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dissertation entitled

IMAGE PROCESSING ENHANCEMENTS FOR SCANNING
PROBE RECOGNITION MICROSCOPY

presented by

YUAN FAN

has been accepted towards fulﬁllment
of the requirements for the

Ph.D. degree in Electrical Engineering

 

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IMAGE PROCESSING ENHANCEMENTS FOR SCANNING PROBE
RECOGNITION MICROSCOPY

By

Yuan Fan

A DISSERTATION

Submitted to
Michigan State University
In partial fulﬁllment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Electrical Engineering

2009

ABSTRACT

IMAGE PROCESSING ENHANCEMENTS FOR SCANNING PROBE
RECOGNITION MICROSCOPY

By
Yuan Fan

The family of scanning probe microscopy (SPM) techniques has revolutionized
studies of micro and nano objects. Nanobiology is one ﬁeld which is being dramatically
impacted by the newly available direct information provided by SPM techniques.
Although SPM has great potential in nanobiology, it is important to realize that it also has
challenges: image artifacts; slow scanning speed; difﬁculty in efﬁcient recognition of the
region of interest; optimization of scanning parameters. A new mode of SPM operation,
Scanning Probe Recognition Microscopy (SPRM), has been developed by our group in
partnership with Veeco Instruments Inc. Scanning Probe Recognition Microscopy is a new
scanning probe microscopy technique which allows us to adaptively track individual
structures using a ﬁne resolution scan restricted to the region of interest, and providing
statistically signiﬁcant data for multiple properties. Two implementation methods, an off-
line processing scheme and an on-line dynamically adaptive multi-resolution scanning
mode, are developed and presented in this thesis.

A second challenge in AF M data is the distortion of the measured image due to tip—
sample interaction which is signiﬁcant in nanoscale metrology. Two approaches for
deconvolution are investigated and applied for the ﬁrst time in the estimation of true
topological shape of nanoscale features from the measured height data. The ﬁrst approach
is based on morphological image processing and uses the geometrical tip and sample

information. The second approach is a physics based deconvolution method and involves

the modeling and characterization of tip/ sample interaction forces. Initial results based on
modeling only Van der Waals component of the over all tip-sample interaction, show the
feasibility of the method for determining true topographic shapes of the sample.

SPRM was developed within an application framework for two reasons. One was
to challenge the instrument development with real versus ideal problems. Another reason
was to immediately use the new SPRM capability to investigate signiﬁcant problems.
Tissue scaffolds built from electrospun carbon nanoﬁbers whose purpose is bridging
injuries in damaged spinal cords were characterized in terms of properties that inﬂuence
neural cell growth and attachment, such as surface roughness and elasticity. The results of
SPRM investigations of the surface roughness and elasticity of tissue scaffolds are
presented. SPRM provided the ﬁrst capability to acquire force curves directly along an
individual nanoﬁber under optimal conditions where the tip and hence applied force is
exactly normal to the curved nanoﬁber surface. Statistical methods based on histograms
were developed to analyze the surface roughness and elasticity properties of the tissue
scaffold nanoﬁbers. This is the ﬁrst time that statistically meaningful information has been
extracted along individual nanoﬁbers using an automatic procedure that maintains

uniformity of experimental conditions.

To my beloved wife and parents

iv

Acknowledgement

I would like to express my sincere gratitude to Dr. Lalita Udpa and Dr. Virginia
Ayres for the continuous guidance and encouragement they has provided throughout the
present study. Particularly, my very special thanks to Dr. Lalita Udpa, who gave me the
opportunity to pursue the Ph.D degree. I am grateful for her intellectual and ﬁnancial
support, inspiration, freedom of work, invaluable advice and above all trust that gave me
the conﬁdence and guided me to take the right decisions throughout my graduate studies. I
also sincerely thank my coadvisor Dr. Virginia Ayres for her intellectual guidance,
discussions and encouragement in many aspects of my graduate studies. She taught me the
Scanning Probe Microscopy and its application. I am glad to work with my advisors and I
have learned science and many invaluable moral values working with them.

I would like to thank my committee members Dr. Satish Udpa and Dr. S.D.Mahanti
for taking the time to serve on my committee and for providing invaluable comments and
suggestions to enhance the quality of this dissertation.

I would like to thank Ms. Qian Chen for the intellectual discussions and dedicated
team work on SPRM experiments. My special thanks to my friend Dr. Zhiwei Zeng for the
help on the numerical model computation. I would like to thank Shiva Arun Kumar for the
intellectual discussions and team work on geometric AF M image deconvolution algorithm.
I would also like to thank Ms. Xin Liu for the intellectual discussions on inverse problem.

I am thankful to Benjamin W. Jacobs for providing nano circuit sample.

We collaborated with Dr. Sally Meiners of UMDNJ-Robert Wood Johnson
Medical School in application of SPRM in tissue scaffolds. I would like to express my
gratitude to the collaborators for providing tissue scaffold sample and helpful discussion.

Once again I thank each person related to this work directly or indirectly for the
successful completion of the dissertation.

Finally, I would like to thank my wife Jun Chen and my parents, Peilian Fan and
Yuede Shen, for their unconditional support, love and caring. To them, I dedicate this

dissertation.

vi

TABLE OF CONTENTS

LIST OF FIGURES .......................................................................................................... IX
CHAPTER 1 INTRODUCTION ........................................................................................ 1
1.1 Motivation ........................................................................................................... 1
1.2 Overview of Scanning Probe Microscope Family .............................................. l
1.3 SPM Family ........................................................................................................ 3
1.4 Atomic Force Microscopy .................................................................................. 5
1.4.1 AFM System ...................................................................................................... 6
1.4.2 Imaging Modes ................................................................................................ 10

1.5 Applications of AF M ........................................................................................ 13
1.6 Summary of the Later Chapters ........................................................................ 15
CHAPTER 2 IMAGE PROCESSING CHALLENGES IN AFM .................................... 17
2.1 Analysis Challenge ................................................................................................. 17
2.1.1 Imaging Artifacts ............................................................................................. 17
2.1.2 Region of Interest Recognition ........................................................................ 19

2.2 Implementation Challenge ...................................................................................... 21
2.2.1 Scan Speed ....................................................................................................... 21
2.2.2 Scanning Parameters Optimization .................................................................. 24

2.3 Challenges and Opportunities for Data Fusion ....................................................... 25
CHAPTER 3 DEVELOPMENT OF SPRM ..................................................................... 27
3.1 Off-line Processing Mode ....................................................................................... 29
3.1.1 Multi Scale Analysis ........................................................................................ 31
3.1.2 Skeleton analysis .............................................................................................. 32

3.2 Online Scanning Mode ........................................................................................... 39
3.2.1 Online Scan Plan Generation ........................................................................... 39
3.2.2 Fine Resolution Scan Plan ............................................................................... 43

3.3 Real Time Display .................................................................................................. 47

CHAPTER 4 IMAGE RECONSTRUCTION BASED ON GEOMETRIC

DECONVOLUTION ........................................................................................................ 49
4.1 Deconvolution in Atomic Force Microscopy ......................................................... 50
4.2 Morphological Processing Technique for Surface Reconstruction ........................ 51
4.3 Legendre Transform Technique for Sample Surface Reconstruction ..................... 55
4.4 Blind Tip Estimation ............................................................................................... 60
4.5 Example Applications of Deconvolution for Nanobiology .................................... 62
4.6 Conclusrons ......................... 65

CHAPTER 5 DECONVOLUTION BASED ON THE TIP-SAMPLE INTERACTION
FORCE MODEL .............................................................................................................. 67

vii

5.1 Summary of Tip Sample Interaction ....................................................................... 67

5.2 Van der Waals Force Model ................................................................................... 71
5.2.1 Model Equation ................................................................................................ 74
5.2.2 Parameter Estimation and Model Validation ................................................... 77

5.3 Numerical Result of Van der Waals (VDW) Force Model ..................................... 82
5.3.1 Surface Discretization ...................................................................................... 83
5.3.2 Numerical Model Validation ........................................................................... 89

5.4 Model Based Deconvolution of AFM Image .......................................................... 93

5.5 Implementation Results .......................................................................................... 95

CHAPTER 6 APPLICATION OF SPRM TO TISSUE ENGINEERING ..................... 101

6.1 Introduction ........................................................................................................... 101

6.2 Materials and Methods .......................................................................................... 103

6.3 Surface Roughness ................................................................................................ 104

6.4 Elasticity ............................................................................................................... 111

6.5 Discussion ............................................................................................................. 124

CHAPTER 7 SUMMARY OF RESULTS AND FUTURE WORK .............................. 126
REFERENCE: ................................................................................................................. 130

viii

List of Figures

Figure 1.1 Block diagram of the SPM ................................................................................ 2
Figure 1.2 Lateral Force Microsc0py .................................................................................. 4
Figure 1.3 Magnetic Force Microscopy .............................................................................. 4
Figure 1.4 Schematic of the AF M system .......................................................................... 7
Figure 1.5 Tip-sample interaction force VS. distance ........................................................ 8
Figure 1.6 Quad-Photodiode orientation ............................................................................. 8
Figure 1.7 Schematic of FM-AFM ................................................................................... 13

Figure 2.1 Example of the dilation artifact (Solid line: experimental proﬁle; Dash line:
theoretical proﬁle) ............................................................................................................. 18

Figure 2.2 AFM image of biological sample with two different types of ROI. AF M
images by Y. Fan and Q. Chen. Cell and tissue samples from S. Meiners, college of

Medicine UMDNJ ............................................................................................................. 20
Figure 2.3 Typical scanner piezo tube and X-Y—Z electrical conﬁgurations [59] ............ 22
Figure 2.4 Schematic of traditional raster scan pattern on a tissue scaffold sample ........ 23
Figure 2.5 AFM image of DNA structure, Courtesy J. Reed, UCLA ............................... 23
Figure 3.1 Block diagram of the dynamic scanning system. ............................................ 27
Figure 3.2 Signal Access Module [60] ............................................................................ 28
Figure 3.3 AFM image of DNA molecules (Image size: 0.5x0.5 umz) [61] .................... 30
Figure 3.4 Result of ofﬂine processing [62] ..................................................................... 32
Figure 3.5 AF M image of DNA structure, Courtesy J. Reed, UCLA ............................... 33
Figure 3.6 Flow chart of the Contour-Pruned skeletonization algorithm ......................... 35
Figure 3.7 Object and inscribed circle .............................................................................. 36

ix

Figure 3.8 Skeletonization results: (a) raw DNA image; (b) binary image; (c) radius of
the maximum inscribed circle; ((1) image of length of segmented perimeter; (e) skeleton

image; (f) skeleton image shown in original DNA image. ............................................... 38
Figure 3.9 Skeleton of the DNA image (a) without pruning (b) with pruning ................. 39
Figure 3.10 Online multi-ROI scan plan ﬂowchart .......................................................... 41
Figure 3.11 Schematic of single ROI scanning mode ....................................................... 42

Figure 3.12 Fine scan without prediction (a) Conventional AFM image of the nanoﬁber
(b) Coarse Scan picks up the ﬁrst nanoﬁber; (c) Fine scan only on the ﬁrst nanoﬁber ((1)
Finish the ﬁne scan and retum to coarse scan to ﬁnd another region of interest; (e) Coarse
Scan picks up the second nanoﬁber; (1) Fine scan only on the second nanoﬁber (g) Finish
the high resolution ﬁne scan only on the second nanoﬁber .............................................. 43

Figure 3.13 AF M image of the tissue scaffold sample with cross section area. .............. 44

Figure 3.14 SPRM scan plan of intersecting tissue scaffold sample. 1(a)-(d) shows SPRM
scan without prediction; 2(a)-(d) shows corresponding SPRM scan with prediction ...... 46

Figure 3.15 SPRM scan image of the nanoﬁber. (a) Conventional AFM image of the
nanoﬁber (b) Coarse Scan picks up the ﬁrst nanoﬁber; (c) Finish high resolution ﬁne scan
only on the ﬁrst nanoﬁber and return to coarse scan to ﬁnd another region of interest; ((1)
Coarse Scan picks up the second nanoﬁber; (e) Finish the high resolution ﬁne scan only
on the second nanoﬁber and return to coarse scan to ﬁnd another region of interest; (1)
Coarse Scan picks up the third nanoﬁber; (g) Finish the high resolution ﬁne scan only on
the third nanoﬁber ............................................................................................................. 48

Figure 4.1 Morphological dilation Model of AF M image data with sharp surface features

( Note : The tip surface is reﬂected about its origin in accordance with equation (4.3)) [73,
74] ..................................................................................................................................... 52

Figure 4.2 Surface reconstruction using grayscale morphological erosion [74]. ............ 53

Figure 4.3 Results of Morphological Processing (a) True (known) Specimen Surface (b)
Simulated AFM Image (c) Reconstructed Specimen Surface (d) Proﬁle Comparison 55

Figure 4.4 A schematic of tip surface, sample surface and image surface [76] .............. 56

Figure 4.5 Relationship between the Legendre Transform of the sample surface (black
bold), image surface (dotted) and tip surface [73] ............................................................ 59

Figure 4.6 Application of the Legendre transform to an artiﬁcial AF M height image(a)
True surface image of a cylindrical structure of500nm diameter and 800nm high. (b)

Simulated AF M image using 20nm parabolic tip. (0) Reconstructed image. ((1) Proﬁles
of measured and reconstructed images [73] ...................................................................... 59

Figure 4.7 Blind tip estimation results at different iterations (a) initial guess,(b) lst
iteration,(c) 2nd iteration & ((1) ﬁnal estimate of the tip shape aﬁer convergence [73] ..... 62

Figure 4.8 AFM images of NRK2 cell on polymer tissue scaffolding (a) top view and (b)
surface plot. Two ambiguous features are circled (l) the actual width of the scaffold

ﬁbers and (2) a sharp feature on the cell surface [73] ....................................................... 63
Figure 4.9 Comparison of line scans in (a) Regionl and (b) Region 2 of Figure 4.8

showing deconvolution of ﬁber width [73]. ..................................................................... 64
Figure 5.1 Schematic of the liner, time invariant system ................................................. 67
Figure 5.2 Force curve. ..................................................................................................... 68

Figure 5.3 Integration of the interaction force between two arbitrarily shaped bodies 72

Figure 5.4 Schematic of the tip model. R is the radius of the spherical cap. a is the angle
include the spherical cap, [3 is the cone angle, 20 is the distance between the tip end and

sample. .............................................................................................................................. 74
Figure 5.5 Schematic of the spherical cap ........................................................................ 75
Figure 5.6 Schematic of the tnmcated cone ...................................................................... 76
Figure 5.7 schematic of the tip and sample position in z direction ................................... 78
Figure 5.8 Ten experimental force curves in same sample position. ................................ 80

Figure 5.9 A scheme showing the estimation of the unknown parameters and comparison

of the theoretical force curve with the experimental data ................................................. 81
Figure 5.10 Schema of Van der Waals force calculation .................................................. 82
Figure 5.11 Discretization of spherical cap. ..................................................................... 84
Figure 5.12 (a) Schematic of elements in spherical cap (b) Cross section of spherical cap

in x-z plane (c) Cross section of spherical cap in x-y plane. ............................................ 85
Figure 5.13 Mesh in truncated cone .................................................................................. 87

Figure 5.14 (a) Schematic of the mesh in truncated cone (b) Cross section of truncated
cone in x-z plane (c) Cross section of truncated cone in x-y plane. ................................. 88

xi

Figure 5.15. Mesh of the tip and sample .......................................................................... 90

Figure 5.16 Force vs. Size of integration area in sample surface ..................................... 91
Figure 5.17 Force vs. Size of integration area in tip surface ............................................ 92
Figure 5.18 Force vs. tip-sample distance ........................................................................ 93
Figure 5.19 Schematic of AF M image deconvolution using force model ........................ 94
Figure 5.20 Procedure of AFM image deconvolution using force model. ....................... 94
Figure 5.21 Schematic of the tip and sample surface ....................................................... 96
Figure 5.22 Mesh of the sample surface ........................................................................... 96
Figure 5.23 Line scan of the scan image and initial guess image ..................................... 97
Figure 5.24 Result of the image deconvolution using VDW force model ........................ 98
Figure 5.25 Schematic of the tip and sample .................................................................... 99
Figure 5.26 Result of the image deconvolution using VDW force model ...................... 100

Figure 6.1 (a) AP M image of electrospun carbon nanoﬁber tissue scaffold. The scan area
is 5 square microns and the z-height projection is 1500 nanometers. (b) SEM image of
electrospun carbon nanoﬁber tissue scaffold. The scan area is 20 square microns, images
by Q. Chen and Y. Fan [70]. ........................................................................................... 106

Figure 6.2 SPRM scan image of the nanoﬁber. (a) Conventional AF M image of the
nanoﬁbcr (b) Coarse Scan picks up the ﬁrst nanoﬁber; (c) Finish high resolution ﬁne scan
only on the ﬁrst nanoﬁber and return to coarse scan to ﬁnd another region of interest; (d)
Coarse Scan picks up the second nanoﬁber; (e) Finish the high resolution ﬁne scan only
on the second nanoﬁber and return to coarse scan to ﬁnd another region of interest; (I)
Coarse Scan picks up the third nanoﬁber; (g) Finish the high resolution ﬁne scan only on

the third nanoﬁber. Images by Y. Fan and Q. Chen [109] .............................................. 107
Figure 6.3 Circle ﬁt based on Kasa method [70] ............................................................ 108
Figure 6.4 (a) Characteristic tip-dilation artifacts (b) The cross section of a real AF M

nano ﬁber image and the best ﬁt circle [70] ................................................................... 109
Figure 6.5 Surface roughness map along individual ﬁber [109] .................................... 110
Figure 6.6 Histogram of surface roughness map [109] ................................................... l 11

xii

Figure 6.7 Approach force curve and corresponding tip sample distance ...................... 113

Figure 6.8 Traditional AF M force volume image ........................................................... 114
Figure 6.9 (a) Tissue scaffold surface the tip contact point (b) 6 points were acquired

along the individual nanoﬁber ........................................................................................ 115
Figure 6.10 SPRM force curve signal timing waveform ................................................ 117
Figure 6.11 Force curve collected by the second PC ...................................................... 117
Figure 6.12 Approace force curve after average ﬁlter .................................................... 118
Figure 6.13 Force-distance curve and corresponding force-distance curve ................... 119
Figure 6.14 Force curve in contact region (a) and corresponding ﬁtting result (b) ........ 123
Figure 6.15 Box plot of the estimated Young’s modulus ............................................... 124

xiii

Chapter 1 Introduction

1.1 Motivation

The family of scanning probe microscopy (SPM) techniques has revolutionized
studies of nanostructures. The key capability of scanning probe microscopy is that,
through a controlled combination of feedback loops, detectors and piezoelectric actuation,
it enables direct investigations of micron, nanometer to atomic scale phenomena. One
important emerging area of application for SPM is in nanobiology. The main advantages
of SPM in nanobiology are that it requires minimal sample preparation, and reaches
macromolecular resolution under near life;like conditions. Although SPM has great
potential in nanobiology, it is important to realize that it also has some drawbacks. These
challenges include: image artifacts; slow scanning speed; difficulty in efﬁcient
recognition of the region of interest; optimization of scanning parameters. Furthermore,
from the different types of information provided by the SPM it would be desirable to
construct a composite picture representative of a living specimen’s perception of its
environment. These challenges are addressed in this thesis via development and
application of appropriate signal processing and pattern recognition algorithms which are
integrated with SPM to build a system that we refer to as the scanning probe recognition

microscope (SPRM).

1.2 Overview of Scanning Probe Microscope Family

The farrrily of scanning probe microscopy techniques started with invention of the

scanning tunneling microscope (STM) in 1981 [1], which offered the capability for high

resolution imaging of surfaces of conducting and semiconducting materials [2, 3]. The
invention of STM was considered so signiﬁcant that it was awarded the Nobel Price in
Physics in 1986, one of only four such prizes given for the development of an instrument.
It received a signiﬁcant extension in 1986 with the invention of the atomic force
microscopy [4] which brought the power of the SPM analysis to non-conductive samples
in air and liquid environments [5]. The SPM family has since made a dramatic impact in
many ﬁelds such as materials science, semiconductor physics, biology, electrochemistry,
biochemistry, organic chemistry, catalysis, micromechanics, and medical implant
technology etc [6]. The SPM provides three-dimensional, real-space images of surfaces at
nanoscale spatial resolution. Images are based on the local inter-atomic forces of

interaction between a small probe tip and surface features.

 

Microscope
Probe
'— -— —- Detector

Piezo Controller
I z
¢———-»

va

Vibration Isolation ‘

Figure 1.1 shows a block diagram of a Scanning Probe Microscope. Instead of using light

 

Sample

 

‘I

 

 

 

 

 

 

 

 

Figure 1.1 Block diagram of the SPM

or focused electrons, scanning probe microscopes use a tiny needle like probe attached to
a cantilever that is scanned across the specimen surface. The interactions between probe
and sample are recorded and processed to form an image. Scanning probe microscopes
can visualize a sample surface, in micro/nano/atomic resolution in three dimensions and

generate images which are spatial maps of sample properties such as thermal conductivity,

ﬁ‘iction, hardness, elasticity, magnetic permeability and chemical binding etc. The
operational environment of SPM can be ambient air, liquid or vacuum. Each SPM
technique (STM, AF M etc) includes a family of microscopy modalities i.e. constant
current imaging in addition to constant height imaging. Different modalities of SPM
measurements provide different types of information about physical surface, topography,

electronic structure, electric or magnetic ﬁelds and many other local properties.

1.3 SPM Family

Since its invention in 1981, SPM has developed intoa family of instruments. Different
modalities of SPM measurements provide different types of information about physical
surface, topography, electronic structure, electric or magnetic ﬁelds and other local
properties as described below:

Scanning Tunneling Microscopy

Scanning tunneling microscopy (STM) monitors the ttmneling current between the tip
and sample. As the tip scans the sample surface, it encounters sample features of different
heights, resulting in corresponding changes in the tunneling current. However STM has
some limitations, most signiﬁcant of which is that the surface of both the tip and sample
must be good conductors. This severely limits the type of materials that can be studied.
Atomic Force Microscopy

The atomic force microsc0py (AF M) [4] initially developed to overcome the
limitations of the STM in imaging the non-conducting materials. AF M operates by
scanning a tip attached to the end of a cantilever across the sample surface while

monitoring the change in cantilever deﬂection with a split photodiode detector.

Lateral Force Microscopy

Lateral force microscopy (LF M) [7-9] measures lateral deﬂections of the cantilever
that arise from shear/friction forces on the cantilever normal to the z direction. LF M
studies are useful for imaging variations in surface friction that can arise from

inhomogeneity in surface material.

Scan
Direction
Sample I g g I
Horizontal I I I I

Deﬂection . . .
Dr.“ Hugh fnctlonal
,¢.‘.¢ areas

Figure 1.2 Lateral Force Microscopy
Magnetic Force Microscopy
Magnetic Force Microscopy (MFM) [10] images the spatial variation of magnetic
forces on a sample surface. For MFM, the tip is coated with a ferromagnetic thin ﬁlm.
The system operates in non-contact mode, detecting changes in the resonant frequency of
the cantilever induced by the magnetic ﬁeld/s depending on tip-sample separation. MFM
can be used to image naturally occurring and deliberately written domain structures in

magnetic materials.

 

Scan
Direction
Magnetically
coated tip

S<'a""r>'eI:-+-+ ILLLI .l. I‘m-*1

Magnetic I
Force ———I___I—_

Figure 1.3 Magnetic Force Microscopy

 

 

Electric Force Microscopy

Electric force microscopy (EFM) [1 1-13] applies a voltage between the tip and the
sample while the cantilever hovers above the surface, not touching it. The cantilever
deﬂects when it scans over static charges. EFM plots the locally charged domains of the
sample surface. EF M is used to study the spatial variation of surface charge carrier
density.

Scanning Capacitance Microscopy

Scanning capacitance microscopy (SCM) [14-16] images spatial variations in
capacitance. The cantilever operates in non-contact, constant-height mode. A special
circuit monitors the capacitance between the tip and sample. SCM studies can image
variations in the thickness of a dielectric material on a semiconductor substrate. SCM can
also be used to visualize sub-surface charge carrier distributions.

Other forms of SPM include Surface Potential Microscopy [17-19], Electrochemical
STM & AFM [20], Scanning Thermal Microscopy [21, 22], Photon Scanning Tunneling
Microscopy [23] and Near-ﬁeld Scanning Optical Microscopy [24] etc. This thesis
focuses on the application of one SPM technique, namely, Atomic Force Microscopy

(AFM).

1.4 Atomic Force Microscopy

The principle of STM makes it not suitable for imaging largely nonconductive
biological samples, and this led to the development of the AF M for nanbiological
research. Because of its ability to provide active and high resolution probing of
specimens with minimal sample preparation and under nearly lifelike conditions, the
potential of AF M for use in investigating minimally conductive biological surfaces was

immediately recognized.

A brief description of the operating principles of AF M is given in this section. More
detailed information related to instrumental aspects of the AF M can be found in several
excellent reviews [25, 26].

In an Atomic Force Microscope, a minute tip is mounted at the end of a ﬂexible
micro-cantilever and is maintained in gentle ‘contact’ with the sample surface. As
investigated within this thesis, ‘contact’ is really a precise summation of all possible
Coulomb interactions between the tip and the sample. When the term ‘contact’ is used in
this thesis, the more precise summation tip-sample interaction force is implied. The tip
scans the sample in a raster fashion. The tip movement is performed with sub-angstrom
accuracy by a piezoelectric actuator. AF M is capable of generating 3D images of surface
topography with nanometer resolutions. It can operate in vacuum, ambient air and liquid.
With the tip in direct contact with a biological specimen, AF M offers insight into cellular
and sub-cellular features. With its sensitivity down to tens of pico-newtons, AF M can

also make nano mechanical measurements of elasticity [27].

1.4.1 AFM System

Figure 1.4 shows a schematic representation of the different components in an AF M.

 

 

 

 

 

 

 

   

Control Display

Piezo drive
Monitor , Monitor

signal

 

 

 

 

 

 

 

-__1 __

____:;7 _____

Computer

System
Vibration Isolation

Figure 1.4 Schematic of the AFM system

 

A generic AFM comprises the following components: scanning system; probe system;
sensor system; vibration isolation; controller; computer system.

The AF M measures the interaction force between the sample and a very sharp tip
which is attached to a spring cantilever typically micro-fabricated from silicon or silicon
nitride with length of the cantilever ranging from several microns to hundreds of microns.
When the cantilever tip is brought close to the sample surface, the interaction force
between the tip and sample surface causes the cantilever to bend, or deﬂect. Different
types of tip sample interaction force can be measured depending on the distance between
the tip and sample as shown in Figure 1.5. When the tip is far away the sample surface
(>several tens of nanometers), long-range attractive interactions, such as the electric and
magnetic forces, may be the main source of the tip-sample interaction. When the tip-
sample distance is one to several tens of nanometers, the mid-range attractive force, Van
der Waals force, usually dominate the tip-sample interaction. As the tip is brought close
to ‘contact’ the sample surface at about lnm, the short-range ion-ion repulsive force

dominates the tip sample interactions.

Repulslve
Force +

Ti p-sample distance (nm)
I

    

100.0
Attractive

Force -

 

Figure 1.5 Tip-sample interaction force VS. distance
A laser beam shines on and reﬂects off the back of the cantilever onto a quad-
photodiode to measure the cantilever deﬂection both in vertical and lateral direction.

Figure 1.6 shows the schematic of a quad-photodiode.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

,
I I
<
S
B _.
A s.
o.
(D
a
c D g
g.
l I
,
Lateral deﬂection

 

 

V V

Figure 1.6 Quad-Photodiode orientation

The vertical deﬂection is calculated as:

_(A+B)—(C+D)

 

 

- 1.1
v A+B+C+D ( )
The lateral deﬂection is calculated as:
D : (A+C)—(B+D) (1.2)

A+B+C+D

The sample is mounted on the top of a piezoelectric scanner that provides sub-
angstrom motion increments in the lateral (x, y) and vertical (2) directions.

A controller provides the interface between the computer, sensor system and scanning
system. The controller converts the photodiode output analog voltage signal to digital
signal and sends it to the computer. The controller also generates the voltage drive signal
for the piezoelectric scanner to control the sample movement in all directions. In the x
and y direction the piezo drive signal may be generated by an open loop control circuit
according to the scan command sent by computer, while the z directional drive signal is
generated by a proportional integral (PI) close loop controller. The 2 feedback loop can
maintains a speciﬁc quantity, such as force on the tip, amplitude of tip oscillation or
frequency of tip oscillation, at a constant user speciﬁed value by changing the z piezo
voltage drive signal which moves the sample up or down.

Mechanical vibrations are a large component of the system noise, and it is a major
challenge to reduce the vibration noise while maintaining the system sensitivity down to
tens of pico-newtons. These vibrations can originate from the building, the chamber or
the table on which the microscope sits. To achieve the highest resolution, the microscope
must be vibrationally isolated from its surroundings. The low frequency vibration mainly
comes from the building. An effective way to damp vibration is to suspend the

microscope on long tension wires. This can be accomplished by suspending a massive

table from the ceiling by cords. The length of the cord, the mass of the table, and the
spring constant of the cords can be varied to achieve maximum attenuation at the
frequency of concern. A second approach to damping low frequency vibration is to
levitate the system on air cushioned feet. In our lab, the AF M system is put in a mass
table as an effective but simple way for isolating AF Ms from ﬂoor vibrations and from
acoustic vibration sources, while the STM system is isolated using tripod based
suspension mount.

A computer drives the scanner system, acquires, processes, displays and analyzes the
data produced. The computer also provides a user interface for operator to set scan
parameters.

In this research, the AF M used is Digital Instrument’s Multirnode Nanoscope Illa.

1.4.2 Imaging Modes

The AF M works in three different imaging modalities or modes. These are contact
mode; tapping mode; non-contact mode.

Contact Mode:

The ﬁrst imaging mode that was developed is the contact mode. Contact mode AFM
operates by scanning a tip attached to the end of a cantilever across the sample surface
while monitoring the change in cantilever deﬂection with a split photodiode detector.
During scanning, in ambient air which is the easiest and most commonly used scample
preparations, the tip contacts the surface through the humidity ﬂuid layer on the sample
surface. In 2 direction, a feedback loop maintains a constant cantilever deﬂection, to user

“set-point” deﬂection value, by moving the scanner, vertically up or down, at each (x, y)

10

data point. The force between the tip and sample can be calculated from the cantilever
deﬂection using Hooke's Law:

F = k-x (1.3)

where F: Force;
k: sprint constant;
x: cantilever deﬂection.

Maintaining a constant cantilever deﬂection implies that the force between the tip and
the sample remains constant. By recording the close-loop voltage applied to the z-axis
piezo simultaneously with the sample’s x and y position, the t0pography or height image
of the sample surface can be inferred and stored in the computer. In contact mode, the
deﬂection of the cantilever that occurs prior to re-establishing the constant force via the
z-feedback loop, is also recorded and displayed as deﬂection image data. The deﬂection
image is more sensitive to sharp sample feature. This mode of operation can take place in
ambient air and liquid environments.

Tapping Mode:

In the tapping mode, which is also called intermittent contact mode, the cantilever is
oscillated at or near its resonance frequency with amplitude ranging typically from 20nm
to 100nm. The tip taps lightly on the sample surface during scanning, contacting the
surface at the bottom of its swing. The tip oscillation amplitude changes in response to
the tip-sample distance from its initial free oscillation to a different amplitude and
frequency that reﬂects some property of the sample surface. The feedback loop maintains
constant oscillation amplitude based on constant RMS amplitude as recorded by the four-

cell photodiode. The vertical position of scanner at each (x, y) point that maintains the

11

‘setpoint’ amplitude is recorded by the computer to generate a topographic or height
image of the sample surface. The frequency change of the tip oscillation near the sample
surface relative to the free resonant frequency of cantilever oscillation can also be
recorded by computer at the same time to generate a phase shift or phase image. The high
sensitivity of the phase shifts due to material and topographic properties has made phase
images a very useful tool in many applications. However, since it is difficult to isolate the
different sample properties responsible for the phase shift, quantitative analysis of the
sample properties using phase image is still limited. The tapping mode operation can be
performed in vacuum, ambient and liquid environments although the dumpling effects of
the liquids on cantilever oscillation must be taken into account.

N on-contact Mode

Non-contact mode of AF M operation is very similar to the tapping mode except that
the tip does not contact the sample surface but oscillates above the sample surface. The
resonance frequency, amplitude and phase shift of the tip vibration are related to the tip-
surface interaction. The feedback loop can use any of these values as a parameter to
maintain a constant tip-sample separation by vertically moving the scanner at each point
(x, y) and generate a topography image. There are two major non-contact AF M modes,
amplitude modulation atomic force microscopy (AM-AF M) [28-30] and frequency
modulation atomic force microscopy (F M-AFM) [30, 31]. In AM-AF M, the z direction
feedback loop maintains the amplitude of cantilever oscillation at the “set-point” value to
generate the sample surface topography image. The drive signal of the cantilever
oscillation is a constant amplitude and frequency excitation. While in FM-AF M, the

cantilever is a self-driven oscillator. The cantilever oscillates with constant amplitude at

12

its current resonance frequency which is different from the free cantilever resonance

frequency due to the tip-sample interaction. Figure 1.7 shows a schematic of F M-AF M.

 

 

Z-axis ¢ ’ Osicllatior

Controller 0 Laser Controller
Split 0¢

Photodiode

Detector 4 -
ﬂ/ Oscillator drive

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

I ll . signal
Piezo drive piezo
signal 2
> i
<——>
x,y

 

 

 

Figure 1.7 Schematic of FM-AFM

Two feedback loops are used by the controller. One feedback loop keeps the
oscillation amplitude at the constant value by changing the cantilever oscillation drive
signal. The difference between the current resonance frequency and that of the free lever,
Af, is used as the z—direction feedback loop parameters. By moving the sample up and
down, the z-direction feedback loop maintains the constant value for Af. The distance
that the scanner moves vertically at each (x, y) position is stored in the computer to
generate a topographic image of the sample surface. Currently, the non-contact mode
AFM mostly performs in ultra high vacuum (UHV) because of the very weak forces

involved.

1.5 Applications of AFM

l3

The family of Scanning Probe Microscopy techniques have revolutionized studies of
semiconductors [32-34], polymers [3 5-3 7], nanostructures [3 8] and biological systems
[39—43]. This thesis will focus on study of SPM applications for imaging biological
samples.

The potential of scanning probe microscopy for use in biological studies was
immediately recognized, and research efforts began shortly after the invention of STM.
The original nano-Amp STM was not suitable for imaging largely nonconductive
biological samples, and this led to the development of the atomic force microscope (AF M)
for nanbiological research. As the nano-Newton tip-sample interaction forces of AF M
proved to be sufficient to damage soft biological tissues, pico-Newton imaging systems
based on perturbations to a freely oscillating cantilever were developed (Tapping Mode
or non-contact AFM). Liquid environment systems that greatly reduced Van der Waals
and smface adhesive forces were also developed [44, 45]. The successful operation of
AF M techniques in liquid ambient environments also provides another important
capability for biological investigations: the ability to conduct direct investigations under
nearly life-like conditions [46].

AF M contributions in nanobiology and medicine has been revolutionary in that it
includes: the ﬁrst direct observations of DNA and RNA [47, 48], the ﬁrst direct
investigations of membrane proteins [49], the ﬁrst direct investigations of ligand binding
by ftmctionalized tip AF M [50] and many more important ﬁrst direct studies. A
persuasive argument for the use of AF M techniques in nanobiology is that it is a direct
investigative technique in a ﬁeld that has largely relied on indirect or aﬁer-the-fact

observations. Recognition of the importance of AF M techniques for medically relevant

l4

nanobiological investigations is growing rapidly [51]. Examples of recent studies include
high resolution combined topographical and mechanical studies for multiple living cells
types [51-53], direct investigations of the growth cones on living neurons [51], and,
opening up an very important nanobiological research area, the ﬁrst direct single
molecule investigations [40, 51, 54].

The main advantages of AFM in nanobiology are that it easily reaches
macromolecular resolution, with minimal sample preparation, and under nearly life-like
conditions. A drawback of AF M is that it has been a surface technique requiring
complementary investigations to provide sub-surface information. However, sub-cellular
AF M is also under development [51, 55]. Although AF M has considerable potential in
molecular and nanobiology, it is important to realize that accurate data collection is often
challenged by several limitations and difﬁculties associated with existing commercial

systems.

1.6 Summary of the Later Chapters

The challenges addressed in this thesis are introduced in Chapter 2. Chapter 3
addresses the need for improved scanning efﬁciency. Two implementation methods,
namely, off-line processing scheme and an on-line dynamically adaptive multi-resolution
scanning mode, are presented. A dynamic or adaptive, site speciﬁc scanning feature is
developed and mechanisms for incorporating this feature in commercial AF M systems
are also discussed. The nature and source of image artifacts are described in Chapter 4 in

detail with respect to operation of AFM in contact mode. Two different classes of

15

methods that are widely used in AF M image deconvolution, namely, mathematical
morphology [56] and Legendre transforms [57], are discussed. An alternate approach for
AF M data restoration is physics based deconvolution which includes the modeling and
characterization of the tip and sample artifact sources. Investigations that model the tip
sample interaction are presented in the Chapter 5. An iterative procedure based on the tip-
force interaction model is proposed to deconvolve the image. And results of two different
samples are shown and compared with the result of geometrical deconvolution method.
Chapter 6 introduces the application of SPRM in tissue scaffold engineering. Two import
properties of the bio sample, surface roughness and elasticity, are introduced and the role

of deconvolution in each is identiﬁed. The future works are summarized in chapter 7.

l6

Chapter 2 Image processing challenges in AFM

The main advantages of AFM in nanobiology are that it easily reaches
macromolecular resolution, with minimal sample preparation, and under nearly life-like
conditions. A drawback of AFM is that it has been a surface technique requiring
complementary investigations to provide sub-surface information. However, sub-cellular
AFM is also under development [51, 5 5]. Although AF M has considerable potential in
molecular and nanobiology, it is important to realize that accurate data collection is often
challenged by several limitations and difﬁculties associated with existing commercial
systems.

These limitations are the main focus of this research. Limitations include: image
artifacts; slow scanning speed; lack of automated recognition of region of interest (ROI);
not optimized scanning parameters. These difﬁculties can be addressed by incorporating
a number of image and signal processing solutions to the raw data acquired by the AF M.
Further, due to the multi-modal nature of data provided by SPM systems, a composite
picture representative of a sample environment can be obtained using data fusion
algorithms. This thesis attempts to address many of these disadvantages within the

framework of the Scanning Probe Recognition Microscope.

2.1 Analysis Challenge
2.1.1 Imaging Artifacts

In atomic force microscopy, a sharp tip is brought within nanometers of a sample

surface by the z-motion of a piezoelectric scanner and held there by a z-feedback loop.

17

Any tip shape introduces signiﬁcant artifacts in the form of physically missed region
information. In addition to missed regions, contact at any point other than the tip will
result in an image smearing or dilation artifact. Figure 2.1(a) shows an example of the
dilation artifact. In the ﬁgure, the red dashed line shows the theoretical proﬁle of the
sample surface and black line shows the corresponding proﬁle in the experimental

scanned image data.

 

(a) (b)

Figure 2.1 Example of the dilation artifact (Solid line: experimental proﬁle; Dash line: theoretical
profile)

The sample surface may also contribute missing region and dilation artifacts of its
own as shown in Figure 2.1 (b).

The AFM tip-sample interaction is caused by the summation of all possible Coulomb
forces between the tip and the sample, summed along the physical structure of the tip and
a local region of the sample surface. These forces can introduce distortions into the
information that represents some given aspect of the sample surface. In the case of a
yielding or soft sample, which is the case in cellular imaging, any deformation of the
sample surface can dynamically change the interaction forces in play. This means that
for fully understanding the acquired data a dynamic model that takes into account

contribution of the electrostatic force component in the tip-sample interaction at each

18

position of the tip, is needed [51-53], since an a priori model of such highly individual
conditions cannot exist. Another common artifact is due to drag through a surface water
layer which introduces torsioning of the cantilever that is due to the water layer not to the
sample topography. Also when a tip is raised or lowered through the surface layer while
maintaining its z-feedback condition, it feels vertical adhesive forces as well. Therefore,
tip shape, surface shapes, surface environment and yielding surfaces can all result in
information artifacts.

Physics based approach for enhancing accuracy of measurements include the work by
Grimellec et al [5 8], where effort is made to reduce the tip-sample interaction for
increasing the accuracy of height imaging data. J iao and Schaffer [52] use additional
information about the mechanical properties from spatially resolved force curve at each
pixel to obtain accurate height and volume information of soft samples. Touhami et al [5 3]
use a similar approach for mapping of elasticity of microbial cells. Physics based
approaches are often developed where a problem with imaging artifacts has required that
careful attention be paid to data interpretation. A new signal processing research ﬁeld
could evolve from the systematic integration of physics based information with powerful
image processing and deconvolution techniques to increase both the extraction and the

reliability of the data.

2.1.2 Region of Interest Recognition

In scanning probe microscope investigation, because a tip is in actual direct interaction

with a nanoscale object rather than viewing its image, this gives the system itself the

19

potential for site-speciﬁc probing, in addition to its current high-resolution imaging.
Figure 2.2 shows two examples of AFM imaging of biological samples. Figure 2.2 (a)
shows an ordinary AFM image of an NIH 3T3 ﬁbroblast cell. Figure 2.2 (b) shows an
ordinary AFM image of a tissue scaffold of the type used for cell re-growth in
regenerative medicine. These two examples show two different types of region of

interest (ROI) problems in ordinary SPM imaging.

   

o 10.0 pm

(a) (b)

Figure 2.2 AFM image of biological sample with two different types of ROI. AFM images by Y. Fan
and Q. Chen. Cell and tissue samples from S. Meiners, college of Medicine UMDNJ

Figure 2.2 (a) shows AFM image of ﬁbroblasts grown on plastic 2D surface. The
traditional SPM will scan the whole area while the region of interest in the image is only
the cell. Figure 2.2 (b) shows an AFM image of the tissue scaffold sample, in which
analysis of the properties of individual nanoﬁbers which affect their biocompatibility is
the goal. As shown in the Figure 2.2 (b), the ordinary AFM image contains data point (1),
off the nano ﬁber, data point (3), on the side of the nanoﬁber, and data point (2) in the

center of the nanoﬁber. When imaging the nanoﬁber, the ROI is along the individual

20

nanoﬁber. While analysis the surface roughness of the nanoﬁber, only the top of
nanoﬁber is not limited by geometric dilation and provide reliable data. The ROI thus is
only the top of the individual nanoﬁber in this case. While investigating the elasticity of
nanoﬁber, only the center line of the nanoﬁber is the ROI since only in this place tip is
normal to the sample surface.

To rapidly and reliably detect the region of interest is a highly desirable goal. In order
to achieve this goal the Scanning Probe Microscope system itself should be given the
ability to return to a speciﬁc nanoscale feature of interest by recognizing the way that site
is detected by the SPM system rather than by the way the site looks to a human operator.
Such a capability can be realized if the system has the ability to combine Scanning Probe
Microscope piezoelectric implementation with on-line image processing and dynamically

adaptive learning algorithms

2.2 Implementation Challenge

2.2.1 Scan Speed

In traditional SPM, the tip scans inside a regular rectangular area following a raster
pattern. In virtually all scanning probe microscopes, a piezoelectric scanner is used as an
extremely high resolution positioning stage to move the probe over the sample (or the
sample under the probe). Figure 2.3 shows typical scanner piezo tube and X-Y-Z

electrical conﬁgurations.

21

 

Figure 2.3 Typical scanner piezo tube and X—Y-Z electrical conﬁgurations [59]

The scan motion in the x-y plane is controlled by applying AC voltage to the scanner’s
piezoelectric crystal X-Y axes as represented in Figure 2.3. In this example, the
horizontal axis presented on the display monitor is referred to as the “fast axis" or X-axis
and scans at a preset scan rate entered by the user. The orthogonal axis is known as the
“slow axis” or Y-axis.

In the SPM, an AC voltage applied to the x-y Piezo scanner produces a raster pattern
in the x—y scan plan. Figure 2.4 shows a traditional raster scan pattern on a tissue scaffold
sample. Tire scanner moves across the ﬁrst line of the scan (fast axis), and back. It then
steps in the perpendicular direction (slow axis) to the second scan line, moves across it
and back, then to the third line, and so forth. The path differs from a traditional raster
pattern in that the alternating lines of data are acquired in opposite directions. SPM data
are collected in only one direction—commonly called the fast-scan direction——to

minimize line-to-line registration errors that result from scanner hysteresis.

22

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Figure 2.4 Schematic of traditional raster scan pattern on a tissue scaffold sample
The traditional raster scanning pattern is a time consuming procedure, especially when
the region of interest is non regular or only a very small part of the rectangular boundary
area. Figure 2.5 shows an AF M image of a DNA sample which has the same ROI
problem discussed in section 2.2, Figure 2.2 (a). In order to get the AFM image of the

DNA, the AF M has to scan the whole rectangular area.

 

 

 

Figure 2.5 AFM image of DNA structure, Courtesy J. Reed, UCLA

23

In the normal scanning operation, the SPM uses the same scan speed for the whole
image. In the DNA image, the actual DNA structure is only a very small part of the
whole image. It is therefore very wasteful to use the SPM to collect high resolution data
in the background region. If the SPM can automatically use high scan speed in the
background area and only use low scan speed in the region of interest, the system can be
utilized more effectively. The total area scan time can be decreased thereby increasing the

overall efﬁciency and scan speed for samples.

2.2.2 Scanning Parameters Optimization

In SPM system a sharp tip is used to scan across the sample. The scan parameters such
as scan speed, set point, scan angle control the quality of scan image. Since the shape of
the tip is not symmetric in each direction, the scan angle is known to have a signiﬁcant
effect in optimizing imaging conditions. The system should generate the scan plan based
on different scan angle and ﬁnd the optimized scan angle.

Optimized scan angle also can help to reduce the image artifact. As discussed in
section 2.1.1, the AF M tip-sample interaction is caused by the summation of all possible
Coulomb forces between the tip and the sample, summed along the physical structure of
the tip and a local region of the sample surface. These forces can introduce distortions
into the information that represents some given aspect of the sample surface. One of the
physics based approach for enhancing accuracy of measurements is to reduce the tip-
sample interaction for increasing the accuracy of surface height which in turn means to
reduce the tip-sample contact region. The optimized scan angle can reduce the contact

area between the tip and sample.

24

2.3 Challenges and Opportunities for Data Fusion

AF Ms provide several types of data. In contact mode, the distance that the scanner
moves vertically at each (x,y) data point is stored in the computer to form a topographic
(height) image of the sample surface. The deﬂection of the cantilever at each data point is
also stored as a deﬂection image. The deﬂection image will give more local detail. The
lateral torsioning of the cantilever at each data point is also stored as the friction image.
The ﬁiction image can provide a measure of comparative surface roughness. In contact
mode, SPM system also provides the friction image which shows the lateral force at each
(x, y) point-

In the tapping mode, the tip is oscillating above the sample at or near its resonance
frequency. The tip lightly “taps” on the sample surface during scanning, contacting the
surface at the bottom of its swing. In addition to a ‘sharper’ height image with less
distortion due to lateral torsioning, the phase shift of the cantilever oscillation, is also
stored as a phase image and provides valuable information that detects variations in
composition, adhesion, friction, viscoelasticity, and numerous other properties.

AF M is also capable of even more complementary operational modes which provide
information on other surface properties, such as stiffness, hardness, friction, or elasticity.
It can record the amount of force felt by the cantilever as the probe tip is brought close to
— and even indented into — a sample surface and then pulled away. This technique can
be used to measure the long range attractive or repulsive forces between the probe tip and
the sample surface, revealing local chemical and mechanical properties like adhesion and

elasticity, and even thickness of adsorbed molecular layers or bond rupture lengths.

25

While all these information provide different properties of the sample, the system does
not present a comprehensive map of the object. By virtue of this multi-modal nature of
the data, the AF M serves as an ideal candidate for data fusion applications. Data fusion
techniques can be utilized to synergistically combine mechanical, topographical and

curvature information into a composite picture representative of a specimen.

26

Chapter 3 Development of SPRM

The traditional raster scanning procedure performed in scanning probe microscopy
(SPM) is an extremely time consuming procedure, especially when the area of interest is
non regular and/or occupies a very small part of the rectangle scan area selected. While in
the traditional SPM, the tip scans inside a regular rectangle area following a raster pattern,
in this thesis we develop a new and innovative capabilities for direct investigations of the
speciﬁc sites and interactions that control healthy or dysﬁrnctional cell regulation. We
propose a novel recognition and motion control scan system, scan probe recognition
microscopy (SPRM) that achieves the goal of site-speciﬁc.

The key underlying idea is to replace the current x-y raster scan with a machine-based
auto-focus strategy that allows scanning, data collection and subsequent processing to be
restricted to site-speciﬁc investigation. Figure 3.1 shows the schematic block diagram of

the SPRM dynamic scanning system in its prototype implementation.

 

 

 
 
  
    
   

Signal
\L‘CC\\ Controller : Computer
Module

 

 

 

 

 

 

 

 

 

 

x,y Piezo z} '0‘.” I
I drive signal 061 659/
I 939 $7 Control
I‘— — — 0&9/ Iviurriiur
Piezo Piezo drive 0/

 

 

 

 

z A signal
‘

 

deﬂection...

 

Figure 3.1 Block diagram of the dynamic scanning system.
The SPRM prototype system consists of three major components: the scanning probe

microscope system; Signal Access Module (SAM); Data processing computer. Detailed

27

information about the basic SPM system has been discussed in Chapter 1. The SAM
enables SPM users to make direct connections to the microscope’s electronics. Figure 3.2

shows a photograph of the SAM used in our system.

 

Figure 3.2 Signal Access Module [60]

The SAM is provided with BNC connectors which interface with most standard
laboratory instruments. Twenty-ﬁve separate SPM signals are available. Toggle switches
enable the user to switch each line separately between a normal, uninterrupted
conﬁguration and an external input signal. Output BNC connectors permit monitoring of
both conditioned and uninterrupted signals for use in experiments.

The data processing computer is used to collect the data from SAM via an Analog-to-
Digital converter, analyze the data and generate a scan plan. There are two ways to
control the SPM tip motion. One method is through the signal access module. In this
method, the data processing computer directly generates the piezo drive signals which are
high voltage signals. The signals are added directly in the piezo via the SAM. Since the
voltage range of the piezo drive signal is between -220v and +220v, this method requires

very careful attention. A second method is to use the SPM built-in lithography command

28

to control the tip movement. The nanolithography feature allows tip motion in nano scale
increments. In our research, we choose the second method and use the data processing
computer to analyze the data and generate appropriate scan control commands.

Site speciﬁc scan plan generation can be accomplished either in off-line processing or
on-line processing mode. In the off-line processing mode SPRM ﬁrst scans the entire
sample area at a coarse resolution. The collected data are processed off-line to determine
the region of interest and a scan plan is generated which will guide the tip to scan inside
the region of interest (ROI) in a subsequent scan at a higher resolution. In the on-line
processing mode the pattern recognition and scan plan generation are performed as the
data is acquired. The algorithm analyzes the current collected data and generates the scan
command for the next scan step. In either strategy, the two major steps are ROI

recognition and motion control.

3.1 Off-line Processing Mode

In the off-line processing mode, the SPM ﬁrst scans a large area in the sample which
includes the region of interest (ROI) and obtains a coarse resolution image of the
specimen. The SPM measurements of sample features are processed to recognize the
different landmarks and their locations in terms of integer pixel coordinates, which in
turn can be converted to coordinates in nanometers. These coordinates are used to
redirect the tip to the ROI for further investigation. The overall recognition algorithm
consists of: (i) preprocessing for enhancing image quality; (ii) ROI detection; (iii) scan

plan generation.

29

In a conventional AFM raster-scanned image, not all data points represent an ROI, ie a
cell, a DNA strand etc. Figure 3.3 shows AFM image of DNA molecules. The overall
measured image can be segmented into background (substrate) and ROI (DNA object)
pixels. These are superimposed with noise and artifacts due to operational parameters.
Hence it is important to process the AFM image data to remove noise to facilitate
identiﬁcation of the ROI. Histogram equalization is applied in order to increase local
contrast of the image.

Based on the shape of structure that is being imaged, two different algorithms are used

to detect the ROI: multi scale analysis and skeleton analysis.

Background

 

Figure 3.3 AFM image of DNA molecules (image size: 0.5x0.5 pmz) [61]

30

3.1.1 Multi Scale Analysis

Images in general consist of several scales and features in the image can be broadly
classiﬁed in terms of its scale. For instance, a cell belongs to larger scale than the nucleus,
and a receptor site belongs to smaller scale than a nucleus. A multi scale analysis exploits
the scale information to allow the object to be analyzed at different resolution levels. In
this research, multiscale analysis is implemented using the continuous wavelet
transformation. A continuous wavelet transform is a scale based two-dimensional

transformation deﬁned as:

 

Wra.r1,r2)=§ ij(x,y)w'(x:1 ,y jam» (3-1)

where o is the scale parameter, 1?] and 12 are the translation parameters in the x and y

directions , * denotes complex conjugation, and \y is the mother wavelet function. We use
a differential Gaussian function mother wavelet because this function enhances edge
information. Figure 3.4 shows the results of offline processing. A rectangular region of

interest (R01) is represented in terms of coordinates {(Jcmin , ymin ), (Jr:max , ymax )} .

31

(xlllllli ,Vllllll)
.<§“"' as;

(xiimx- Finn)

 

y 3’

Figure 3.4 Result of oﬂ'line processing [62]

Once a rectangular region of interest in the image has been identiﬁed for further
investigation, the coordinates of the boundary pixels are obtained and used to control the
tip to perform a raster scan only inside the region of interest. The SPRM automatically
ﬁnds the ROI, scans inside the ROI and provides continuous, reliable and high resolution
information of ROI. However the off-line processing mode cannot provide the reliable
ROI coordinate information if the shape or location of sample is dynamically changing

during the scanning process.

3.1.2 Skeleton analysis

In the AFM image of DNA, as shown in Figure 3.5, the actual DNA structure is a long
thin string and occupies a very small part of the whole image of scanned region. It is
therefore wasteful to use the SPM to collect high resolution data in the background region.

On detecting of the ROI, the SPM is controlled to scan only inside the ROI with high

32

resolution to save operation time and obtain accurate, high resolution data. Also as
previously discussed in Chapter 2, the scan angle controls the quality of scan image.
Since the shape of the tip is not symmetric in each direction, the scan angle is known to
have a signiﬁcant effect in optimizing imaging conditions. The SPRM system should
ideally generate scan plans using different scan angles and ﬁnd the optimized scan angle.
By obtaining the orientation information of the DNA chain, we can also control the
scan angle to maximize image accuracy. In this thesis, skeletonization algorithm is used
to detect both location and orientation information. The notion of skeleton was
introduced by H. Blum as a result of the Medial Axis Transform (MAT) or Symmetry
Axis Transform (SAT) [63, 64]. Tire skeleton points are deﬁned as centers of maximal
circles contained in the original object. Three techniques have been developed to
generate skeletons or medial axes, namely, morphological thinning [65], distance

transform [66] and Voronoi diagram [67].

 

Figure 3.5 AFM image of DNA structure, Courtesy J. Reed, UCLA

33

Morphological thinning is a layer by layer erosion method, identifying points whose
removal does not affect the object’s topology. Although this technique is relatively
straightforward, the skeleton generated by thinning methods does not always form a
connected object. Distance transform method includes three steps. The data is ﬁrst
converted into a binary image with the object (1) and background (0). In the distance map,
each pixel represents the distance to the nearest feature element (edge pixel). Skeleton
points are deﬁned along the singularities (ridges). However the detection of singularities
in the distance map is difﬁcult. A third class of methods calculate Voronoi diagram of the
discrete samples of the boundary. The Voronoi diagram of a set of discrete points
(deﬁned as generating points) in a given space is a partition of the given space so that
each partition contains only one generating points and all points which are nearer to this
generating point than any other generating points. If we choose the boundary points as
generating points and the number of the generating points goes near to inﬁnite, the
Voronoi diagram of the these boundary points converges to the skeleton. This method can
generate an accurate connected skeleton. However it is complex to implement and is
computationally expensive.

This research develops a skeletonization algorithm using the Contour-Pruned
skeletonization algorithm [68]. Figure 3.6 shows the ﬂow chart of the Contour-Pruned

skeletonization algorithm.

34

 

Raw Image

 

I

 

Median Filter

 

I

 

Binary Image

 

I

 

Extra Boundary

 

T

 

Calculated length and
radius of maximal
inscribed circle

 

I

 

 

Remove noise based
on the length of
perimeter cut off by
inscribed circle

 

I

 

 

Extract skeleton using
morphological
thinning operation

 

Figure 3.6 Flow chart of the Contour-Pruned skeletonization algorithm

A median ﬁlter is ﬁrst used to remove the salt and pepper noise. The ﬁltered image is
then converted into the binary image in which the boundaries of the DNA chains are
easily extracted. Inside the boundary of DNA chain, the distance of each pixel to the
nearest edge pixel is calculated to obtain the radius of the maximal inscribed circle
centered at that pixel. The boundary points of the object are labeled clockwise. The
perimeter of the object is deﬁned by the difference between the ﬁrst and last boundary
pixels which is the same as the number of boundary pixels. The length of perimeter cut
by the inscribed circle is deﬁned as the difference between the perimeter and the largest
gap between the inscribed circle’s contact points. Figure 3.7 shows an example of the

inscribed circle in the object. In Figure 3.7, the length of the perimeter is equal to 20. The

35

 

 

inscribed circle has three contact points at boundary nodes 5, 9 and 17. The gaps between
these contact points are 4, 8 and 8. The length of perimeter cut by the inscribed circle is

deﬁned as

Pcutoﬁ" = Pboundary - maX(gap) = 20 — 8 =12 (3-2)

 

 

 

 

 

 

 

 

11
12
19181716I15I1413

 

 

 

 

 

 

 

 

 

Figure 3.7 Object and inscribed circle
This procedure is repeated for each pixel inside the boundary and a new image is
generated in which each pixel represents the length of perimeter inside the inscribed
circle. Figure 3.8 (c) shows the map of the radius of the maximal inscribed circle in the
DNA image and Figure 3.8 ((1) shows the image of length of perimeter cut off by the
inscribed circle in each pixel.

The pruning algorithm is implemented by using the length of the perimeter cut by the
inscribed circle. In the image of length of perimeter cut by the inscribed circle, a
threshold value is manually set to remove the noise pixel which typically has a small
segment of the perimeter length within the circle. A morphological thinning operation is

used to ﬁnd the skeleton in the image of the perimeter lengths cut by each inscribed circle.

36

This is also the skeleton of the same DNA chain. Figure 3.8 (f) shows the skeleton
superimposed on the DNA image.

The advantage of this method is the pruning technique, which is based on the length of
perimeter cut by a maximal inscribed circle. This method makes it easy to prune noisy
skeleton branches while leaving signiﬁcant features intact. Figure 3.9 shows the results of
skeletonization with and without the pruning technique. As is seen, the pruning technique
provides a more accurate skeleton of the object.

Once the skeleton of the DNA chain is found, the position and orientation of the DNA
chain can be deﬁned in terms of the scan plan. The new scan plan then controls the tip to
perform a scan around the DNA chain with different scan angle between the tip and DNA
chain. The SPRM automatically moves to the start of the DNA chain, scans cross the
DNA chain and provides continuous, high resolution information image data. By
controlling tip scan angle as it crosses the DNA strand, the SPRM can provide more
reliable and detailed information. However, as mentioned before in the case of multi
scale off-line processing, this method cannot provide the reliable ROI coordinate

information if the shape or location of target and hence R01 is continually changing.

37

 

(6)

Figure 3.8 Skeletonization results: (a) raw DNA image; (b) binary image; (c) radius of the maximum
inscribed circle; (d) image of length of segmented perimeter; (e) skeleton image; (f) skeleton image
shown in original DNA image.

38

 

(a) (b)

Figure 3.9 Skeleton of the DNA image (a) without pruning (b) with pruning

3.2 Online Scanning Mode

Unlike the off-line processing mode which requires a low resolution pre-scan image of
the entire scan area prior to identifying the ROI, the online scanning mode implements
the recognition operation in real time. The ROI recognition algorithm and scan plan
generation algorithm run in conjunction to adaptively detected features of the ROI and

use these to control the tip motion to get high a resolution image of the ROI.

3.2.1 Online Scan Plan Generation

Unlike the off-line processing mode which require low resolution pre-scan image of
the entire scan area before recognition of the ROI, the online scanning mode implements
the recognition operation in the real time. The ROI recognition algorithm and scan plan
generation algorithm run in conjunction to adaptively detect features of the ROI and to

control the tip motion to get high a resolution image of the R01.

39

In online scanning mode there are two types of scan commands, namely, ﬁne
resolution scan and coarse resolution scan. The ﬁne resolution scan command controls
are used when the tip scans inside the ROI where a ﬁne or small step size and low scan
rate are used to get a high resolution image. The coarse resolution scan control
commands are used to scan the background region where a large step size and fast scan
rate are used to save scan time. The resultant image will have high resolution in the ROI
and low resolution in the background region [69, 70].

Two types of online scan plans are proposed for addressing speciﬁc applications.

1. Multi ROI scan plan

2. Single ROI scan plan

The ﬁrst type of online scan plan is multi-ROI scan plan. The ﬂow chart of the
multi-ROI scan plan is shown in Figure 3.10. This scan plan also starts with the coarse
resolution scan. The system begins from the top left comer of the scan area with the
initial coarse resolution (rough) scan command. Data acquired in the coarse resolution
scan is processed for ROI detection. Once the recognition algorithm detects an ROI, the
system stops the rough scan, stores the coordinate of the last point on the coarse scan.
The ﬁne resolution scan procedure is started from the upper left corner and the ﬁne scan
command is used to get the high resolution image within the ROI. After completing the
scan of the current ROI, the system resumes the coarse scan from the stored coarse scan
point. When the system encounters the second ROI the above process is repeated to get
the high resolution image of the second ROI. This multi resolution scan procedure

continues until the tip reaches the scan size limit.

40

 

Initiates tip position to
left-upper corner

 

 

 

 

 

 

 

Move to next line

Rough scanning along x-

 

 

 

 

 

axis

 

 

 

 

   

 

Finish scanning

 

 

 

 

 

 

 

 

 

 

 

 

Move to next line

 

 

 

I

N Finish ﬁne

 

 

scanning?

Figure 3.10 Online multi-ROI scan plan flowchart

41

 

Move to next line

 

 

———> Rough scanning along x

 

 

  

Finish scanning

 

 

 

 

Initiates tip position to
left-upper corner

I

 

 

 

 

 

 

 

 
   

  
      

Inside the
unscanned object?

 

 

 

 

Move back to ﬁne
scanning starting positon

 

 

 

 

 

Fine scanning along x 4

 

 

 

 

 

Finish line scan?

     

 

Move to next line

I

 

 

 

W

Figure 3.1] Schematic of single ROI scanning mode

W N

 

V

In order to study small dynamic changes in a speciﬁc site, for example, the

dynamics of living cell structures, a single ROI scan plan is generated. In the single ROI

mode, once the system detects an ROI, the scan will auto-track within the ROI and

provides continuous reliable real-time detail information of the living cell’s dynamic

processes. Figure 3.11 shows the ﬂow chart of the continuous dynamic scanning mode. In

42

the single ROI scan plan, the SPRM starts with coarse resolution scanning until the ROI
(cell structure) is detected. Once the system detects the ROI, the SPRM will initiate the
ﬁne resolution scan within the ROI. After the ROI scan is completed, instead of resuming
the coarse scan, system will re-scan the ROI in the reverse direction to continue
collecting high resolution information inside the current R01 to hack real time dynamic

changes in the ROI. This process continues until a pre-set condition is reached.

3.2.2 Fine Resolution Scan Plan

In the ﬁne resolution scan stage, the system uses a smaller step size and appropriate
scan speed to control the SPM tip movement. The tip follows the raster scan pattern with
variable fast axis length. Fine resolution scan plan is operated in two modes, namely with

prediction and without prediction.

3.2.2.1 Fine Scan without Prediction

 

Figure 3.12 Fine scan without prediction (a) Conventional AFM image of the nanoﬁber (b) Coarse
Scan picks up the ﬁrst nanoﬁber; (c) Fine scan only on the ﬁrst nanoﬁber (d) Finish the ﬁne scan and
return to coarse scan to find another region of interest; (e) Coarse Scan picks up the second
nanoﬁber; (0 Fine scan only on the second nanoﬁber (g) Finish the high resolution ﬁne scan only on
the second nanoﬁber

In this mode, the R015 are separated and there is no crossing over between two ROIs.
Figure 3.12 shows the ﬁne scan result of two ROIs which don’t have crossing section.
Once the system detects the ROI, it automatic focuses on the ROI and obtains a high

resolution image of the ROI.

3.2.2.2 Fine Scan with Prediction

This scan mode is used in samples where the R015 intersect each other. This is a
particularly challenging problem where the tip is required to track a single ﬁber in a
tissue scaffold, for example, as shown in Figure 3.13(a). In such a case we use the prior
knowledge of the R01 to incorporate a prediction algorithm into the scan plan generation.
Figure 3. 13(a) shows a typical AF M image of the tissue scaffolding sample, where the
R015 are two intersecting nano ﬁber, identiﬁed by the arrow. Figure 3.13(b) shows the
result of SPRM scan on one nanoﬁber passing through the intersection region and

maintaining its original path.

SPRM

Incorporation of linear predictive coding
(LPC) in SPRM for handling cross-over
points

,,

a ., ..LL,.__‘

0 5.00 “1.00

mm

 

Figure 3.13 AF M image of the tissue scaffold sample with cross section area.

44

The prediction algorithm can, for example, be based on the linear regression of
detected boundaries in the previous lines. The linear regression model is deﬁned as
Y = aX + b + a (3-3)

where a is the slope, b is the intercept, 3 is the “residual” random variable with zero mean

and unknown variance oz, 8 ~ N (0, 021) . Using least squares method [71], we get the

predicted boundary points in the next scan line.

Figure 3.14 shows SPRM image of tissue scaffold sample. l(a)-(d) shows the SPRM
scan plan generated without prediction. When the tip meets the intersection area, the scan
plan in this case, jumps to the second ﬁber. While with the prediction algorithm the scan
plan is as shown in 2(a)-(d). The tip scans past the intersection and stays on the original

nano ﬁber to complete the data collection on the same nano ﬁber.

45

 

Figure 3.14 SPRM scan plan of intersecting tissue scaffold sample. l(a)-(d) shows SPRM scan
without prediction; 2(a)-(d) shows corresponding SPRM scan with prediction

46

3.3 Real Time Display

When using the lithography command to control the tip movement, the prototype
SPRM system uses the SAM to access the SPM controller system to collect the real time
scan data as shown in Figure 3.1. The SAM provides the access to monitor most of the
SPM signals such as set point, vertical deﬂection, lateral deﬂection, 2 position, STM
preamp output etc. In addition, the SAM provides four user-deﬁned low voltage analog
output ports. User can set the output voltage in the lithography script command by using
the command ‘LithoSetOutput’. In our system we use the 2 position information. The
SAM LV-Z output signal port is used to monitor the 2 position information. The SAM’s
low voltage output signal port Ana3 is used to trigger data collection by the data
processing PC

The A/D card used in the prototype system is NI PCI-MIO-16E-4 where data length is
12 bits. The sampling rate is 1000 Hz. A custom Matlab program is used to control the
A/D card and display the sampled data. Once the system ﬁnishes scanning the whole area,
the program will display the collected data according to the stored coordinates ﬁle.

Figure 3.15 shows the SPRM scan image of tissue scaffold sample. Adaptive scanning
enables SPRM to follow along an individual nanoﬁber even when it crosses another as
shown in Figure 3.15 (b)-(g). Therefore, the three nanoﬁbers, or whole nanoﬁber mesh

becomes the region of interest. The output is generated in real time.

47

 

O

10.0 mm

 

(e) (s)

Figure 3.15 SPRM scan image of the nanoﬁber. (a) Conventional AF M image of the nanoﬁber (b)
Coarse Scan picks up the ﬁrst nanoﬁber; (c) Finish high resolution fine scan only on the ﬁrst
nanof'iber and return to coarse scan to ﬁnd another region of interest; ((1) Coarse Scan picks up the
second nanoﬁber; (e) Finish the high resolution fine scan only on the second nanoﬁber and return to
coarse scan to ﬁnd another region of interest; (0 Coarse Scan picks up the third nanoﬁber; (g) Finish
the high resolution fine scan only on the third nanoﬁber

48

Chapter 4 Image Reconstruction Based on Geometric
Deconvolution

In atomic force microscopy, a sharp tip is brought within nanometers of a sample
surface by the z-motion of a piezoelectric scanner and held there by a z-feedback loop, as
discussed in Chart]. The AF M tip-sample interaction is caused by the summation of all
possible Coulomb forces between the tip and the sample, summed along the physical
structure of the tip and over a local region of the sample surface. These forces can
introduce distortions into the information that represents some given aspect of the sample
surface. A tip shape introduces signiﬁcant artifacts in the form of physically missed
region information. In addition to missed regions, contact at any point other than the tip
will result in an image smearing or dilation artifact. The sample surface may also
contribute missing region and dilation artifacts of its own, depending on its surface
roughness. In the case of a yielding sample, which is the case for cellular imaging, any
deformation of the sample surface also dynamically changes the interaction. While this
does not necessarily introduce a missed region artifact, it does mean that dynamic
modeling of the contribution of each electrostatic force component in the tip-sample
interaction becomes necessary [51-53]. The x-y raster motion takes place in the ambient
environment within 10’s of nanometers of the sample surface. A very common artifact is
due to drag through a surface layer which introduces torsioning of the cantilever. When a
tip is raised or lowered through the surface layer while maintaining its z—feedback
condition, it feels vertical adhesive forces as well. Therefore, tip shape, surface
roughness, surface environment and yielding surfaces can all result in information

artifacts.

49

This chapter discusses the application of image processing techniques for
deconvolving artifacts due to tip shape from the SPM measurements, whereas physics

based methods for deconvolution are described in chapter 5.

4.1 Deconvolution in Atomic Force Microscopy

In general, by modeling the AF M measured data as the output of a linear time
invariant system, the surface measured by the AF M can be interpreted as the convolution
of the sharp nanoscale surface features, with a transfer function that depends on the
properties of the tip. When the tip properties are accurately known, the true image can be
reconstructed by a linear deconvolution of the measured surface. Two of the most
important factors that affect AF M resolution are the apex angle/radius and aspect ratio of
the scanning tip. The ﬁrst tips used by the inventors of the AFM were made by gluing
sharply faceted diamond chips onto aluminum foil. Current tips are rrricrofabricated from
silicon or silicon nitride. Contact mode tips have an apex radius of curvature of about 25-
30 nm and tapping or non contact mode tips have an apex radius of curvature of about 5-
10 nm. Standard AFM research probes are tetrahedral with a 35° apex angle. The apex
and aspect ratio may be modeled using a parabola to describe an overall tip shape. New
tip shapes are under experimental development such as STING probe features additional
narrow and long extratip provided by Mikromasch Corp. motivated by the issues
discussed here. The redesign of the tip shape can reduce the imaging artifact but only
deconvolution really addresses the problem.

This chapter concentrates on the effects of the tip shape convolved with the sample

surface features, without considering the complexity introduced by the sample plasticity

50

or the surface environment. Two different classes of methods that are widely used in

AF M image processing, namely, mathematical morphology [56] and Legendre
transforms [57], are investigated. These techniques essentially serve to reconstruct, from
the measured image, the sample surface if the tip geometry is known, or the tip geometry

if the sample surface is known.

4.2 Morphological Processing Technique for Surface
Reconstruction

The approach based on mathematical morphology for surface reconstruction, derived
by Villarrubia [72] takes into account the effects of a ﬁnite probe tip size. It is assumed
here that the image distortion is due to dilation of the image features by the ﬁnite area of
the probe tip. The section below discusses the inherent relationship that exists between
AFM image and the ﬁeld of morphological image processing and describes a procedure
to obtain the best possible reconstruction of the original sample surface using
morphological deconvolution of the measured AF M image. The AFM image formation
can be described in terms of morphological operations as below:

The notations in two dimensions are as follows:

0 s(x, y) : true sample surface

0 i(x ’, y') : measured AFM image surface

0 t(x-x ’, y-y') : arbitrary position of probe tip relative to the sample surface s(x, y).
As the probe is moved, the height of the tip above the sample surface is the measured

height data (Figure 4.1) and can be modeled as

i(x’,y') = min{t(x -x',y -y') -S(x,y)} (4-1)
x

51

This is equivalent to the grayscale morphological operation of dilation

1 =S€BP (4.2)

where ‘ EB ’ is dilation operator and set S = [(x,y,z) / 2 SS (x, y)], is referred to as the
‘top’ of s(x, y). Similarly I and P are sets corresponding to measured surface i(x ’, y’) and
the probe tip t(x, y). When the probe apex is in contact with the sample, the AF M output
measures the true height, i.e. i(x ’, y’) = s(x, y). However, when the point of contact is
other than the probe apex, there is a distortion in the measured surface height and i(x ’, y ')
¢s(x, y). Figure 4.1 shows various translates of the parabolic tip, t(x-x ’, y-y ’) relative to
the sample, the corresponding points of contact and the resultant measured surface. The
dotted lines represent the simulated image obtained by the process of dilation which

results in the rounding artifact seen in measured AF M data.

 

I I I

11. an

V'V'V V'V'V V'V'V 'VVV'V VV

—

—Reﬂected TIp Surface —
‘8‘ Original Specimen Surface
Simulated Image —

 

 

 

l l I I l

 

Figure 4.1 Morphological dilation Model of AFM image data with sharp surface features (Note : The
tip surface is reflected about its origin in accordance with equation (4.3)) [73, 74]

From the above image model, the algorithm for ‘deconvolving’ the distortion due to
the tip shape can be obtained using a grayscale morphological erosion (inverse of dilation)

operation deﬁned as

Sr(x, y) = min[i(x + u, y + v) — p(u,v)] (4.3)
u,v

52

where the minimum operation is carried out over those coordinates where both tip and
image are deﬁned. In terms of the corresponding sets, deﬁned above, equation (4.3) can

be written as
S, = I (~)P (4.4)
where 6) denotes the morphological erosion operator and S, is the reconstructed
surface. Figure 4.2 depicts the process of erosion of measured surface with a parabolic
tip surface. It is important to note that the reconstruction procedure described above can

also be used for estimating an unknown tip surface from the measurement of a well

characterized sample geometry as P, = IOS.

 

I I ‘ e I 1. I I

. I’ I’
._ .\ _ \ _-i_ /‘ /

t. . . Positionl Position 2

—— TIp Surface

—e— Original Specimen Surface
_ . —A- Reconstructed Surface

- - Simulated Image

1 1 1 J L
Figure 4.2 Surface reconstruction using grayscale morphological erosion [74].

 

 

 

Two properties from mathematical morphology are useful for showing that S r is the
least upper bound of S.

Property 1: (A69 B) G) B :_> A

Property2:(A€BB®B)GBB=AEBB

Property 1 implies that S r 2 S and property 2 ensures that S ,. is the least upper bound

of S. Hence in the reconstructed image, S,(x, y) = S(x, y) in some parts and Sr(x, y) >

53

S (x, y) in others. Figure 4.2 also indicates that narrow regions of the sample that are
inaccessible to the tip cannot be reconstructed. In order to identify the regions in which
the reconstruction is exact, Pingali and Jain [75] suggest procedures for constructing a
certainty map c(x, y) as a measure of the conﬁdence in the reconstructed surface. The
certainty map c(x, y) is deﬁned as below:

0 (x, y) = I when Sr(x, y) = S(x, y) (4.5)

c (x, y) = 0 when Sr(x, y) at S(x, y) (4.6)

In Figure 4.2 we can see that at tip position 1, t(x, y) touches the reconstructed surface
at one point, (x, y) where i(x, y) + t(u, v) = Sr(x + u, y + v) . Hence the certainty map in
this location is set to 1. In position 2, the tip contacts the sample at multiple points and
hence the certainty ﬁrnction is deﬁned as C(x, y) = 0 in this location. Figure 4.3 shows the
performance of surface reconstruction obtained using morphological erosion on a

simulated surface. The simulated AF M height image in Figure 4.3(b) was generated using

morphological dilation operation on the known sample surface depicted in Figure 4.3(a).

54

—True Surface Proﬁle

"9 Simulated Image Proﬁle

+Reoonstructed Surface
Proﬁle

 

Figure 4.3 Results of Morphological Processing (a) True (known) Specimen Surface (1:) Simulated
AFM Image (c) Reconstructed Spedrnen Surface (d) Proﬁle Comparison

4.3 Legendre Transform Technique for Sample Surface
Reconstruction

An alternate approach for deconvolving the effect of tip shape/size is developed by
Keller and is based on the Legendre transform of the measured image. This technique
exploits the fact that the relationship between the measured surface and true surface is
nonlinear as seen by the schematic in Figure 4.4. When the slope of the sample surface is
large relative to that of the tip, the probe touches the sample at a point other than the
nominal tip apex position. The AFM image consequently shows a surface that is smeared

and corners that are more rounded. The true image can be reconstructed from the

55

measured image if the true contact point between probe and sample can be calculated
from the image surface and tip shape. This involves the calculation of two quantities,
namely, the lateral distance between true and apparent contact points (Ax), and the

vertical distance between true and apparent contact points (As).

       
    

I
I,
Image Surface I

i(x’) I True Surface
I
5(X)

  

"I?

 

Figure 4.4 A schematic of tip surface, sample surface and image surface [76]

In one-dimension we deﬁne the following notation,

0 s(x) : true sample surface

i(x’) : measured AFM image surface

Ax : lateral error between true point of contact x and apparent point of contact x’

0 As : corresponding vertical error between x and x’

t(Ax ) : tip surface described as a function of Ax
These equations can be easily extended to a two-dimensional image case in a

straightforward manner. At the true point of contact the probe and sample surfaces have

56

the same tangent line so that the slope of the tip surface equals slope of the true sample

surface, i.e. s(x) and t(Ax) have the same derivative at contact.

EAx—(Ax)-dx ‘ — 6150‘) (4-7)

As the tip moves, x’ changes and so does Ax, i.e. Ax a Ax (x’).
Speciﬁcally, Ax = x — x’ or x = x’ + Ax(x ’). Taking derivative of x w .r. t.x’ we get

d" —= +113 (4.8)

dx' dx'

From the deﬁnition of true surface we have

s(x) = i(x') + As(x') (4.9)
where As(x’) = t(Ax(x ’))

The derivative of equation (4.9) w. r. t. x’ is given by

 

ﬂ = di(x') + dAs(x')

4.10
dx' dx' dx' ( )

Using equations (4.8) and (4.9) in (4.10), we get

di__(_x')= dsdx _d_As_(x') _ds(dx_ _d__Ax)
dx' dxdx' dx' dx dx' dx'

which results in

L0” =§ (4.11)
dx' dx
Equation (4.11) indicates that the slope of the measured image at apparent point of
contact x’ is equal to the slope of the true sample surface at the point of contact x.

Equation (4.11) can be inverted to determine Ax(x ’) and hence As(x’) if t(Ax) is known.

These values are then substituted in Equation (4.9) to reconstruct the true surface s(x). A

57

. . . . . dAx
quantitative measure of the distortion due to probe surface 18 deﬁned to be equal to E'— ,

which can be calculated as

dAx_ d2i(x')/dx'2
dx' d2t(Ax)/dAx2

 

(4.12)

Equation (4.12) simply states that when the tip has a high curvature, the distortion is
less and vice versa. In terms of Legendre transform the reconstruction can be expressed
in a very simple manner. The Legendre Transform, L(/(x)) of a function ﬁx) is deﬁned as

the intercept on y-axis made by the tangent to ﬁx) at x which can be expressed as [77]:
Ltf (0) =50") =f (X(m))-mx(m) (4-13)

df (x) df
air

where m is the slope deﬁned by m = and x(m) is the solution of m = Z(x(m)) .

The inverse Legendre transform for computing f(x) from b(m) is then given by
f (X) = m(x)X+b(m(X)) (4.14)
db(m)

where x is found according to —x = -—d—— and m(x) is the solution of
m

—x = 37:— (m(x)) .

From Figure 4.5 we can see that the Legendre transforms of true surface (bold),

measured surface (dotted) and probe tip surface are related by

L[S(X)] = 11le ')l + 1110315)] (4-15)

58

 

-bﬁp;

 

Tip Surface

 

 

 

 

 

 

\\ '

Figure 4.5 Relationship between the Legendre Transform of the sample surface (black bold), image
surface (dotted) and tip surface [73]

-— Measured Image

‘9' Reconstructed
, Image

 

 

 

Figure 4.6 Application of the Legendre transform to an artiﬁcial AFM height image(a) True surface
image of a cylindrical structure of500nm diameter and 800nm high. (b) Simulated AFM image using
20nm parabolic tip. (c) Reconstructed image. (d) Proﬁles of measured and reconstructed images [73].

59

di .
where all the transforms are evaluated at m = -d—x-'. The true surface rs therefore

obtained simply by inverse Legendre transformation, which is equivalent to the

operations in equations (4.7) through (4.11).
Figure 4.6 shows the surface reconstruction that results from applying the Legendre

transform to simulated AF M height data of a known surface proﬁle and a known tip
'I

geometry using linear interpolation in the inaccessible region. The simulated image in

F " "‘ "Ii—An.t

Figure 4.6 (b) is obtained by the morphological dilation procedure described in equation

(4.2).

4.4 Blind Tip Estimation

The reconstruction algorithms discussed so far require accurate knowledge of the tip
surface. However tips can abrade or pick up debris from the sample surface during a scan.
In such cases, the tip surface needs to be ﬁrst estimated using a known calibration sample.
In general it is a signiﬁcant challenge to produce an accurately characterized reference
artifact to nanometer tolerances. This in turn introduces an error in the estimated tip
shape and hence we can at most estimate the upper and lower bounds of the actual tip
shape. The upper bound of the tip surface allows the estimation of the lower bound of the
sample surface with the measured image serving as the upper bound. Altemately the
surface can be reconstructed using iterative blind deconvolution algorithms [78, 79]. The
iterative blind reconstruction algorithm proposed by Villarrubia [78] is based on the
rationale that the tip essentially serves to broaden any protrusion on the sample surface.

Since the tip is assumed to be relatively narrow, independent features in the image can be

60

 

treated as separate images each of which sets an upper bound on the tip shape so that the
true tip surface is sharper than the tightest of these bounds. Intersection of all the bounds
results in the least blunt estimate of the tip that is consistent with the observed image. The
iterative procedure for blind tip estimation is derived in [78]and is summarized below

Assume initial estimate for the probe tip surface P0.
Locate features on the image surface.

(i + I)“ iteration: Get a bound on the tip surface based oni’h image feature .

P;(X) = Bn(X — I) where x is the location of the feature of interest.

The (i + I)”, estimate is computed as

Pi+1=ﬂ[(1-x)®1i(x)lﬂft (4.16)
At convergence we have the resulting estimate for the tip surface as

PR = .lim P, (4.17)
l-—)oo

The parameters involved in this algorithm are mainly the initial tip surface and initial
values for the tip height, i.e. tip shape. It can be proved that each iteration produces a
result that is smaller or equal to the preceding result. At convergence the ﬁnal result gives
a minimum upper bound of the true tip surface. Given an image and estimated tip
geometry, the morphological erosion procedure is used for sample surface reconstruction
according to equation (4.3). The performance of blind tip estimation depends strongly on

the sharpness of the sample features.

61

 

Figure 4.7 Blind tip estimation results at different iterations (a) initial guess,(b) lst iteration,(c) 2"d
iteration & (d) ﬁnal estimate of the tip shape after convergence [73].

Typical results of blind tip estimation on synthetic data are shown in Figure 4.7. The
coordinate system is chosen such that z = 0 at the tip apex, hence setting all values to
zero provides an initial upper bound as shown in Figure 4.7(a). Using features in the
synthetic image in Figure 4.3(a), the blind estimation procedure results in the tip shape

estimate shown in Figure 4.7(d).

4.5 Example Applications of Deconvolution for Nanobiology

The application of the morphological deconvolution and Legendre transform

approaches, without and with blind tip estimation are applied to an AF M measurement of

62

cell growth on tissue scaffolding. Experimental AFM images of a rat kidney cell (type
NRK2) attached to an electrospun carbon nanoﬁber tissue scaffold are shown in Figure
4.8. Figure 4.8 (a) and (b) are different presentations of the same data set. Two features
of interest and some ambiguity to a human investigator are identiﬁed by the circles 1 and
2. These are: (1) the apparent versus the real width of an average nanoﬁber within the
tissue scaffold network, and (2) a conspicuous projection on the cell surface which may
be a real feature due the coagulating proteins of a dying cell, or an artifact caused by a
sharp surface protrusion imaging the tip.

In the problem of apparent versus the real width of an average nanoﬁber within the
tissue scaffold network, a horizontal line section through the raw AFM data in circled

region “1” is shown as the blue line in Figure 4.9(a), and it indicates that a tip-shape

based rounding artifact is distorting the width measurement.

 

 

 

 

 

 

Figure 4.8 AFM images of NRK2 cell on polymer tissue scaffolding (a) top view and (b) surface plot.
Two ambiguous features are circled (l) the actual width of the scaffold ﬁbers and (2) a sharp feature
on the cell surface [73].

Deconvolution of the image using both the (a) Legendre transform (LT) and (b)
mathematical morphology (MM) methods was performed and the corresponding line
sections through the nanoﬁber are shown next to the blue line in Figure 4.9(a). Legendre

transform result is shown in black and the mathematical morphology deconvolution is in

63

red. The difference in the two results is due to the fact that in the LT method, the
parabolic tip is of unlimited height, which gets wider with the height of the tip, where as
in MM the probe tip is of ﬁnite height. Consequently when the aspect ratio of feature is
comparable with that of the tip, the two methods produce similar results but when the
aspect ratio is larger than the tip’s, the MM method produces a sharper estimate than the

LT method as in the case of the nanoﬁber.

 

   

  
   
   
 

 

 

 

 

  
   
   
 

(a)
-340 - -
—400 ~ —
_Measured Surface Proﬁle
“460 ' +Reconstructed Surface Proﬁle-MM '
*Reconstructed Surface Proﬁle-LT
-520 l I I I l l l
0 20 4O 60 80
1000 i I I
(b)
600 ~ -
200 — -
-200 _ _Measured Surface Proﬁle q
+Reconstructed Surface Proﬁle-MM
“‘Reconstructed Surface Proﬁle-LT _
-400 x 1 r J

 

 

 

200 400 600
Figure 4.9 Comparison of line scans in (a) Region] and (b) Region 2 of Figure 4.8 showing
deconvolution of fiber width [73].

64

The nanoﬁber widths were estimated as 354.25nm for the measured image, 334.01nm
after deconvolution using LT and 328.42 nm after deconvolution using MM method.

Next we consider the conspicuous projection on the cell surface, circled region “2” in
Figure 4.8. The Legendre transformation and the mathematical morphology
deconvolutions are used in conjunction with blind tip estimation procedure to analyze the
data. Figure 4.9 (b) shows horizontal line scans across region 2 in Figure 4.8 before and
after deconvolution. The lack of improvement using LT deconvolution method implies
that the feature is wider than the parabolic tip curvature estimated by the blind tip
estimation procedure. Also, the difference in the LT and MM results indicate that the
feature is taller than the assumed tip height (100nm). However the blind tip estimation
described here is rather simplistic and yields a tip shape that depends on the sharpest
feature in the image. Hence if the true tip shape is known, deconvolution would yield an
impulse feature as the result, which in turn will resolve the ambiguity, stated in the

beginning of this section.

4.6 Conclusions

The restoration of image features in cellular and molecular images is a crucial problem
in nanobiological investigations. The distortion of the measured image due to tip-sample
interaction is a major challenge for nanoscale metrology and signal processing solutions
are needed for increasing the accuracy and reliability of the data. Two existing
approaches that are not physics based, have been described in detail for modeling the tip

sample interaction from a topographical perspective, The approaches have been

65

 

implemented for reconstructing the sample surface, assuming the tip geometry. When the
aspect ratio of feature is comparable with that of the tip, the two methods produce similar
results but when the aspect ratio is larger than the tip’s, the MM method produces a
sharper estimate that the LT method. When the tip geometry is not known, blind tip
estimations methods are needed for iterative estimations of tip and sample surfaces.

An alternate approach for AF M data restoration is physics based deconvolution. A key
component of the physics based approach is the modeling and characterization of the tip ;.
and sample artifact sources for use in subsequent deconvolution algorithms. Attempts to

model the tip sample interaction are presented in the next chapter.

66

Chapter 5 Deconvolution based on the tip-sample
interaction force model

The deconvolution methods discussed earlier focus mainly on effects due to tip
size and geometry. For example, in contact mode AF M, the measured sample topography
is assumed to depend only on the contact point between the tip and sample and

independent of the geometry of the tip away the sample. However in atomic force

microscopy, the AFM tip-sample interaction is caused by the summation of all possible
Coulomb forces between the tip and the sample areas, summed along the physical
structure of the tip and over a local region of the sample surface. Therefore a physics
based model of the tip sample interaction should provide an estimate of the impulse

response of the assumed linear, time invariant (LTI) system as summarized in Figure 5.1.

 

 

 

h(r-t)

X(l') Y0) i
Impulse Response —§ '
Sample Topography f ip-sample interactio Measured Imagew

 

 

 

Figure 5.1 Schematic of the liner, time invariant system
The scanned image which is the output of the LT] system is shown as
y(?') = W“) * h(r -t) (5.1)
where * represents the convolution operation.
A force model of the tip/sample interaction is used in the deconvolution algorithm

described in this chapter.

5.1 Summary of Tip Sample Interaction

67

A variety of tip-smface interactions can be detected by an atomic force
microscope, depending on the separation distance between tip and sample. The forces
include the Van der Waals forces, electrostatic forces, mechanical contact force, capillary
forces, and other variations of Coulomb forces. Coulomb forces are separation-dependent
which translates into height-dependent in an SPM system. Figure 5.2 shows a force-
distance curve which represents the force measured at different tip positions in z direction.
In this ﬁgure, the tip-sample distance is divided broadly into to 3 regions. In region lor
zero force region, the tip is far away from the sample and the mean value of the total
force does not depend on the distance. Region 2 is the within 10’s of nm of the sample
surface before the tip contacts the sample. In this area the total force is attractive and the
tip is pulled toward the sample surface. Van der Waals force is the dominant force in this
region. The force curve situated to the left of contact point is region 3. The ion-ion
interaction now dominates. The total force in this region is repulsive and the tip is

pushed away the sample surface.

Region 3 Region 2 Region 1

VDeflection
15.66 nm/div

Setpoint

(lunuclpouu

 

0-00 = z — 27.58 rim/div 551-56

Figure 5.2 Force curve.

68

In Region 2 active Van der Waals force between atoms and /or molecules consists
of three components: polarization, induction, and dispersion [6, 80]. Polarization refers to
permanent dipole moments and is also known as the Keesom potential. Induction refers
to the contribution of induced dipoles and is known as Debye potential. Dispersion is due
to instantaneous fluctuations of dipoles on the tip and sample surfaces and is the most
important contribution to Van der Waals force. The total Van der Waals force is the sum
of the three terms. At distance of a few nanometers, Van der Waals forces are sufﬁciently
strong to move macroscopic objects such as AF M cantilevers.

In Regions 2 and 3 electrostatic forces arise from the surface charges at interfaces.
Ambient air use is the most common operation for AFM systems as there is almost no
sample preparation required. However in ambient air condition, a humility layer develops
on the sample surface. Surface dissociation or adsorption of a charged species in water is
very common due to the fact that water has a high dielectric constant. The surface charge
is balanced by dissolved counter-ions which are attracted back to the surface by the
electric ﬁeld. Together the ions and the charged surface are known as the electric double
layer. The electrostatic force is produced from the electrical double layers, and the
associated ion gradients, as a charged probe is brought near a charged sample surface.
The general relation describing the force experienced by a tip above the homogeneous
surface for electrostatic interaction is described by

26C

1
F electrostatic = ‘5“ V) 32‘ (52)

where AV=Vtip-Vsa,m,1,3 , is the difference in potential between sample and tip, C is the

tip-sample capacitance as a function of separation z [6].

69

Capillary force is attributed to the water bridge between the tip and sample. Under
ambient environmental conditions (room temperature, atmospheric pressure, and ambient
air) the sample surface is invariably covered with a thin layer composed essentially of
water and miscellaneous hydrocarbons. Considering the nano size contact region and
assuming the tip end is a sphere of radius R, the adhesion capillary force can be
calculated as [80]:

F z 47rRyL cos 6 (5.3)
where 7 L is the surface energy of the liquid, 0 is the angle of the tip-sample contact
region.

After the tip ‘contacts’ the sample surface, meaning that the ion-ion repulsion
now dominates the tip-sample interaction, the sample and/or tip are deformed. The force
between the tip and sample may now be deﬁned as mechanical contact force, which
depends on both the material properties and geometry of the surface. Several theories
describing the contact force have been deve10ped by Hertz [81], J ohnson-Kendall-
Roberts (JKR) [82], and Derjaguin-Muller-Toporov (DMT) [83, 84]. The difference
between the three models is the adhesion of the sample is neglected in the Hertz model
whereas the DMT model considers it outside the contact region and JKR model
calculates it inside the contact region.

In this work we consider only the attractive part of Van der Waals force as the
main tip-sample interaction force which is applicable only in region 2 of the force-

distance curve shown in Figure 5.2.

70

5.2 Van der Waals Force Model

D. Sarid [85] modeled the tip as a molecule, a sphere, or a cylinder in his work on
Van der Waals force—distance relations. In Y. N. Moiseev et al published a paper [86],
where the tip is modeled by a paraboloid. U. Hartmann [87] investigated the Van der
Waals interaction between ﬂat sample surface and sharp probes such as a cylinder, a
paraboloid and a cone. J. L. Hutter and J. Bechhoefer [88] use the theoretical force—
distance relation for a sphere above a plate which they compared with experimental data
(although the tip in use is in fact close to a pyramid). In C. Argento and R. H. French’s
paper [89] the tip images obtained from scanning electron microscopy suggests a
parametric tip model which consists of a cylindrical part and a conical part covered by
the spherical cap. The parametric tip model was also used for estimating the pyramidal
tip shape. In this thesis, we use the same parametric tip model for calculating the Van der
Waals force between the tip and sample.

If we only consider the attractive part of the Van der Waals force between the

sample and tip, the potential energy of interaction w(d) is deﬁned as:

_C .
W) = 56’3" (5.4)

 

where Cdisp is the interaction constant deﬁned by London [90]. The interaction force

between the sample and tip is given by the gradient of interaction potential deﬁned as
f = —Vw (5.5)
Hamaker performed the integration of the interaction potential to compute the total

interaction force between macroscopic bodies with three assumptions [9]]:

71

(l) Additivity: the total interaction can be obtained by the pairwise summation of the
individual contributions;

(2) Continuous medium: summation can be replaced by an integration over the
volumes of the interacting bodies assuming that each ‘molecule’ occupies a
volume dv with number density p;

(3) Constant material properties: the number density p and the interaction coefﬁcient

are constant over the volume of the bodies

 

Figure 5.3 Integration of the interaction force between two arbitrarily shaped bodies
The total force between two arbitrary shaped bodies as shown in Figure 5.3 is

given by:
F=p1p2 L2 Llﬂdwvldvz =—p1p2L2 [1dev1dv2 (5.6)

where pland p2 are the number densities of bodies 1 and 2.
Details of the six-dimensional volume integration found in [92] is summarized below:

Using the gradient theorem ( LVadV : (Lads = (is ands ), we get

F = #3192 [,2 L‘dendvz = #91sz1 [52 wnAzdszdvr (5.7)

where n; represents the normal to the body 2.

72

Let G be a vector ﬁeld deﬁned as

V -G = —w (5.8)
Substituting equation (5.8) into (5.7), we get:

F = -p1p2 [,2 [VIdevrdvz = -p1p2 L1 [32 wadszdn =p1p2 [,1 [52(V-Gﬁdv2dw

(5.9)

Using the divergence theorem ( LV-AdV = (is A-dS = (is A-ndS ), a double-surface

integration is obtained as
F =P1P2 [V1 [2(V-G)nzdvde1 =P1P2 [52 [SI (Gn1)n2d91d92 (5.10)

where n1, n2 represent the normals to bodies 1 and 2.

Hamaker constant is deﬁned as:
_ 2
A — 7: C plpz (5.11)

Substituting equation (5.11) into (5.10), we get the Van der Waals force between two

bodies as:
A A A A A
F: (Corr )n dsds =— (G-n )n dsds (5.12)
’01szle 1 212 chLZ'Ll l 212

This integration calculates equivalent distributed forces over the surface of body 2 that
represents a weighted average of the inﬂuence of the surface of body 1. The vector ﬁeld
G is obtained from the interaction potential of two molecules. Consider the Van der

Waals interaction potential

“’(d) _ ‘Cdisp _ ’Cdisp _ _Cdisp (5 13)
_ 6 _ ‘ ” 1/2 6 — " " 3 '
61 (OM) ) (WC)

 

73

where it is the vector from a point in body 2 to a point in body 1. The solution of
vector ﬁeld G in equati0n(5.8) is

_ Cdisp;

G = -
3(x-x)3

 

(5.14)

The double surface integration is in general difficult to execute both analytically
and numerically. To simply the problem, we will start with the simple sample, a ﬂat

sample surface and assume the parametric tip model.

5.2.1 Model Equation

The schematic of the tip model is shown in Figure 5 .4.

A

Z Tip

 

Truncated cone

Spherical cap
V

 

A I

     

 

 

 

Figure 5.4 Schematic of the tip model. R is the radius of the spherical cap. a is the angle include the
spherical cap, [3 is the cone angle, 10 is the distance between the tip end and sample.

Let body 1 in equation (5.6) represents the sample and body 2, the tip. For a ﬂat

sample, we only need to calculate the vertical component of the interaction force since all

74

other components are zero due to symmetry of the problem. Therefore n1 = (0, 0, 1),

substituting equation (5.14) into equation (5. 12)

 

A A
F=— 3d): d9 (5.15)
2L2 (”313022 +y2 +2 23) 050112 2

In S] , integrating over appropriate limits for x and y, (-oo, +oo) yields

7r

 

Z
[S 2 dxay = (5.16)

13(x2 +y +22)3 623 ,
Substituting the equation (5.16) into (5.15) we get the interaction force as:

F =— —n2ds2 (5.17)

Considering symmetry of the problem, we only need to integrate the vertical component
of equation (5.17) over the tip surface. The integration over the surface is the sum of two

parts, spherical cap and truncated cone.
For the spherical cap, 2 can be written as a ﬁmction of 20 and (o as shown in Figure 5.5:

z=zO+R—Rcosa) (5.18)

 

 

 

 

 

 

b--ID---------

 

 

Sample

 

Figure 5.5 Schematic of the spherical cap

75

The component of the normal 112 along the z direction is
n22 =—cosco (5.19)
The inﬁnitesimal element of the surface dSz on the spherical surface is

as, = 27rerw= 27m" sin wdco (5.20)

The force contributed by the spherical cap is

 

 

F256: ﬂ—Az- ”3n; 22d: — $.61 3(—cosa))27rR2sinaxiw
32 62 » 6(20 +R— Rcosw)
Fzsc = AR2(1—cosa)(Rcosa—zocosa-R—zo) (5.21)

623 (R + 20 — R cos 0:)2

The second part is the force contributed by the cone area. Figure 5.6 shows the schematic

of the truncated cone part.

 

 

 

 

Z0+R(1-cosa)

 

 

 

 

Sample

 

 

 

 

Figure 5.6 Schematic of the truncated cone

Expressing 2 as a function of r and 20

76

z = 20 +R(1—cosa)+tana(r—Rsina) (5.22)
The component of the normal 112 along the z direction is
n22 = —cosa (5.23)

The inﬁnitesimal element of surface dSz on the spherical surface is

 

dS2 = 2’” dr (5.24)
COSCI

Substituting equation (5.22)-(5.24) into equation (5.17), we get the force
contribution of the cone as:

cmone = —A[zo cos a + R cos a — R(cos 2a)] (5.25)

 

6tanasina(zo + R —Rcoscz)2
Adding equations (5 .21) and (5 .25), the total force between the tip and sample can

be calculated as:

F2 = F296 + FZCONQ
_ AR2 (1 — cos a)(R cos a — 20 cos a — R -— 20) + —A[zo cos a + R cos a — R(cos 2a)] (5°26)
6z(%(R+zo—Rcosar)2 6tanarsina(zo+R—Rcosa)2

 

where the Hamaker constant - A and the distance between the tip end and sample - 20 are
unknown parameters. Reference [93] lists different methods proposed to calculate the

Hamaker constant for different materials and conﬁgurations.

5.2.2 Parameter Estimation and Model Validation

In the ﬁnal expression for tip-sample interaction force there are two unknown

parameters. One unknown parameter is Hamaker constant A that depends on both the

77

sample and tip material properties. Another unknown parameter is the distance between

the tip and sample, 20. The distance between the tip and sample can be expressed as
20 = z — do (5.27)
where do is the position of contact point, and z is the position of the tip as illustrated in

Figure 5.7. The unknown parameters are therefore A and do and equation (5.26) can be

written as:

_ sc cone

= AR2(1—cosa)[Rcosa—(z —d0)cosa—R —(2 —d0)] +
6(z—d0)2(R +z-d0 —Rcosar)2
-A[(z - d0)cosa + Rcosa — R(cos 2a)]
6tanasina(z—d0 +R —Rcosa)2

(5.28)

 

 

 

 

 

do

 

Sample

 

 

0 _.
Figure 5.7 schematic of the tip and sample position in z direction

In this work, we use a least squares estimation procedure to determine A and 20

by minimizing the error in equation (5.29) with respect to unknown parameters A and 20

78

 

1 N th exp 2
0' = W Z (Fm — Fm ) (5.29)
i=1

. . ex . . . .
where srgma rs the rms error, — Fvarlz) rs the measured force in region 2 and F52" IS the

model predicted force in equation (5.28).

Experiments for measurement and characterization of Van der Waals force with
different tip-sample systems are reviewed for different systems in [94] and [95]. Here we
follow the same measuring procedure as described in reference [96]. The experiment was
performed using Veeco Instruments Nanoscope IIIa operated in ambient air with a
standard silicon nitride tip. A gold layer was selected for evaluationg the model since this
is a standard surface used by many groups. The gold layer was a (500nm X 500 nm)
photolithographically generated pattern of about 25 nm thickness, with about 5 nm
buffer layer of Titanium on a silicon wafer surface with oxide layer. The sample was
mounted on the scan stage. Then the piezoelectric scanner was extended along z-axes
with an applied voltage, decreasing sample distance until contact. A plot of cantilever
deﬂection is obtained as a function of sample displacement. The force corresponding to
each value of deﬂection is calculated using Hooke’s law. The above procedure was
repeated 10 times to get 10 force curves at same position as shown in Figure 5.8(a). Each
force curve contains 2048 experimental data points. In the experimental force curve, data
points in region 1 are used to calculate the zero force as shown in Figure 5.8(b). The data
points in region 2 shown in Figure 5.8(c) are used to estimate and validate the force

equation (5.28).

79

 

 

0.5

 

 

 

 

 

 

 

 

Zero force

  
 

(b)

Region 2

 
  
 

,, Contact point

 

 

    

 

0 1 ﬂ ‘2500'2'5 o T 256
0+.**‘.*..‘c*.' . . q 0 "
Average force curve ‘ Ten force curves
(c) . (d)
-o.35 4 '2-5 .. . . . i . . .
0 35 0 35

Figure 5.8 Ten experimental force curves in same sample position.

Ten force curves are averaged at each sample position and a total of 33 data

points are obtained in region 2. Six data points are used to estimate the unknown

parameters A and do in equation (5.28) as shown in Figure 5.9(b). The radius of the

spherical cap, R, was set to 100nm and angle 0., to 35°. The RMS values estimated are

Hamaker constant A = 0.01867nNnm and position of the contact point do = 37.56nm. For

model validation, these parameter values are used in equation (5.28) to calculate the force

at the remaining 28 points. The validation results are presented in Figure 5.9 (c).

80

-0.05 "

-0.1

-045_
412

-0.25
-0.3

 

 

 

 

 

 

 

 

0. 1 t L t’ *L 1' [
- ﬁr 1r
_0.05‘ (a) etgw’“, * s are e 5
*t-
tr
-01- .4 .
tr
iv
'0.15~ b -
t
-0.2- r -
tr
‘0.25L 1,. .4
-0.3t 1' .
'0-35' 1 r r J r L J r r >
39 40 4142 43 44 45 46 47 48 49
. I ‘C 1 I t .I’ * “l
, _~+——-
«-005 (C) . sent—M .. .
. 93),".
v; 1
-0.1 a)“
, J
-0.15 [’4‘
-02 /" E ' a
. . , y . xpenmental data
_Eﬁiimental data .025 2"" 0 Training data
- f — Fit curve
413 o
l
40 43 ' I ‘46 39 43 46 49

 

 

 

 

 

Figure 5.9 A scheme showing the estimation of the unknown parameters and comparison of the
theoretical force curve with the experimental data

The theoretical Van der Waals force is shown in red and the experimental data are

shown as blue stars. The red stars are the data used for estimating the unknown

parameters. From Figure 5.9(c) we can see the theoretical model predictions agree with

the experimental data very well which validates the Van der Waals model in equation

(5.28).

81

5.3 Numerical Result of Van der Waals (VDW) Force Model

The analytical model for Van der Waals force between a parametric tip and a ﬂat
sample has been calculated and validated using the experimental AF M data. The next
step is to extend the VDW model for interactions between a parametric tip and a non-ﬂat
sample. In the case of a non-ﬂat sample, the double surface integration is very difficult to
evaluate analytically and numerical methods must be developed for generating a model of

the Van der Waals force as outlined in Figure 5.10.

 

 

 

Tip & Sample Discrete VDW Model VDW Force
Discretization Matrix Equation Image

 

 

 

 

 

 

 

 

 

Figure 5.10 Schema of Van der Waals force calculation

As deﬁned previously in section 5 .2, let 31 represent the surface of sample, and 52
represent the tip surface. The parametric tip surface can be divided into two parts: 321 -
surface of spherical cap and 322- the surface of truncated cone. The integration in
equation (5 .12) can be expressed as the sum of two double surface integrations as:

F = 34—, l. L(G°£i)a;d91d92 = %< ] L<G~£>E£dsldszl + [- I (047152341422
c7: 2 czz' 321 322 5‘1
(5.30)

The surfaces of the tip and sample are ﬁrst discretized into a ﬁnite number of
small square elements. The double surface integration can then be calculated as double
sum of the pairwise interaction forces between each element on sample surface 51 and tip

surface 32 as shown below:

82

A A A
F='C72‘ZZ(GL2'“1)“25152

A $1 32 A A A A A (5.31)
= —2- 2 Z (01,21'01)112131321 + ‘7 Z 2 (01.22 '“1 )“2251522
672' 31 321 0” S] 522

5.3.1 Surface Discretization

The discretization of spherical cap and truncated cone surfaces are described below.
i). Spherical cap: Figure 5.12 shows a schematic of the spherical cap. The (x, y, z)

coordinates of each point (x, y, 2) on the spherical cap surface, is expressed as:

x = x0 + R - sin(a)z) - cos(co,y) (5.32)
y = yo + R - sin(a)z)-sin(a)xy) (5.33)
z = 20 +R—R-cos(a)z) (5.34)

where (x0, yo,zo) is the tip apex coordinate, (oz varies from 0 to a and 02,0, varies from 0

to Zn.
Consider four points, all, a12, a21, a22 on the spherical cap surface as illustrated in
Figure 5.12 (a). The coordinates of these four points are expressed as below.

all:

xall = x0 + R'Sin(wza11)'°05(wxya1 1)
yall =y0 +R'Sm(wzall)'5in(wxyall) (5.35)
2011 = 20 +R-R'COSWza11)

a12:

xa12 = x0 + R ' Sin(wza12) ' cos(a)xy012)
you = yo + R ' Sin(wza12)'sm(wxya12) (5-36)
za12 = 20 + R —R-cos(wzalz)

83

a21:

xa21 = X0 + R ' Sin(wz¢121)' cos(wxyaZI)
ya21 = J’o + R ' Sin(wzaZI) 'Sin(wxy021) (5-37)
2021: 20 +R—R ‘cos(a)za21)

a22:

J‘azz = x0 + R ' Sin(wza22) ' 008(wxya22)
yaZZ = J’o + R ' Sin(“’zaZZ) 'sm(wxyaZZ) (5-38)
Za22 = 20 + R — R 'COSWzazz)

where wza11= wza12,wza21= wzazz, wxya11= coxyazl and mxya12= wxyazz- Figure 5-11

shows the tessellation of the spherical cap.

 

 

 

 

 

 

 

-100 -100

Figure 5.1] Discretization of spherical cap.

84

 

 

 

 

 

 

 

 

>
(XOaYOaZO)
x
(a)
A y
A Z
(x050) '
R wxy T
(oz x
z
20
(b) (C)

Figure 5.12 (a) Schematic of elements in spherical cap (b) Cross section of spherical cap in x-z plane
(c) Cross section of spherical cap in x-y plane.

85

ii). Truncated Cone:

A schematic of the truncated cone is shown in Figure 5.14. As illustrated in Figure 5.14
(b) and (c), the (x, y, z) coordinate of each point on the truncated cone surface is

expressed as:

x=xo +r-cos(a)xy) (5.39)
y : yo + r ' sin(a)xy) (540)
2:20+R(l—cosa)+tana(r-R5ina) (5 41)

where (xo, yo, zo) is the tip apex coordinate, r is the cone radius and coxy varies from 0 to

Zn. Consider four points (all, a12, a21, a22) on the truncated cone surface. From Figure
5.14 (a), the coordinates of these four points are deﬁned as:

all:

xall = 3‘0 +rall 'COS(wxya11)
yall = yo +rall 'Sin(wxya11) (542)
2a” = 20 +R(l—cosa)+tana(ra11—Rsina)

a12:

x012 = x0 + r012 'Cos(wxya12)
J’alz = yo + ra12 'Sin(wxya12) (5-43)
2012 = 20 + R(l — cos a) + tan a(r012 — R sin a)

a21:

x021 = 9‘0 + r021 'COSnyazr)
ya21 = Yo + ra21'sm(wxya21) (5.44)
2021: 20 + R(l —COS(Z) + tana(r021 —RSIII a)

a22:

86

x022 = x0 + r022 '°°S(wxya22)
ya22 = Yo “a22 'Sin(wxya22) (5-45)
2022 = 20 + R(l — cos a) + tan a(ra22 — R sin a)

where r311= r312, ra21= T2122, mxy311= 03xya21 and wxya12= rowan. Figure 5.13 shows a

mesh of the tnmcated cone.

400

 

 

 

 

 

 

0 ' '
-600 -600 400

Figure 5.13 Mesh in truncated cone

87

 

 

(X0. Yo. Zo)

 

 

 

 

 

(a)
z
A r_con_end 11 y
r ;
‘RsirF G
(X. y)
R (Xo Yo) r w
I < ' xy
m >
(X0. Y0. 20) x

 

Z0+R(1-cosa) B

 

 

 

 

r Sample 1

(b) (C)

Figure 5.14 (a) Schematic of the mesh in truncated cone (b) Cross section of truncated cone in x-z
plane (c) Cross section of truncated cone in x-y plane.

88

5.3.2 Numerical Model Validation

In order to establish the validity of the model we ﬁrst compare the numerical
model simulation result with the analytical result, obtained for a ﬂat sample same as in

section 5.2.

Ideally, the double sum in the VDW model equation (5.31) should be calculated

_"fl

numerically on the entire surface of sample and tip to obtain the most accurate result.

gr _qna

However, since the force between tip and sample decreases as distance increasing,
regions of the sample and tip that are very far ﬁ'om each other can be neglected. We
deﬁne the area where the force between tip and sample cannot be ignored as valid
integration areas of both tip and sample. Hence in order to save computation time without
affecting accuracy of the calculated force, equation (5.31) needs to be calculated only
within the valid integration area.

In order to ﬁnd the optimal size of valid integration area on the sample and tip
surfaces, the double sum VDW models equation (5.31) is evaluated with gradually
increasing areas of integration. Figure 5.15 shows the mesh of the integration tip and a
square area on the sample surface. Figure 5.16 (a) shows a plot of Van der Waals force
calculated with different size of integration area on sample surface for a ﬁxed tip surface.
The x—axis represents side of the square integration area on sample surface. The plot in
Figure 5.16 (b) shows that the force increases with the integration area and saturates at a
square of size 1500nm. Further increase in the area of integration does not change the
force value signiﬁcantly. In this thesis, we set the width of the valid integration area on

sample surface to be 1500nm.

89

 

 

 

 

 

.ﬂ

 

 

 

\800

 

-1000 -800 ’

Figure 5.15. Mesh of the tip and sample

Similarly, the optimal integration area on tip surfaces estimated. Starting with

initial area that includes the whole spherical cap, the maximum radius of the truncated

cone represents the size of the integration area of tip surface. Figure 5.17 (a) shows Van

der Waals force calculated with gradually increasing integration areas of tip surface. The

x-axis represents the radius at the truncated end of cone, T_con_end- Figure 5.17 (b) shows

that the force increases with increasing r con end- When the maximum radius cone is

larger than 900nm, the force increase is negligible. In this research, we choose the

90

Force: nN

Force difference: nN

-0.07

-0.08

-0.09

-0.1

-0.11

-0.12

-O.13

«0.14

-0.15

-0.16

-0.01

-0.02

-0.03

—0.04

-0.05

-0.06

 

 

 

 

 

 

 

 

4000

 

 

 

Width of integration area in sample surface: nm

Figure 5.16 Force vs. Size of integration area in sample surface

91

If (a)
t in
l l‘ f I' f I' I L I
500 1000 1500 2000 2500 3000 3500
Width of integration area in sample surface: nm
I I l * T *
(b)
L. -
l- -
l l f l f l’ J L ’
500 1000 1500 2000 2500 3000 3500 4000

 

force: nN

force difference: nN

 

 

0.017 r I I >

(a)
-0.018

I
I

-0.019

T
l

-0.02

-0.021

I
1

-0.022

I
1

-0.023

I
l

-o.o24 L 4

-0.025

I
I

-0.026

 

 

 

-0.027 ' '
0

 

 

 

 

500 1000 1500

rcon_end' "m

Figure 5.17 Force vs. Size of integration area in tip surface

92

0.11 t t x r .
+ Numerical result
0.1 ~ —9—Analytical result “

 

 

 

 

 

0.09

I

0.08

0.07

0.06

0.05

0.04

Attractive force in z direction: nN

0.03 -

r

 

0.02

 

 

4 I

t
10 15 20 25 30 35
Tip sample distance: nm

0.01 i '

 

Figure 5.18 Force vs. tip-sample distance

The numerical model is validated by comparing the simulation results of the same
geometry using the numerical double sum VDW model equation (5.31) and analytical
VDW model equation (5.28). Figure 5.18 shows the result of validation. The x-axis is the
distance between the tip apex and sample and the y-axis is the corresponding force in z

direction.

5.4 Model Based Deconvolution of AFM Image

Once the Van der Waals model is validated, the model can be used for a physics
based deconvolution of the AF M image data. Figure 5.19 shows a schematic of the AFM

image deconvolution procedure using the Van der Waals force model.

93

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Measured force
\ Deconvolution Sam le sha e
. —-> Usin p p
Tip shape g (True)
/ VDW model
Initial guess

 

 

 

Figure 5.19 Schematic of AFM image deconvolution using force model
First the tip is positioned at a distance from sample surface so that the force detected will
fall in region 2 dominated by the attractive part of Van der Waal force (Figure 5.2). Then
the contact mode AF M is used to scan the sample to acquire the force measurements that
yield sample topography with artifacts. With the Van der Waals force model and tip
model, AF M image deconvolution can be formulated as an inverse problem which can be

solved using the forward Van der Waals force model in an iterative framework as shown

 

 

 

 

 

 

 

 

 

 

 

  

 

 

 

 

 

 

 

 

 

 

 

in Figure 5 .20.
T d l VDW force
'9 mo e of true sample
Initial . I , VDW force True
Sample shape VDW model Calculated Sample Shape
] N
Sample shape :
Update

 

 

 

Figure 5.20 Procedure of AFM image deconvolution using force model.

1. The measured image data is used to derive the initial guess of the true sample

(0).

shape s
Iteration n

(n)

2. With the sample shape 5 and tip model, we calculate the VDW force using

the validated forward model.

94

 

d:
be

(111

3. The error between the model calculated force and the measured force of the

true sample is determined. If the error is within a prescribed threshold — STOP

()2

and s is the true shape of the sample.

(n+1)

4. Otherwise, the sample shape is updated to s so the error in step 3 is

minimized. Since we know a priori that the measured image is dilation of the
true shape by tip shape, the updating procedure simply involves sharpening the

edge. Go to step 2.

5.5 Implementation Results

The above procedure for deconvolution is applied to a sample with an edge and
corresponding AFM data generated using morphological dilation to introduce the artifacts.
To simplify the overall procedure the error between model prediction and measurement is
computed using the values at one position of the tip. Figure 5.21 shows a schematic of the
tip and true sample topography for calculating the VDW force using the forward model.
We use the parametric tip model as discussed before. The tip is placed above the sample
at the distance of lOnm. Figure 5.22 shows the mesh of the sample surface.

The initial guess for the true sample shape was generated using the simulated
AFM data and is shown in Figure 5.23. The edge was parameterized using a single
parameter, namely the slope of the edge. Figure 5.24 shows the results of the image
deconvolution using iterative deconvolution procedure. Figure 5 .24 (a) shows the error
between model and measured force values at single position in each iteration with

different updated sample shapes. The successive updated sample edge shape in each

95

iteration and the ﬁnal converged deconvolved sample edge shape are shown in Figure
5 .24 (b) and compared with deconvolution result obtained using mathematic morphology

described in Chapter 4.

 

zo=10nm

 

/ Sample

 

 

 

'H———I-
30nm
Figure 5.21 Schematic of the tip and sample surface

 

Figure 5.22 Mesh of the sample surface

96

 

 

 

 

 

 

 

 

 

0. . tr t 1% (II-
—-III— Scan Image

-2 - —9— Initial Guess -

.4 - ..

-6 r -

-8 F -
-10 - 4
-12 M 4
-14 - ..
-15 .. .
'18 ’ * I’ * I g f I t ’

-100 -80 -60 -40 -20 0 20 40 60

Figure 5.23 Line scan of the scan image and initial guess image

The deconvolution procedure was then implemented on the data from a second
sample edge which is piecewise linear as shown in Figure 5.25. The initial guess is
derived from samples of the (measured) simulated AFM data. In each iteration the error

is calculated using the model prediction and measured force values at a single position of

the tip. In nth iteration, the sample shape is deﬁned as s" = (28 ,21" , - . 323,). The updating

of sample edge shape is carried out as below:

 

 

n-l—R_JR2_(x;;-1 2
_ m 3

m > n (5.46)

0 m<n

n
zm

97

Error

 

0.014 1 l x I

0.012

0.01

0.008

0.006

0.004

0.002

 

 

 

I I I I

 

o I I l f
3

3.5 4

No. of iteration

 

Height: nm

 

 

,, 9.1' ,
-40 -20

    

 

+ Scan Image

-—t'— True sample surface
+ Sample surface-MM
Updated sample surface
—e— Sample surface-IP

r _, ,_ I

0 20

 

 

 

 

 

,l’..¥

40

X coordinate: nm
Figure 5.24 Result of the image deconvolution using VDW force model

98

 

 

 

 

 

 

 

 

 

 

z I) r _/
R
a
zo=10nm ..
30nm 15nm 26nm
sample
30nm ’

Figure 5.25 Schematic of the tip and sample

Figure 5.26 shows the results of the image deconvolution using iterative
deconvolution procedure. The error between model predicted and measured force values
at single position in each iteration with different updated sample shapes are shown in
Figure 5.26 (a). Figure 5 .26 (b) shown the updated sample edge shape in each iteration,
the ﬁnal converged deconvolved sample edge shape and compared with deconvolution
result obtained using mathematic morphology described in Chapter 4.

The force-model based deconvolution algorithm has been developed and initial
results show the feasibility of the method for determining true topographic shapes of the
sample. However currently, the algorithm is applied to minimizing the error between
model and measurement data at one position of the tip. The results will be much more
accurate if the error is computed using VDW force calculations and measurements on a

larger scan area centered at each point.

99

 

0.005

 

 

I’ I f I‘ f
4 5 6 7 8
No. of Iteration

 

 

_L
ML
03

 

15 r r r

: + Scan Image (b)

10 ~ —|— True sample surface '
+ Sample surface-MM
5 ~ — Updated sample surface —
. —9— Sample surface—1P

 

 

 

Height: nm

 

 

 

   

X coordinate: nm

Figure 5.26 Result of the image deconvolution using VDW force model

100

Chapter 6 Application of SPRM to Tissue Engineering

6.1 Introduction

From its inception, SPRM was developed within an application framework for
two reasons. One was to challenge the instrument development with real versus ideal
problems. As will be discussed in detail in this chapter, the evaluation of the properties of
tissue scaffolds used for regenerative medicine provided a challenging example which
contributed greatly to the development of SPRM. The second reason was to introduce the
large potential users community to the newly availably SPRM capability. This is best
accomplished by demonstrating the power of the technique to investigate signiﬁcant
research problems in new and better ways.

Tissue scaffold engineering is an active and successful research ﬁeld [97-99] in
biological studies. Tissue engineering is the use of a combination of cells, engineering
materials, and suitable biochemical factors to improve or replace biological functions
[100]. The ﬁeld of tissue engineering merges the expertise of life sciences, physical
sciences, and engineering to develop functional tissues that can maintain, restore, or
improve damaged organs [101]. Biomaterials have played a crucial role in the
development of tissue engineered organs. Cells are 'seeded' into an artiﬁcial structure
capable of supporting three-dimensional tissue formation. These artiﬁcial structures,
usually referred to as scaffolds, allow the cell attachment and migration. The scaffolds
deliver entrained growth and can even exert certain mechanical and biological inﬂuences

to modify the behavior of the cell phase. The success of tissue engineering has helped in

101

clinical implant work within complex tissues such as bladders [97] and cartilage [98].
However, despite such successes much fundamental understanding is still needed to
design scaffolds with the most appropriate mechanical, topographical and chemical
properties for particular cells or cell classes.

Actin-based cells can actively probe their environment through lamellipodia and
ﬁlopodia extension. The leading edge of such extensions corresponds to tens of
nanometers sensing area at the cell’s extremities. The environmental triggers that cause
extension/retraction/re-direction through actin polymerization/depolymerization should
therefore be assessed on a comparable scale. With nanometer-scale resolution, atomic
force microscopy is suitable to be used to investigate minimally conductive biological
surfaces [5 1].

Recently two important mechanical properties, surface roughness and elasticity,
are found to be important for cell growth. Deligianni et al have published the effect of
surface roughness of hydroxyapatite on human bone marrow cell grow [102]. Their
experiment discovered that surface roughness affected cellular response, cell adhesion
and proliferation. Engler A.J. et a1 investigated the correlations between substrate
stiffness and cell adhesion [103]. Their experimental result shows that the adhesive
spreading of cells correlates broadly with the effective stiffness of substrate tissues and
stiffer materials tend to promote spreading of smooth muscle cells. These two mechanical

properties are investigated using SPRM in this work.

102

6.2 Materials and Methods

(A) Tissue Scaffold Samples

Tissue scaffolds fabricated from electrospun [104, 105] carbon nanoﬁbers was
obtained from the Donaldson Company. The nanoﬁbers were electrospun using an
adapted electrospinning probe procedure described in Reference [106]. No further
information about the tissue scaffolds samples was provided.

(B) Nanoscope IIIa Special SPRM Modiﬁcation

The scanning probe microscopy (SPM) experiments were performed using a
Veeco Instruments Nanoscope IIIa operated in atomic force microscopy contact mode in
ambient air [4, 6, 41, 51]. The system has a special modiﬁcation developed by our
research group in partnership with Veeco Instruments. SPRM system is used to scan the
sample. The SPM system itself is given the ability to auto-focus on regions of interest
through incorporation of recognition—based tip control, described as Scanning Probe
Recognition Microscopy (SPRM). The recognition capability of SPRM is realized using
algorithms and techniques in computer vision, pattern recognition and signal processing
ﬁelds. Adaptive learning and prediction are also implemented to make detection and
recognition procedure quicker and more reliable. The integration of recognition makes
the SPRM system more powerful and ﬂexible in investigating speciﬁc properties of

samples.

103

6.3 Surface Roughness

The surface roughness of the substrate has been shown to inﬂuence cell
attachment. It is therefore important to obtain this information accurately and
conveniently along tissue scaffold nanoﬁbers. In the majority of studies, the surface
roughness is the Root Mean Square (RMS) of height values in a region of interest as

deﬁned in equation (6.1).

 

g (Zi - Zave)2

RMS = ‘=1 ,
N (6 1)

For AFM-based measurements, N is the number of total pixilated data points in

 

1 N
this region; Z,- is the height value at each pixel and Z ave = 7V .21 21' is the average
1:

value of all height values.

In conventional atomic force microscopy, the surface roughness information is
acquired through manual application of a rectangular region of interest box [107]. The
surface roughness within the box is then calculated using equation (6.1). There are
several problems with the conventional approach to surface roughness investigation when
the sample is a tissue scaffold nanoﬁber.

(1) The shape of the region of interest (ROI) may not be rectangular, necessitating
the application of several small ROI boxes which follow the curvature of the nanoﬁber.

(2) Only a single value is provided for each time of operation. Therefore, in order
to get surface roughness along a nanoﬁber, this operation would need to be repeated for

many times.

104

(3) Height data, Z, is used to calculate the surface roughness. This is acceptable
for samples whose surfaces are relatively ﬂat because then the variation in height data
will reﬂect the variation in their surface roughness. This assumption is no longer
appropriate for tissue scaffolds because the nanoﬁbers have a cylinder shape. Therefore,
the variation of height data, Z, includes not only its surface roughness variation, but also
the variation caused by the shape.

In the SPRM system, a recognition-based scan plan can be generated to auto-
focus tip motion along an individual nanoﬁber [69, 108]. Adaptive scanning enables
SPRM to follow along an individual nanoﬁber even when it crosses another as shown in
Figure 3.13. Therefore, the whole nanoﬁber, or whole nanoﬁber mesh becomes the
region of interest.

Figure 6.1 (a) shows the Atomic force microscope (AFM) images of tissue scaffold
sample. Figure 6.1 (b) shows the seaming electron microscope (SEM) images to ensure
that the AF M results were representative over larger scaffold areas. SPRM were then used

to scan the same sample to provide more reliable and accurate surface roughness detail.

105

 

 

Figure 6.1 (a) AF M image of electrospun carbon nanofiber tissue scaffold. The scan area is 5 square
microns and the z-height projection is 1500 nanometers. (b) SEM image of electrospun carbon
nanoﬁber tissue scaffold. The scan area is 20 square microns, images by Q. Chen and Y. Fan [70].

In the SPRM system, a recognition-based scan plan can be generated to auto-focus
tip motion along an individual nanoﬁber as discussed in chapter 3. Figure 6.2 shows the
conventional AF M image of the nanoﬁber and the SPRM scan image of the nanoﬁber. The
SPRM system starts with coarse scan and picks up the ﬁrst nanoﬁber as shown in Figure
6.2 (b). During the ﬁne scanning, adaptive scanning algorithm enables SPRM to follow
along an individual nanoﬁber even when it crosses another nanoﬁber as shown in Figure
6.2 (d). Therefore, the whole nanoﬁber, or the whole nanoﬁber mesh becomes the region
of interest. After ﬁnishing high resolution ﬁne scan only on the ﬁrst nanoﬁber, SPRM
system returns to coarse scan to ﬁnd another region of interest. This coarse-ﬁne-coarse

scan procedure will keep going on until SPRM system ﬁnish scanning the whole region.

106

  
   
 

1000 1000 1 000

  
   

(b)

600

200
200

(e) m1000 1000

 
  
 

600

200

-200 -200

-600 -600

Figure 6.2 SPRM scan image of the nanoﬁber. (a) Conventional AFM image of the nanoﬁber (b)
Coarse Scan picks up the first nanoﬁber; (c) Finish high resolution ﬁne scan only on the ﬁrst
nanoﬁber and return to coarse scan to find another region of interest; (d) Coarse Scan picks up the
second nanoﬁber; (e) Finish the high resolution ﬁne scan only on the second nauoﬁber and return to
coarse scan to ﬁnd another region of interest; (0 Coarse Scan picks up the third nanoﬁber; (g) Finish
the high resolution ﬁne scan only on the third nanoﬁber. Images by Y. Fan and Q. Chen [109].

In Scanning Probe Recognition Microscopy, distance data, D, instead of height
data, Z, was used to get the real roughness of the sample surface. The Kasa circle ﬁt
method [110] was implemented to get the center (xcemer, Zcenrer) of the most ﬁtted circle
as shown in Figure 6.3. Then the distance Di between each point on the surface and the

ﬁtted circle center was evaluated and used to calculate the surface roughness maps and

histograms.

 

2 2
Di = \/(Zi ‘ Zcenter) + (X i ’ X center) (6-2)

107

 

 

 

 

 

 

 

 

(xoenterr Zcenter)

Figure 6.3 Circle in based on Kisa method [70]

Only the center part of the height data was used to ﬁnd the best ﬁt circle. The
boundary regions are unreliable due to tip-shape dilation effects. Dilation, or broadening
of the image, is a result of the side of the tip coming into contact with the curved side of
the nanoﬁber [72, 76]. When an SPRM scan is focused on an individual nanoﬁber, both
the edge and center data is acquired. However, only the center part of the nanoﬁber
provides reliable data because of the tip convolution effect [56, 73]. The ideal AFM
would have an inﬁnitely sharp tip to reach as much of the surface as possible and an
inﬁnitely sharp impulse response in its feedback system to instantly adjust the height of
the tip as it is scanned over the surface. However in reality, the tip has a pyramidal or
conical shape with some ﬁnite end radius so it is durable enough to withstand the surface
interaction forces. The effects of the tip shape cannot be avoided and these result in
characteristic tip-dilation artifacts, as shown in Figure 6.4 (a). The nanoﬁber properties

evaluations are restricted to regions of reliable data through the use of an erosion

108

operation [111]. This is an important consideration when analyzing tissue scaffold

nanoﬁber geometries using AF M-based methods (instead of planar substrates).

 

 

 

 

 

 

 

 

 

 

(a)
/ True Curvature
450» I (b) l I ‘ * ~ I ' —Scanned Image
—O-—Reconstructed Image
K .
_ .5 R'- '
300) _ . _ . '4 i f: 1 f 1 I E"; I 9' .
1500 240°
Kasa Circle Fit

...
a a
~'."Oocca IIII“.......

Figure 6.4 (a) Characteristic tip-dilation artifacts (b) The cross section of a real AFM nano ﬁber
image and the best ﬁt circle [70]

Using data obtained by SPRM along individual nanoﬁbers, the surface roughness

was calculated on each pixel based on a local neighborhood region using below equations:

 

 

N .—
Era—DY
Roughness: M N (6.3)
_ 1 N
and D=FZDi (6.4)
i=1

109

The shape and size of the local neighborhood region can be adjusted by the user,
which makes the system adaptable to different sample shapes. In this research, a
rectangular box around each pixel is chosen as the local neighborhood region, with a
width of box size of 219.76 nm (close to the nanoﬁber diameter) [108]. Multiple sets of
overlapping surface roughness information were generated, with the provision that any
box that extended outside the nanoﬁber boundaries was automatically truncated. Total
564267 data points are used to calculate the surface roughness map. A surface roughness

map along individual nanoﬁber was then generated as shown below.

 

500 2000
Figure 6.5 Surface roughness map along individual ﬁber [109]

The histogram of the surface roughness map is shown in Figure 6.6. From the

histogram, we can get the mean value as 4.57nm, the mode value as 2.0mm, the variance
value as 7.15 nmz, and the range is 0.8nm~19.7nm. The histogram also shows the

distribution of the surface roughness while an individually applied ROI box would be most

likely to return the mode value. When comparing the surface roughness of different

110

samples, the mode value may not show the true difference. However, the variances and

distributions will show the true difference between surface roughness of the samples [70,

 

 

 

 

 

108].
4
X 10
8 L I. L I. '
7 ~ 5
6 M s
m
0
o
g 5 ~ 5
(D
E
a 4~ -
H
.8
5 3~ 1
Z
2 M ..
1 R IlllllllIl-u '
0 ' “-..—J _ "
0 5 10 15 20 25
Surface roughness (nm)
Figure 6.6 Histogram of surface roughness map [109]
6.4 Elasticity

Atomic force microscopy can be used to measure elastic properties by collecting
force curves over points on the surface of the sample. AF M has been used to study the
elasticity of cells [53, 112-116], bacteria [117], monkey eyes [27], gelatin ﬁlms [118],
human platelet [119] and tissue scaffold [70, 109, 120]. Analyzing the collected force
curve with theoretical models can provide quantitative information on sample elasticity

(i.e. Young’s modulus, spring constant).

111

Force curve measurement consists in approaching and withdrawing an AF M tip
from a surface and measuring the cantilever deﬂection that is induced by the interaction
force between the tip and the sample surface. Figure 6.7 shows the approach force curve
and corresponding tip sample position. In Figure 6.7, x axis is the tip position in z
direction which is movement of electrical piezo in z direction. The y axis is the
interaction force between the tip and sample. As introduced in chapter I, the force is
given by the measured cantilever deﬂection multiplied by the force constant of the
cantilever. The approach curve starts with the tip far away from the surface. At these
large distances the attractive long-range interaction between the tip and the sample is
extremely small and there is no detectable deﬂection of the cantilever. This is the so-
called ‘force free’ region shown as region ‘A’ in Figure 6.7. When the tip moves toward
the sample in z direction, the tip will ‘jump’ to contact the sample due to the attractive
Van der Waals force shown as contain point B in ﬁgure. When tip moves further toward
the sample, the tip will indent into the ample surface shown as contact region ‘C’ in the

Figure 6.7.

112

'f‘ﬁ- I” ~

 

 

 

 

12 ,
10 ~ i
Z 8 _. ”'75 a
c .-
S .
z: 6 r- - '4
8 ‘- A
E '7'; ’ Free Force’ Region
4 H C —» a
Contact Region E V—
2 r: ﬂ
RR. v
Contact Point '
.2 bf f 1' I' r

 

l' l’ r I' I" _ ’
0 20 40 60 80 100 120 140 160 180 200
2 position: nm

Figure 6.7 Approach force curve and corresponding tip sample distance

An array of force curves can be collected across the sample surface at regular
intervals and this is known as force volume imaging. Figure 6.8 shows a traditional force

volume imaging.

113

FZWKTT‘T‘

FV Image

 

0 10000.0 nm
Data Type Height
Z range 102.27 urn
Z scan 1000 um
Z position 15.24 nm/div

 

0 10000.0 nm
Data Type Height
2 range 3.80 urn

AFM 0 . 3.80 um Force Plot
FV .wm nm

Figure 6.8 Traditional AF M force volume image

 

There are several serious problems when using the conventional force volume

imaging in the nanoﬁber sample to collect the force curve for analyzing the elasticity

property.

(1) In conventional atomic force microscopy, the force volume imaging
scans the entire scan area irrespective of the shape of the region of
interest. This mode is slow and wasteful.

(2) In conventional force volume imaging applied to tissue scaffolds, force

curves acquired at regular intervals may not always be on a nanoﬁber.
It will hit anywhere inside the scan region where may be not inside the

region of interest which in tissue scaffold sample is the nanoﬁber.

114

(3) The cross-section of the nanoﬁber is a circle shape. When the tip scans
a point on the side of the nanoﬁber the sample surface normal is at an
angle to the direction of the tip-sample interaction force.
In order to get a reliable measurement of the elasticity, the force curve must be
collected at the top of the nanoﬁber where the force vector is exactly normal to the

sample surface as shown in Figure 6.9.

 

(a) (b)

Figure 6.9 (a) Tissue scaffold surface the tip contact point (b) 6 points were acquired along the
individual nanoﬂber

Force volume imaging using SPRM overcomes all of these difﬁculties. SPRM
will provide capability to collect a wealth of surface roughness information extracted
along many individual nanoﬁbers using an automatic procedure that maintains uniformity
of experimental conditions. SPRM will also provide the ﬁrst capability to acquire force
curves directly along an individual nanoﬁber so that the applied force is exactly normal to
the curved nanoﬁber surface, therefore ﬁilﬁlling conditions for appropriate use of the
Hertz model elasticity analysis.

The SPRM system will ﬁrst recognize the left and right edges of the nanoﬁber
during the ﬁne scanning and then detect the highest position in the section of nanoﬁber.

Then tip is moved to that position. The tip position in z direction is recorded as the

115

 

sample surface height at that x-y location. After turning off the z-feedback loop, the tip is
controlled to move in z direction to generate the force curve at this location. In the
current experiment, the tip is ﬁrst moved up from the normal tip sample contact point to a
tip ‘free-force’ position where there is no strong interaction between the tip and sample.
The system then sends a trig signal to inform the second PC to start collect the force and
2 position information. Tip is ﬁrst brought down to the sample in z direction. After tip
hits the sample surface and moves Snm further, SPRM system will move the tip back to
the ‘free-force’ position. When the tip moves toward and away from the sample, the
second pc records the force in the tip and 2 position of the tip. A force curve is then
generated at that x-y location. Figure 6.10 shows the signal timing waveform recorded
by the second PC. Figure 6.11 shows the collected force curve at that location. The red
one is the approach force curve which collected when the tip is brought down to the
sample surface and the blue one is retract force curve which is collected when the tip is
moving away from the sample. Using the same procedure, a set of force curves along the

most reliable area in the nanoﬁber can thus be collected for calculating elasticity.

116

 

3 l l I. I l l l l

 

¢——— Sampling trig signal

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

>
2)
§ ‘ ‘ ‘ .
o
>
Deﬂection signal
I l l‘
6 7 8 9
4
x 10
Time: ms
Figure 6.10 SPRM force curve signal timing waveform
1 K
0
E
c
.9
g -1
F:
O
-2
0.55 0.85

0.615 ' 0.7'5
Tip Position (v)

Figure 6.11 Force curve collected by the second PC

117

Figure 6.11 shows one recorded force curve collected in the reliable region. As we
can see, in the same 2 position several deﬂection values are collected because of the
limited resolution in the 2 position. The force curve is ﬁrst passed the average ﬁlter which
takes the average deﬂection value in each 2 position. The collected raw deﬂection value
is the voltage output signal of the detection photodiode as introduced in chapter 1. By
multiplying the sensitive constant, the voltage signal can be converted to the tip
deﬂection in nm. Figure 6.12 shows the collected average force curve.

The force curves collected record the cantilever deﬂection versus the 2 position of
the tip. Rather than using the tip 2 position, it is more useful to use the distance (D)
which is the relative separation between the tip and the sample surface, and this is known
as a force-distance curve. A force-distance curve (PD) is deﬁned as the cantilever
deﬂection force versus the absolution distance (D) between the tip and sample surface.

Figure 6.13 shows force-distance curve collected in the reliable region.

 

14 L L L L L L L L L
~

“3*

Deﬂection: nN

 

 

 

 

_2 P r r r r r r r 1 r '
20 40 60 80 100 120 140 160 180 200
2 position: nm

Figure 6.12 Approace force curve after average ﬁlter

118

 

14p L L f L

 

10*-

Deﬂection: nN

 

 

 

 

~50 0 50 100 150 200
Z-d : nm

Figure 6.13 Force-distance curve and corresponding force-distance curve
To analysis the elasticity property, different methods have been developed to interpret
the force-distance curve.
The simplest way is to use the slop of the force curve in the contact region. In this
method, the elastic response of the ample is assumed linear and an effective force constant,

spring constant, then can be deﬁned to characterize the elasticity of the sample. The spring

constant of the sample K5 is deﬁned as

 

_ Kcs

K
S l—s

(6.5)

where K C is the spring constant of the cantilever, s is the slope of the force curve [121,
122}

Another method is called Force Integration to Equal Limits (FIEL) proposed by A-
Hassan [69, 116, 117, 120]. FIEL method uses the Hertz model [81] to calculate the force

between the tip and sample. If the tip of an AP M is approximated by a sphere, then the

119

 

force on the cantilever (F) can be deﬁned from the indentation (5), elastic modulus (E),

Poisson ration (v) and radius of the probe sphere

= 4EJ§ 53/2

6 3(1_v) (6.6)

To compare the elastic properties at two different positions, a pair of force-distance

curves is collected at positions P1 and P2 using the relative trigger mode [59]. At these

I"
points, the force F 1 equals force F2. The work done by the cantilever at each position is g
i.
the area under a force-distance curve, and is given by i-
w: K’Force-d6=§-£615/2 (6.7)
15 7rk

Therefore, the relationship between the elasticity and the force-distance curve at two
different data positions is

[C 2/3
XI. = [_1] (6.8)
“’2

l— v . . . . .
where k = -—E- is inversely proportional to E, the elastic constant which represents the
7!

local elasticity of the sample. The area under the force-distance curve can be calculated
and used to represent the inverse relative elasticity of the tissue scaffolding.

This method has the advantage of being independent of the tip-sample contact point,
and of not requiring calibration of the AF M cantilever’s spring force constant. However
this method requires each force curve has the same force value at the end of indentation
which is hard to achieve. FIEL method can provide the comparison result between

different samples only if each sample is tested in same experimental conditions.

120

In this research, the wildly used Hertz (or Sneddon) model [27, 53, 103, 112, 118,
119, 123] is applied to quantify the contact part of force curve (region ‘0’ in Figure 6.7).
Since the tip is much harder than the sample, the elastic deformation of the sample can be
related to its Young’s modulus in the contact part of the force curve. The Hertz model
describes the elastic deformation of two surfaces touching under a load force which was
ﬁrst treated by Hertz in 1881 [81]. The general force-indentation relation can be

,.
expressed as [95, 124]: l

 

F = 255 (6.9) m
where F is the loading force and 5 is the indentation depth. The term A and exponent
[3 are parameters decided by the two touching surfaces. The sample surface can be

considered as a ﬂat soft sample. Two different geometries seem to be appropriate to

describe the AFM tip.
1. Tip as a sphere of radius R, Hertz model is deﬁned as [53, 124]:
4 E
Fsphm = -3-——2J1—263’2 (6.10)
(1-# )

where F sphere is the measured force, E is the Young’s modulus, ,u is the Poisson’s

ratio and (5 is the indention depth.

2. Tip as a cylindrical cone of opening angle 2a, hertz model is deﬁned as [53, 113,
125k

2 E

_ 2 m(a)52 (6.11)
”(l-x1 )

F

cone =

 

where F cone is the measured force, E is the Young’s modulus, p is the Poisson’s

ratio and 6 is the indention depth.
As we discussed in chapter 5, we assume the tip end is sphere with the radius 100nm,

the Hertz model we used is equation (6.10). The indentation 6 was calculated as follows:

121

5=(z—zO)—(d—d0) (6.12)
Where 2 is the sample height, 20 is the contact point where tip touches the sample, (1
is the cantilever deﬂection and do is the deﬂection of the free cantilever when the
cantilever is far from sample surface. To simplify the problem, the nonlinear force
(F sphere) and indentation (6) equation can be converted to linear equation of

2/3

(F sphere) and 6 by substituting equation (6.12) to equation (6.10):

4 E
Fspherf’?’ =<-3——,—~/§)2’3[(z—zo)—(d—do)1 (6.13)
(l -# )
In equation(6. l 3), nghere , 2, d and do can be obtained ﬁ'om the experimental force

curves. As we discussed in chapter 5 the radius of the sphere in the tip’s end can be
chosen as 100nm. Typically, the Poisson’s ration can be assumed as 0.5 for soft materials
[124-127]. The unknown parameters are Young’s modulus E and the tip-sample contact

point 20 . In this work, we use a least squares estimation procedure to determine E and

20 by minimizing the error in equation (6.14) w.r.t unknown parameters E and 20

 

1 N 2/3 2
0’ = J? 2:1((F;:here)2/3 " (Es-322m) ) (6-14)
I:

Where 0 is the rms error, F 5;; e is the measured force in contact region ‘c’ and

F share is the force calculated using equation(6.]3). Figure 6.14 shows the contact part

force curve and the ﬁtting result using equation (6.13) and (6.14). Figure 6.15 is the box
plot of the Young’s modulus (E) estimated from six experiment force curves which
shows the lower quartile, median, and upper quartile E values. The mean value of

Young’s modulus along the nanoﬁber is about 4675 Pa.

122

P-m‘xm'mmr aim

 

14

12

Deﬂection: nN

 

(a)

 

 

Z-dznm

100

 

 

 

 

 

+ Experimential data
Fit cum

 

 

 

 

 

-1000’
-40

-20

0

100

Figure 6.14 Force curve in contact region (a) and corresponding ﬁtting result (b)

123

 

 

 

 

 

 

 

 

4750 ~ —— -
4700 - -

U)

2

3

8 4650 ~ -

2

_ID

0)

C

3

O

> 4600 - -
4550 ~ -

_T

 

 

 

Figure 6.15 Box plot of the estimated Young’s modulus

6.5 Discussion

SPRM provided the ﬁrst capability to collect statistically meaningful surface
roughness information extracted along many individual nanoﬁbers using an automatic
procedure that maintained uniformity of experimental conditions. More importantly,
histograms showing the distribution in the surface roughness values as well as the mode
value were generated from the analysis of many individual nanoﬁbers. The usual AF M
individually applied ROI box would be most likely to return the mode value. However,
the variances and distributions between samples under investigation can prove to be the

real difference between them [70].

124

SPRM also provided the ﬁrst capability to acquire force curves directly along an
individual nanoﬁber under conditions such that the applied force was exactly normal to
the curved nanoﬁber surface, therefore closing to conditions for appropriate use of the
Hertz model elasticity analysis. This method is presently being reﬁned and calibrated by
our group and will lead to the statistically meaningful elasticity information extracted
along many individual nanoﬁbers using an automatic procedure that maintains uniformity

of experimental conditions.

125

Chapter 7 Summary of Results and Future Work

Scanning Probe Recognition Microscopy (SPRM) is an innovative and valuable
extension of the capabilities of existing scanning probe microscopes. The SPRM allows
adaptively track along individual structures within the scan area and provides statistically
signiﬁcant data for multiple properties by ﬁne resolution scan restricted to the region of
interest. Two implementation methods, namely, off-line processing scheme and an on-
line dynamically adaptive multi-resolution scarming mode, are developed.

SPRM has the obvious advantage of saving operation time by scanning only regions
of interest and ignoring other parts of the sample. This is especially useful for
investigations of tissue scaffold properties, as a scaffold is composed of many individual
nanoﬁbers.

F irst-time SPRM investigations of tissue scaffold properties were performed directly
along individual nanoﬁbers. The results of a SPRM investigation of the surface roughness
and elasticity of tissue scaffolds are presented. These investigations on curved nanoﬁber
surfaces were enabled by the new SPRM ability to auto-track a restricted region of interest
(ROI). For the surface roughness investigation, the R01 is the top area of the nanoﬁber.
For the elasticity investigation, the R01 is only the central line of the nanoﬁber where the
force applied by the tip is norm to the nanoﬁber surface thus providing meaningful force
curves.

Deconvolution methods were developed and used for data accuracy along curved
nanoﬁber surfaces. Geometric deconvolution, speciﬁcally the mathematical morphology

method, was applied to the problem of surface roughness extraction. This was essential

126

........._._.__._,

for extraction of the true surface roughness along the nanoscale curved surface. An
alternate approach for AF M data restoration, physics based deconvolution which includes
the modeling and characterization of the tip and sample artifact sources, is also developed
and applied to model systems. Initial results show the feasibility of the method for
determining true topographic shapes of the sample.

The SPRM approach provided a wealth of data. Statistical methods based on
histograms were developed to analyze the surface roughness and elasticity properties of
the tissue scaffold nanoﬁbers. The mode, mean, variance and distribution of surface
roughness and elasticity were analyzed. This is the ﬁrst time that statistically meaningﬁil
information has been extracted along individual nanoﬁbers using an automatic procedure
that maintains uniformity of experimental conditions.

Future work

One of the key components in the SPRM system is automatic detection of ROI. In
this thesis, the height information alone is used to recognize an area of interest. In any
SPM system many additional pieces of information are also provided. These include
deﬂection, lateral force, phase etc. Based on the sample properties, these additional
pieces of information can also be used to detect the ROI with greater accuracy and guide
the SPM scan.

The SPRM can also be used in a purely recognition mode to study the conformational
changes of features such as the ‘open’ and ‘closed ‘state of ion channels. This feature
can be extremely helpful in providing greater ﬂexibility for handling a wide array of

nanobioligcal investigations that involve conformational changes.

127

In the present work on surface roughness calculations, a Kasa circle ﬁt method is
used to acquire the true surface roughness on a curved surface. Deconvolution operation
based on mathematical morphology methods was applied as the inverse operation to
reverse the tip-shape dilation artifacts observed in AF M section measurements. In future
work, the mathematical morphology deconvolution operation may be replaced by the
force model based deconvolution procedure introduced in chapter 5.

The force-model based deconvolution algorithm has been developed and initial
results show the feasibility of the method for determining true topographic shapes of the
sample. However currently, the algorithm is applied to minimizing the error between
model and measurement data at one position of the tip. The results will be much more
accurate if the error is computed using VDW force calculations and measurements on a
larger scan area centered at each point.

In this thesis, the force-model based deconvolution was performed on synthetic data
due to lack of a calibration sample with well characterized shape information that can be
used for generating measurements. The force based deconvolution should be validated
with actual experimental data for which the true sample and tip shape information is
available. Finally the force based model should be extended to include other components
of the overall force that contribute to the tip sample interaction.

SPRM also provides the ﬁrst capability to acquire force curves directly along an
individual nanoﬁber under optimal conditions where the tip and hence applied force is
exactly normal to the curved nanoﬁber surface. Methods for computing accurate values
of the Young's modulus are currently under development. In particular two issues need to

be addressed. The force-curve collected by SPRM is modeled to extract Young's modulus.

128

 

The model used in this work is the simple Hertz model which assumes the tip to be a
sphere of radius = 100nm. The ﬁrst issue is that the Hertz model does not consider the
adhesion force between the tip-sample contact regions. In Hertz model, the sample
surface is assumed to be ﬂat which is not always true for tissue scaffold samples which
nanoﬁbers. Future work should be focused on a more accurate model of the force curve
for estimating the Young’s modulus. The second issue is calibration. In order to get
accurate results, the model should be calibrated with a standard elastic sample.

Any property that can be investigated by scanning probe microscopy can be
investigated by Scanning Probe Recognition Microscopy with auto-track on a region of
interest. Work is also in progress to develop SPRM-based surface chemistry
investigations, as this is known to be an important property for characterizing cell
motility and adhesion [128]. Future work will develop data ﬁision methods that combine
surface roughness, elasticity and surface chemistry information into a composite picture

more truly representative of a cell’s perception its environment.

129

 

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