRP sample; (b) damage from 20 J impact; (c) damage from 40 J impact; (d) damage
from 80 J impact.

results qualitatively for further experimental validation of the OTS system. The self-referencing
capabilities of pulse-echo UT and OTS can be exploited to normalize the scans of impact damage and
compare the results using a common metric. The process of acquiring UT and OT measurements
is schematically shown in Fig. 1.23. The amplitude of a plane longitudinal UT wave reflected from
the top surface of the GFRP specimen can be expressed using Beer-Lambert law [40]:

AUT
1 = AUT
0

· RWC · e−2·κw·2· χw,

(1.16)

where AUT
is the acoustic wave intensity generated by the piezoelectric transducer; RWC is the
0
reflection coefficient of water-composite interface; κw is the attenuation constant for ultrasound
in water; and 2 · χw is the total wave path in the water that includes forward and backward wave
propagation equaling double the distance from the transducer to the sample. Note that Eq. (1.16)
does not account for losses associated with the spread of the ultrasonic beam.

31

Figure 1.21: Damage contours identified using the UT ToF difference: (a) healthy GFRP sample;
(b) damage from 20 J impact; (c) damage from 40 J impact; (d) damage from 80 J impact.

A portion of the ultrasonic wave energy propagates through the GFRP specimen, reflects from
its bottom surface and leaks back into water. Assuming some energy losses occur in the bulk GFRP
material, the amplitude of back wall reflection from a healthy sample sensed by the piezoelectric
transducer is defined as:

(cid:16)

(cid:17)

AUT
2

= AUT
0

H

· TWC · RWC · TCW · e−2·κw·2· χw · e−2·κc·2· χc,

(1.17)

where TWC is the transmission coefficient of the water-composite interface; RCW = 1 − TCW and
TCW = 1 − RCW are the reflection and transmission coefficients of the composite-water interface,
respectively; κc is the attenuation constant for ultrasound in the GFRP material; and 2 · χc is the
total path travelled by the UT wave in the GFRP specimen that equals the doubled thickness of the
specimen.

32

Figure 1.22: Binary union of damage contours estimated from the amplitude and ToF UT measure-
ments: (a) healthy GFRP sample; (b) damage from 20 J impact; (c) damage from 40 J impact; (d)
damage from 80 J impact.

Figure 1.23: (a) Ultrasonic reflections from the top surface of the sample and from interlaminar
delaminations in case of immersion UT inspection in pulse-echo mode; (b) transmission of elec-
tromagnetic radiation through healthy and delaminated regions of the test sample in case of OTS
inspection.

33

Similarly, whenever the UT wave is incident onto a region of the sample with delaminations,

the amplitude of the received back wall reflection can be expressed as:

(cid:16)

(cid:17)

AUT
2

= AUT
0

D

· TWC · RWC · TCW ·(cid:16)

1 − RUT
D

(cid:17)2N · e−2·κw·2· χw · e−2·κc·2· χc,

(1.18)

where RUT
D is the reflection coefficient of a single delamination that accounts for both its top and
bottom interfaces, and N is the number of delaminations at a scanning point. It is worth mentioning
that it can be sometimes difficult to extract the amplitude of the back wall reflection by the time
gating, since the observed wave packet has small amplitude and also contains contributions from
reflections at the upper delaminations. The reflection coefficient of each delamination also depends
on whether the interlaminar interface is filled with water or air. For instance, for a composite-water
interface, the ratio between the incident and reflected UT intensities is defined by the Fresnel
law [40]:

(cid:18) ZW − ZC

ZW + ZC

(cid:19)2 ≈ 0.36,

RCW = IREF
IINC

=

(1.19)

where IINC and IREF are the intensities of incident and reflected UT waves; ZW and ZC are the
acoustic impedances of air and GFRP composite. The acoustic impedance of the GFRP material
used in the impact tests was estimated experimentally by measuring its density ρC and velocity of
longitudinal wave propagation ϑC and using the well-known approximation:

Similarly, for water and air we have:

kg/

.

(cid:16)
m · s2(cid:17)(cid:105)
m · s2(cid:17)(cid:105)
(cid:16)
m · s2(cid:17)(cid:105)

.

kg/

(cid:16)

ZC = ρC · ϑC = 1900 · 3100 = 5.89 × 106(cid:104)
ZW = ρW · ϑW = 1000 · 1480 = 1.49 × 106(cid:104)
(cid:104)
(cid:19)2 ≈ 1.

ZA = ρA · ϑA = 1.225 · 343 = 420.18

(cid:18) ZA − ZC

RC A =

kg/

ZA + ZC

,

(1.20)

(1.21)

(1.22)

(1.23)

34

Consequently, the reflection coefficient of a composite-air interface is:

Hence, if a delamination is filled with air, very little UT wave intensity propagates through the
interface owing to the large acoustic impedance mismatch, and the bottom layer delaminations or
back wall reflection may not be detected. However, this is not the case with optical transmission
scanning, as the experimental results demonstrate. Considering the top and back wall UT reflections,
the optical amplitude attenuation coefficient for a healthy composite sample can be defined as:

(cid:33)

(cid:32) AUT

2
AUT
1

AUT
0

=

H

αUT
H =

· TWC · RCW · TCW · e−2·κw·2· χw · e−2·κc·2· χc

AUT
0

· RWC · e−2·κw·2· χw

TWC ·(cid:0)1 − TCW

=

(cid:1) · TCW · e−2·κc·2· χc
(cid:17)2N · e−2·κc·2· χc

1 − TWC

,

(1.24)

(1.25)

Similarly, for the case with delaminations, we have:

(cid:33)

(cid:32) AUT

2
AUT
1

=

D

αUT
D =

TWC ·(cid:0)1 − TCW

(cid:1) · TCW ·(cid:16)

1 − RUT
D

1 − TWC

where RUT
D is the reflection coefficient for a single delamination taking into account losses at both
interfaces. The procedure for comparing the UT and OTS measurements adopted in this paper
included normalization of all UT amplitude ratios with respect to those obtained on the healthy
region of the test sample, such that the attenuation inside the healthy composite is compensated
and only the attenuation introduced by the impact damage is obtained:

(cid:16)

(cid:17)2N

˜αUT =

αUT
D
αUT
H

=

1 − RUT
D

In the case of OTS, the amplitude of radiation power transmitted through a healthy GFRP can be
calculated as:

(cid:16)

(cid:17)

AOTS
2

= AOTS

0

H

· TAC · TC A · e−ηc· χc,

0

where AOTS
is the output power of the radiation source, TAC is the transmission coefficient of an
air-composite interface, TC A is the transmission coefficient of a composite-air interface, ηc is the
attenuation constant for electromagnetic radiation in the GFRP material, and χc is the thickness of
the GFRP specimen.

35

(1.26)

(1.27)

(cid:16)

(cid:17)

· TAC · TC A ·(cid:16)

The corresponding expression for the case of the GFRP with delaminations takes the following
form:

0

D

AOTS
2

= AOTS

(1.28)
= R1 = R2 = · · · = RN is the reflection coefficient of a single delamination taking
where ROTS
into account losses at both interfaces, and N is the total number of delaminations. Hence, the OTS
attenuation constants of healthy GFRP and GFRP with delaminations are defined as:

D

D

1 − ROTS

(cid:17) N · e−ηc· χc,

αOTS
H

=

(cid:33)

(cid:32) AOTS

2
AOTS
0

=

D

AOTS
0

αOTS
D

=

(cid:33)
(cid:32) AOTS
· TAC · TC A ·(cid:16)

2
AOTS
0

=

H

AOTS
0

· TAC · TC A · e−ηc· χc

AOTS
0

(cid:17) N · e−ηc· χc
= TAC · TC A ·(cid:16)

1 − ROTS
AOTS
0

D

,

(1.29)

(cid:17) N · e−ηc· χc

(1.30)

1 − ROTS

D

If the OTS self-referencing capability is used, all power measurements at the photodetector should
be normalized by the corresponding values obtained on the healthy regions of the composite sample,
as follows:

(cid:16)
(cid:16)

(cid:17)
(cid:17)

(cid:16)

˜αOTS =

αOTS
D
αOTS
H

=

AOTS
2
AOTS
2

=

D

H

1 − ROTS

D

(cid:17) N

(1.31)

As mentioned above, post-processing of OT-scans relies on the key assumption that the reflection
coefficients of all delaminations are reasonably close to identical. The transmission coefficient of
a single delamination, was obtained experimentally from OT-scans of a mode I sample:

TOTS
D

= 1 − ROTS

D

≈ 0.61

(1.32)

In the case of UT, on the other hand, the transmission coefficient of a single delamination filled
with water can be estimated as

D =(cid:0)1 − RCW

(cid:1) ·(cid:0)1 − RWC

(cid:1) ≈(cid:0)1 − RCW

(cid:1)2 ≈ 0.41

D = 1 − RUT
TUT

(1.33)

36

Consideration of the amplitude attenuations defined by Eq. (1.26) and Eq. (1.31) suggests that the
UT and OT scans can be compared qualitatively through the following relationship:

(cid:16)
˜αUT(cid:17)
˜αOTS(cid:17) =
(cid:16)

ln

ln

(cid:20)(cid:16)
(cid:20)(cid:16)

ln

ln

(cid:17)
(cid:17)

1 − RUT
D
1 − ROTS

D

(cid:16)
(cid:16)

1 − RUT
D

(cid:17)2N(cid:21)
(cid:17) N(cid:21) = 2 ·
(cid:16)
(cid:16)
˜αOTS(cid:17)2· ln

ln

D

1−RUT
D
1−ROTS

D

1 − ROTS

ln

ln

(cid:17)
(cid:17)

(cid:16)

˜αUT =

(1.34)

(1.35)

However, it should be noted that Eq. (1.35) is only an approximation. It does not account for such
factors as different footprints and divergences of the ultrasonic and laser beams as well as some
challenges in extracting correct amplitudes from the ultrasonic A scans. Fig. 1.24 and Fig. 1.25
show the post-processed images of structural damage obtained with the UT and OTS techniques.
These normalized versions of the scans demonstrate good agreement for all impact energies. In
particular, the outer damage contours are quite similar; and the slight variations of damage severity
can be attributed to the challenges in UT data processing described earlier. The obtained results
additionally validate the OTS technique and prove its worthiness for NDE of GFRP composites.
Compared to water immersion pulse-echo UT, the OTS is fully non-contact, and it offers rapid
scanning capabilities, because the photodetector generates a DC voltage output that is directly
proportional to transmitted radiation. UT, on the other hand, requires sampling and post-processing
of the entire ultrasonic waveform (A-scan) record.

1.2.3.1 UV DPT of impacted GFRP samples

The results of the UV DPT are shown in Fig. 1.26. As seen from the images, the damage
patterns on the top surface exhibited a cruciate form, which followed the directions of the glass
fibers in the samples, [0/90]4. On the other hand, damage on the bottom side of the samples
was distributed quasi-uniformly in the circumferential direction. Because the position of the UV

37

Figure 1.24: Normalized UT C-scans showing ˜αUT for: (a) healthy GFRP sample; (b) GFRP
sample subjected to 20 J impact; (c) GFRP sample subjected to 40 J impact; (d) GFRP sample
subjected to 80 J impact.

lamp varied during the tests, the digital images had slightly different brightness levels. Therefore,
the post-processing of the results included their normalization by the maximal image intensity, as
shown in Fig. 1.27. Damage contours were then obtained by image thresholding. The threshold
level was estimated from the averaged intensity measured in the healthy regions of all samples, and
was applied to all images. The damage distributions determined from the top and bottom surfaces
of the test specimens are shown in Fig. 1.28.

The total damage extent was identified in each case by combining the damage contours for both
the top and bottom surfaces for each sample. Note that in all the figures showing the UV DPT
results, all bottom side images were mirrored along the vertical axis. Fig. 1.29 demonstrates that
adding the rear side images mostly increased the damage area between the principle fiber directions.
The total damage extent can be estimated from each combined figure by considering the union of
yellow and dark brown contours.

38

Figure 1.25:

(cid:16)
(cid:16)
˜αOTS(cid:17)2· ln

(cid:16)

ln

(cid:17)
(cid:17)

1−RUT
D
1−ROTS

D

Normalized OT-scans

adjusted according to Eq.

(1.35)

that

show

for: (a) healthy GFRP sample; (b) GFRP sample subjected to 20 J im-

pact; (c) GFRP sample subjected to 40 J impact; (d) GFRP sample subjected to 80 J impact.

1.2.3.2 Quantitative comparison of OTS and other NDE methods in estimation of the total

damage area

The extent of the impact damage was independently estimated for all GFRP specimens by the
OTS, UT and UV DPT, as described in the previous sections. The summary of results shown in
Fig. 1.30 demonstrates good overall agreement for all three of these NDE techniques. In particular,
the percent difference in estimation of the total damage area between the OTS and other techniques
was generally small, as shown in Table 1.2. The largest relative difference was observed for all
techniques in the case of the impact with the smallest energy of 20 J. In the case of OTS and UT,

39

Figure 1.26: Images of damaged GFRP samples soaked in UV dye and illuminated with UV light:
(a) top surface, E = 20 J; (b) top surface, E = 40 J; (c) top surface, E = 80 J; (d) bottom surface,
E = 20 J; (e) bottom surface, E = 40 J; (f) bottom surface, E = 80 J.

Technique E = 20 J E = 40 J E = 80 J
UT
UV DPT

14.89% 1.51%
19.70% 2.43%

8.76%
2.13%

Table 1.2: Absolute percent difference in estimation of the total damage area between the OTS and
other NDE techniques.

this can be attributed to the differing footprints of the ultrasonic and laser beams, which resulted in
different averaging areas and transition regions. Hence, the edge smoothing introduced by the finite
beam width had more effect on the smallest damage and was less pronounced for bigger damage,
as expected. Some discrepancies in estimation of the overall damage extent between the OTS and
UV DPT were apparently caused by excessive dye penetrant, which was not completely removed
by surface cleaning. At the same time, there is also a possibility that the UV dye did not penetrate
into all internal defects.

40

Figure 1.27: UV DPT images of damaged GFRP samples after normalization of image intensity:
(a) top surface, E = 20 J; (b) top surface, E = 40 J; (c) top surface, E = 80 J; (d) bottom surface,
E = 20 J; (e) bottom surface, E = 40 J; (f) bottom surface, E = 80 J.

1.2.4 Conclusions

In this Section, OTS was successfully validated by comparing inspection results with two
conventional NDE techniques, including pulse-echo UT and UV DPT. The damage extent was
determined for GFRP samples after low velocity impacts at three different energies of 20, 40 and
80 J. The experimental results demonstrated good agreement for OTS, UT, and UV DPT. OTS and
conventional water immersion pulse-echo UT provided similar evaluations of the severity of dam-
age inside the GFRP samples. In addition, post-processing of OT-scans helped to better quantify
impact damage by determining the total number of delaminations at each scan position. The dam-
age areas corresponding to either one or two delaminations were found to increase dramatically for
higher impact energy, but there was no significant difference in damage areas when delaminations
were more numerous.

41

Figure 1.28: Damage contours identified from normalized UV DPT images of GFRP samples: (a)
top surface, E = 20 J; (b) top surface, E = 40 J; (c) top surface, E = 80 J; (d) bottom surface,
E = 20 J; (e) bottom surface, E = 40 J; (f) bottom surface, E = 80 J.

Figure 1.29: Total damage area evaluated as a union of UV DPT images taken from top and bottom
sides of GFRP samples: (a) E = 20 J; (b) E = 40 J; (c) E = 80 J.

It was demonstrated that OTS combines cost-effectiveness and the fast NDE capabilities of quali-
tative techniques (e.g., UV DPT) with the more robust and comprehensive data analysis provided
by quantitative methods (e.g., UT). Overall, the results obtained with the developed OTS system
are promising and encouraging.

42

Figure 1.30: Comparison of damage areas obtained by the OTS, UT, and UV DPT for different
impact energy levels.

1.3 Feasibility of OTS for Quality Control and NDE of GFRP Composite

Structures

Results presented in this Section demonstrate that defects and certain microstructural variations
in GFRP composites can be easily identified by OTS, because the technique is sensitive to localized
changes of optical properties such as radiation absorption and scattering. The applications of OTS
are extended to GFRP plates with improperly mixed resin, inclusions, and delaminations. We
also demonstrate the capability of the technique to evaluate the distribution of adhesive and detect
fatigue damage in adhesively bonded GFRP joints.

1.3.1 Materials and methods

1.3.1.1 Manufacturing of GFRP samples with improper cured resin component proportions

An eight layer GFRP plate was manufactured using the previously described resin transfer
molding (RTM) process. However, in this case some regions of the plate had improper ratios of
part A and part B of the epoxy, which resulted in non-uniform matrix properties. On one edge of
the specimen, the component ratio was nearly optimal, and on the opposite edge the epoxy lacked

43

the hardener. Hence, the epoxy component proportions in the middle of the plate fell somewhere
between the values at the opposite edges, with an unknown gradiation over the extent of the plate
that depended on the local degree of mixing. The standard cure cycle was implemented, which
likely left only partially cured those areas where the hardener proportion was below optimal. Three
rectangular samples (100×50×4.7 mm) were cut from the left, middle and the right areas of the plate,
and then were labeled as “properly mixed”, “semi-mixed” and “badly mixed”, correspondingly (see
Fig. 1.34).

1.3.1.2 Manufacturing of GFRP samples with inclusions

The plate manufacturing process was implemented twice to allow two different types of inclu-
sions in the composite specimens. In the first sample (100×100×4.7 mm), small pieces of resin
transfer medium were intentionally left between plies during the manufacturing. The average size
of such objects was about a few millimeters. The inclusions were of a red color as shown in
Fig. 1.32a. In the second GFRP plate (360×85×4.7 mm) foreign objects were simulated as glass
fibers dyed black (Fig. 1.33a). The sample also had piezoelectric wafer elements bonded to its top
surface for exciting ultrasonic guided waves, which was a part of another study for defect detection
using guided waves [41,42].

1.3.1.3 Manufacturing of double cantilever beam samples and mode I fracture tests

Mode I fracture tests were performed using double cantilever beam (DCB) samples in accor-
dance with ASTM standard D5528. The samples were fabricated using the materials and procedures
described in Section 1. A Teflon sheet was placed in the middle of the sample during layup to
introduce the initial crack. The cured plates were cut to required dimensions and the piano hinges
were attached using high-strength cyanoacrylate glue (see Fig. 1.35a).

44

1.3.1.4 Manufacturing of adhesively bonded GFRP joints and fatigue tests

Two 430×45 mm lap-joints with bond area lengths of 50 mm were manufactured from 4.7
mm thick quasi-isotropic GFRP composite plates bonded with FM-94K adhesive film as shown
in Fig. 1.31. The thickness of the adhesive layer was intended to be 0.4 mm for both specimens.
Prior to placing the lap-joints into the oven, the adherends of the first lap-joint were clamped
together using stiff backing plates so as to establish quasi-uniform distribution of the adhesive. The
adherends of the second lap-joint were clamped by a C-clamp in the center of the bond area, which
allowed the plates to flex slightly so as to create a nonuniform adhesive thickness.

Figure 1.31: Side view of the manufactured GFRP lap-joint.

The sizes of the lap-joints did not meet the relevant ASTM standards, because the same lap-
joints were used as waveguides for ultrasonic wave propagation in another study [26]. The second
lap-joint was subjected to fatigue testing to introduce gradual failure of the adhesive at the edges
of the bond area. Fatigue testing was performed at 30% of the ultimate tensile strength (UTS), and
the rate of cyclic loading was set to 2 Hz. The UTS of the lap-joint was approximately 70 kN,
this value being determined from prior tensile tests of similar specimens. The sinusoidal load was
applied in tension to avoid buckling effects. The relative displacement between the two adherends
was measured using appropriately placed laser reflectors and a laser extensometer. Fatigue testing
was stopped at approximately 20000 cycles due to time considerations.

45

1.3.2 Experimental Results and Discussion

1.3.2.1 Detection of foreign object inclusions in GFRP plates

The GFRP plate with foreign object debris simulated as pieces of resin transfer media is shown
in Fig. 1.32a, where the circles show the locations of the debris. The corresponding OT-scan
demonstrated in Fig. 1.32b revealed that some areas of the plain weave GFRP plate with no
inclusions had higher transmittance than other areas, which was caused by thickness variations
of the sample and glass fiber irregularities. The transmitted power was minimal when radiation
propagated via clusters of fibers.
In contrast, the highest transmitted power corresponded to
propagation of radiation via resin-rich areas.

Figure 1.32: (a) GFRP sample with red inclusions (small pieces of resin transfer medium); (b)
OT-scan of the same sample. Inclusions are highlighted by circles in both images.

The inclusions of resin transfer medium reduced the averaged transmitted power by 33%, which
in some cases was comparable with the transmitted power reduction due to variations of the GFRP
structure. As seen in Fig. 1.32a, the inclusions were of red color, which matched the wavelength
of laser radiation. Hence, the sensitivity of OTS to red foreign objects was mainly determined by
scattering at their interfaces rather than by radiation absorption of the material.

46

Figure 1.33: (a) 8-layer GFRP sample with black fiber inclusions and impact damage; (b) OT-scan
of the same sample.

In contrast, OT-scans of the GFRP sample with black-dyed fibers showed that the transmitted
radiation power at the receiver was reduced up to 80% compared to healthy GFRP structure
(Fig. 1.33).
In this case, inclusions of black fibers caused not only scattering, but significant
absorption of laser radiation at 640 nm wavelength. These results demonstrate that an OTS system
can be designed to characterize both the shapes and the materials of foreign objects if several
scanning wavelengths are employed.

47

1.3.2.2 Evaluation of GFRP plates having improper proportions of matrix components

OTS was used to evaluate three GFRP specimens cut from a plate with local variations of part A
to part B epoxy ratios, as explained in Section 1. Digital images of the top surfaces of the samples are
presented in Fig. 1.34. The first sample, shown in Fig. 1.34a, was manufactured with a proper epoxy
mixture, while the second and third samples lacked the hardener in smaller and larger amounts. To
the eye, all three samples appear to be fabricated with the proper resin proportions. OT-scans of all

Figure 1.34: Evaluation of 8-layer GFRP samples and QC detection of faulty resin component
ratios using OTS: (a) Photo of GFRP sample having proper resin proportions; (b) Photo of GFRP
sample having moderate error in resin proportions; (c) Photo of GFRP sample having extreme
error in resin proportions; (d) OT-scan GFRP sample having proper resin proportions; (e) OT-scan
of GFRP sample having moderate error in resin proportion; (f) OT-scan of GFRP sample having
extreme error in resin proportions.

48

three samples were acquired at the same laser power of 8 mW. The results obtained demonstrated
that afaulty resin proportions affects the optical transmittance, although all three specimens looked
quite similar visually. The voltage outputs from the photodetector averaged over sample areas with
no supports were 5.02 V, 5.83 V and 8.13 V, respectively. Hence, the transmitted power increased
by 16% for “semi-mixed” composite and by 62% for “improperly mixed” composite. In addition,
the “semi-mixed” sample had non-uniform optical transmittance over the scan area (see Fig. 1.34e),
apparently owing to the local variations of part A to part B component ratio. These results, while
largely qualitative in nature, demonstrate that the OTS technique is promising for detection of
improper proportioning or mixing of the matrix components in GFRP composites.

1.3.2.3 Monitoring of crack propagation in DCB samples

Accurate determination of crack length in DCB samples is critical for reliable estimation of
fracture toughness of GFRP material. In this section, we demonstrate the suitability of OTS for
crack imaging and characterization of interior interfaces in GFRP DCB samples. Typical OT-scans
of DCB samples are presented in Fig. 1.35b and Fig. 1.35c.

Experimental results demonstrated that 15.4% of the radiation propagated through the Teflon
insert embedded between the GFRP adherends. Subsequent to cyclic loading causing crack growth,
the detailed crack profile was visible. The transmission coefficient of a tight crack,T, is around
0.6, apparently owing to the diffuse surface of the crack interface. The transmission coefficient is
calculated as the ratio of the radiation intensities averaged over the healthy region of the sample to
the intensities measured in the area of a crack (blue and orange regions in Fig. 1.35c, respectively).
As demonstrated in Section 1, knowledge of T allows for successful characterization of impact
damage and determination of the total number of delaminations in GFRP plates after low velocity
impacts.

49

Figure 1.35: (a) GFRP DCB mode I test sample); (b) OT-scan of the DCB sample before cyclic
load test; (c) OT-scan of the DCB sample after crack growth caused by cyclic load.

1.3.2.4 Detection of non-uniform adhesive distribution and fatigue damage in adhesively

bonded lap-shear joints

Fig. 1.36 demonstrates OT-scans of composite lap-joints and adhesive bonds obtained at dif-
ferent laser radiation powers. As seen from Fig. 1.36a, the properly proportioned, cured, and
distributed adhesive transmits incident radiation quite uniformly across most of the bond area.
In this case, the lap-joint was cured using measures to assure consistent adhesive thickness, as
mentioned above. Poor bonding is evident close the edges. In contrast, Fig. 1.36b presents the
OT-scan of a similar lap-joint, where the adherends were fixed using a single C-clamp in the center
of the bond area. The non-uniform pressure resulted in a apparent low-quality bonding everywhere

50

Figure 1.36: OT-scans of composite lap-joints: (a) properly cured adhesive bond, quasi-uniform
pressure applied to adherends, P = 150 mW; (b) lap-joint before fatigue tests, manufactured using
a single C-clamp, non-uniform pressure applied to the adherends when curing, P = 150 mW; (c)
adherends of a lap-joint (output radiation power, P = 3 mW); (d) lap-joint pictured in (b) after
20000 fatigue cycles, manufactured using a single C-clamp, non-uniform pressure applied to the
adherends during curing, P = 150 mW.

51

but directly under the clamp. The effect of fatigue degradation is illustrated in Fig. 1.36d. The
adhesive started to fail at the edges and damage progressed towards the center of the bond area. This
created microcracks that increased optical scattering and reduced the radiation power registered at
the downstream photodetector.

1.3.3 Conclusions

These experiments highlighted the broad capabilities of the OTS system for QC and NDE
of GFRP composite structures. OTS successfully detected foreign object inclusions between
the plies. As expected, the technique was more sensitive to black inclusions rather than to red
inclusions because the red ones have a lower transmission coefficient at the inspection wavelength
of 640 nm. The results have also demonstrated that the OTS could easily identify GFRP samples
with improperly proportioned epoxy resin, because mixing the epoxy with different ratios of part A
and part B components affected the optical transmittance of the manufactured composite material
as well as leading to incomplete curing. OT-scans of DCB GFRP samples revealed the true profiles
of cracks introduced after mode I fracture toughness tests. Finally, the OTS showed excellent
results in determining the uniformity of adhesive distribution in adhesively bonded GFRP lap-
joints. Variation of the optical transmittance in the bonded area of a lap-joint was minimal when
quasi-uniform pressure was applied to GFRP adherends in the bonding process. Conversely, a
wide variation of clamping pressure was created when the GFRP adherends were tightened with
a single C-clamp in the center of the bond area likely causing the adhesion to be weak near the
edges. This uneven distribution of adhesive was clearly reflected in the OT-scans. Applying cyclic
loading to the same lap-joint introduced gradual failure of the adhesive bond, which progressed
from the edges towards the center. This fatigue damage was successfully captured by the OTS as
optical transmittance was reduced in the damaged regions. Overall, the results obtained in Section
3, while largely qualitative in nature, demonstrated the considerable potential of the OTS technique
to reliable QC and NDE problems.

52

1.4 Robust Implementation of OTS and Advanced NDE Features

1.4.1 OTS system with advanced scanning capabilities

A new version of a system for OTS was assembled at General Photonics Corporation (Chino,
CA) for developing advanced scanning features. Functional block diagram of a new system OTS-
1000 is shown in Fig. 1.37. OTS-1000 uses collimated or focused radiation from an optical source
for NDE of composite samples. In terms of optical bandwidth, the source can operate at a fixed
wavelength, or can be tunable. For inspection of different materials and localization of various
defects, optical source can also operate in UV, visible, near-IR, and/or IR ranges.
In terms of
geometry of generated beam, a radiation source in the system can be point-like, line, or a plane
source. Hence, the list of compatible light sources includes, but is not limited to lamps (UV,
visible, and IR); broad spectrum sources such as superluminescent diodes, or ultrafast lasers (fiber,
solid state, or gas lasers); diode lasers, IR emitters and many more. The attenuator in Fig. 1.37

Figure 1.37: Block-diagram of OTS-1000 system for NDE of GFRP composites.

provides necessary reduction of radiation power in case the system is equipped with a high-power
source, but the inspected samples are thin or highly transmissive. In general, an attenuator can
be assembled based on a manually tuned, motorized, step-wise variable, or continuously variable
optical element that uses absorption, reflection, diffusion, scattering, deflection, diffraction, or

53

Figure 1.38: OTS-1000 system for NDE of GFRP composites.

dispersion mechanisms to adjust the level of output power. Optical filter 1 controls the bandwidth
of radiation incident onto the test sample. Similarly, filter 2 is used to control the bandwidth of
radiation registered on the opposite side of the sample by the photodetector. Both filters can be
absorptive, interference or dichroic. In Fig. 1.37 polarization state generator (PSG) controls the
state of polarization (SOP) of radiation emitted by source, and polarization state analyzer (PSA)
determines the SOP of radiation tramsnitted through the sample to identify possible defects. Both
PSG and PSA can be implemented as a rotating wave plate and polarizer, or can be made with
binary magneto-optic (MO) polarization rotators, as described in [43–45]. The diaphragms 1 and
2 adjust the sizes of optical beams on both sides of the test sample. These can be pinholes, or iris
diaphragms controlled mechanically or electrically. Variable focus lens/telescopes 1 and 2 control
the focal spot and beam divergence. Lenses can be made of glass, crystals or liquid polymers, and
may have fixed or variable focal lengths. Transmitted radiation is registered with suitable single
point, 1D, or 2D detector, which can be optical, light, imaging, or photon sensor. Two detectors,
P-detector and S-detector are used to register ˆp and ˆs polarizations, respectively. In OTS-1000, the

54

sample is moved in plane perpendicular to the direction of incident radiation using motorized 2D
stage. The photo of the new OTS system is shown in Fig. 1.38. The updated experimental setup
has the following features:

• Rugged hardware and stable software for rapid scanning of relatively large samples.

• Optical resolution of 100 µm.

• Positioning accuracy up to 50 µm.

• Scan speed up to 285 mm/s.

• Variable laser beam focusing.

• Ability to acquire OT-scans in regular lab environment outside of a dark room.

• Modular structure for easy switching between different light sources and photodetectors.

1.4.2 Multi-wavelength evaluation of GFRP structures

OTS setup can be operated at different inspection wavelengths providing complete character-
ization of complex structures with two or more components. Since optical attenuation depends
on the inspection wavelength, the use of multiple wavelengths (e.g. light source array or tunable
light source), allows for more detailed evaluation of materials under test. For instance, different
types of defects may have different optical transmittances at a particular wavelength. Moreover,
multi-wavelength approach allows for NDE of complex structures with two or more materials, such
as adhesively bonded joints.

A technique for evaluation of bond-line thickness in lap-shear joints is provided here as an
example. The adherends and the adhesive are considered homogeneous, hence Eq. (1.9) can be
used to evaluate the optical transmittance of the bond-line section. Fig. 1.39 illustrates the geometry
of a lap-joint. The thickness of adhesive layer is ha, and combined thickness of the adherends is
hp = hp1 + hp2.

55

According to Eq. (1.4), radiation power transmitted through the bond-line for i-th inspection
wavelength is

−(cid:16)

Pi = P0 · e

(cid:17)

−(cid:16)

(cid:17)

αpi hp1+αai ha+αpi hp2

= P0 · e

αpi hp+αai ha

,

(1.36)

where P0 is the power of incident radiation, and αpi and αai are known attenuation coefficients for
i-th inspection wavelength of homogeneous adherend (plate) and adhesive, respectively. OT-scans
at two inspection wavelengths are needed to solve for ha and hp.

Hence, we have:

where P1 and P2 are optical powers transmitted through adhesive bond-line at wavelength λ1 and
λ2, respectively.

Figure 1.39: Geometry of adhesively bonded lap-joint.

,

P2 = P0 · e

−(αp1 hp+αa1 ha)
−(αp2 hp+αa2 ha)

P1 = P0 · e
ln
(cid:16) P0
(cid:17)
(cid:17)
(cid:16) P0
(cid:17) · αp1 = αp1 · αp2 · ha − αa2 · αp1 · ha
(cid:16) P0
(cid:17) · αp2 − ln
(cid:17) · αa2 − ln
(cid:17) · αa2 = αa2 · αp1 · hp − αa1 · αp2 · hp
(cid:16) P0

= αp1hp + αa1ha
= αp2hp + αa2ha

P2

ln

P1

P2

P2

ln

ln

(cid:16) P0
(cid:16) P0

P1

P1

(1.37)

(1.38)

(1.39)

Let’s rearrange equations in the following way:

56

Combining expressions with logarithms in Eq. (1.39) yields

(cid:17)
αa1 · αp2 − αa2 · αp1
αa1 · αp2 − αa2 · αp1

(cid:17)

= ln

P1

= ln

P1

ha ·(cid:16)
−hp ·(cid:16)

ha ·(cid:16)
hp ·(cid:16)
ha ·(cid:16)
hp ·(cid:16)



αa1 · αp2 − αa2 · αp1

αa1 · αp2 − αa2 · αp1
(cid:17)
(cid:17)

αa1 · αp2 − αa2 · αp1

αa1 · αp2 − αa2 · αp1

P2

P2

= ln

= ln

P1

P2

P1

(cid:17)αp2 − ln
(cid:16) P0
(cid:17)αp1
(cid:16) P0
(cid:16) P0
(cid:17)αa2 − ln
(cid:17)αa1
(cid:16) P0
(cid:18) P0
(cid:19)αp2


(cid:17)
(cid:19)αp1
(cid:18) P0
(cid:18) P0
(cid:19)αa2


(cid:17)
(cid:19)αa1
(cid:18) P0



(cid:17)
P2
αp2−αp1
0
(cid:17)
−αp1
αp2
·P
P
2
1
αa1−αa2
0
−αa2
αa1
·P
P
2
1

 P
 P
(cid:17) · lnP0 − ln
(cid:17) · lnP0 − ln

(cid:16)
(cid:16)

= ln

= ln

(cid:16)
(cid:16)

αp2
P
1
αa1
P
2

−αp1
· P
2
−αa2
· P
1

(cid:17)
(cid:17)

Finally, we can find expressions for the thicknesses

ha ·(cid:16)
hp ·(cid:16)

(cid:17)
(cid:17)

(cid:16)
(cid:16)

αa1 · αp2 − αa2 · αp1
αa1 · αp2 − αa2 · αp1

=

=

αp2 − αp1
αa1 − αa2

ha =

hp =

(αp2−αp1)·lnP0+αp1·lnP2−αp2·lnP1
(αa1−αa2)·lnP0+αa2·lnP1−αa1·lnP2

αa1·αp2−αa2·αp1
αa1·αp2−αa2·αp1

(1.40)

(1.41)

(1.42)

(1.43)

(1.44)

Following all steps from Eq. (1.37) to Eq. (1.44), the thicknesses of the adhesive bond-line and
adherends (ha and hp) can be obtained from two OT-scans acquired at λ1 and λ2, respectively. It
should be noted that if composite structure consists of more than two materials, more OT-scans at
different wavelengths need to be acquired.

57

1.4.3 State of polarization measurements

Adding polarization state generator (PSG) and polarization state analyzer (PSA) to the OTS
system allows for measuring local changes of SOP at each scan step in order to better characterize
defects. The schematics of PSG and PSA are shown in Fig. 1.40 and Fig. 1.41, respectively.

Figure 1.40: Polarization state generator based on 4 magneto-optic rotators.

Figure 1.41: Polarization state analyzer based on 6 magneto-optic rotators.

Both PSG and PSA can be built on pairs of magneto-optic (MO) rotators. MO rotator has the
following properties:

• when a positive magnetic field exceeding the strength of saturation field is applied, the rotator
rotates the SOP by 22.5◦ .

• when a negative magnetic field is applied beyond the saturation point, the rotator rotates the
SOP by −22.5◦ .

58

Hence, when both rotators in each pair rotate in the same direction, the net rotation of SOP is
+45◦ or −45◦ . However, if two rotators rotate in opposite directions, their modifications of SOP
cancel each other, and the net SOP rotation is zero. Assuming that the polarizer is aligned with the
c-axis of the λ
4 plate, the following SOPs can be generated by PSG (referenced with respect to the
polarizer’s direction):

• A linear SOP at 0◦ when the rotators in both pairs rotate in opposite directions.
• A linear SOP at +45◦ when the rotators in the first pair rotate in opposite directions, but the
rotators in the second pair both rotate +22.5◦.
• A linear SOP at 45◦, when the rotators in the first pair rotate in opposite directions but the
rotators in the second pair both rotate −22.5◦.
• Right hand circular (RHC), when the rotators in the first pair both rotate 22.5◦.
• Left hand circular (LHC), when the rotators in the first pair both rotate −22.5◦.

Note that 4 distinct polarization angles produce 16 SOP combinations. However, only 5 SOP states
are unique and the rest are degenerate. In principle, only 4 SOPs are required for calculation of the
Mueller matrix. However, some applications may require 6 distinct SOPs for better accuracy. To
generate 6 SOPs another MO rotator pair can be added to the PSG to produce additional +45◦ and
−45◦ rotations, similarly to PSA shown in Fig. 1.41. Note that this 6-bit device (with 6 binary MO
switches) can theoretically generate 64 states; however, only 6 states will be non-degenerate.

The Mueller matrix M of inspected composite sample can be obtained using a combination of

PSG and PSA shown in Fig. 1.37. Let the Stokes vector of the i-th output of the PSG be:

(1.45)

(cid:169)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:171)

SPSG
0i
SPSG
1i
SPSG
2i
SPSG
3i

(cid:170)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:172)

SPSG
i

=

59

Corresponding Stokes vectors measured by the PSA after the radiation passes through the sample
are related to Mueller matrix M by:

(cid:169)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:171)

SPSA
0i
SPSA
1i
SPSA
2i
SPSA
3i

(cid:170)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:172)

(cid:169)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:171)

SPSA
i

=

=

m00 m01 m02 m03
m10 m11 m12 m13
m20 m21 m22 m23
m30 m31 m32 m33

(cid:170)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:172)

·

(cid:169)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:171)

SPSG
0i
SPSG
1i
SPSG
2i
SPSG
3i

(cid:170)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:172)

(1.46)

At least 4 non-degenerate SOPs must be generated by the PSG and analyzed by the PSA to
completely determine the Mueller matrix M by solving Eq. (1.46). In such a case, i = 0,1,2,3
in Eq. (1.45) and Eq. (1.46). However, for higher accuracy, we require that as many as 6 non-
degenerate SOPs would be generated by the PSG and analyzed by the PSA, so that i = 0,1,2 . . . 5.
Let’s define a new matrix SPSA as:

SPSA =

(cid:169)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:171)

=

(cid:170)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:172)

SPSA
03
SPSA
13
SPSA
23
SPSA
33

SPSA
02
SPSA
12
SPSA
22
SPSA
32

SPSA
01
SPSA
11
SPSA
21
SPSA
31

SPSA
00
SPSA
10
SPSA
20
SPSA
30
m00 m01 m02 m03
m10 m11 m12 m13
m20 m21 m22 m23
m30 m31 m32 m33

(cid:169)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:171)

(cid:170)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:172)

(cid:169)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:173)(cid:171)

·

SPSA
04
SPSA
14
SPSA
24
SPSA
34
SPSA
00
SPSG
10
SPSG
20
SPSG
30

SPSA
05
SPSA
15
SPSA
25
SPSA
35
SPSA
01
SPSG
11
SPSG
21
SPSG
31

SPSA
02
SPSG
12
SPSG
22
SPSG
32

SPSA
03
SPSG
13
SPSG
23
SPSG
33

SPSA
04
SPSG
14
SPSG
24
SPSG
34

SPSA
05
SPSG
15
SPSG
25
SPSG
35

(cid:170)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:174)(cid:172)

= M · SPSG (1.47)

Consequently, the Mueller matrix M of the inspected sample can be obtained from

M = SPSA ·(cid:16)

SPSG(cid:17)T ·

(cid:20)

SPSG ·(cid:16)

SPSG(cid:17)T(cid:21)−1

,

(1.48)

is the transpose of matrix SPSG. More detailed Mueller matrix analysis is
where
provided in [34, 35]. The changes in SOP parameters may be attributed to the superstructure,
defects, or introduced stresses inside the tested sample.

(cid:16)

SPSG(cid:17)T

60

1.4.4 Separation of ballistic and scattered photons

Separation of scattered photons from the ballistic photons is important in applications, where
scattering properties of studied material are evaluated. Basic ways to accomplish this are based
either on spatial or temporal separation. In the first case, ballistic photons can be split from scattered
photons spatially by using a pinhole or 2D detector. Ballistic photons are registered in the center of
the photodetector, and fraction of scattered photons is easily calculated by subtraction of radiation
power of the ballistic photons from the total radiation power. Another way is to separate ballistic

Figure 1.42: Spatial and temporal discrimination of ballistic and scattered photons.

and scattered photons in time domain by using a high-speed photodetector. In this case, ballistic
photons will contribute to the registered signal with characteristic spike, while scattered radiation
will have broad envelope following the peak from ballistic photons. Both spatial and time domain
discrimination concepts are illustrated in Fig. 1.42.

In addition, if scattering of radiation inside the test sample is well described by mechanisms of
Rayleigh scattering, which depends on the inspection wavelength, the light source array or tunable
light source would also provide the ability to discriminate scattered photons from ballistic photons.
If absorption spectrum of the studied material is known, and Rayleigh scattering proportional to

61

4 is taken into account, transmitted radiation for two inspection wavelengths λ1 and λ2 can be
λ
approximated as:

,

(1.49)

where A1 and A2 are known absorption constants, B is the fraction of ballistic photons, and S is
proportional to the number of scattered photons. The solution to Eq. (1.49) yields:

(cid:33)
(cid:33)

(cid:32)
(cid:32)

B + S
λ4
1
B + S
λ4
2



(cid:16)

P1 ≈(cid:0)1 − A1
(cid:1) ·
P2 ≈(cid:0)1 − A2
(cid:1) ·
(cid:34) P1λ4

(cid:17) ·

1
1 − λ4
λ4
2

(cid:35)

1
1 − A1

− P2λ4
2
1 − A2

(1.50)

B ≈

1.4.5 Feasibility of 3D imaging

3D scanning should be implemented in order to determine the exact location of the defect in the
transect of the inspected sample. One way to perform such scanning is to analyze the dependence
of the transmitted power on the position of the focal plane. In this case, the beam focus is shifted
from the front to the rear surface of the sample manually or using a variable focus lens. Fig. 1.43

Figure 1.43: 3D scanning concept using variable focus lens.

62

illustrates an example of scattering from a defect inside the sample. When focal position is in the
vicinity of defect (Position 1), most of the radiation will scattered away from the photodetecor, and
minimal power will be registered. In contrast, when the beam is focused at Position 2, only a small
portion of the incident radiation is scattered by the defect, and registered power is maximal.

Figure 1.44: 3D scanning concept using scattering pattern correlation.

Another way to locate the position of defect in the transect of the sample is to correlate the
2D scattering pattern with defect depth while the focus of the optical lens is fixed at an optimal
position. In this case, the distribution of transmitted power is measured using a 2D photodetector.
In the example illustrated in Fig. 1.44, optical focus hits the defect at Position 1 prior to the defect
at Position 2. Assuming scattering occurs at the same solid angle for both defects, the 2D power
distribution corresponding to defect at Position 1 will be more spread out compared to that of at
Position 2. This is explained by different distances from two defects to the same photodetector.
Fig. 1.45 illustrates a simple experimental setup for validation of a 3D scanning concept. In this
case, power of transmitted radiation was measured as a function of focal distance along the vertical
scanning axis. Pig tailed light source was focused on the surface of the sample, and the focal point
was changed by moving the source with the Z-axis motor of the OTS-1000. The sample was a

63

Figure 1.45: Schematic of the experimental setup for measuring the power of transmitted radiation
as a function of focal distance along Z-axis.

Figure 1.46: Measured signal as a function of focal distance along Z-axis.

GFRP sandwich panel with two 2-mm skins and empty core. The gap between top and bottom skins
was 6 mm. Positions of the sample and the photodetector were fixed as they were mounted on a
separate mechanical fixture. Obtained results are demonstrated in Fig. 1.46. Apparently, two lobes
of measured signal correspond to top and bottom GFRP interfaces. High-frequency oscillations are
probably caused by vibrations, as the light source wasn’t perfectly mounted on the Z-axis fixture
of the gantry. Hence, the results being largely qualitative in nature, still demonstrate the sensitivity
of the technique to changes of internal structure of tested samples along their thickness, and show
potential for further refinement of OTS by implementing scanning along depth.

64

1.4.6 Detection of fiber breakage, lack of infusion, air voids and fiber waviness

Performance of the OTS system was successfully validated on various GFRP samples with
macro- and microscopic defects. For instance, Fig. 1.47 demonstrates the OT-scan of a GFRP
sample with dry fibers owing to lack of infusion, and cracks. Other details such as black marks,
left overs of tape and scratches are also visible. The scan resolution is 100 µm for both axes.

Figure 1.47: OT-scan of GFRP sample with lack of infusion (dry spots) and cracks.

Figure 1.48: GFRP sample with irregular distribution of chopped glass fibers. Region with air
bubbles is highlighted with red ellipse.

65

Fig. 1.48 shows a GFRP composite plate manufactured with chopped glass fibers. Major defects
detected in this sample were:

• a bundle of long glass fibers on the left;

• insertion of carbon fibers in the bottom of the test sample and on its right side;

• film insert in the upper part of the sample;

• agglomerations of air voids.

Resin-rich areas corresponded to brighter regions of the OT-scan, while fiber-rich areas were darker
on current gray scale colormap. Air bubbles present in the sample appeared as dark dots owing to
scattering of incident radiation. The average size of these dots was approximately 0.5 mm.

Fig. 1.49 and Fig. 1.50 show detailed OT-scans of another GFRP composite with chopped
fibers acquired at 640 nm and 1310 nm (visible versus infrared ranges). No apparent defects are
present, but uneven distributions of fibers and matrix are well captured. Interestingly, the 1310 nm
OT-scan is more sensitive to irregularities of matrix distribution, while fibers are seen much better
on a 640 nm OT-scan. Apparently, this is explained by different transmission coefficients of fibers
and matrix at selected inspection wavelengths. Zooming into different segments of the OT-scan
shown in Fig. 1.47 allows for detailed visualization of individual glass fiber tows (see Fig. 1.51).
In Fig. 1.51 fibers seem to be well aligned. However, when looking at Fig. 1.52, one may notice
that fibers are wavy. Fiber waviness is highlighted with red dotted line.

1.4.7 Conclusions

In this Section, a new robust version of OTS system was presented. Advanced NDE features
such as high-spatial scan resolution, high-speed scanning using array sources, multi-wavelength
measurement capability, SOP measurements, separation of ballistic and scattered photons, and 3D
imaging of defects by means of laser beam focusing were discussed. OTS was succesfully used for
detection of fiber breakage, lack of infusion, air voids and fiber waviness in GFRP samples.

66

Figure 1.49: OT-scan of GFRP sample with chopped glass fibers (640 nm wavelength).

Figure 1.50: OT-scan of GFRP sample with chopped glass fibers (1310 nm wavelength).

67

Figure 1.51: Zoomed region of the OT-scan shown in Fig. 1.47. Individual fiber tows are visible
and fibers are well aligned.

Figure 1.52: Zoomed region of the OT-scan shown in Fig. 1.47. Wavy fibers are detected.

68

CHAPTER 2

OPTICAL FREQUENCY DOMAIN REFLECTOMETRY FOR SHM OF STRUCTURAL

COMPOSITES

2.1 Fiber-optic sensing

Data logging with fiber-optic sensors is one of the actively researched areas in SHM [46].
Optical fibers are made by drawing glass (silica) or plastic to a diameter slightly thicker than
that of a human hair (on the order of µm), such that embedding them into a host specimen does
not affect its intrinsic properties to any appreciable degree. Measuring the properties of light
propagating through such fibers provides essential information about the state of the surrounding
structure (Fig. 2.1). These key features along with immunity to electromagnetic interference and
light weight make fiber-optic sensors very appealing for health monitoring of structural composites.
Fiber-optic sensors can be divided into two major categories: point and distributed sensors. Point

Figure 2.1: Categories of fiber-optic sensors and main interrogation techniques.

sensors provide signals from a single location, and can be broadly classified as Fiber Bragg-grating
(FBG) sensors and interferometeric sensors [47]. FBG is a sensing element written in the fiber

69

by UV exposure, which reflects a resonant wavelength called Bragg wavelength. The Bragg
wavelength is intrinsically sensitive to temperature, strain, or any other perturbations that modulate
the refractive index, n of the fiber or change the grating period, Λ. By sending a broad-band
radiation into an FBG and by monitoring the resonant wavelength shift, the local temperature or
strain can be extracted. Interferometeric sensors are based on mode coupling theories where two
or more modes of radiation propagating in the fiber undergo different optical paths and recombine
at a certain point. Hence, variations of temperature or strain affect optical paths, which results in
optical wavelength shifts or power variations. Recently, performance of FBG sensors and many
interferometeric sensors (e.g. Sagnac, Fabry-Perot, Michelson, Mach-Zehnder and others) have
been successfully demonstrated in different applications. However, the major drawback of sensing
signals at a single point is that structural damage or other events occurring outside the sensing area
will be missed. For instance, in the case of FBG, possible ways to alleviate this issue are:

• combine FBGs with different Bragg wavelengths into arrays through Wave-Division Multi-

plexing (WDM);

• use quasi-distributed sensors (e.g. continuously written fiber Bragg-gratings (CFBG));

• implement hybrid sensing techniques (as demonstrated in Chapter III).

Unlike point sensors, distributed fiber-optic sensors can be interrogated along their whole length.
This key advantage makes them suitable for monitoring of complex structures (e.g. vehicles,
bridges, pipelines, etc.), where knowledge of exact strain distribution is critical.
In a simple
case, an optical fiber itself may serve as a distributed sensor, if right interrogation technique is
implemented [48]. When radiation propagates along the optical fiber, small amounts of it are
reflected back through different physical mechanisms known as Raman, Brillouin and Rayleigh
back scattering. Major techniques for distributed sensing are optical time domain reflectometry
(OTDR) [49], optical frequency domain reflectometry (OFDR) [50] and optical low coherence
reflectometry (OLCR) [51] .

70

2.2 Scattering of radiation in optical fibers

A spontaneous scattering spectrum of solid state medium is schematically shown in Fig. 2.2.
Most photons are elastically scattered by atoms or molecules of the medium. However, a small
portion of photons (approximately 1 in 10 million) is scattered inelastically. In this case, scattered
photons have different frequencies and energies compared to incident photons.

Figure 2.2: Typical spectrum of scattered radiation in solid state medium.

From the perspective of solid state physics, Brillouin scattering is an interaction between an
electromagnetic wave and crystalline lattice waves in the medium (e.g. mass oscillation or acoustic
modes). The scattering is inelastic meaning that the photon may lose energy (Stokes process) and in
the process create a quasiparticle (phonon) or it may gain energy (anti-Stokes process) by absorbing
a quasiparticle. Such a shift in photon energy, corresponding to a Brillouin shift in frequency, is
equal to the energy of the released or absorbed quasiparticle. Thus, Brillouin scattering can be used
to measure the energies, wavelengths and frequencies of various atomic chain oscillation types.

Raman scattering is another phenomenon that involves inelastic scattering of light caused by the
vibrational properties of matter. The detected range of frequency shifts and other effects are very

71

different compared to Brillouin scattering. In Raman scattering, photons are scattered by the effect
of vibrational and rotational transitions in the bonds between first-order neighboring atoms, while
Brillouin scattering results from the scattering of photons caused by large scale, low-frequency
phonons. The effects of the two phenomena provide very different information about the sample:
Raman spectroscopy can be used to determine the transmitting medium
s chemical composition
and molecular structure, while Brillouin scattering can be used to measure the material
s properties
on a larger scale such as its elastic behavior.

Rayleigh scattering is known as the scattering of radiation due to non-propagating fluctuations
of density, composition and orientation of molecules within the optical fiber, and hence of its
refraction index. The difference between Brillouin scattering and Rayleigh scattering is that the
former involves only the random and incoherent thermal fluctuations, in contrast with the correlated,
periodic fluctuations (phonons).

Figure 2.3: Weak FBG model describing Rayleigh scattering as superposition of point-like reflectors
along the fiber.

Optical fiber can be treated as a series of infinitesimally short segments, where each segment
acts as a random point-like scatterer. Hence, Rayleigh back-scattering profile along the optical fiber
can be modeled as a sequence of weak Bragg-gratings with randomly varying periods. In the case
of an FBG, the resonant wavelength is determined by grating period and effective refractive index.
Any change in these parameters leads to resonant wavelength shift. The Rayleigh back-scattering
responds in the same manner: changes in refractive index or physical length lead to a resonant
wavelength shift. By measuring the wavelength shifts, one may achieve distributed sensing, which
functions as thousands of FBGs multiplexed.

72

2.3 OFDR operating principle

Recently, OFDR has attracted increased interest in the areas of space resolved characterization
of optical fibers and components thanks to its high spatial resolution and dynamic range. OFDR
has been primarily used for applications that require high spatial resolution (e.g. millimeter and
sub-millimeter) with a relative short measurement range up to a few hundreds of meters. OFDR
has also been implemented in various SHM projects that require distributed strain and temperature
sensing. Hence, OFDR has found its use in such industries as oil and gas, aerospace, automotive
and civil engineering, geophysics, and many more.

Figure 2.4: Schematics of the OFDR system for measuring Rayleigh back-scattered radiation in
single-mode optical fibers.

Typical schematic of OFDR set-up is illsutrated in Fig. 2.4. OFDR system for detection
of Rayleigh scattering and Fresnel reflections consists of a tunable laser source (TLS), a main
interferometer with polarization diversity receiver, and auxiliary interferometer, which is optional.
Radiation from TLS is split into two beams at the coupler C3. At this point, 99% of incident power
goes into the main interferometer, while 1% power is sent into auxiliary interferometer.

73

At coupler C1, radiation power is split equally between the circulator
s input and polarization
controller (PC). Incident radiation propagates into the fiber under test (FUT) through the second
port of the circulator, and back-reflected radiation is outputted at the third port. The back-scattered
radiation from FUT interferes with radiation from TLS at the coupler C2, which produces fringe
patterns. The output of C2 is split into two orthogonal polarization components ( ˆp and ˆs) by
a polarization beam splitter (PBS). Intensities of beat patterns are measured by corresponding
photodetectors (PD) connected to a data acquisition card (DAQ).

Figure 2.5: Perfect linear TLS tuning (ω is instantaneous optical frequency, ω0 is initial optical
frequency, and γ is tuning rate).

The auxiliary interferometer is used for real-time tracking of TLS optical frequency as it usually
diverges from ideal curve (see Fig. 2.5). Electric circuitry generates clock signals at each “zero-
crossing” position of the optical interference fringe signals, which is needed for proper data sampling
by DAQ. The auxiliary interferometer is typically implemented as Michelson interferometer with
Faraday rotation mirrors (FRM) and optical delay line. Such scheme mitigates tuning nonlinearity
of TLS, which may severely deteriorate acquired reflectance measurements. However, perfect TLS
tuning is assumed in this report, and the compensation of TLS nonlinearities is left as future work.

2.4 Theory of polarization diverse OFDR

This section presents theoretical formulation of OFDR operating principles. We shall first
define the electric field at coupler C1 as a starting point for the analysis. Assuming the TLS

74

generates radiation with an optical frequency ω(t) and instantaneous phase of ϕ(t) (as shown in
Fig. 2.5), the electric field at coupler C1 can be expressed as

√−1. Note that the instantaneous phase of

(2.1)

E(t) = E0(t)e jϕ(t),

(cid:90)t

0

where E0 is the magnitude of the electric field, and j =
the electric field is given by the following expression:

ϕ(t) =

ω(t)dt + ϕ0,

(2.2)

where ϕ0 is the initial phase of the radiation generated by the TLS. Generally, if radiation propagates
in the optical fiber, the electric field at a distance l from the output of TLS is given by

E(τ, t) = A√
2

E0(t − τ)e jϕ(t−τ)e−αl,

(2.3)

where τ is a propagation time delay, α is the attenuation constant, and A is a complex constant that
defines phase shift of electric field introduced by couplers, circulators or other optical components
along the fiber length. In Eq. (2.3), τ is defined as

τ = l
v

=

l · ng
c

,

(2.4)

where v is the group velocity, ng is the group refractive index, and c is the speed of light in vacuum.
Let’s evaluate the electric field at the end of the top arm of the main interferometer. In our case,
this is the optical fiber of length lb between couplers C1 and C2. Using Eq. (2.3), electric field at
the first input of C2 can be expressed as

E(τb, t) =

Ab√
2

E0(t − τb)e jϕ(t−τb)e−αlb,

(2.5)

where τb is the corresponding propagation time delay. Now let’s consider the propagation of
radiation from the circulator to an arbitrary point z0 along the length of the fiber under test (FUT).
If the circulator is taken as origin, the electric field at location z0 is given by
−αlz0 .

t−τz0

(2.6)

jϕ

e

(cid:16)

(cid:17)

(cid:17)

(cid:16)

(cid:17)

e

(cid:16)

E

τz0, t

=

Az0√
2

E0

t − τz0

75

Taking into account Rayleigh back-scattering at z0, the radiation returned back to circulator is
expressed as

(cid:16)

(cid:16)

(cid:17)

(cid:17)

(cid:16)

(cid:17)

E

2τz0, t

= r(z0)

A2z0√
2

E0

t − 2τz0

jϕ

e

t−2τz0

−α2lz0,

e

(2.7)

where r(z0) is a complex Rayleigh back-scattering coefficient that describes local variation of
refractive index in the FUT. Now, similarly to Eq. (2.5), we need to obtain an expression for the
electric field at the second input of coupler C2 referenced to coupler C1 as origin. For simplicity,
let’s assume that lengths of fiber sections between coupler C1 and circulator, and between circulator
and coupler C2 are equal to la
2 . Then the radiation from C1 will propagate through the circulator
to the FUT, Raleigh-back scattering will take place at location z0, and the resulting electric field
registered at coupler C2 will be defined as

(cid:16)

(cid:16)

(cid:17)

(cid:17)

(cid:16)

(cid:17)

E

2τz0 + τa, t

=

A(2z0+la)

√
2

E0

t − (2τz0 + τa)

jϕ

e

t−(2τz0+τa)

−α

e

2lz0+la

,

(2.8)

where τa is the combined time delay due to fiber optic paths C1-circulator and circulator-C2.
Applying the weak FBG model, each point along the FUT will act as an independent reflector.
Hence, Rayleigh back scattering from all points will contribute to the value of the electric field at
the second input of coupler C2:

(cid:16)

(cid:17)

Ea(t) = Aa√
2

(cid:88)

z

(cid:104)

r(z)E0 (t − (2τz + τa)) e jϕ(t−(2τz+τa))e−α(2lz+la)(cid:105)
r(z)E0 (t − (2τz + τa)) e jϕ(t−(2τz+τa))e−α(2lz+la)(cid:105)
(cid:104)
(cid:88)

.

The electric field at the output of C2 is given by Jones matrix:

E(t) = Ea(t) + jEb(t) = Aa√
2

z

(2.9)

+ j

Ab√
2

E0(t − τb)e jϕ(t−τb)e−αlb.

(2.10)

The OFDR block diagram shown in Fig. 2.4 features polarization diverse measurement scheme to
eliminate polarization dependent losses (PDL) in the fiber. This is done by splitting the radiation
at the output of C2 in two orthogonal components ˆp and ˆs, and by registering them independently
using two optical photodetectors PD1 and PD2, respectively.

76

Hence, ˆp and ˆs components of the electric field are given by the following relations:

z

(cid:32)(cid:88)
(cid:32)(cid:88)

(cid:104)

rp(z)E0 (t − (2τz + τa)) e jϕ(t−(2τz+τa))e−α(2lz+la)(cid:105)
rs(z)E0 (t − (2τz + τa)) e jϕ(t−(2τz+τa))e−α(2lz+la)(cid:105)

+ j AbE0(t − τb)e jϕ(t−τb)e−αlb

(cid:104)

Ep(t) = ˆp

Tpe jϕp

2

Aa

Es(t) = ˆs

Tse jϕs

2

Aa

z

+ j AbE0(t − τb)e jϕ(t−τb)e−αlb

(cid:33)

(cid:33)

,

(2.11)

,

(2.12)

where ˆp and ˆs are orthogonal unit vectors; Tp and Ts are the split coefficients of PBS; ϕp and ϕs
are the phase shift coefficients of PBS; and rp and rs are the Rayleigh back-scattering coefficients
for ˆp and ˆs electric field components, respectively.
Let’s consider the ˆp component of the electric field’s intensity registered by photodetector PD1:

Ip(t) = Ep(t) · Ep(t)∗

(2.13)

As the DC part of Ip(t) contains no useful information about the Rayleigh back-scattering profile
of the FUT, only the AC part is taken into account [52]:

(cid:33)

I AC
p (t) =

p Aa A∗
T2
4

b

(cid:32)

(cid:88)

z

e−α(2lz+la+lb)rp(z)E0 (t − (2τz + τa)) E∗

0(t − τb)

(cid:16)

ϕ(t−(2τz+τa))−ϕ(t−τb)

j

× e

(cid:17)

+ c.c.,

(2.14)

(cid:90)t

0

(cid:90)t

0

where c.c. denotes the complex conjugate of the first term in the equation. Assuming linear tuning
of optical frequency by TLS (see Fig. 2.5), the instantaneous optical phase is given by:

ϕ(t) =

ω(t)dt =

(γt + ω0)dt =

1
2 γt2 + ω0t + ϕ0,

(2.15)

where ϕ0 is the initial optical phase of TLS output. Using Eq. (2.15), the phase term of a complex
exponential in Eq. (2.14) can be simplified into
ϕ(t − (2τz + τa)) − ϕ(t − τb) =

2 γ(cid:0)τb − τa − 2τz(cid:1)(cid:0)2t − (2τz + τa + τb)(cid:1)

1

(cid:0)τb − τa − 2τz(cid:1)

(2.16)

+ ω0

77

Since τa and τb are time delays due to sections of optical fibers inside the OFDR instrument, they
can be adjusted to have the same length l0 = la = lb, so that τ0 = τa = τb. In this case, we have:

ϕ(t − (2τz + τa)) − ϕ(t − τb) = −2γτz(t − (2τz + τ0)) − 2ω0τz

Thus, Eq. (2.14) is now reduced to

I AC
p (t) =

p Aa A∗
T2
4

b

e−α(2lz+2l0)rp(z)E0

(cid:32)

(cid:88)

z

0

(cid:1)

(cid:0)t − τ0

(cid:0)t − (2τz + τ0)(cid:1) E∗
× e−j(cid:0)2γτz(t−(τz+τ0))+2ω0τz(cid:1)(cid:33)
(cid:0)t − τ0
0(t)e−j(cid:0)2γτz(t−(τz+τ0))+2ω0τz(cid:1)(cid:33)

+ c.c.,

where c.c. denotes the complex conjugate of the first term. If output of the TLS is stable over long
period of time, then E0
p Aa A∗
T2
4

(cid:0)t − (2τz + τ0)(cid:1) ≈ E(t) and E∗
(cid:32)
(cid:88)

e−α(2lz+2l0)rp(z)E0(t)E∗

0(t). Eq. (2.18) becomes

(cid:1) ≈ E∗

I AC
p (t) =

+c.c.,

(2.19)

0

b

z

where c.c. denotes the complex conjugate of the first term. Let’s group all phase terms related
OFDR optical frequency tuning and Rayleigh back-scattering:

(2.17)

(2.18)

(2.20)

(2.21)

Θp(z) = 2τz(ω0 − γτz(τz + τ0)) − θrp(z),

Factoring out complex amplitude constants, we have:

mp(t) = |mp(t)|·e jψp(t) =

TpAa A∗

b

4

|E0(t)|2

Eq. (2.19) can be now expressed as
−j

I AC

p (t) =(cid:88)
(cid:32)
= 2(cid:88)

z

z

+ψp(t)−θrp(z)

|rp(z)|·|mp(t)|e

(cid:32)
(cid:16)
|rp(z)|·|mp(t)|e−2α(cid:0)lz+l0
= 2(cid:88)

2γτzt+2τz(cid:0)ω0−γτz(τz+τ0)(cid:1)(cid:17)
(cid:1)

(cid:33)
(cid:1)(cid:1) + ψp(t) − θrp(z)
cos(cid:0)2γτzt + ψp(t) + Θp(z)(cid:1)(cid:33)
mp(t, z) cos(cid:0)2γτzt + ψp(t) + Θp(z)(cid:1)(cid:33)

2γτzt + 2τz(cid:0)ω0 − γτz(cid:0)τz + τ0
|rp(z)|·|mp(t)|e−2α(cid:0)lz+l0
=(cid:88)

+ c.c.

(cid:1)
(cid:32)

cos

(cid:32)

(cid:16)

z

,

(cid:17)(cid:33)

(2.22)

z

78

where mp(t, z) = |rp(z)|·|mp(t)|e−2α(cid:0)lz+l0

(cid:1)

is the magnitude of measured field intensity, and
jθrp(z) is a complex reflection coefficient owing to Rayleigh back-scattering at
rp(z) = |rp(z)|·e
coordinate z. Assuming that strain and temperature fields applied to the FUT are quasi-static
(e.g.
strain and temperature distributions along the fiber stay constant during a single OFDR
measurement), mp(t, z) ≈ mp(z) and ψp(t) = 0. Finally, Eq. (2.22) turns into

I AC

p (t) =(cid:88)
(cid:16)

mp(z) cos(cid:0)2γτzt + Θp(z)(cid:1) .
e jΘp(z)δ (ω − 2γτz) + e−jΘp(z)δ (ω + 2γτz)(cid:17)

mp(z)

z

(2.23)

(2.24)

Fourier transform of Eq. (2.23) yields

(cid:88)

z

√
2π
2

I AC
p (ω) =

Since generation of only positive frequencies is physically feasible, only the first summand in
Eq. (2.24) is considered for reflectance measurement:

(cid:88)

z

√

2π
2

I AC
p (ω) =

mp(z)e jΘp(z)δ(ω − 2γτz) =(cid:88)

z

κ(z)δ(ω − 2γτz)

(2.25)

where κ(z) defines local reflection coefficient that accounts for reflections from optical components
and for Rayleigh back-scattering, and δ(ω − 2γτz) is an impulse function specifying the beat
frequency ωz = 2γτz directly related to a position z along the fiber. Thus, as explained in the
previous section, optical fiber under test is indeed treated as superposition of point reflections along
its length when OFDR technique is used. Similar results can be obtained for the ˆs component of
the electric field registered by the photodetector PD2. Then two measurements will be combined
together to provide the total power of back reflected field at each point along the FUT.

2.5 Strain sensing approach based on detection of physical shifts of point-like

reflectors

Flowchart of conventional algorithm for strain sensing using OFDR reflectance data [53] is
presented in Fig. 2.6. Baseline measurement B of size L is taken prior to applying any displacements
to the FUT. The second measurement M is acquired when the FUT or some of its sections are
strained. Both B and M are then windowed by a moving rectangular window w, and are partitioned

79

into s cropped segments. Note that windows may or may not overlap depending on how many
points for measuring strain the user wants to assign.

Figure 2.6: Conventional approach for strain measurement using OFDR.

Windowing operation is described by Eq. (2.26) and Eq. (2.27):

ˆBs[k] = B[k]w[k − l · s],

ˆMs[k] = M[k]w[k − l · s],

(2.26)

(2.27)

where B is the baseline, M is reflectance measurement in a strained state of FUT, l is window shift
(in samples), and s is an index of windowed segment. Window w is defined as:

(cid:20) k − X

(cid:21)

N

(cid:20)

(cid:21)

(cid:20)

(cid:21)

w[k] = Rect

= u

k − X + N
2

− u

k − X − N
2

,

(2.28)

(cid:107)

(cid:106) L

where X is window’s center (usually X = N
2 ), N is window’s length in points (even positive integer),
u[k] is the Heaviside step function. Note that depending on how much overlap between neighboring
windows is required, l ∈ [1, N + 1], hence the maximal number of partitioning segments ranges
from
Windowed segments are transferred back to the wavenumber domain by applying the inverse
discrete Fourier transform (iDFT):

to L − N.

N

bs[n] =

1
N

ˆBs[k]e j 2πkn
N ,

(2.29)

ms[n] =

(2.30)
where n = 0,1...N−1. Note that fast inverse Fourier transform (iFFT) is used in actual computations
to speed-up the algorithm.

k=0

1
N

ˆMs[k]e j 2πkn
N ,

N−1(cid:88)
N−1(cid:88)

k=0

80

Wavenumber shift between the obtained signals is calculated using cross-correlation as

R(s)
bm[h] =

∞(cid:88)
(cid:17)
n=−∞ bs[n]ms[n − h],

(cid:16)

R(s)
bm[h]

,

Ps = argmax

h

(2.31)

(2.32)

bm is the cross-correlation coefficient in wavenumber space, and Ps is the shift that is

where R(s)
experimentally calibrated to strain εs in the FUT.

In this dissertation, an alternative approach for strain measurement is proposed. The corre-
sponding flowchart is demonstrated in Fig. 2.7. The main difference between Fig. 2.6 and Fig. 2.7
is the absence of the iFFT. Instead, the cross-correlation is directly applied to windowed reflectance
data. Hence, the algorithm detects mechanical shifts of local scatterers rather than modulations of
wavenumber.

Figure 2.7: Alternative approach for strain measurement using OFDR.

Signal processing approach shown in Fig. 2.7 does not require phase information, and provides
displacement measurement directly, if x−axis of reflectance measurement is mapped accurately to
spatial coordinates along the FUT:
R(s)
BM[h] =

∞(cid:88)

(2.33)

k=−∞

BM is the cross-correlation coefficient in spatial domain. Local displacement Ds is given

where R(s)
by the following expression

(cid:12)(cid:12) ˆBs[k](cid:12)(cid:12) ·(cid:12)(cid:12) ˆMs[k − h](cid:12)(cid:12) ,
(cid:16)

(cid:17)

R(s)
BM[h]

Ds = argmax

h

Finally, strain in each fiber segment can be easily calculated as

εs = Ds
N

81

(2.34)

(2.35)

If OFDR reflectance measurements are corrupted with noise, computed displacement vector is
passed through the Hampel filter as shown in Fig. 2.7. The filter uses the three-sigma rule of
statistics to remove outliers from the signal. For a given sequence x1, x2, ...xn and a sliding window
of length k, the following condition is evaluated:

(cid:12)(cid:12)xi − mi

(cid:12)(cid:12) > nσσi,

(2.36)

(2.37)

where mi is the local median, σi is the standard deviation, and nσ is the threshold specified by user.
the local median and standard deviation are defined as

mi = median(cid:0)xi−k, xi−k+1, ...xi, ..., xi+k−1, xi+k
(cid:12)(cid:12)(cid:1) ,
(cid:12)(cid:12) , ...,(cid:12)(cid:12)xi+k − mi
σi = κ · median(cid:0)(cid:12)(cid:12)xi−k − mi

(cid:1) ,

(2.38)
≈ 1.4826. If condition in Eq. (2.36) is met, the Hampel filter

√
2·E f rc−1·1
2

where coefficient κ =
declares xi an outlier and replaces it with mi.
2.6 Validation of signal processing technique for strain sensing using OFDR

1

Measurements of Rayleigh back-scattered radiation in single mode (SM) optical fibers were
performed at General Photonics Corporation (Chino, CA) using the polarization analyzing OFDR
system PA-OFDR-1000. This section presents data acquisition approach and signal processing
technique for calculating displacements and strains induced in the fiber. Experimental setup for
validating the OFDR system is shown in Fig. 2.8. PA-OFDR-1000 unit was connected to Agilent
81607A tunable light source, and the whole setup was controlled from a lap-top with LabView
drivers. Agilent TLS were driven at a scanning rate of 20 nm/s, and the wavelength tuning range
spanned from 1500 nm to 1580 nm that provided spatial resolution of approximately 20 µm, when
interrogating SM optical fibers. Output power of the TLS was approximately 3 mW. Optical fiber
under test consisted of three sections: an SM fiber (1 m long), a piezoelectric fiber stretcher FST-005
(with 35 m long fiber inside), and an SM fiber with 500 continuously written Bragg-gratings (8 m
long). Fiber stretcher was used to introduce nearly uniform strains in the corresponding section of
the FUT. FST-005 was controlled by a DC voltage source and piezo-amplifier that supplied up to

82

Figure 2.8: OFDR experimental setup at General Photonics Corporation.

Figure 2.9: Radiation intensity sensed by photodetector PD1 (ˆs-polarized component).

300 V to the PZT crystal around which the fiber was wounded inside the instrument. All sections
of FUT were connected with angle physical contact (APC) connectors.
Fig. 2.9 demonstrates
typical intensities of fringe patterns registered by the photodetectors and sampled by embedded
high-speed DAQ inside the PA-OFDR-1000 module. The signal was averaged 8 times. As seen
from Fig. 2.9, strong beating is observed around 1522 nm, which corresponds to Bragg wavelengths
of continuously written FBGs at the end of the FUT. Note that signal presented in Fig. 2.9 contains

83

Figure 2.10: Typical OFDR measurement showing reflectance of FUT: single mode fiber, PZT fiber
stretcher and optical fiber with CBFGs.

Figure 2.11: Fresnel reflection at APC connector.

approximately 8 · 106 data points. Fast Fourier transform of the beat signal shown in Fig. 2.9
provides reflectance along the FUT length. Fig. 2.10 demonstrates Rayleigh back-scattering from
the optical fiber inside the FST-005 stretcher, reflections from CFBGs and APC connectors. Also,
the x-axis of Fig. 2.10 starts at approximately 3.3 m in order not to show reflections from fibers
inside the OFDR unit itself.

84

Figure 2.12: Reflections from continuously written Bragg-gratings.

Figure 2.13: Shift of reflection from APC connector at different strain states.

Fig. 2.12 illustrates typical reflections from Bragg-gratings in the last 8-m section of the FUT.
As results demonstrate, reflectivity of different Bragg-gratings varies up to 5 dB, but their period
remains constant. Fig. 2.11 is a another version of Fig. 2.10 zoomed into the region around the
APC connector. Fig. 2.11 reveals that some side lobes or “ghost” reflections are present near the
true peak. This issue is caused by non-constant TLS tuning rate γ, and can be compensated for
by applying the deskew filter, non-uniform Fourier transform or other advanced signal processing
techniques.

85

Fig. 2.13 shows the effect of uniform displacement field applied to the FUT section by the
FST-005 piezoelectric fiber stretcher. Fig. 2.13 is centered around the reflection from the APC
connector on the output of FST-005. Two increased voltages (w.r.t.
initial voltage of 110 V) on
the inputs of FST-005 generated higher strains in the fiber, which resulted in physical shifts of
point-like Rayleigh reflectors, ∆x1 and ∆x2, respectively.

Figure 2.14: Cross-correlation of segments of back-scattering profile at the end of the fiber stretcher.
Baseline reflectance measurement is compared to a measurement after applying 190 V to the input
of FST-005.

Hence, it was concluded that identifying shifts of local Rayleigh back-scattered radiation patterns
should help recover displacement along the whole FUT length. This was easily implemented by
partitioning the reflectance measurement in small segments (windows) and by calculating local
cross-correlations with respect to baseline measurement in undisturbed state of the FUT as per
Eq. (2.33). This simple approach was notably different from commonly used technique where the
same segmentation is applied, but the cross-correlation is performed in the K-space by taking the
inverse FFT first.

OFDR measurements were acquired for 23 different strain states in subsequent experiments.
Reflectance profiles (see Fig. 2.10) were segmented into 12-mm long windows. Then the cross-
correlations were computed for all windows with respect to a baseline measurement in a strain-free

86

state, when the fiber stretcher was turned off. Windows were also allowed to have 50% overlap for
smoother output. Typical cross-correlation between windowed section of the FUT at the end of the
fiber stretcher in the strained state and strain-free state is presented in Fig. 2.14. In this case, nearly
4-mm reflector displacement was detected, when 190 V were applied to the FST-005.

Figure 2.15: Displacement profiles along the 35-m long optical fiber section inside the FST-005
fiber stretcher.

Applying the same signal processing procedure to a complete set of 23 OFDR measurements
allowed for recovering of respective displacement profiles along the FUT length as shown in
Fig. 2.15. Obtained results agreed perfectly with factory specifications of FST-005. It should be
noted that calculated displacements had some spurious single-point spikes, apparently caused by
measurement noise that shifted cross-correlation peaks to wrong locations. These spikes were
successfully removed with a Hampel filter. Based on displacement profiles shown in Fig. 2.15,
corresponding strain profiles were calculated (see Fig. 2.16).

87

Figure 2.16: Strain profiles along the 35-m long optical fiber section inside the FST-005 fiber
stretcher.

2.7 Conclusions

Chapter II described the development of advanced signal processing techniques for distributed
displacement and strain sensing in SM fibers using the OFDR. An approach for measuring strain
using Rayleigh back-scattering was proposed. In contrast to conventional techniques that detect
applied axial strain as a modulation of wavenumber, reflectance measurements were analyzed in
spatial domain, and local displacements along FUT were identified as shifts of point-like scatterers.
The new signal processing technique was successfully validated using the PA-OFDR-1000 system
at General Photonics Corporation.
In the experimental setup, one section of the FUT had the
piezoelectric fiber stretcher that introduced nearly uniform axial strain, which was accurately
measured by the algorithm with a 4-mm spatial resolution. In addition, the acquired measurements
were denoised that allowed to use reflectance data with less averaging. Overall, the obatined results
demonstrated that the OFDR technique along with advanced signal processing is a promising tool
for NDE and SHM of composite structures.

88

CHAPTER 3

HYBRID ACOUSTO-OPTIC HEALTH MONITORING OF STRUCTURAL

COMPOSITES USING GUIDED WAVES AND CFBG-FPI SENSORS

3.1 Proposed approach for hybrid acousto-optic SHM

Rapid and cost-effective damage detection using multiple sensing techniques is one of the
emerging paradigms in SHM. This chapter is focused on developing a novel hybrid approach
for SHM of structural composites that combines benefits of ultrasonic and optical sensing. The
proposed work uses use current successes in aforementioned techniques as launch-pad to propel
the development of a new system that will utilize reusable surface-bonded or embedded arrays of
optical fibers with strategic ability to sense ultrasonic guided waves. The synergy of this hybrid
approach aims at eliminating the limitations of each of the approach while making it cost-effective
and reusable.

Figure 3.1: Overall approach for hybrid acousto-optic SHM of structural composites.

89

The overall approach proposed in this work is schematically shown in Fig. 3.1. Arrays of
Fabry-Perot interferometric sensors formed by pairs of chirped fiber Bragg-gratings (CFBG-FPI)
are surface-mounted or embedded in safety critical areas of composite structure [54]. Guided waves
(GW) are excited by active sources, such as thin surface-bonded PZT wafers or external devices
for non-contact generation of ultrasound (e.g. air-coupled transducers or a laser) and are sensed
by CFBG-FPI receivers. In a passive mode, CFBG-FPI sensors are used for in-situ monitoring of
slowly varying strains, loads or temperature changes in the host structure. In contrast, when the
active mode is triggered for event-based or schedule-based inspection, guided waves are excited
and CFBG-FPI interrogator is switched to the high-sampling rate regime. The system is controlled
through the onboard PC, and pre-programmed signal processing algorithms are used on the acquired
data for identifying damage signatures. Potential advantages of the proposed hybrid acousto-optic
SHM approach are summarized in Fig. 3.2. The detailed descriptions of GW theory and GW sensing
with CFBG-FPIs are given in the following sections, since the SHM approach is experimentally
validated for cases of defect detection in aluminum plates.

3.2 Guided wave theory

This section introduces the fundamental equations describing guided waves in isotropic plate-
like structures. Since the topic is well documented in the literature, only the key results are
presented. The constitutive relations describing guided waves in plates can be thought of as a
special case of elastic wave propagation in unbounded media. The differential equation of motion
in three-dimensional solids is known as Navier’s equation [55]:

∂x2 + ∂
µ( ∂
∂x2 + ∂
µ( ∂
µ( ∂
∂x2 + ∂

∂ y2 + ∂
∂ y2 + ∂
∂ y2 + ∂

∂z2 )ux + (λ + µ) ∂
∂z2 )uy + (λ + µ) ∂
∂z2 )uz + (λ + µ) ∂

∂x

∂x

∂x

( ∂
∂x
( ∂
∂x
( ∂
∂x

+ ∂
∂ y
+ ∂
∂ y
+ ∂
∂ y

+ ∂
∂z
+ ∂
∂z
+ ∂
∂z

90

)ux = ρ

)uy = ρ

∂ux
∂t2
∂uy
∂t2
∂uz
∂t2

)uz = ρ

(3.1)

Figure 3.2: Unique features of the proposed hybrid acousto-optic SHM.

91

Eq. (3.1) can be concisely expressed in vector form:

µ∇2u + (λ + µ)∇(∇ · u) = ρ

∂u
∂t2

(3.2)

where u = iux + juy + kuz is the particle displacement vector, ρ is the material density, µ and λ are
the Lame constants, the ∇ is a del differential operator and ∇2 is a vector Laplacian.

It should be noted that Navier’s differential equations governing wave propagation are based
upon three fundamental relationships from linear elasticity theory. These include strain-displacement
relations (Eq. (3.3)), equation of motion also known as Newton’s generalized second law (Eq. (3.4))
and constitutive stress-strain relations or Hooke’s law (Eq. (3.5)). Their expressions in tensor no-
tation are:


i j =

1
2
∂σi j
∂xi

(uj,i + ui,j)

= ρ

∂ui
∂t2

(3.3)

(3.4)

(3.5)
where i, j = 1,2,3; 
i j − the strain tensor and ci jkl − the stiffness tensor; repeated indexes imply
summations and commas imply partial derivatives.

σi j = ci jkl 
kl

Therefore, Navier’s equation combines three equilibrium equations, six strain-displacement
equations, and six constitutive equations from Eq. (3.3)−Eq. (3.5). Navier’s equation can be solved
with the help of Helmholtz vector and scalar potentials H and Φ :

u = ∇Φ + ∇ × H

∇ · H = 0

Upon the substitution of Eq. (3.5) and Eq. (3.6) into Eq. (3.1) we get

(λ + 2µ)∇2Φ − ρ∇(cid:220)Φ = 0

µ∇2H − ρ (cid:220)H = 0

92

(3.6)

(3.7)

(3.8)

(3.9)

The rearrangement of Eq. (3.8) and Eq. (3.9) yields the equation of wave propagation in 3D
homogeneous solids in terms of scalar and vector potentials

2∇2Φ = (cid:220)Φ
cl
2∇2H = (cid:220)H

cs

(3.10)

where cl = (2µ + λ)/ρ and cs = µ/ρ. Double dot operator represents the second order time
derivative. It can be shown that the total solution for displacement vector u has three components
[55]:

u = uL + uSH + uSV

(3.11)

where uL corresponds to longitudinal or pressure wave whose particle displacement is parallel to
the direction of propagation, uSH and uSV define the shear horizontal and shear vertical waves.
Motion of particles for these solutions is perpendicular to the direction of wave propagation. The
snapshots of S-wave and P-wave are shown in Fig. 3.3.

Figure 3.3: Shear vertical and pressure waves in solids.

Shear vertical and pressure wave solutions are of particular importance if Navier’s equations
are solved for practical cases when the structure has some geometric bounds. In particular, the
interaction of shear vertical and pressure waves in thin plates and shells gives rise to guided waves.
In this section we consider the derivation of Lamb wave equations for two-dimensional plates of
infinite length. For simplicity of analysis it is possible to assume that the wave potentials are
invariant to the z-direction along the wave front [55].

93

Figure 3.4: Isotropic plate of infinite length and thickness 2d. Wave propagates in x-direction.

In this case ∂/∂z = 0 and uSH accepts only shear displacement uz. In contrast, uL with uSV
accept ux and uy displacements, which depend only on scalar potential Φ and a z-component of a
vector potential Hz. Therefore, Navier’s equation in terms of scalar and vector potentials for uL,
uSV possible solutions and the geometry in Fig. 3.4 takes the form:

cl

2∇2Φ = (cid:220)Φ
cs2∇2Hz = (cid:220)Hz

p2 = ω2
q2 = ω2

cp2 − ξ2
cs2 − ξ2

94

where cl and cs are longitudinal and shear wave speeds. Introducing the simpler notation Φ = φ
and Hz = ψ we get a classical formulation for guided wave equations in the potential form:

∂2φ
∂x2 + ∂2φ
∂2ψ
∂x2 + ∂2ψ

∂ y2 + ω2
∂ y2 + ω2

cp2 φ = 0
cs2 ψ = 0

Assuming harmonic solution e−i(ωt−ξ x), the system of equations Eq. (3.13) becomes:

∂ y2 + ( ω2
∂2φ
∂ y2 + ( ω2
∂2ψ

cp2 − ξ2)φ = 0
cs2 − ξ2)ψ = 0

(3.13)

(3.14)

In Eq. (3.14), ξ = ω/c defines a wavenumber. At this point we can introduce the more compact
notation for convenience:

(3.12)

(3.15)

Hence,

∂2φ
∂ y2 + p2φ = 0
∂2ψ
∂ y2 + q2ψ = 0
The general solution for the above system takes the form:

φ = A1 sin py + A2 cos py
ψ = B1 sin qy + B2 cos qy

(3.16)

(3.17)

where A1, A2, B1 and B2 are constants to be determined from the boundary conditions.

3.2.1 Symmetric solution

Symmetric solution implies that ux component of the displacement vector and shear stresses

are symmetric about the midplane across the thickness of the plate, namely

ux(x,−d) = ux(x, d)
uy(x,−d) = −uy(x, d)

τyx(x,−d) = −τyx(x, d)
τyy(x,−d) = τyy(x, d)

Symmetric boundary conditions also include traction free surfaces

τyx(x,−d) = −τyx(x, d) = 0
τyy(x,−d) = τyy(x, d) = 0

(3.18)

(3.19)

Using the general solution for potentials in Eq. (3.17) and formulas for displacements and stresses
from the Appendix A, Eq. (3.19) can be expressed as

−2iξ A2 sin pd + B1(ξ2 − q2) sin qd = 0

A2(ξ2 − q2) cos pd − 2iξB1 cos qd = 0

(3.20)

(3.21)

(3.22)

A non-trivial solution for the above linear system of equations exists if the determinant in Eq. (3.20)
vanishes:

(cid:77)S= (ξ2 − q2)2 sin qd cos pd + 4ξ2pq cos qd = 0
Rearranging Eq. (3.21) yields the dispersion relation for symmetric modes:

where p and q are given in Eq. (3.15).

tan pd
tan qd

= −(ξ2 − q2)2
4ξ2pq

95

3.2.2 Antisymmetric solution

Antisymmetric solution requires that displacements and stresses are antisymmetric with respect

to the midplane

ux(x,−d) = −ux(x, d)
uy(x,−d) = uy(x, d)

τyx(x,−h) = τyx(x, h)
τyy(x,−h) = −τyy(x, h)

The antisymmetric boundary conditions are the following

τyx(x,−d) = τyx(x, d) = 0
τyy(x,−d) = −τyy(x, d) = 0

(3.23)

(3.24)

Using the general solution for the potentials in Eq. (3.17) and formulas for the displacements and
stresses from the Appendix A, Eq. (3.24) can be expressed as

(3.25)

(3.26)

(3.27)

2iξ A1 cos pd + B2(ξ2 − q2) cos qd = 0

A1(ξ2 − q2) sin pd + 2iξB2 cos qd = 0
A non-trivial solution exists if determinant in Eq. (3.25) vanishes:

(cid:77)A= (ξ2 − q2)2 sin pd cos qd + 4ξ2pq cos qd sin qd = 0

Finally, we obtain Lamb wave equation for antisymmetric modes:

tan pd
tan qd

= − 4ξ2pq
(ξ2 − q2)2

It can be noticed that the right-hand side of Eq. (3.22) is reciprocal to that of Eq. (3.27).

3.2.3 Phase velocity and group velocity dispersion curves

It can be noticed that solutions of Rayleigh-Lamb equations in Eq. (3.22) and Eq. (3.27) define
the dispersion curves or the relationship between the phase velocity, cph and the actuation frequency,
ω. Since p and q also depend on ω, the phase velocity should be evaluated numerically at each
frequency step for a fixed value of a plate thickness 2h.

96

Figure 3.5: Phase velocity dispersion curves of 3-mm thick aluminum plate.

Figure 3.6: Group velocity dispersion curves of 3-mm thick aluminum plate.

cgr =

c2

c − f d ∂c
∂( f d)

(3.28)

The example of phase velocity dispersion curves is presented in Fig. 3.5. It follows that the solution
is not unique, and at high frequency-thickness products multiple symmetric and antisymmetric
modes exist in the plate. However, the knowledge of group velocity dispersion curves (Fig. 3.6)
can be considered even more important, since the group velocity, cgr determines how fast the
wavefront of each mode propagates. This enables one to calculate the Time-of-Flight (ToF) and
distance traveled by wave packets in the structure, which is essential for locating damage sites.
Group velocity dispersion curves can be obtained from the phase velocity data using Eq. (3.28).

97

3.3 Detection of guided waves with FBG and CFBG-FPI sensors

Fiber Bragg-grating (FBG) sensors are manufactured by inscribing a systematic variation of
refractive index into the core of the conventional optical fiber (see Fig. 3.7). Hence, an FBG is a
sandwich-like distributed reflector, which acts as an optical filter that transmits the entire spectrum
of the light source and reflects back the resonant Bragg wavelength, given by the following equation:

where n is the effective refractive index of the fiber core; and Λ is the period of Bragg-grating.

λB = 2nΛ

(3.29)

Figure 3.7: Operation principle of the fiber Bragg-grating sensor.

The sensor resolution is determined by the spectral bandwidth of the back-reflected radiation
that depends on the effective refractive index of the fiber core and Bragg-grating period. As
the strain inside the structure varies so does the spacing between the gratings, which results in a
shift of the Bragg wavelength. Hence, the strain response of the FBG arises from both the physical
elongation of the sensor and the change in effective fiber refractive index due to photoelastic effects.
Similarly, a thermal response is driven by the inherent thermal expansion of the fiber material and
the temperature dependence of the refractive index. The wavelength-encoded nature of the FBG

98

output provides a built-in self-referencing capability for the sensor. Since the wavelength is the
fundamental parameter, the output does not depend directly on the total light levels, losses in the
connecting fibers and couplers, or source power.

Figure 3.8: Principle of FBG wave division multiplexing.

Many FBG sensors in the same fiber can be interrogated using wave division multiplexing
(WDM). In this case, all FBGs have unique Bragg wavelengths, and their corresponding reflectance
spectra don’t overlap as shown in Fig. 3.8. The dynamic interrogator is tuned on each Bragg
wavelength in a round robin fashion to acquire all data.

Figure 3.9: Design of the Fabry-Perot interferometer based on a pair of chirped fiber Bragg-grating
sensors (CFBG-FPI).

Fabry-Perot (FP) cavities, which are realized by inscribing multiple FBGs in a single fiber,
have wide applications in optical fiber communication systems, optical fiber sensing systems and
photonic generation. The structure of Fabry-Perot interferometer based on chirped FBGs (CFBG-

99

FPI) is shown in Fig. 3.9. Two identical chirped FBGs of lengths LCFBG are cascaded with a
short offset LS between them [54]. Typically, CFBG sensors feature wider reflectance spectrum
than regular FBGs. Writing a pair of CFBGs in a sequence introduces approximately equally
spaced fringes to the resulting reflectance spectrum as shown in Fig. 3.10(a). Free spectral range
(FSR) of the fringes can be set by selecting the appropriate length, chirp rate and offset between
the CFBGs. Similar to regular FBGs, the spectrum of radiation reflected by the CFBG-FPI will
undergo wavelength shifts proportional to applied strain and/or temperature fields along the fiber.

Figure 3.10: (a) Spectrum of radiation reflected from a CFBG-FPI sensor; (b) approach for high-
resolution strain sensing by modulating the intensity of radiation back-reflected from CFBG-FPI.

Hence, a CFBG-FPI structure in the optical system can act as a filter that modulates the intensity
of radiation reflected from it as a function of external thermo-mechanical input [54]. This concept
is used in present work for dynamic detection of ultrasonic vibrations in aluminum plates. The
approach for strain sensing using the CFBG-FPI is illustrated in Fig. 3.10(b). Once the CFBG-FPI

100

sensor has been strategically deployed on the structure, its reflectance spectrum is measured with
Optical Spectrum Analyzer (OSA) to identify all notches. Then the tunable light source (TLS)
is set to output monochromatic radiation with center wavelength at the midpoint of one of the
edges of the sharpest notch. Applying strain to the CFBG-FPI will shift the position of the notch,
thus modulating the intensity of reflected radiation. Sharpness of the notch and its magnitude will
determine the sensitivity and linear range for GW detection.

Figure 3.11: Block diagram of the setup for GW detection using surface-mounted CFBG-FPI
sensors.

Fig. 3.11 shows a block diagram of the experimental setup based on a CFBG-FPI and laser-
intensity demodulation with smart feedback control for detection of ultrasonic signals under large
low-frequency background strains [54]. The TLS can be a low-cost semiconductor laser, such
as a distributed feedback laser diode or a discrete mode laser diode, whose wavelength is tuned
with high speed through current injection in a wavelength range slightly larger than the FSR of
the CFBG-FPI. The laser is locked to one of the spectral notches within its tuning range for GW
detection. Radiation from TLS propagates to CFBG-FPI through the single-mode fiber, polarization
controller (PC) and circulator. PC is required to manually adjust the state of polarization (SOP)
of incident radiation for getting the sharpest notches in the reflection spectrum of the CFBG-FPI
sensor. This adjustment is particularly useful in cases when CFBG-FPI is bonded to the structure
directly using tapes or adhesives, since adhesive bonding introduces deformation of the sensor prior
to GW detection. Radiation reflected from CFBF-FPI is channeled to the coupler C1, which splits

101

it in two parts. Most of the radiation power (≈ 95%) goes to the photodetector 1 (PD1), and a
small portion of it (≈ 5%) is sent to the photodetector 2 (PD2). Radiation registered by PD1 is
converted to voltage that is sampled by the data acquisition device (DAQ). Output of the PD2 is
fed to a feedback control module of the TLS. The external TLS controller is designed to account

Figure 3.12: Experimental setup for GW detection using the CFBG-FPI sensors.

for quasi-static background strains caused by structural loads or ambient temperature drifts causing
significant shifts of notches in the CFBG-FPI reflectance spectrum. Large background strains may
push out the operating point well beyond the limits of TLS tuning range. However, if the bandwidth
of TLS around the operating wavelength is wider than the FSR between the spectral fringes, other
spectral notches will enter this window, and the controller will re-lock the TLS on the new notch.
In this case, the sensitivity of the system to propagating GWs may change depending on the slope
and amplitude of the new notch.

Experimental setup for GW detection in a 3-mm thick aluminum plate using the CFBG-FPIs is
demonstrated in Fig. 3.12. Guided waves are excited in the plate with a 7-mm wide and 0.2-mm

102

thick round piezoelectric transducer made of PZT-5A material. The PZT crystal resonates at 300
kHz, and it is driven with a 5-cycle tone burst from DDS function generator. The amplitude of the
excitation signal is 20 Vpp. Three 1545 nm CFBG-FPI sensors were fabricated in three separate

Figure 3.13: Aluminum plate with CFBG-FPI sensors, piezoelectric transducer and surface-bonded
reflector: (a) drawing with exact dimensions; (b) photo of the test setup.

single-mode fibers using a 193 nm excimer laser and a linearly chirped phase mask with a chirp
rate of 2 nm/cm. Each CFBG-FPI sensor was 1.1 cm long as it consisted of two 5-mm CFBGs
separated by 1-mm gap. CFBG-FPIs were bonded to the surface of the plate directly using the
Scotch tape in the locations shown in Fig. 3.13. Since the system was not wave division multiplexed
(WDM), CFBG-FPI sensors were connected to the circulator via the APC connectors one-by-one
to measure propagating GWs. Ultrasonic signals registered by the PD1 were amplified with a
broadband 20-dB pre-amplifier from Physical Acoustics. Initially, three baseline GW signals were
acquired by CFBG-FPI sensors, and after that an external reflector was bonded to the plate using the
Krautkrammer acoustic gel as illustrated in Fig. 3.13(b). The measurement process was repeated
in the presence of simulated damage. GW signals from CFBG-FPI sensor 3 are shown in Fig. 3.14.
The signals represent two single measurements that were not averaged in time, but were only passed
through a zero-phase band-pass filter with cut-off frequencies of 100 kHz and 500kHz. Actuation
waveform shown in Fig. 3.14 is not filtered.

103

Figure 3.14: Guided waves registered with the CFBG-FPI sensor 3.

Obtained results demonstrate that two wave packets are clearly visible. The first wave packet
with ToF around 38 µs corresponds to the fundamental S0 mode, and the second wave packet with
ToF of approximately 58 µs corresponds to the A0 mode in the 3-mm thick plate. The group
velocities of S0 and A0 modes agree well with the dispersion curves from Fig. 3.6. The S0 wave
packet resembles the excitation signal better than the A0 wave packet, since the S0 mode is less
dispersive around 300 kHz. At the same time, the A0 mode is more sensitive to a glued reflector.
3.4 Delay-and-Sum diagnostic imaging

In this chapter, the delay-and-sum (DAS) algorithm was used for data fusion from multiple
guided wave paths [56]. The first step of the DAS imaging is computation of the wave scatter from
damage. This task is accomplished by subtracting the baseline measurement from the measurement
obtained after introduction of structural damage:

ˆri j = si j(t) − bi j(t)

(3.30)

In Eq. (3.30), it is assumed that in a general case, the sensor system may have multiple GW
transmitters and receivers. Hence, i denotes the index of the transmitting PZT; and j denotes the
index of the receiving CFBG-FPI sensor; bi j are the baseline signals, and si j are the GW signals
in the damaged state of the structure.

104

The envelope of the residual signal due to damage is defined as

ri j = | ˆra

i j|= | ˆri j + jH(ˆri j)|,

(3.31)

where ˆra
i j is the analytic signal, and H(ˆri j) is the Hilbert transform. In the next step, the energies
of the computed residual signals are mapped onto each point on the image. The arrival time of the
single mode wave packet traveling from the transmitting PZT at (xi; yi) to the image pixel (x; y)
and on to the receiver at (xj; yj) can be calculated as
(xi − x)2 + (yi − y)2 +
cgr

(xj − x)2 + (yj − y)2

ti j(x, y) =

(cid:113)

(cid:113)

(3.32)

,

where cgr is the group velocity of the selected GW mode. Assuming there are P sensors in the

P!

2!(P−2)! unique actuator-sensor pairs, envelopes of residuals computed in
Eq. (3.31) are windowed using the corresponding time-delays tm(x; y) and are averaged over all
pairs:

2

(cid:16)

(cid:17)

R(t; x, y) =

rmw

t − tm(x, y)

,

(3.33)

array, and M =(cid:169)(cid:173)(cid:173)(cid:171)P

(cid:170)(cid:174)(cid:174)(cid:172) =

M(cid:88)

m=1

1
M

(cid:16)

(cid:90)T

0

where w(t) is a Gaussian window function, whose time support T is equal to the time support of
the actuation signal. Finally, the intensity of the diagnostic DAS image at a pixel (x, y) is given by
the energy of R(t; x, y):

I(x, y) =

R(t; x, y)

dt

(3.34)

(cid:17)2

Note that Eq. (3.34) defines a family of concentric ellipses around the actuator-sensor pair. Such
approach is best suited for diagnostic imaging of structures with circular PZT elements that have
uniform sensitivity to all directions of GW propagation. However, the algorithm will need to be
modified in the future work to account for unidirectional sensitivity of CFBG-FPI along their length
only.

Fig. 3.15 illustrates the DAS image of the plate with surface bonded reflector (see Fig. 3.13).
The presence of reflector is better captured by the the CFBG-FPI-3 rather then CFBG-FPI-1 and
CFBG-FPI-2. This happens because the scatter from damage propagates at angles to the sensors

105

Figure 3.15: DAS image of aluminum plate with the surface-bonded reflector. Location of PZT
actuator is marked as a black dot, CFBG-FPI sensors are marked as black squares, and location of
damage is marked by a white circle with a cross.

1 and 2, and FBG-based fiber optic receivers provide the highest sensitivity to GWs along their
length. Directional sensitivity of CFBG-FPIs should be incorporated into the DAS algorithm
for more accurate damage localization. Another way to improve damage detection is to increase
the number of pick-up sensors. It should be also noted that multiple CFBG-FPI sensors can be
multiplexed in a single fiber using the WDM technique, and CFBG-FPI sensors may not be directly
bonded to the structure. In general, it suffices to bond any open section of the optical fiber to the
structure, and GWs will leak into it propagating to CFBG-FPI receivers through the fiber core and
cladding.

106

3.5 Conclusions

Chapter III presented a hybrid approach for acousto-optic SHM of materials and structures.
Online monitoring of structural health is accomplished by using surface-bonded or embedded
arrays of optical fibers with strategic ability to sense ultrasonic guided waves. In this case, chirped
Bragg-gratings inscribed in fiber core serve as receivers of ultrasonic signals. Pairs of CFBGs
form Fabry-Perot cavities, whose spectra of back-reflected radiation have sharp transitions. Laser
source is tuned to output radiation with a wavelength centered around these transitions. Hence,
propagating UT waves shift the spectra of CFBG-FPI, which in turn results in modulation of
radiation reflected by such optical sensor. In contrast to OFDR or local strain sensing using regular
FBGs, hybrid GW/CFBG-FPI approach allows for detecting structural imperfections away from
the fiber as guided wave reflections carry all necessary information instead. Proposed acousto-
optic SHM technique was successfully validated on aluminum plates with damage simulated as
surface-bonded reflector. Three CFBG-FPI sensors were used for receiving S0 and A0 GW modes
generated by the piezoelectric transducer. Measurement in defect-free and damaged states were
acquired by all CFBG-FPIs to generate a diagnostic image of the plate using the DAS algorithm.
Since the damaged area was correctly highlighted, obtained results demonstrated the feasibility of
the proposed hybrid GW/CFBG-FPI approach for SHM of metal and composite structures.

107

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