Spectral / Fourier Domain Doppler Optical Coherence
Tomography in the Rodent Retina
by
Jonathan Jaoshin Liu
B.S., Electrical Engineering
National Taiwan University, 2005
Submitted to the
DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
September 2008
@2008 Massachusetts Institute of Technology
All rights reserved
Signature of Author:
/lepartment of Electrical Wineering and Computer Science
August 2008
A
Certified by:
/
James G. Fujimoto
Professor of Electrical Engineering and Computer Science
Thesis Supervisor
A
I
Accepted by:
,-
-
Terry P. Orlando
Chair, Department Committee on Graduate Students
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
OCT 222008
ARCHIVES
Spectral / Fourier Domain Doppler Optical Coherence Tomography
in the Rodent Retina
by
Jonathan Jaoshin Liu
Submitted to the Department of Electrical Engineering and Computer Science
on August 29, 2008 in Partial Fulfillment of the
Requirements for the Degree of Master of Science in
Electrical Engineering and Computer Science
Abstract
Optical Coherence Tomography (OCT) is an emerging imaging technique based on
low-coherence interferometry for noninvasive, high-resolution, cross-sectional imaging in a
variety of biomedical fields. In ophthalmology, OCT has rapidly become a standard clinical
diagnostic tool for retinal diseases, providing visualization of the retina with unprecedented
detail. However, conventional time domain OCT systems are limited by low imaging speeds.
Conventional time domain OCT systems use a mechanically scanned reference mirror to adjust
the reference arm path length in time. Spectral / Fourier domain OCT systems use a
spectrometer to detect the interference spectrum and do not require mechanical scanning of the
reference mirror. This technology significantly improves imaging speed and sensitivity.
Spectral / Fourier domain OCT detection methods enable imaging speeds -50-100x faster than
conventional time domain OCT systems, providing the capability for three dimensional retinal
imaging and blood flow quantification using Doppler OCT measurements.
A pre-objective scanning spectral / Fourier domain OCT system for in vivo rodent retinal
imaging is designed and built. The system includes a broadband light source to achieve ~-3gm
resolution and a CCD camera spectrometer with imaging speed at 25,000 axial scans per second.
Applications of spectral / Fourier domain OCT for in vivo rodent retinal imaging are illustrated,
including three-dimensional OCT imaging of retinal structure, OCT imaging of the retina preand post-injection, and Doppler OCT imaging providing quantitative measurements of pulsatile
blood flow in a retinal vessel. These results demonstrate the ability of spectral / Fourier domain
OCT to visualize rodent retinal structure in vivo, perform longitudinal studies by evaluating
disease progression in an individual animal, and quantitatively measure rodent retinal blood flow.
Thesis Supervisor: James G Fujimoto
Title: Professor of Electrical Engineering
Acknowledgments
I would like to thank my thesis advisor Professor James Fujimoto for the guidance and resources
to perform this work.
I am most grateful for the opportunity to work in the Laser Medicine and
Medical Imaging Group at MIT.
I would also like to thank all my colleagues, especially Vivek Srinivasan and Iwona Gorczynska
for all their help and guidance.
They have truly been my mentors.
Finally, I thank my family, my girlfriend, and friends for all the unconditional support.
Table of Contents
Abstract..........................................
3
Acknowledgm ents ....................................................................................................................
4
Table of Contents ...................................................................................................................
5
Chapter 1 Introduction and Overview ....................................................... 7
1.1 Introduction ..................................................................................................................... 7
1.2 OCT in Ophthalm ology ........................................... ................................................. 11
1.3 Doppler O CT ...........................................................................................................
13
1.4 Scope of Thesis ..............................................................................................................
14
References ............................................................................................................................
15
Chapter 2 O CT Theory ..............................................................................................................
21
2.1 The M ichelson Interferom eter ................................................................................... 21
2.2 Time Domain Interferometer with Low-Coherence Light ..................................... 23
2.3 Spectral / Fourier Dom ain OCT ......................................................
26
2.3.1 M easurem ent Range .................................................................................
29
2.3.2 Spectrom eter Roll-off ...........................................................................
...
30
2.3.3 Dispersion Com pensation...............................................
31
2.3.4 Doppler O CT .................................................................................................... 33
2.4 Noise and Sensitivity .........................................
..............................................
34
2.4.1 Shot Noise Lim it........................................... ................................................. 35
2.4.2 Excess Intensity noise ..............................................................................
35
2.4.3 Receiver Noise ..................................................................................
36
...
2.4.4 Sensitivity............................................................................................................ 36
2.4.5 Dynam ic Range ............................................ ................................................. 37
2.4.6 Doppler Range and Sensitivity .........................................
References .................................................
.............. 38
39
Chapter 3 Pre-Objective Scanning Small Animal OCT System...............................
3.1 Overview ...................................................
41
41
3.2 Spectrometer Design ............................................................................................... 42
3.3 Light Source ..................................................................................................................
42
3.4 Interferom eter ............................................................................................................... 44
3.5 Sample Arm Optics ................................................................................................. 45
3.6 Image Acquisition and Processing .........................................................................
46
3.7 System Performance ............................................................................................... 51
3.7.1 Sensitivity Measurement ........................................................................
51
3.7.2 Dynamic Range Measurement.............................................................
52
3.7.3 Sensitivity Roll-Off....................................................................................... 52
3.7.4 Doppler Measurement Range .................................................................
References ..................................................
Chapter 4 OCT Imaging and Data Analysis.................................................................
53
54
57
4.1 Overview ................................................................................................................. 57
4.2 B ackground ...................................................................................................................
57
4.3 3D OCT Imaging of Rat Retina ................................................................................ 58
4.4 Diabetic Macular Edema Study .....................................................
61
4.5 Doppler Flow Calculation ...................................................................................... 63
Referen ces ............................................................................................................................
67
Chapter 1
Introduction and Overview
1.1 Introduction
Optical Coherence Tomography (OCT) is a non-contact non-invasive imaging technology that
can perform micron-scale, tomographic
microstructure in vivo and in real time.' 6
cross-sectional
imaging of biological tissue
OCT imaging is analogous to ultrasound B-mode
imaging, except that OCT measures the intensity of backscattered light rather than acoustical
waves.
Cross-sectional images are generated by scanning the optical beam and the
backreflected or backscattered light from internal tissue microstructures is measured as a
function of axial range (depth) and transverse position using interferometric correlation
techniques.
Since the propagation speed of light is much faster than photodetector response times, light echo
time delays cannot be measured electronically as in ultrasound.
Instead, OCT uses a
fundamentally different technique based on a Michelson interferometer, also known as
low-coherence interferometry.
Figure 1-1 illustrates the principle of low-coherence
interferometry with a generic OCT system schematic implementing a simple Michelson
interferometer. Light from a source is divided into a scanning reference path and a sample path.
The backscattered light reflected from the sample arm is recombined with the reflected light
from the reference arm at a photodetector to produce interference fringes. If the light source is
monochromatic, interference is seen over a wide range of sample and reference arm path length
mismatches.
When using a low-coherence broadband light source, interference is only seen
when the reference arm path length matches the sample arm path length to within the coherence
length of the light source.
Low-coherence light can be generated by superluminescent
semiconductor diodes or other sources, such as solid state lasers. Higher axial resolution can be
achieved by increasing the bandwidth of the light source.7 Low-coherence interferometry
permits the echo delay time (or optical path length) and magnitude of the light reflected
from
internal tissue microstructures to be measured with extremely high accuracy and sensitivity.
RA2
t
bA
Reference
I
A AA
Long Coherence Length AIc >> Am
A/2
pie
Short Coherence Length Alc < Am
Figure 1-1.
Schematic illustrating the principle of low-coherence interferometry
using a Michelson interferometer. Light is divided into the reference and sample
paths and the reflected light is recombined.
For monochromatic light sources,
interference is seen over a wide range of sample and reference arm path length
mismatches. For low-coherence broadband light sources, interference is only
seen when the reference path length matches the sample path length to within the
coherence length of the light source.
The principal of generating two-dimensional images using OCT is shown
in Figure 1-2.
Scanning the reference arm path length and plotting the envelope of the
interference as a
function of this path length generates a map of the backscattered light intensity
from the sample.
Additionally, translating the sample with respect to the incident beam
or scanning the incident
beam across the sample results in a two dimensional array dataset which
represents the optical
backscattering or reflections within a cross sectional slice of the sample.
Transverse Scanning
1
I
Backscatter Intensity
II
I II
i
I
Cn,
0
CD
_0
D
Figure 1-2.
I•
G2
f
y CaI;
S
l
Formation of an OCT image.
mapped as a function of depth.
i
IIIIt;
I
. IJpLI;dal DdLcksi
dLLCatrl
The backscattered intensity is
A two-dimensional image is formed by scanning
the incident beam with respect to the sample.
Standard resolution OCT imaging systems can achieve axial image resolutions of 10-15 tm. 2
With the development of ultrahigh-resolution (UHR) OCT imaging using state of the art laser
technologies, axial resolutions of -3 gtm in the human eye and -1 ptm in other applications have
been achieved. 8-12 The axial resolution in OCT depends on the coherence length of light and is
inversely proportional to the optical bandwidth of the light source. Ultrahigh resolution OCT
imaging requires extremely broad bandwidths. Superluminescent diode light sources
are
commonly used in OCT because of their compact size and low cost. However, traditional
superluminescent diode light sources have limited bandwidths and axial image resolutions
are
typically 10 gm. Femtosecond lasers are ideal light sources for ultrahigh resolution
OCT
because they can generate the extremely broad bandwidths necessary for ultrahigh resolution
imaging.
Recently, significant advances in the field of superluminescent diodes have enabled
ultrahigh OCT image resolution performance approaching femtosecond lasers. 13 , 14
Conventional OCT systems use a mechanically scanned reference mirror to adjust the reference
arm path length.1' "5'
The magnitudes of light echoes from the sample arm with sequentially
different delays are detected at different times as the reference path length is scanned.
these systems are known as "time domain" systems.
Hence,
Recently, novel OCT detection techniques
have emerged which do not require mechanical scanning and achieve very high detection
sensitivities, enabling OCT imaging with a -15 to 50x increase in imaging speed over standard
resolution OCT systems and -100x over conventional ultrahigh resolution OCT systems.
In
contrast to standard OCT, which detects light echoes at different delays sequentially, spectral /
Fourier domain detection measures all of the light simultaneously.
Fourier domain techniques measure the echo time delay of light by Fourier transforming the
interference spectrum of the light signal. 16 '
17
Different echo time delays of light produce
different frequencies of fringes in the interference spectrum.
Fourier domain OCT detection
can be performed in two ways: spectral OCT using broadband light source and a spectrometer
with a multichannel analyzer16 20
- or swept source OCT using a rapidly tunable, narrow linewidth
laser source2 1-2 5. Additionally, Fourier domain optical coherence tomography offers significantly
improved sensitivity and imaging speed compared to time domain OCT.'18
26-28
Spectral and swept source Fourier domain OCT significantly improve imaging speeds of
conventional time domain OCT and are therefore promising for ultrahigh resolution imaging.
With high imaging speeds of Fourier domain OCT, it is possible to acquire three-dimensional
maps of the sample.2 9-32
In addition, Fourier domain OCT has the advantage of providing direct
access to the spectral fringe pattern, enabling a wide range of novel applications.
Fourier
domain OCT can be used for absorption measurement 33 and the complex Fourier domain signal
can be directly measured to double the axial measurement scan range 34 ' 18,35.
Spectral domain
and swept source OCT are also especially well suited for numerical dispersion compensation
correcting for resolution loss due to mismatched dispersion in the sample and reference arms.
Fourier domain OCT also provides convenient access to phase information after Fourier
transformation of the spectrum, therefore Doppler OCT techniques can be directly applied to
image motion.
36-50
1.2 OCT in Ophthalmology
OCT is now considered a standard diagnostic tool in ophthalmology. OCT has a number of
features which make it attractive including its high probing depth, high resolution approaching
that of histopathology, contact-free and non-invasive operation, and the possibility to create
various function dependent image contrasting methods.
In ophthalmology, OCT is able to
acquire high-definition images with detail that is impossible to obtain by any other noninvasive
technique.
Standard resolution commercial OCT systems such as the StratusOCT (Carl Zeiss
Meditec) can achieve -10 p.m axial image resolutions with 128 axial scan (transverse pixel)
images acquired in 0.32 seconds or 512 axial scan (transverse pixels) images acquired in -1.3
seconds.
Using state of the art laser technologies, ultrahigh resolution OCT imaging with axial
image resolutions of 2-3 gpm in the eye and resolutions as fine as 1 gpm in animals have been
demonstrated.8 -12 Ultrahigh resolution enables the direct visualization of retinal architectural
morphology and pathology in individual layers of the retina.
Recent advances in OCT technology provide a 50 to 100x increase in imaging speed, enabling
high-speed acquisition of OCT cross-sectional images. 16'
17
High-speed OCT imaging also
allows three-dimensional mapping of the retina while significantly reducing eye motion artifacts.
This enables the acquisition of high transverse pixel density images which have improved image
quality and enables a wide range of new imaging protocols based on three-dimensional (3D)
imaging and mapping.
Additionally, 3D OCT images can be analyzed using quantitative image
processing techniques and algorithms which yield quantitative information.5 1
This greatly
facilitates statistical analysis and the development of objective diagnostic criteria. Furthermore,
Doppler OCT measurements of quantitative blood flow can be performed for high transverse
pixel density images, providing information on retinal perfusion.5 0
OCT has become a standard clinical tool for the diagnosis and management of a wide variety of
ocular diseases.,' 52 OCT images enables the visualization of retinal pathology at resolutions not
possible with other noninvasive imaging techniques and are permit the delineation of retinal
substructure in vivo.3 ' 53' 54' 4, 55,56
OCT has been applied to a wide range of ophthalmic diseases
including macular holes, glaucoma, age-related macular degeneration, macular edema, and
diabetic retinopathy.
Since OCT provides direct information on the dimensions of retinal
structures, it permits the quantitative measurement of the nerve fiber layer (NFL) for glaucoma
diagnosis and monitoring. 5 ' 57
In addition, OCT can image and quantitate retinal structure
enabling a wide range of applications for the diagnosis and monitoring of retinal disease. 52
Ultrahigh resolution OCT can achieve resolution comparable to histopathology enabling the
direct visualization of retinal architect morphology and pathology and detecting changes that are
below the threshold for detection on a standard ophthalmoscopic examination of the fundus.
High-speed OCT significantly reduces motion artifacts, and enables acquisition of high
transverse pixel density images and new imaging protocols based on three-dimensional retinal
structure imaging and quantitative mapping. 3 1
Research on ocular diseases is often limited by the restrictions on studying pathophysiologic
processes in the human eye.
Also, many human ocular diseases are genetic in origin, but
oftentimes appropriate subjects are not available for genetic studies.
Murine (rat and mouse)
models of ocular disease provide powerful tools for analysis and characterization of disease
pathogenesis and response to treatment.
The murine retina is similar in structure to the human
retina, and is frequently used in research involving oxygen modulation or electroretinogram
recordings.
Animals are sacrificed before undergoing enucleation and histological examination, therefore
each animal only contributes to a single time point for monitoring disease progression or
morphological changes in the retina.
Such studies are inherently cross-sectional, and do not
evaluate disease progression in individual animals.
While enucleation and histology are the
gold standard for characterization of microstructural changes in animals, non-invasive structural
imaging has the potential to reduce the need for sacrifice and histology in many studies.
Non-invasive in vivo examination of the animal retina without euthenization provides the ability
to perform longitudinal studies by monitoring disease progression in individual animals.5 8
High-speed UHR-OCT enables high quality in vivo imaging of the murine retina and the
visualization of all major intraretinal layers including the photoreceptors.
protocols
using high-definition,
high
transverse
pixel density imaging,
OCT imaging
as well
as
three-dimensional (3D-OCT) imaging with dense raster scanning have been demonstrated. 59
Raster scan protocols enable volumetric imaging and comprehensive coverage of a region of the
retina. An OCT fundus image, akin to a fundus photograph, can be directly generated by axial
summation of 3D-OCT data. This enables precise registration of individual OCT images or
measurements to fundus features.
Segmentation algorithms along with three-dimensional
imaging enable quantification of retinal structure, which promises to allow repeated,
non-invasive measurements to track disease progression, reduce the need for sacrifice and
histology.60
This capability can accelerate the translation from basic research studies in rats and
mice into clinical care.
One limitation in the development of treatments for macular edema is the lack of appropriate
animal models.
In evaluating anti-vascular permeability agents for treatment of diabetic
macular edema in humans, an animal model that exhibits quantifiable edema is desired. Optical
coherence tomography (OCT) has become the clinical standard for quantifying diabetic macular
edema in humans, 56 and is therefore the preferred method for characterization of retinal edema in
animal models.
Animal studies may also help to determine surrogate markers for early disease
progression. The availability of clinical surrogate markers would help in the design of clinical
trials with shorter time frames.
These markers would also help to elucidate mechanisms by
which hyperglycemia and diabetes cause changes in retinal hemodynamics and metabolism. By
identifying appropriate animal models of diabetic retinopathy and imaging tools for
characterization, future studies will aid in identification of surrogate markers for early
progression of diabetic retinopathy.
1.3 Doppler OCT
Doppler motion imaging is a functional extension developed for OCT.61
3
In OCT, the
frequency of the interferometric signal is shifted by motion in the sample enabling the detection
of motion using Doppler OCT methods and algorithms. Since OCT performs depth ranging and
is a tomographic technique with high special resolution, depth-resolved cross-sectional flow
imaging of in vivo tissues can be obtained. Doppler OCT has been demonstrated to detect
motion and blood flow of tissue in vivo.64 , 65, 37,66,67,38
In ophthalmology, retinal hemodynamics is important for investigating diseases such as
glaucoma, diabetic retinopathy, and age-related macular degeneration. 68-70 Many measurement
technologies have been developed for in vivo retinal blood vessel imaging and blood flow
detection.
Fluorescein angiography (FA) and indocyanine green angiography (ICGA) are
standard clinical diagnostic methods for retinal diseases.71
Both methods allow visualization of
retinal blood vessels, while choroidal vasculature is more effectively displayed in ICGA due to
the longer excitation wavelength.
However, these methods are invasive since they require
intravenous injections of fluorescence dye. Noninvasive blood flow measurement techniques
based on laser Doppler velocimetry have been used to investigate retinal blood vessels. 72-76
Other noninvasive methods such as laser Doppler flowmetry, laser speckle photography, and
laser speckle flowgraphy can perform two-dimensional mapping of blood flow.77 -80 Nonetheless,
these techniques demonstrate poor ability to resolve depth structure.
OCT has the advantage of
providing three-dimensional structural OCT intensity images along with the ability to extract
vessel structure and blood flow measurements from the Doppler OCT images.
1.4 Scope of Thesis
This thesis focuses on the development of spectral / Fourier domain OCT technologies for in vivo
rodent retinal imaging.
Conventional time domain OCT has had significant clinical impact in
ophthalmology. However, difficulty in registering the images and motion artifacts limited the
use of time domain OCT in rodent retinal imaging.
Spectral /Fourier domain OCT detects the
interference spectrum directly without mechanically scanning the reference mirror in time,
enabling a dramatic increase in imaging speed and thereby allowing 3D imaging of the rodent
retina for precise registration and quantification of retinal layer thickness.
Moreover, Doppler
OCT measurements can be performed to obtain retinal blood flow.
Chapter 2 presents an introduction to spectral / Fourier domain OCT theory.
is discussed and compared with spectral / Fourier domain OCT.
compensation and Doppler OCT theory are described.
sensitivity in spectral / Fourier domain OCT is provided.
Time domain OCT
Numerical dispersion
In addition, analyses in noise and
Chapter 3 discusses development and characterization of the spectral /Fourier domain OCT
system for rodent retina. A prototype high-speed, ultrahigh resolution OCT instrument with a
pre-objective scanning long working distance microscope design for performing in vivo imaging
of the murine retina is proposed and developed.
Using a compact, multiplexed
superluminescent diode light source having a bandwidth of -150 nm centered near ~900 nm, an
axial resolution of -3 tm is achieved. A -11 /m transverse resolution in air is obtained using a
pre-objective scanning long working distance microscope.
The prototype OCT instrument
using spectral / Fourier domain detection has imaging speed of 25,000 axial scans per second, an
improvement of -~100xover previous UHR-OCT systems.
Chapter 4 demonstrates the spectral / Fourier domain OCT system for high resolution, in vivo
3D-OCT imaging in the rat retina. High-resolution retinal images of normal rats before and
after intravitreal saline and kallikrein injection is demonstrated.
Doppler OCT methods and
results measuring blood flow in a normal rat retinal vessel showing pulsatility is presented.
References
1.
D. Huang, E.A. Swanson, C.P. Lin, J.S. Schuman, W.G. Stinson, W. Chang, M.R. Hee, T.
Flotte, K. Gregory, C.A. Puliafito, and J.G. Fujimoto, "Optical Coherence Tomography,"
Science, vol. 254, pp. 1178-1181,1991.
2.
J.G Fujimoto, M.E. Brezinski, GJ. Tearney, S.A. Boppart, B. Bouma, M.R. Hee, J.F.
Southern, and E.A. Swanson, "Optical biopsy and imaging using optical coherence
3.
4.
5.
6.
7.
8.
tomography," Nature Medicine, vol. 1, pp. 970-972,1995.
M.R. Hee, J.A. Izatt, E.A. Swanson, D. Huang, J.S. Schuman, C.P. Lin, C.A. Puliafito,
and J.G Fujimoto, "Optical coherence tomography of the human retina," Archives of
Ophthalmology, vol. 113, pp. 325-332,1995.
C.A. Puliafito, M.R. Hee, C.P. Lin, E. Reichel, J.S. Schuman, J.S. Duker, J.A. Izatt, E.A.
Swanson, and J.G Fujimoto, "Imaging of macular diseases with optical coherence
tomography," Ophthalmology, vol. 102, pp. 217-229,1995.
J.G Fujimoto, C. Pitris, S.A. Boppart, and M.E. Brezinski, "Optical coherence
tomography: an emerging technology for biomedical imaging and optical biopsy,"
Neoplasia,vol. 2, pp. 9-25,2000.
J.G Fujimoto, "Optical coherence tomography for ultrahigh resolution in vivo imaging,"
NatureBiotechnology, vol. 21, pp. 1361-1367,2003.
J.M. Schmitt, "Optical coherence tomography (OCT): a review," IEEE Journal of
Selected Topics in Quantum Electronics, vol. 5, pp. 1205-15,1999.
B. Bouma, GJ. Tearney, S.A. Boppart, M.R. Hee, M.E. Brezinski, and J.G Fujimoto,
"High-resolution optical coherence tomographic imaging using a mode-locked Ti:A1203
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
laser source," Optics Letters, vol. 20, pp. 1486-1488,1995.
B.E. Bouma, GJ. Tearney, I.P. Bilinsky, B. Golubovic, and J.GXFujimoto,
"Self-phase-modulated Kerr-lens mode-locked Cr:forsterite laser source for optical
coherence tomography," Optics Letters, vol. 21, pp. 1839-1841,1996.
W. Drexler, U. Morgner, F.X. Kartner, C. Pitris, S.A. Boppart, X.D. Li, E.P. Ippen, and
J.G Fujimoto, "In vivo ultrahigh-resolution optical coherence tomography," Optics
Letters, vol. 24, pp. 1221-1223,1999.
W. Drexler, U. Morgner, R.K. Ghanta, F.X. Kartner, J.S. Schuman, and J.G Fujimoto,
"Ultrahigh-resolution ophthalmic optical coherence tomography," Nature Medicine, vol.
7, pp. 502-507,2001.
I. Hartl, X.D. Li, C. Chudoba, R.K. Hganta, T.H. Ko, J.G Fujimoto, J.K. Ranka, and R.S.
Windeler, "Ultrahigh-resolution optical coherence tomography using continuum
generation in an air-silica microstructure optical fiber," Optics Letters, vol. 26, pp.
608-610,2001.
B. Cense, N. Nassif, T.C. Chen, M.C. Pierce, S. Yun, B.H. Park, B. Bouma, G Tearney,
and J.F. de Boer, "Ultrahigh-resolution high-speed retinal imaging using spectral-domain
optical coherence tomography," Optics Express, vol. 12, pp. 2435-2447,2004.
T.H. Ko, D.C. Adler, J.G. Fujimoto, D. Mamedov, V. Prokhorov, V. Shidlovski, and S.
Yakubovich, "Ultrahigh resolution optical coherence tomography imaging with a
broadband superluminescent diode light source," Optics Express, vol. 12, pp.
2112-2119,2004.
E.A. Swanson, J.A. Izatt, M.R. Hee, D. Huang, C.P. Lin, J.S. Schuman, C.A. Puliafito,
and J.G. Fujimoto, "In vivo retinal imaging by optical coherence tomography," Optics
Letters, vol. 18, pp. 1864-1866,1993.
A.F. Fercher, C.K. Hitzenberger, G. Kamp, and S.Y. Elzaiat, "Measurement of Intraocular
Distances by Backscattering Spectral Interferometry," Optics Communications, vol. 117,
pp. 43-48,1995.
G Hausler and M.W. Linduer, ""Coherence radar" and "spectral radar"-new tools for
dermatological diagnosis," Journalof Biomedical Optics, vol. 3, pp. 21-31,1998.
M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A.F. Fercher, "In vivo
human retinal imaging by Fourier domain optical coherence tomography," Journal of
Biomedical Optics, vol. 7, pp. 457-463,2002.
M. Wojtkowski, T. Bajraszewski, P. Targowski, and A. Kowalczyk, "Real-time in vivo
imaging by high-speed spectral optical coherence tomography," Optics Letters, vol. 28,
pp. 1745-1747,2003.
M. Wojtkowski, V.J. Srinivasan, T.H. Ko, J.G Fujimoto, A. Kowalevicz, and J.S. Duker,
"Ultrahigh resolution, high speed, Fourier domain optical coherence tomography and
methods for dispersion compensation," Optics Express, vol. 12, pp. 2404-2422,2004.
S.R. Chinn, E.A. Swanson, and J.G Fujimoto, "Optical coherence tomography using a
frequency-tunable optical source," Optics Letters, vol. 22, pp. 340-342,1997.
B. Golubovic, B.E. Bouma, G.J. Tearney, and J.G Fujimoto, "Optical frequency-domain
reflectometry using rapid wavelength tuning of a Cr4+:forsterite laser," Optics Letters,
vol. 22, pp. 1704-1706,1997.
S.H. Yun, C. Boudoux, G.J. Tearney, and B.E. Bouma, "High-speed wavelength-swept
semiconductor laser with a polygon-scanner-based wavelength filter," Optics Letters, vol.
28, pp. 1981-1983,2003.
24.
S.H. Yun, C. Boudoux, M.C. Pierce, J.F. de Boer, GJ. Tearney, and B.E. Bouma,
"Extended-cavity semiconductor wavelength-swept laser for biomedical imaging," IEEE
Photonics Technology Letters, vol. 16, pp. 293-5,2004.
25.
26.
27.
28.
29.
30.
31.
32.
R. Huber, D.C. Adler, and J.G Fujimoto, "Buffered Fourier Domain Mode Locking
(FDML): Unidirectional swept laser sources for OCT imaging at 370,000 lines per
second," Optics Letters, vol. In Press,2006.
M.A. Choma, M.V. Sarunic, C.H. Yang, and J.A. Izatt, "Sensitivity advantage of swept
source and Fourier domain optical coherence tomography," Optics Express, vol. 11, pp.
2183-2189,2003.
J.F. de Boer, B. Cense, B.H. Park, M.C. Pierce, G.J. Tearney, and B.E. Bouma, "Improved
signal-to-noise ratio in spectral-domain compared with time-domain optical coherence
tomography," Optics Letters, vol. 28, pp. 2067-2069,2003.
R. Leitgeb, C.K. Hitzenberger, and A.F. Fercher, "Performance of Fourier domain vs.
time domain optical coherence tomography," Optics Express, vol. 11, pp. 889-894,2003.
N.A. Nassif, B. Cense, B.H. Park, M.C. Pierce, S.H. Yun, B.E. Bouma, GJ. Tearney, T.C.
Chen, and J.F. de Boer, "In vivo high-resolution video-rate spectral-domain optical
coherence tomography of the human retina and optic nerve," Optics Express, vol.
12,2004.
M. Wojtkowski, T. Bajraszewski, I. Gorczynska, P. Targowski, A. Kowalczyk, W.
Wasilewski, and C. Radzewicz, "Ophthalmic imaging by spectral optical coherence
tomography," Am J Ophthalmol,vol. 138, pp. 412-9,2004.
M. Wojtkowski, V. Srinivasan, J.G Fujimoto, T. Ko, J.S. Schuman, A. Kowalczyk, and
J.S. Duker, "Three-dimensional retinal imaging with high-speed ultrahigh-resolution
optical coherence tomography," Ophthalmology, vol. 112, pp. 1734-46,2005.
B. Wabbels, M.N. Preising, U. Kretschmann, A. Demmler, and B. Lorenz,
"Genotype-phenotype correlation and longitudinal course in ten families with Best
vitelliform macular dystrophy," Graefes Archive for Clinical and Experimental
33.
34.
35.
36.
37.
38.
Ophthalmology,vol. 244, pp. 1453-1466,2006.
R. Leitgeb, M. Wojtkowski, A. Kowalczyk, C.K. Hitzenberger, M. Sticker, and A.F.
Fercher, "Spectral measurement of absorption by spectroscopic frequency-domain optical
coherence tomography," Optics Letters, vol. 25, pp. 820-2,2000.
M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A.F. Fercher, "Full range complex
spectral optical coherence tomography technique in eye imaging," Optics Letters, vol. 27,
pp. 1415-17,2002.
P. Targowski, M. Wojtkowski, A. Kowalczyk, T. Bajraszewski, M. Szkulmowski, and W.
Gorczynska, "Complex spectral OCT in human eye imaging in vivo," Optics
Communications,vol. 229, pp. 79-84,2004.
R.A. Leitgeb, L. Schmetterer, W. Drexler, A.F. Fercher, R.J. Zawadzki, and T.
Bajraszewski, "Real-time assessment of retinal blood flow with ultrafast acquisition by
color Doppler Fourier domain optical coherence tomography," Optics Express, vol. 11, pp.
3116-3121,2003.
B.R. White, M.C. Pierce, N. Nassif, B. Cense, B.H. Park, GJ. Teamey, B.E. Bouma, T.C.
Chen, and J.F. de Boer, "In vivo dynamic human retinal blood flow imaging using
ultra-high-speed spectral domain optical Doppler tomography," Optics Express, vol. 11,
pp. 3490-3497,2003.
R.A. Leitgeb, L. Schmetterer, C.K. Hitzenberger, A.F. Fercher, F. Berisha, M.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
51.
52.
53.
Wojtkowski, and T. Bajraszewski, "Real-time measurement of in vitro flow by
Fourier-domain color Doppler optical coherence tomography," Opt Lett, vol. 29, pp.
171-3,2004.
T.C. Chen, B. Cense, M.C. Pierce, N. Nassif, B.H. Park, S.H. Yun, B.R. White, B.E.
Bouma, G.J. Tearney, and J.F. de Boer, "Spectral domain optical coherence tomography:
ultra-high speed, ultra-high resolution ophthalmic imaging," Arch Ophthalmol, vol. 123,
pp. 1715-20,2005.
B.H. Park, M.C. Pierce, B. Cense, S.H. Yun, M. Mujat, GJ. Tearney, B.E. Bouma, and J.F.
de Boer, "Real-time fiber-based multi-functional spectral-domain optical coherence
tomography at 1.3 mu m," Optics Express, vol. 13, pp. 3931-3944,2005.
M.A. Choma, S. Yazdanfar, and J.A. Izatt, "Wavelet and model-based spectral analysis of
color doppler optical coherence tomography," Optics Communications, vol. 263, pp.
124-128,2006.
S. Makita, Y. Hong, M. Yamanari, T. Yatagai, and Y. Yasuno, "Optical coherence
angiography," Optics Express, vol. 14, pp. 7821-7840,2006.
H.W. Ren, T. Sun, D.J. MacDonald, M.J. Cobb, and X.D. Li, "Real-time in vivo
dblood-flow imaging by movingscatterer-sensitive spectral-domain optical Doppler
tomography," Optics Letters, vol. 31, pp. 927-929,2006.
Y.C. Ahn, W. Jung, and Z.P. Chen, "Quantification of a three-dimensional velocity vector
using spectral-domain Doppler optical coherence tomography," Optics Letters, vol. 32, pp.
1587-1589,2007.
A.H. Bachmann, R. Michaely, T. Lasser, and R.A. Leitgeb, "Dual beam heterodyne
Fourier domain optical coherence tomography," Optics Express, vol. 15, pp.
9254-9266,2007.
A.H. Bachmann, M.L. Villiger, C. Blatter, T. Lasser, and R.A. Leitgeb, "Resonant
Doppler flow imaging and optical vivisection of retinal blood vessels," Optics Express,
vol. 15, pp. 408-422,2007.
B.A. Bower, M. Zhao, R.J. Zawadzki, and J.A. Izatt, "Real-time spectral domain Doppler
optical coherence tomography and investigation of human retinal vessel autoregulation,"
JBiomed Opt, vol. 12, pp. 041214,2007.
D. Morofke, M.C. Kolios, I.A. Vitkin, and V.X.D. Yang, "Wide dynamic range detection
of bidirectional flow in Doppler optical coherence tomography using a two-dimensional
Kasai estimator," Optics Letters, vol. 32, pp. 253-255,2007.
C.J. Pedersen, D. Huang, M.A. Shure, and A.M. Rollins, "Measurement of absolute flow
velocity vector using dual-angle, delay-encoded Doppler optical coherence tomography,"
Optics Letters, vol. 32, pp. 506-508,2007.
Y. Wang, B.A. Bower, J.A. Izatt, O. Tan, and D. Huang, "In vivo total retinal blood flow
measurement by Fourier domain Doppler optical coherence tomography," J Biomed Opt,
vol. 12, pp. 041215,2007.
J.S. Schuman, M.R. Hee, A.V. Arya, T. Pedut-Kloizman, C.A. Puliafito, J.G. Fujimoto,
and E.A. Swanson, "Optical coherence tomography: a new tool for glaucoma diagnosis,"
Current Opinion in Ophthalmology, vol. 6, pp. 89-95,1995.
J.S. Schuman, C.A. Puliafito, and J.G. Fujimoto, Optical coherence tomography of ocular
diseases, 2nd edition. 2004, Thorofare, NJ: Slack Inc.
M.R. Hee, C.A. Puliafito, C. Wong, J.S. Duker, E. Reichel, J.S. Schuman, E.A. Swanson,
and J.G. Fujimoto, "Optical coherence tomography of macular holes," Ophthalmology,
vol. 102, pp. 748-756,1995.
54.
M.R. Hee, C.A. Puliafito, C. Wong, E. Reichel, J.S. Duker, J.S. Schuman, E.A. Swanson,
and J.G Fujimoto, "Optical coherence tomography of central serous chorioretinopathy,"
American Journalof Ophthalmology, vol. 120, pp. 65-74,1995.
55.
56.
57.
58.
59.
M.R. Hee, C.R. Baumal, C.A. Puliafito, J.S. Duker, E. Reichel, J.R. Wilkins, J.G Coker,
J.S. Schuman, E.A. Swanson, and J.G Fujimoto, "Optical coherence tomography of
age-related macular degeneration and choroidal neovascularization," Ophthalmology, vol.
103, pp. 1260-1270,1996.
M.R. Hee, C.A. Puliafito, J.S. Duker, E. Reichel, J.G Coker, J.R. Wilkins, J.S. Schuman,
E.A. Swanson, and J.G Fujimoto, "Topography of diabetic macular edema with optical
coherence tomography," Ophthalmology,vol. 105, pp. 360-370,1998.
J.S. Schuman, T. Pedut-Kloizman, E. Hertzmark, M.R. Hee, J.R. Wilkins, J.G Coker, C.A.
Puliafito, J.G Fujimoto, and E.A. Swanson, "Reproducibility of nerve fiber layer
thickness measurements using optical coherence tomography," Ophthalmology, vol. 103,
pp. 1889-1898,1996.
M. Ruggeri, H. Webbe, S.L. Jiao, G Gregori, M.E. Jockovich, A. Hackam, Y.L. Duan,
and C.A. Puliafito, "In vivo three-dimensional high-resolution imaging of rodent retina
with spectral-domain optical coherence tomography," Investigative Ophthalmology &
Visual Science, vol. 48, pp. 1808-1814,2007.
V.J. Srinivasan, T.H. Ko, M. Wojtkowski, M. Carvalho, A. Clermont, S.E. Bursell, Q.H.
Song, J. Lem, J.S. Duker, J.S. Schuman, and J.G. Fujimoto, "Noninvasive volumetric
Imaging and morphometry of the rodent retina with high-speed, ultrahigh-resolution
optical coherence tomography," Investigative Ophthalmology & Visual Science, vol. 47,
60.
pp. 5522-5528,2006.
B.B. Gao, A. Clermont, S. Rook, S.J. Fonda, V.J. Srinivasan, M. Wojtkowski, J.G
Fujimoto, R.L. Avery, P.G Arrigg, S.E. Bursell, L.P. Aiello, and E.P. Feener,
"Extracellular carbonic anhydrase mediates hemorrhagic retinal and cerebral vascular
permeability through prekallikrein activation," Nature Medicine, vol. 13, pp.
181-188,2007.
61.
62.
63.
64.
65.
66.
X.J. Wang, T.E. Milner, and J.S. Nelson, "Characterization of Fluid-Flow Velocity by
Optical Doppler Tomography," Optics Letters, vol. 20, pp. 1337-1339,1995.
J.A. Izatt, M.D. Kulkami, S. Yazdanfar, J.K. Barton, and A.J. Welch, "In vivo
bidirectional color Doppler flow imaging of picoliter blood volumes using optical
coherence tomography," Optics Letters, vol. 22, pp. 1439-41,1997.
Y. Zhao, Z. Chen, C. Saxer, S. Xiang, J.F. de Boer, and J.S. Nelson, "Phase-resolved
optical coherence tomography and optical Doppler tomography for imaging blood flow in
human skin with fast scanning speed and high velocity sensitivity," Optics Letters, vol. 25,
pp. 114-16,2000.
Z. Chen, T.E. Milner, S. Srinivas, X. Wang, A. Malekafzali, M.J.C. van Gemert, and J.S.
Nelson, "Noninvasive imaging of in vivo blood flow velocity using optical Doppler
tomography," Optics Letters, vol. 22, pp. 1119-21,1997.
S. Yazdanfar, A.M. Rollins, and J.A. Izatt, "Imaging and velocimetry of the human retinal
circulation with color Doppler optical coherence tomography," Optics Letters, vol. 25, pp.
1448-50,2000.
V.X.D. Yang, M.L. Gordon, E. Seng-Yue, S. Lo, B. Qi, J. Pekar, A. Mok, B.C. Wilson,
and I.A. Vitkin, "High speed, wide velocity dynamic range Doppler optical coherence
67.
68.
69.
70.
71.
72.
73.
74.
75.
76.
77.
78.
79.
80.
tomography (Part II): imaging in vivo cardiac dynamics of Xenopus laevis," Optics
Express, vol. 11,2003.
S. Yazdanfar, A.M. Rollins, and J.A. Izatt, "In vivo imaging of human retinal flow
dynamics by color Doppler optical coherence tomography," Archives of ophthalmology,
vol. 121, pp. 235-9,2003.
V. Patel, S. Rassam, R. Newsom, J. Wiek, and E.Kohner, "Retinal blood flow in diabetic
retinopathy," Bmj, vol. 305, pp. 678-83,1992.
E. Friedman, "A hemodynamic model of the pathogenesis of age-related macular
degeneration," Am J Ophthalmol,vol. 124, pp. 677-82,1997.
J. Flammer, S. Orgul, V.P. Costa, N. Orzalesi, G.K. Krieglstein, L.M. Serra, J.P. Renard,
and E. Stefansson, "The impact of ocular blood flow in glaucoma," Prog Retin Eye Res,
vol. 21, pp. 359-93,2002.
J.D.M. Gass, "Stereoscopic Atlas of Macular Diseases: Diagnosis and Treatment". 1987,
CV Mosby: St. Louis, Missouri. p. 46-65.
G.T. Feke and C.E. Riva, "Laser Doppler measurements of blood velocity in human
retinal vessels," J Opt Soc Am, vol. 68, pp. 526-31,1978.
B. Eberli, C.E. Riva, and G.T. Feke, "Mean circulation time of fluorescein in retinal
vascular segments," Arch Ophthalmol, vol. 97, pp. 145-8,1979.
G.T. Feke, D.G. Goger, H. Tagawa, and F.C. Delori, "Laser Doppler technique for
absolute measurement of blood speed in retinal vessels," IEEE Trans Biomed Eng, vol. 34,
pp. 673-80,1987.
C.E. Riva, S. Harino, B.L. Petrig, and R.D. Shonat, "Laser Doppler flowmetry in the
optic nerve," Exp Eye Res, vol. 55, pp. 499-506,1992.
C.E. Riva, S.D. Cranstoun, J.E. Grunwald, and B.L. Petrig, "Choroidal blood flow in the
foveal region of the human ocular fundus," Invest Ophthalmol Vis Sci, vol. 35, pp.
4273-81,1994.
J.D. Briers and A.F. Fercher, "Retinal blood-flow visualization by means of laser speckle
photography," Invest Ophthalmol Vis Sci, vol. 22, pp. 255-9,1982.
Y. Tamaki, M. Araie, E. Kawamoto, S. Eguchi, and H. Fujii, "Noncontact,
two-dimensional measurement of retinal microcirculation using laser speckle
phenomenon," Invest Ophthalmol Vis Sci, vol. 35, pp. 3825-34,1994.
G. Michelson and B. Schmauss, "Two dimensional mapping of the perfusion of the retina
and optic nerve head," Br J Ophthalmol, vol. 79, pp. 1126-32,1995.
G. Michelson, B. Schmauss, M.J. Langhans, J. Harazny, and M.J. Groh, "Principle,
validity, and reliability of scanning laser Doppler flowmetry," J Glaucoma, vol. 5, pp.
99-105,1996.
Chapter 2
OCT Theory
2.1 The Michelson Interferometer
Consider the schematic of the Michelson interferometer shown in Figure 2-1.
An input optical
wave generated from the light source is divided by a beamsplitter into reference and sample
beams.
Waves reflected from the reference and sample mirrors recombine at the same
beamsplitter and produce an output incident on the detector.
The sample and reference mirror
are positioned Is and IR from the beamsplitter, respectively.
Assuming a monochromatic
light source, the electric field at the detector can be given by:
E=ER +Es
(2.1)
where ER and Es are the monochromatic electric field components from the reference and
sample arms.
The fields may be expressed by:
ER = ARe - j 2 kRlR
and Es = As e - j 2ks's
(2.2)
Where k is the propagation constant. AR and As are the amplitudes of the light reflected
from the reference and sample mirrors. The round trip propagation of the waves to and from
the sample and reference mirror generates the factor of two multiplying the phase constants.
J
lR,ER
ple
ER+ Es
Detector
Figure 2-1.
The Michelson interferometer.
In general, the photo electron density I at the detector is given by:
=7e ER +Es.
(2.3)
2r0
ha
where 77 is the detector quantum efficiency, e is the electronic charge, hw is the photon
energy, and 770 is the intrinsic impedance of free space.
For monochromatic fields, equation
(2.3) can be rewritten as
I27e
[IAR
2+
AS
2
2 ReEE
DC
int
(2.4)
The intensity returned from the sample arm is usually small compared with the intensity from the
reference arm.
Therefore, the term describing the variation of photocurrent with positions, lint ,
can be obtained by subtracting the intensity AR
intensity As
2
from the sample arm:
2
from the reference arm and ignoring the
i,oc ReERE}
(2.5)
(
By substituting ER and Es with equation (2.2),
lint oc ARAs cos(2 kRls - 2 kslR)
(2.6)
In free space, the propagation constants are equal for both the reference and sample fields, giving
kn = k 3 = 2
(2.7)
and
2cARA
cos(
2Al)
s
Ii., cCARAs cos(-.
2A)
(2.8)
1%
where Al = ls -lR
is the mismatch in distance between the reference arm and sample arm beam
paths.
Since all of the interference information is contained in the cross-spectral term
Re EREE
s
, subsequent analysis will focus on calculating this term only.
2.2 Time Domain Interferometer with Low-Coherence Light
A low-coherence light source consists of a finite bandwidth of frequencies corresponding to
different wavelengths.
Therefore, the reference and sample arm electric fields can be written as
functions of wavelength:
' ")1L
ER (o) = AR (o)e-i2 kR() /R and EL (o)= AL (o)e-j2kL(
(2.9)
For time domain OCT, the interference signal at the photodetector is the sum of the interference
from all frequecies:
ER (o)Es (c) do = Re
Iint oc Re
(2.10)
S(o)e jA¢(,)doe
where
S(co) =AR(c)As (o)
(2.11)
and
Af(ao) = 2kR (o)l
s
. (2.12)
- 2k s (co)lR
Assume that the sample and reference arms consist of non-dispersive material, and equal
propagation
constants
kR(c) = ks(c) = k(oo) +k'(co)(co-coo) .
bandlimited light source S(wc-co ) is centered at ao frequency.
The spectrum
of the
The phase mismatch in
equation (2.12) can be rewritten as
Aq(co) = k(Co) -2A1 + k'(c)(Co)-
(2.13)
o). 2AI
The interference signal becomes:
int oc
Re e- j k(' o)2A'
S(w
-
- j k '(
)(
o)e w
-o)
-
°2
l
d( 2-
)
This shows that the interference signal consists of a carrier and an envelope wave.
e-
jk
(o)- ' 2 Al
represents the carrier wave with fast oscillation.
S(co - c)e
-CoO
-j
k'((o)(coo)-
2
AI d (
- too)
2;
(2.14)
The term
The slowly varying envelope
determines the axial point spread function of the
interferometer is the inverse Fourier transform of the source power spectrum S(o - co) .
This
is also a statement of the Wiener-Khinchin theorem.
In time domain optical coherence tomography (OCT), the width of the envelope sets the axial
resolution of the imaging system.
To generate an image, the sample arm focus is scanned
laterally at a fixed depth in the sample and the reference arm path length is varied at high speed.
Interference signals are generated when the path length difference between light scattering from
planes in the sample and the position of the reference arm mirror is within the coherence length
of the light source.
Assuming that the light source has a Gaussian power spectral density S(o - co) = -e
2a.2'
where 2a,,is the standard deviation power spectral bandwidth, equation (2.14) becomes:
int xc Re
e
'2A =e
e- j k(%)o)
2
The interference signal oscillates with k(oo).-2Al.
reference and sample arm length Al.
2
(2.15)
cos(k(co) 2Al)
The envelope falls quickly with mismatched
The full width at half maximum (FWHM) of the
interference signal in a free space interferometer, where 1/k'(coo)= c, can be shown to be related
to the center wavelength and spectral FWHM as
A
21n2 202
(2.16)
AlFwHM =
where A2 is the FWHM bandwidth and4 is the center wavelength of the light source.
This
gives the resolution of time domain OCT in terms of wavelength and bandwidth.
For a general non-Gaussian spectrum, the coherence length can be evaluated by determining the
FWHM of its Fourier transformation.
Compared to the Gaussian spectrum, non-Gaussian
spectra will produce broader point spread functions giving worse resolution.
Generation of
sidelobes by non-Gaussian sources can also be a problem for low-coherence interferometry
applications.
2.3 Spectral / Fourier Domain OCT
In spectral / Fourier domain OCT, the interference signal is detected by a spectrometer using a
high-speed multi-element CCD or a photodiode array detector. The delay and magnitude of the
optical reflections from the sample can be detected by Fourier transforming the spectral
interference signal.
spectral / Fourier domain OCT enables reconstructing the depth resolved
scattering profile at a certain point on the sample from a modulation of the optical spectrum
caused by interference of light beams.
In spectral / Fourier domain OCT, the time averaged photoelectron density I at the CCD detector
is given by:
I =q()+T
R
2l
+ A,
0(c)
2
+ 2 ReI Es (co)ER(w)c =
DC+
it
(2.17)
Therefore, the interference signal can be written as:
oc Re ER (o)E (w)*
= Re (S(w)e-jA
}
where S(c) = AR((w)As (co)
and A (w) = 2kR ()lR - 2ks (w)ls .
Note the differences with
equations (2.4) and (2.10).
This is due to the fact that CCD detectors collect photoelectron
int
(2.18)
charges during the exposure time T whereas PIN photo detectors register the continuous
photoelectron current.
Also, the spectral detection method detects the spectrum of the
interference light, while the photodiode in the time domain detects the sum of all light
frequencies.
The total field from the sample arm is assumed to be composed of a superposition of fields
generated by reflections from different delays or depths.
intoc
Re ER (W)
n
Es,n (w)* = Re
Equation (2.18) thus becomes:
n
S,(w)e-JA
)
(2.19)
with
(2.20)
S ())= AR ,()AS, (0)
and
. (2.21)
A&0 (o) = 2kR (o)lR - 2ks (o)1s,n
If
the
sample
and
reference
arms
consist
of
kR (o) = ks (w) = k(c) = k(o) + k'(co)(o - co) and 1/k'(o) = c .
non-dispersive
material
The phase mismatch in
equation (2.21) can be rewritten as
A, (O) = k(coo) . 2Al. + k '(o)( - o)-2Al, =
where Al, = s,n -1R, and O,(Al,)
C
+ (D,(Al,)
is the co independent constant phase term.
(2.22)
Therefore, equation
(2.19) can be rewritten as:
in
Y-"S,(0)cos( 2 A
t
i
-
. +2(Al)))
(2.23)
The mismatch of distance between the reference and sample arms can be obtained by calculating
the inverse Fourier transform of equation (2.23):
I = FAssume that parameters
depth-independent.
{Iint ()}
oc
e-in"(A)G (z) ®S(z ± 2Al, )
(2.24)
such as dispersion and the spectral transfer function are
The resolution of spectral / Fourier domain OCT is therefore determined
by G, (z)= S, (co) -- , linked to the Wiener-Khinchin theorem. Notice the resolution is same
for time domain and spectral / Fourier domain OCT. Also notice the "mirror images" expressed
by 8(z ± Al).
The total number of pixels carrying unique information about the axial scan is
reduced by a factor of two, because the Fourier transform of the real spectrum has conjugate
symmetry about the zero delay.1
=L
S(CqCo"
2r
Assuming that the light source has a Gaussian power spectral density
the resolution is given by
AlFWM =-
21n2
S(-)=
-- 0
A02
;rAA, as shown in section 2.2.
2r2
S(m) = .
e
(c)
F-1 {S(co)}
2A1)
F-' {cos(k(co) -2A1)}
F-1
I
I
I•
AlFWHM
2 In 2
I
,0 2
A
Figure 2-2.
Inverse Fourier transformation of lint .
The inverse Fourier
transform of the Gaussian envelope S(co) is the pointspread function, and
therefore determines the resolution.
On the other hand, the cosine term holds
information on the path length difference Al.
(Wo-W•
0 )2
2,T,,
2
2.3.1 Measurement Range
In spectral / Fourier domain OCT, the multi-element CCD or a photodiode array detector in the
spectrometer has a limited bandwidth or spectral range AA.
If AA is too small and the full
spectrum is not imaged onto the CCD or detector, the axial resolution will be worse than the
theoretical value set by (2.16). If AA is too large, the axial measurement range is reduced
while the axial resolution remains the theoretical value. Therefore, AA must be chosen so that
the optimal resolution in (2.16) is achieved without compromising the axial measurement range.
The measurement range in spectral / Fourier domain OCT depends on the spectral resolution of
the spectrometer. Assume that the number of sampling points N is given by the number of
CCD pixels.
The path length differences in the sample are found by calculating the numerical
Fourier transform (FFT) of the measured signal.
1 2,rAA
According to the Nyquist sampling theorem, the minimal detectable frequency Akin
-
N c)22
From equation (2.16), this corresponds to a maximum path difference
Alax-1
2
N
4 AA
(2.25)
In order to resolve two reflections separated by Az, the axial pixel spacing should be no less than
. Thus, the spectrometer must have a bandwidth or spectral range of
2Az"
2
(2.26)
By combining equations (2.25) and (2.26), the axial measurement range over which reflected
signals can be measured is
Aln2,=I 2 N
Alm x- 2x
(2.27)
This equation shows that, for a given source bandwidth, the axial scan range is limited by the
number of pixels, if optimal resolution is to be achieved. 2
2.3.2 Spectrometer Roll-off
In practice, a significant weakness of spectral / Fourier domain OCT is the depth dependent
signal drop.
The spectrometer enables special separation of light with different k(x) ,
where x denotes a spatial coordinate corresponding to the distribution of the photo-sensitive
elements of the detector.
A diffraction grating followed by a lens and CCD array is usually
used, which obtains a spectrum evenly sampled in wavelength instead of frequency co :
x c iZc
A
21r
k(x) oc x
(2.28)
Since the interference signal is encoded in frequencies of k dependent spectral fringes as in
equation, partial aliasing could occur. The high frequencies of the interference signal are
sampled more sparsely sampled than the low frequencies.
This means that high frequencies
could be aliased in part of the spectrum while the rest of the signal can remain within the Nyquist
limit.
The rectangular characteristic of pixels also results in a suppression of amplitudes of high
frequency components of the interference signal.
Since the spectrum is averaged within a
single pixel, the interference signal is convolved with the rect function
single pixel of the CCD with width 5x.
,,x/2 (x) representing a
After the Fourier transform, the rect function becomes
a sinc function which is related to the decrease of interference signal visibility as a function of
increasing modulation frequency.
An illustration is shown in figure 2-3.
ix/2W
t
I
Fx
1K1
Figure 2-3.
_
Spectrometer roll-off due to spectrometer rectangular characteristic
of CCD pixel.
The green line shows the effect of integration within pixel
width Sx .
Other factors suppressing the high frequency components of the interference signal are the
electronic pixel crosstalk and finite focal spot size.
The charge from a particular pixel is spread
over the neighboring pixels, which causes degradation of the spectrometer resolution.
When
the focal spot size is bigger than the pixel width, the visibility of the interference signal also
decreases. 3-5
2.3.3 Dispersion Compensation
Dispersion causes different frequencies to propagate with nonlinearly related velocities
dependent on the propagation constants for materials.
broaden without proper dispersion compensation.
In ultrafast lasers, a short pulse will
In OCT, the interferometric autocorrelation
will also broaden if there is dispersion mismatch between the reference and sample arms.
Therefore, the dispersion mismatch between the two arms must be compensated to achieve
optimal resolution.
The propagation constant k(co) can be expanded as a Taylor series near the center frequency of
the light source co :
k(w) = k(o)+ k '(coo)(co- o)+
2
(co -Coo)2 + "
6
(C
- Co) 3 +...
(2.29)
The constant term k(co0) is the propagation constant at the center frequency co. In ultrafast
optics, this corresponds to the phase delay of the carrier at cw passing through a material with
propagation constant k(wo0).
The second term k'(co0) is the inverse group velocity. This
determines the group delay, or the temporal delay of a pulse passing through a medium with a
propagation constant varying linearly as a function of frequency.
Higher order terms in the Taylor expansion result in broadening of the point spread function and
loss of resolution.
The third term in function (2.29) describes the group velocity dispersion or a
variation in group velocity with frequency.
This is the term that produces pulse broadening in
femtosecond optics and broadening of the axial resolution in OCT. The fourth term has been
referred to as third-order dispersion, which produces asymmetric pulse distortion in femtosecond
optics and asymmetric distortion of the point spread function in OCT. Higher order terms may
also be present.
Equation (2.23) can be rewritten as
int
oc , S
n
)cos(2+ ,
C
(2.30)
(o,Al,))
The phase term D,(w, Al,) incorporates all non-linear components of the phase in o, as well as
any constant ( w independent) phase.
As the above equations show, the combination of
dispersion and recalibration errors results in two types of phase terms to compensate.
depth dependent ( Al, dependant) phase error.
One is a
The other is a depth independent ( Al
independent) phase error. In most OCT imaging applications, the axial range Al. over which
imaging is performed is short. For spectral / Fourier domain OCT, the axial range Al.m
is
limited by the number of pixels. In scattering tissues, the imaging depth is further limited by
optical scattering and absorption.
Therefore, variation of dispersion over the axial image range
is usually negligible, and dispersion is predominantly caused by fixed material in front of the
axial imaging range. Because the frequency-dependent phase distortion is the same for all
depths in one axial scan, the dispersion is not depth dependent, giving D, (co, Al) = ', ()o).
In spectral / Fourier domain OCT, dispersion compensation can be performed by canceling the
frequency-dependent nonlinear phase, which arises from the dispersion mismatch between the
two arms of the interferometer.
Since the interference signal from the spectrometer is a real
function, a Hilbert transform can be used to generate the imaginary part of the complex analytic
signal Im lint }. Note that this is not equivalent to acquiring the complex interference signal
directly, since the number of pixels carrying unique information about the axial measurement is
reduced by a factor of two from the number of pixels in the spectrum.
The real and imaginary
parts of the interference signal are used to construct the complex analytic representation of the
spectral fringe pattern. The phase of the complex analytic signal is then modified by adding a
phase correction to compensate for dispersion:
6(0) =
2
o- )0 2 a 3 (o -
0)
3
(2.31)
The coefficient -a 2 is adjusted to cancel the group velocity dispersion imbalance (second-order
term) and -a 3 is adjusted to cancel the third-order dispersion imbalance (third-order term).
This method may be generalized to higher orders; however, compensation to third-order is
usually sufficient, assuming that the interferometer arms were approximately dispersion matched
initially. Finally, the corrected spectrum is Fourier transformed to obtain the axial depth scan.
If the appropriate phase correction has been applied, this new axial depth scan is compensated
for dispersion mismatch between the interferometer arms and it has optimum axial resolution.6
2.3.4 Doppler OCT
Doppler OCT can provide information on flow as well as wavelength scale thickness variations
and displacements in samples and tissues in the axial direction. Doppler flow is measured by
performing multiple axial scans at or near the same transverse position and extracting and
comparing the relative interferometric phases of sequential scans.
layer has distance mismatch Al, and velocity v.
Assume that a reflective
Reexamine equation (2.22) using Al, + vr,
where r is the time period between measurements and vr << Al,,
A
= 2(Al,
A
+
Vr) )
C
•- (,(A,) = 2Al
2 n .co
+ 4:vt
4z- +( ,(AlJ)= 2A/n .m + f (v)+n(Al,)
C
A
c
(2.32)
The calculated distance mismatch between the reference and sample arm at the same position
sequential in time can be written as:
I=
{Int (c)}Icc
IF'
e-'
(Al"")-",,(V)G (z) S (z +2Al )
(2.33)
n
Notice the additional phase term
,n(v) compared with equation (2.24).
In spectral / Fourier domain OCT, the phase of the interferometric signal is directly accessible.
The phase data can be used to provide quantitative sub-wavelength measurements of optical path
variations within a sample, or to obtain highly sensitive Doppler flow information.
Flow
velocity in the direction parallel to the axial OCT probe beam is calculated by
(2.34)
v(z) = A(D(z)2
4nt
where AcD(z) is the phase difference between the same transverse position of adjacent scans, A is
the center wavelength, r is the time difference between adjacent scans.7 '8
2.4 Noise and Sensitivity
The minimum detectable reflectivityRs,min, yielding a signal power equal to the noise of the
system, is an important feature of an OCT instrument.
Sensitivity S is defined as the ratio of
the signal power detected from a perfectly reflecting mirror (R = 1) and that detected from
Rs,min.
The signal powers are proportional to the corresponding reflectivities giving:
S=
SNR
where
SNR
isthe
signain-to-noise
ratio.
where SNR is the signal-to-noise ratio.'
(2.35)
The dominating noise sources in OCT are shot noise, excess intensity noise, and receiver noise.
Optimal sensitivity is achieved when the sensitivity is shot noise limited. This occurs when the
shot noise dominates all other sources of noise.
2.4.1 Shot Noise Limit
Photon shot noise is the noise associated with the random arrival of photons at a detector. The
time between photon arrivals is governed by Poisson statistics.
The number of detected
photoelectrons in a time interval T is given by the following distribution:
p(n) =
n" exp(-n)
(2.36)
n!
where n is the number of detected photoelectrons, and n is the expected number of detected
photoelectrons or mean photon count. In spectral / Fourier domain OCT, The expected number
of detected photoelectrons on a N pixel CCD array is given by the average photoelectron
density:
n-
(2.37)
DC
N
Because the variance of a Poisson process is equal to its mean, hot = ni, the number of photons
detected is linearly related to the accuracy of detection."'
2.4.2 Excess Intensity noise
In the case of partially coherent light, fluctuations in optical power / intensity are random.
variance of the photon number has two contributions.
The
One component results from the
association of particles with power or intensity, or Poisson noise.
The second component is
from fluctuations in the classical power or intensity caused by beats between the various
randomly phased Fourier components making up the linewidth. Therefore,
an2
2t +
2ess
(2.38)
where the variance includes an excess noise component.
ecess
In spectral / Fourier domain OCT,
is given as:
(1+ 2)
2
es
=
2T
2
hN
(PRRR +PRS
)2
N
11
(2.39)
AVeff
where Hl is the degree of polarization and Avef is the effective spectral linewidth.3
2.4.3 Receiver Noise
The CCD receiver noise consists of dark current noise, thermal noise, and flicker noise.
For a
given readout configuration and speed, these noise sources are independent of the signal level.
Dark current is the result of imperfections in the depleted bulk region of the silicon or the
silicon-silicon dioxide interface.
This can be minimized by cooling the CCD.
Dark current
non-uniformity results from the fact that different pixels generate different amounts of dark
current. This noise can be eliminated by subtracting a reference frame.
However, the dark
current shot noise remains a problem. Thermal noise is independent of frequency and has
temperature dependence.
It fundamentally originates in the thermal movement of atoms.
Flicker noise or 1/f noise is strongly dependent on frequency.
The read noise and dark noise
in the CCD camera can be estimated by blocking optical power from the interferometer to the
spectrometer.
In this case, the variance e2
of each pixel can be measured over time. 3
2.4.4 Sensitivity
By rewriting equation (2.17) into
I = IDC + lint =
2h[TPRRR
+ Ps R s + 2PRRRPsR
s
cos(2kAl)]
(2.40)
where P, and Ps are the output power in the reference and sample arms, RR and Rs are
reflectivities of the reference and sample mirror.
Taking total noise
2,,s = C,
+
e+ee
into account, the SNR of a spectral / Fourier
domain OCT system is given as:
where the factor of
-
2
(2.41)
N
SNR
20"noise
is due to the DFT, which also could be understood from the fact that
N pixels improve the sensitivity; however, redundant data is generated for positive and negative
sample displacements, decreasing the improvement by a factor of 2.
For shot noise limited detection, where aO
se
=
0,3
ho,,, and assuming the reference arm intensity is
much larger than the sample arm, i.e. RR >> Rs , the SNR can be written as:
( T 2PRRRPsRs
)
SNR = N 2ho
i7T
2
=N
2hA PRRR
IT
PsRs
2hos
(2.42)
Therefore, the sensitivity S of a spectral / Fourier domain OCT system may be written as:
S =N
(2.43)
T Ps
2heo
SNR=I
2.4.5 Dynamic Range
In spectral / Fourier domain OCT setups, the detector records the sum of the DC background
with the interference signal. The dynamic range DR is defined as the ratio of the maximum to
the minimum measurable photocurrent power or the maximum measurable signal to noise ratio:
DR = Pm = SNR
Revisiting equation (2.41), the dynamic range can be written as:
(2.44)
( "RT) 2PRRPsm
DR =
If we assume that P,,f = yP,,, where 0 <y <1 and
(2.45)
mx
2ro sa
N
T PR
1iT
PRRR
2heo
2
, = Ps,mx +PR
+
2 Ps,PR.
Hence, the
maximum sample arm power is given by:"
2
Ps,max =a(1)
sat (I+y-2
Y)
(2.46)
And equation (2.45) can be rewritten as:
DR=
T Pt N ( + - 2
2hc
'
)
(2.47)
(2.47)
2.4.6 Doppler Range and Sensitivity
In a shot-noise limited spectral / Fourier domain OCT system, phase noise is generated by the
random phase of the shot noise.
The shot noise limited phase stability is limited by the phase
angle Sy•,s between Isignal and I=
signal
+
'noise
as shown in figure 2-4.
The phase angle can
be written as
rsIg-na+ise
-sin'
os
I/sens = tan 1
where
'signal
Frand
a
'noise
Isin
f.rand is the random phase of the shot noise with respect to Isignal.
>> lnoisel,
" si
the value of 68ysns < I no
I-
I'signal I
1
NR
(2.48)
If it is assumed that
The minimum observable flow is
limited only by the phase noise on each individual point.
On the other hand, the maximum detectable flow before phase wrapping occurs corresponds to
±;r phase shifts.
8,12
2;r ambiguity arises when the phase difference is larger than ;r, resulting
in a sign change and incorrect measurement of flow.
unwrapping.
This could be corrected by phase
However, the accuracy of phase unwrapping is effected by phase noise.
Imaginary
sin Vkrand
:oS Vrand
Real
Figure 2-4. Phase stability of spectral / Fourier domain OCT. The rotation of
I caused by Inoise defines the phase noise.
References
1.
2.
3.
4.
5.
6.
7.
M. Wojtkowski, A. Kowalczyk, R. Leitgeb, and A.F. Fercher, "Full range complex
spectral optical coherence tomography technique in eye imaging," Optics Letters, vol. 27,
pp. 1415-17,2002.
M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A.F. Fercher, "In vivo
human retinal imaging by Fourier domain optical coherence tomography," Journal of
Biomedical Optics, vol. 7, pp. 457-463,2002.
R. Leitgeb, C.K. Hitzenberger, and A.F. Fercher, "Performance of Fourier domain vs.
time domain optical coherence tomography," Optics Express, vol. 11, pp. 889-894,2003.
N. Nassif, B. Cense, B.H. Park, S.H. Yun, T.C. Chen, B.E. Bouma, GJ. Tearney, and J.F.
de Boer, "In vivo human retinal imaging by ultrahigh-speed spectral domain optical
coherence tomography," Opt Lett, vol. 29, pp. 480-2,2004.
T. Bajraszewski, M. Wojtkowski, M. Szkulmowski, A. Szkulmowska, R. Huber, and A.
Kowalczyk, "Improved spectral optical coherence tomography using optical frequency
comb," Opt Express, vol. 16, pp. 4163-76,2008.
M. Wojtkowski, V.J. Srinivasan, T.H. Ko, J.G Fujimoto, A. Kowalczyk, and J.S. Duker,
"Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and
methods for dispersion compensation," Optics Express, vol. 12, pp. 2404-2422,2004.
R.A. Leitgeb, L. Schmetterer, W. Drexler, A.F. Fercher, R.J. Zawadzki, and T.
Bajraszewski, "Real-time assessment of retinal blood flow with ultrafast acquisition by
color Doppler Fourier domain optical coherence tomography," Optics Express, vol. 11, pp.
8.
9.
10.
11.
12.
3116-3121,2003.
R.A. Leitgeb, L. Schmetterer, C.K. Hitzenberger, A.F. Fercher, F. Berisha, M.
Wojtkowski, and T. Bajraszewski, "Real-time measurement of in vitro flow by
Fourier-domain color Doppler optical coherence tomography," Opt Lett, vol. 29, pp.
171-3,2004.
A.F. Fercher, W. Drexler, C.K. Hitzenberger, and T. Lasser, "Optical coherence
tomography-principles and applications," Reports on Progress in Physics, vol. 66, pp.
239-303,2003.
J.F. de Boer, B. Cense, B.H. Park, M.C. Pierce, G.J. Tearney, and B.E. Bouma, "Improved
signal-to-noise ratio in spectral-domain compared with time-domain optical coherence
tomography," Optics Letters, vol. 28, pp. 2067-2069,2003.
R.A. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl,
and A.F. Fercher, "Ultrahigh resolution Fourier domain optical coherence tomography,"
Optics Express, vol. 12, pp. 2156-2165,2004.
M.A. Choma, A.K. Ellerbee, S. Yazdanfar, and J.A. Izatt, "Doppler flow imaging of
cytoplasmic streaming using spectral domain phase microscopy," Journal of Biomedical
Optics, vol. 11, pp. -,2006.
Chapter 3
Pre-Objective Scanning Small Animal OCT System
3.1 Overview
Figure 3-1 shows a schematic of the OCT system with pre-objective scanning and spectral /
Fourier domain detection for small animal retina imaging. Low coherence light is split equally
into reference and sample arm paths by a fiber optic coupler. The reference arm light passes
through glass for dispersion compensation. The sample is illuminated through a scanning
microscope. In this design, the galvanometer scanners are placed after the collimating lens and
before the focusing microscope objective. Polarization controllers in both sample and reference
arms ensure electric field alignment for maximum interference.
detected with a CCD camera spectrometer.
The interference signal is
Glass Density
Block Filter
rreor
nor
river uoupier
Collimating
ctive
Figure 3-1.
Schematic of high-speed ultrahigh resolution OCT system with a
pre-objective scanning microscope design for small animal retina imaging.
3.2 Spectrometer Design
Figure 3-2 shows a schematic of the CCD camera spectrometer design.
The spectrometer
consists of a 1200 lp/mm diffraction grating and a 12 bit, 28 kHz, 2048 pixel high speed CCD
linescan camera with 141tm pixel size (Atmel Aviiva M2 2014). This design yields a theoretical
detection bandwidth of 209nm on the spectrometer.
A 35mm focal length near infrared barrel
lens (Schneider Optics) is used to collimate the light from the fiber, and a 100mm focal length
f-theta lenses (Sill Optics) is used to focus the light after a grating onto the linescan camera.
The spot size on the CCD detector is therefore -17.5tnm.
Assuming that the spectrometer is
centered at 890nm, the theoretical imaging range is 1.94mm.
Der
'era
Collimating
Objective
Figure 3-2.
Schematic of CCD camera spectrometer.
diffracted with a transmission grating.
Light is collimated and
The diffracted light is finally focused by
the f-theta lens onto the CCD array of the linescan camera.
3.3 Light Source
OCT requires spatially coherent and temporally incoherent light. A spatially incoherent source
such as a light emitting diode generally emits light into a large number of modes, which prevents
efficient coupling to a single mode fiber. For temporally incoherent light, it is important to
achieve emission into a spatial mode. A modelocked short pulse laser is temporally incoherent
and emits spatially coherent light with a single transverse spatial mode. Femtosecond laser
technology provides high-power, broad-bandwidth sources ideal for OCT.1-3
Short pulse lasers
provide bandwidth inversely proportional to the pulse duration.
Femtosecond lasers can
generate bandwidths of hundreds of nanometers can be achieved with 50 - 100mW or more of
output power.
An alternative approach to achieving broadband high power emission into a single spatial mode
is the superluminescent diode (SLD).4 The SLD is presently the most popular light source in
OCT since it provides turnkey operation in a variety of environments.
SLDs emit light through
amplified spontaneous emission and achieve broadband high power emission.
operation is achieved by a waveguide through the active region.
Single mode
Typically SLDs have high
optical gain and must be carefully protected against optical feedback.
Small reflections at the
output facets of the SLD could result in parasitic Fabry-Perot modulation in the output spectrum
or can cause damage to the device.
In the pre-objective scanning small animal OCT system, a multiplexed, two superluminescent
diode light source (Broadlighter D890, Superlum Diodes, Ltd.) with bandwidth BW = 145 nm,
center wavelength Xc = 890 nm was used.
The theoretical resolution calculated for the light
source is approximately 2.4#m in air or 1.8/m in tissue.
Figure 3-3 shows the spectrum
measured from the output of the light source using an optical spectrum analyzer.
Spectrum
1
'
Id
>
c
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
A
750
Figure 3-3.
800
850
900
950
wavelength (nm)
1000
Spectrum measured from Broadlighter D890.
Xc is 890 nm with bandwidth BW 145 nm.
1050
Center wavelength
3.4 Interferometer
A Michelson interferometer configuration with 50/50 coupling is implemented.
The
interferometer uses 800nm single mode fiber with 5.51im core diameter, 1251im cladding
diameter with numerical aperture 0.14.
Polarization controllers are used in both sample and
reference arms.
Flat spectral transmission curves in the circulator and the couplers are optimal for the
interferometer to avoid distortion of the spectra interfering at the detector.
transmission measurement of the coupler is shown in figure 3-4.
The spectral
The plot displays the output
spectrum normalized by the input spectrum.
850nm Fiber Coupler Transfer Function
0.9
0.8
0
0.7
C 0.6
S0.5
. 0.4
0 0.3
0.2
0.1
700
750
800
850
900
950
1000
1050
1100
wavelength (nm)
Figure 3-4.
system.
Spectral transmission measurement for 850nm fiber coupler used in
Measurements made with ANDO AQ-4303B white light source.
Interference only occurs between fields of the parallel polarization.
Birefringence in the optics,
fiber, and the sample can misalign the reference and sample arm electric fields.
Polarization
paddle controllers introduce stress-induced birefringence to alter polarization state.
X/4:X/2:X/4 configuration for the center wavelength is used.
A
The paddles in the reference and
sample arms are set to optimize the incident power onto the sample and interference signal.
3.5 Sample Arm Optics
Figure 3-5 shows a schematic of the sample arm optics. In the sample arm of the OCT imaging
system, light from the fiber is collimated by a 20mm focal length near infrared doublet lens.
The collimated beam is then scanned with a pair of 6mm galvanometer-actuated mirrors (6215H;
Cambridge Technology, Cambridge, MA). A long-working-distance microscope objective (M
Plan 5X; Mitutoyo, Paramus, NJ) refocuses the beam. The objective has a 4cm working
distance, providing enough space between the animal eye and the sample arm optics for
adjustment of the animal position. This design has -2141im depth of focus, and yields a -~114m
spot on the sample.
The spot size is an important parameter for Doppler OCT measurements.
Each axial scan must overlap adjacent axial scans by at least half the spot size in order to obtain
Doppler OCT information.
Finally, the measured power transmission in the sample arm is
-65% single pass or -42% double pass.
Collimatina
OCT
Fiber
Optic
D1 =5.5um
Scanning
Mirror(s)
Mouse
Retina
11um
ONC
20mm
7mm
40mm
Figure 3-5. Detail schematic of pre-objective scanning microscope design.
Compared to post-objective scanning, pre-objective scanning fully utilizes the
long working distance of the objective providing more room to adjust the animal's
position for allignmnet.
There are several alignment procedures which must be performed in order to obtain OCT images.
The OCT beam must be directed through the animal's pupil while scanning range is limited by
vignetting of the OCT beam on the pupil. In order to achieve maximum scanning range, the
animal must be dilated. Therefore, mydriatic imaging yields better results. The OCT
beam
must be focused on the retina to obtain an acceptable signal level.
Finally, the axial range,
known as the "Z-offset," must be adjusted so that the retina is within the measurement range.
The small animal eye presents strong aberrations due to their small size and short focal length.
By pressing a flat microscope cover glass and Hydroxypropyl methylcellulose (Goniosol, 2.5%)
over the animal eye, refraction from the interface at the cornea can be effectively removed
leaving only the weaker refraction from the lens. This enables the OCT beam to be focused
directly on the retina avoiding aberrations and irregularities from the cornea while keeping the
cornea hydrated.5' 6
3.6 Image Acquisition and Processing
The image acquisition is controlled by a personal computer configured with a Horizon Link i2s
Line Scan Imaging Capture Board and a National Instruments PCI-6731 High-Speed Analog
Output.
The imaging capture board controls the CCD camera and streams the captured images
to computer memory.
The analog output provides drive signals to the galvanometer controller
cards and triggering for the CCD camera. Real-time images are created for alignment using
Windows based LabVIEW software.
The LabVIEW software used for the system was created by Dr. Iwona Gorczynska, a Research
Associate in our group and dlls for the software were written in C by Vivek Srinivasan, a senior
PhD student in our group.
The software displays a 512 axial scan X-direction and a 512 axial
scan Y-direction image or a 100x100 pixel OCT fundus image real time.
The software also
provides a variety of scan protocols and the ability to create custom scan protocols.
There are several scan protocols commonly used for murine retinal imaging, illustrated in figure
3-6.
The first protocol acquires a set of three high-definition OCT images with 8192 axial scans
per image in -0.3 seconds per image or a total of -0.9 seconds.
The second protocol acquires
21 high-definition images with 2048 axial scans per image in a raster pattern in -0.07 seconds
per image or a total of -1.4 seconds.
The third protocol acquires three-dimensional OCT
(3D-OCT) data in a dense raster pattern consisting of 180 images with 512 axial scans per image
in a total of -4 seconds.
The three-dimensional OCT (3D-OCT) dataset may be used for
applications such as rendering, OCT fundus image generation, and mapping.
In order to obtain
Doppler OCT information, each transverse spot must be sampled at least twice.
Therefore, it is
spot size for
important that adjacent axial scans do not separate more than half the transverse
data for
Doppler OCT imaging. Oversampling in the transverse direction yields more
averaging and other signal processing techniques, but decreases the imaging area in given
amount of time.
Figure 3-6.
OCT imaging protocols.
This scan consists of 3
(A) Long scan.
high-definition cross-sectional images with 8192 axial scans.
(B) 2D scan.
This scan consists of 21 cross-sectional images with 2048 axial scans. (C) 3D
scan. This scan consists of 180 cross-sectional images with 512 axial scans.
Spectral / Fourier domain OCT samples a spectrally dispersed light intensity uniformly along a
spatial dimension defined by the orientation of the CCD camera in the spectrometer. Typically,
it is assumed that the spatial dimension x is approximately linearly proportional to wavelength
X. In order to apply the discrete Fourier transform (DFT) to reconstruct the axial scan as a
function of z, samples evenly spaced in frequency c
must be obtained by a scale
However, there may be other effects which can complicate the scale
transformation such as the nonlinear angular dispersion of the grating and the deviation of the
scan lens in the spectrometer from the f-theta condition. Therefore, the required scale
transformation.
transformation may deviate from the ideal hyperbolic scale transformation.
A general representation for the w(x) measured by the spectrometer can be given by a Taylor
expansion:
W(x)= ao +ax+ax2 + a3x3 +...
(3.1)
Using this expression for co it is possible to rewrite the expression for the phase corresponding
to an isolated reflection with a path difference Al,:
+ Alon(x)
I(x, Al,) = cdisp (p(x))
(3.2)
As equations (3.1) and (3.2) show, nonlinear sampling is equivalent to a depth dependent
dispersion.
This dispersion will increase with increasing depth, and will therefore be most
prominent for large axial delays.
In order to correct for nonlinear sampling in co, resampling is necessary.
The measured data is
resampled using spline interpolation to obtain samples equally spaced in frequency, followed by
a digital Fourier transform (FFT) to reconstruct the axial scan. The nonlinear sampling may not
always be invertible as aliasing may occur at larger path length delays.
Since aliasing
represents a loss of information, it may not be possible to accurately reconstruct the axial scan at
larger path length delays.
This is one of the reasons behind spectrometer roll-off, as described
in chapter I2. 79
In OCT, the Fourier transform of the detected interference spectrum yields the axial point spread
function. The axial resolution is determined by the full-width at half-maximum of the point
spread function.
The detected interference spectrum, which is affected by the light source,
spectral changes in the reference and sample arms, and detector sensitivity, determines the point
spread function.
A Gaussian spectrum is ideal for OCT since sidelobes in the point spread function are minimized.
Typically, the spectrum of light sources used for OCT has a non-Gaussian shape.
non-Gaussian spectrum yields sidelobes that degrade the resolution.
A
Sidelobes are tolerable up
to the dynamic range of the sample measured. Therefore, spectral shaping may be required to
minimize point spread function sidelobes and achieve optimal resolution as illustrated in figure
3-7.
However, spectral shaping always results in a reduction in sensitivity and signal-to-noise
ratio.
Spectral shaping represents a tradeoff between optimizing point spread function shape
and minimizing degradation of the signal to noise ratio."0
0.9
0.8
0.7
E 0.6
S0.5
C,,
0.4
E 0.3
0.2
0.1
cn
c
0u
800
1000
950
900
850
-0.03
Wavelength (nm)
Figure 3-7.
-0.02uz
-0.01
u
u.u0
u.uI
Mirror Displacement (mm)
Spectral correction and point spread function.
The measured
spectrum and calculated point spread function with noticeable sidelobes are
shown in red. The reshaped spectrum and corresponding point spread function
with suppressed sidelobes are shown in blue.
Figure
Comparison
3-8.
non-compensated
compensation.
image.
of dispersion
compensated
image
(A) OCT image without numerical
versus
dispersion
(B) OCT image with numerical dispersion compensation.
The
dispersion compensation is especially noticeable at the interfaces of retinal layers.
0.0O
In figure 3-8, dispersion is compensated numerically using an iterative procedure
that measures
the sharpness of the image to determine the coefficients in the phase compensation
equation
(2.31), D(w) =-a 2(w-a ) 2 -a 3(w- 0) 3 .
The sharpness metric function M(a ,a )
2 3
measuring the concentration of energy in the image, is maximized when the image
is sharpest.
By varying the second- and third-order coefficients a2anda , which corresponds
to adjusting
3
the group velocity dispersion and the third-order dispersion, M(a2 , a3 )can be maximized. 11 12'8
Doppler OCT is used to acquire flow or wavelength scale displacement information
in the
sample. The phase difference between sequential scans at or near the same transverse
position
can be calculated from the phase information readily available after Fourier transforming
the
interference signal.
Hence, the depth distribution of the phase difference can be obtained.
75x70y
a
13-18
2
-loo10m
0
_ý2
,,
SM
.·:· · ~
; ·:·
-100m I
"
-100pm
I
Figure 3-9.
OCT fundus image and color Doppler cross-sectional images. All
images are generated using a 0.75x0.75mm 3D scan dataset. The OCT fundus
image is generated by summation of axial pixels.
The corresponding positions
of the cross-sectional color Doppler images are labeled.
every 1.5 /m apart.
An axial scan is taken
Doppler OCT measuring blood flow is shown in color scale
overlaying OCT structural images presented in grayscale.
3.7 System Performance
In order to obtain maximum sensitivity, dispersion in the reference and sample paths must be
matched accurately.
Unbalanced dispersion results in the loss of resolution.
To match
dispersion in the system, glass is added to the reference arm path to balance the glass in the
sample arm. Large amount of glass in the microscope objective is problematic since the types
of glass and thickness of the lenses are proprietary information. Therefore, an approximate
matching technique is used.
dispersion compensation.
SFL6 and LakN22 are suitable glass types to be used for
SFL6 is much more dispersive than LakN22, and together the two
glass types provide a coarse and fine adjustment.
or -3.1/lm in tissue as shown in figure 3-7.
The resolution of the system is -4.2jtm in air
Due to lower sensitivity at longer wavelengths on
CCD cameras and loss in the isolator and coupler, the spectrometer is unable to detect the full
spectrum from the light source.
This results in a lower resolution compared with the theoretical
value obtained in section 3.3 using the light source characteristics.
3.7.1 Sensitivity Measurement
System sensitivity is measured with a mirror placed at the focus of the sample arm.
The
galvanometers in the sample arm are not scanned. The incident power on the sample arm
mirror is -1.5mW.
The light incident on the sample arm mirror is attenuated using an neutral
density filter. The attenuation occurs in both forward and reflected light paths and should be
accounted for twice.
The reference arm power is also attenuated to avoid saturating the camera.
The signal-to-noise is measured using the formula:
SNR = 20 -log
{int}peak
std(F_ ({Int}noise)
+2-10. O.D.
(3.3)
Where F1' {Jt}peak is the peak of the measured signal, F-' {Int}n,,o,is the noise floor away from
the position of the sample arm mirror., and O.D. is the optical density of the filer. Using this
formula, the signal-to-noise ratio for the system is measured to be 97.9dB.
3.7.2 Dynamic Range Measurement
Dynamic range is measured by setting the reference and sample arm power at the levels used for
imaging. The incident power on the sample arm mirror is -1.5mW. The reflected light in the
sample arm is attenuated to give the maximum reflected power without saturating the CCD
The dynamic range DR is measured using the formula:
camera.
std(IF-'{
(3.4)
1
intle
The system is measured to have dynamic range 60.9dB.
3.7.3 Sensitivity Roll-Off
Spectrometer roll-off is a measurement of the sensitivity drop with higher frequency interference
signal or larger reference and sample arm distance mismatch as described in Chapter 2.
A
Measurements are performed at different reference and sample distance mismatches.
decrease in the signal amplitude and increase in noise related to distance is seen in figure 3-10.
6dB drop off occurs at -0.9mm.
The imaging range of the system is also measured by reading
the micrometer on the reference or sample arm translation stage.
The imaging range of the
system is 1.95mm.
d
1
0.9
i
r
I
I
'
I
,------
----------,-------r------+--------
0.8 -- -,_____~
,_____~
cu0.6 ------
-----5----//--------4
-----4------
-- --
L-
j___
IL------_ ____
=-30
~-----0.5 -------
0.3
-10
-20
,------
E 0.4
E•
,_____~
,------
I.
.
-..
--------,-----r---------1---E<-40
-50
0.2"
0.1
ik. /
U0
0.2
j
0.4
-60
0.6
0.8
1
1.2
Distance in Air (mm)
Figure 3-10.
imaging depth.
1.4
1.6
1.8
I
0
0.2
0.4
0.6
0.8
1
1.2
Distance in Air (mm)
1.4
1.E3
Spectrometer roll-off. A measurement of sensitivity drop versus
6dB drop in signal occurs at -0.9cm in air.
1.8
3.7.4 Doppler Measurement Range
The maximum absolute Doppler flow directly obtainable before 2;r phase wrapping occurs in
this system will be ).
4r
Since the system has speed -25,000 axial scans per second, the
maximum Doppler flow corresponding to ±+r phase shift is -±5.6mm/s in air or -+4.2mm/s in
tissue.
The minimum phase measurable is vn (z) =
deviation of phases evaluated at a mirror at rest.
4trr
where A(,,t
is the standard
The measured phase standard deviation of the
mirror with the galvanometer scanners turned off is -0.180, corresponding to a variability in
longitudinal velocity of-5.61Lm/s in air or -4.21im/s in tissue.
A problem in phase stability occurs due to movement of the galvanometer scanning mirrors.
The instability is worse when the beam is not perfectly centered on the galvanometer scanning
mirrors. However, it is not possible to center both galvanometer scanning mirrors at the back
focal length of the lens; therefore there is always some path length change, even when the beams
are centered on the mirrors.
Consequently, movement from the scanning mirrors changes the
path length, and is detectable by Doppler OCT. Jittering or resonance from scanners cause
instability in Doppler phase measurements.
With the galvanometer scanners turned on and held
at the center position, the standard deviation of phases is measured to be -36.3'.
Motion from
scanning the mirrors also causes a gradual phase change along a cross sectional scans. These
motion artifacts along with sample bulk motion can be corrected using an averaged-shifted
histogram method with the bin width determined using the Freedman & Diaconis rule, which
takes into account the interquartile range and total number of observations. 19' 20 After applying
the motion correction algorithm, the measured phase standard deviation is reduced to -1.180,
corresponding to a variability in longitudinal velocity of -37.5/tm/s in air or -27.4Lm/s in tissue.
The phase stability remains worse when the scanners are turned on, even with motion correction.
-
Standard Deviation = 0.17844
^^
80
A
40
o 60
LI
S40
.0
0
. 20
'
I •
50
-1
0
1
Phase Difference (degrees)
Standard Deviation = 36.3229"
n ••
Standard Deviation = 1.1765"
3UU
=
0
o
40
0
250
200
> 30
i
S20
C
150
0 100
0
a10
50
n
u
100
-100
0
Phase Difference (degrees)
Figure 3-11.
Phase stability measurements.
10
0
-10
Phase Difference (degrees)
(A) With the galvo scanners
turned off, the system maintains high phase stability.
(B) With the galvo
scanners on, jittering from the scanner causes significant phase variation.
(C)
After motion correction, phase stability improves but is still worse than having the
galvos turned off.
References
1.
2.
3.
4.
W. Drexler, U. Morgner, F.X. Kartner, C. Pitris, S.A. Boppart, X.D. Li, E.P. Ippen, and
J.G. Fujimoto, "In vivo ultrahigh-resolution optical coherence tomography," Optics
Letters, vol. 24, pp. 1221-1223,1999.
U. Morgner, W. Drexler, F.X. Kartner, X.D. Li, C. Pitris, E.P. Ippen, and J.G. Fujimoto,
"Spectroscopic optical coherence tomography," Optics Letters, vol. 25, pp. 111-113,2000.
W. Drexler, U. Morgner, R.K. Ghanta, F.X. Kdirtner, J.S. Schuman, and J.G. Fujimoto,
"Ultrahigh-resolution ophthalmic optical coherence tomography," Nature Medicine, vol.
7, pp. 502-507,2001.
T.H. Ko, D.C. Adler, J.G. Fujimoto, D. Mamedov, V. Prokhorov, V. Shidlovski, and S.
Yakubovich, "Ultrahigh resolution optical coherence tomography imaging with a
broadband superluminescent diode light source," Optics Express, vol. 12, pp.
2112-2119,2004.
5.
Q. Li, A.M. Timmers, K. Hunter, C. Gonzalez-Pola, A.S. Lewin, D.H. Reitze, and W.W.
Hauswirth, "Noninvasive imaging by optical coherence tomography to monitor retinal
degeneration in the mouse," Investigative ophthalmology & visual science, vol. 42, pp.
6.
2981-9,2001.
V.J. Srinivasan, T.H. Ko, M. Wojtkowski, M. Carvalho, A. Clermont, S.E. Bursell, Q.H.
Song, J. Lem, J.S. Duker, J.S. Schuman, and J.G Fujimoto, "Noninvasive volumetric
Imaging and morphometry of the rodent retina with high-speed, ultrahigh-resolution
optical coherence tomography," Investigative Ophthalmology & Visual Science, vol. 47,
pp. 5522-5528,2006.
7.
M. Wojtkowski, R. Leitgeb, A. Kowalczyk, T. Bajraszewski, and A.F. Fercher, "In vivo
human retinal imaging by Fourier domain optical coherence tomography," Journal of
Biomedical Optics, vol. 7, pp. 457-463,2002.
8.
9.
10.
11.
12.
13.
14.
15.
M. Wojtkowski, V.J. Srinivasan, T.H. Ko, J.G Fujimoto, A. Kowalczyk, and J.S. Duker,
"Ultrahigh-resolution, high-speed, Fourier domain optical coherence tomography and
methods for dispersion compensation," Optics Express, vol. 12, pp. 2404-2422,2004.
T. Bajraszewski, M. Wojtkowski, M. Szkulmowski, A. Szkulmowska, R. Huber, and A.
Kowalczyk, "Improved spectral optical coherence tomography using optical frequency
comb," Opt Express, vol. 16, pp. 4163-76,2008.
R. Tripathi, N. Nassif, J.S. Nelson, B.H. Park, and J.F. de Boer, "Spectral shaping for
non-Gaussian source spectra in optical coherence tomography," Optics Letters, vol. 27,
pp. 406-8,2002.
B. Cense, N. Nassif, T.C. Chen, M.C. Pierce, S. Yun, B.H. Park, B. Bouma, G Tearney,
and J.F. de Boer, "Ultrahigh-resolution high-speed retinal imaging using spectral-domain
optical coherence tomography," Optics Express, vol. 12, pp. 2435-2447,2004.
R.A. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl,
and A.F. Fercher, "Ultrahigh resolution Fourier domain optical coherence tomography,"
Optics Express, vol. 12, pp. 2156-2165,2004.
S. Yazdanfar, A.M. Rollins, and J.A. Izatt, "Imaging and velocimetry of the human retinal
circulation with color Doppler optical coherence tomography," Optics Letters, vol. 25, pp.
1448-50,2000.
A.M. Rollins, S. Yazdanfar, J.K. Barton, and J.A. Izatt, "Real-time in vivo color Doppler
optical coherence tomography," JournalofBiomedical Optics, vol. 7, pp. 123-9,2002.
R.C. Wong, S. Yazdanfar, J.A. Izatt, M.D. Kulkami, J.K. Barton, A.J. Welch, J. Willis,
and M.V. Sivak, Jr., "Visualization of subsurface blood vessels by color Doppler optical
coherence tomography in rats: before and after hemostatic therapy," Gastrointestinal
endoscopy, vol. 55, pp. 88-95,2002.
16.
17.
18.
R.A. Leitgeb, L. Schmetterer, W. Drexler, A.F. Fercher, R.J. Zawadzki, and T.
Bajraszewski, "Real-time assessment of retinal blood flow with ultrafast acquisition by
color Doppler Fourier domain optical coherence tomography," Optics Express, vol. 11, pp.
3116-3121,2003.
S. Yazdanfar, A.M. Rollins, and J.A. Izatt, "In vivo imaging of human retinal flow
dynamics by color Doppler optical coherence tomography," Archives of ophthalmology,
vol. 121, pp. 235-9,2003.
R.A. Leitgeb, L. Schmetterer, C.K. Hitzenberger, A.F. Fercher, F. Berisha, M.
Wojtkowski, and T. Bajraszewski, "Real-time measurement of in vitro flow by
Fourier-domain color Doppler optical coherence tomography," Opt Lett, vol. 29, pp.
19.
20.
171-3,2004.
B.R. White, M.C. Pierce, N. Nassif, B. Cense, B.H. Park, G.J. Teamey, B.E. Bouma, T.C.
Chen, and J.F. de Boer, "In vivo dynamic human retinal blood flow imaging using
ultra-high-speed spectral domain optical Doppler tomography," Optics Express, vol. 11,
pp. 3490-3497,2003.
S. Makita, Y. Hong, M. Yamanari, T. Yatagai, and Y. Yasuno, "Optical coherence
angiography," Optics Express, vol. 14, pp. 7821-7840,2006.
Chapter 4
OCT Imaging and Data Analysis
4.1 Overview
The high-speed, ultrahigh resolution OCT system discussed in chapter 3 was applied for in vivo
imaging of the rat retina.
Section 4.2 presents background information on rodent OCT imaging.
Section 4.3 presents OCT imaging of the normal rat retina with 3D visualization.
describes imaging of an animal model for studies in diabetic retinopathy.
Section 4.4
Section 4.5 discusses
the processing and results of Doppler OCT, measuring quantitative pulsatile blood flow in a rat
retinal blood vessel.
All studies adhere to the ARVO Statement for the Use of Animals in Ophthalmic and Vision
Research, and all imaging procedures were performed at Massachusetts Institute of Technology
facilities with a protocol approved by the MIT Committee on Animal Care.
4.2 Background
The murine retina is structurally similar to the human retina. Rat and mouse models provide
powerful tools for characterization of ocular disease pathogenesis and response to treatment.
Therefore, non-invasive imaging technologies for measuring rat and mouse retinal structure and
physiology at the micron scale could be useful tools for biomedical research on ocular disease.
It makes possible monitoring disease progression through its entire course in individual animal
models, enabling longitudinal studies using single animals.'
Spectral / Fourier domain OCT
enables high-speed ultrahigh resolution 3D imaging or volumetric imaging, offering a promising
technique for rat and mouse retinal imaging.2 ,3 Previous studies have demonstrated monitoring
progressive anatomical changes in the mouse retina using spectral / Fourier domain OCT.4
The short-time fast Fourier transformation method from Doppler ultrasound was first utilized to
generate Doppler OCT information in time-domain OCT systems.5 -9 Phase-resolved Doppler
OCT improved Doppler OCT imaging speed and sensitivity of time-domain OCT systems by
using the Hilbert transform to determine phase information for each pixel so that the phase
change between sequential axial scans can be used to calculate the Doppler frequency shift.'10,
In spectral / Fourier domain OCT systems, the phase information is directly accessible after the
Fourier transformation of the interference fringes, further improving the imaging speed and
sensitivity of Doppler OCT.12-16
Recent studies have demonstrated quantification methods for
ocular blood flow in humans using spectral / Fourier domain Doppler OCT systems. 17"
4.3 3D OCT Imaging of Rat Retina
As a demonstration of the potential of spectral / Fourier domain OCT for in vivo rodent retinal
imaging, Long-Evans rat retina was imaged.
Long-Evans rats which have normal retinas were
anesthetized with ketamine (40-50mg/kg IP) and xylazine (5mg/kg IP).
After anesthesia, eyes
were dilated with tropicamide (Mydriacy) (1%) applied topically as drops.
The animals were
placed in a comfortable holder with its head in a mount to reduce eye and head motion.
Hydroxypropyl methylcellulose (Goniosol, 2.5%) was used to preserve corneal hydration, and a
thin coverslip contact lens was gently placed on the cornea to remove curvature and enable
focusing of the OCT imaging beam on the retina.
The angle of incidence of the OCT beam
relative to the cover slip was adjusted to minimize aberrations.
With the pre-objective scanning
along with a long working distance microscope design, OCT fundus images showing blood
vessels and the optic nerve head can be easily obtained.
3D-OCT datasets consisting of 180 images with 512 axial scans over a 2x2mm area were
obtained along with 2mm high-definition cross-sectional scans with 8196 axial scans.
An OCT
fundus image can be is created by summing along the axial direction to form a projection in the
transverse plane.
This image provides a view similar to fundus photography.
In addition to
examining 180 cross-sectional images individually, 3D rendering can be performed using Amira,
a commercially available software platform for visualizing and manipulating 3D datasets.
high-definition scan provides better visibility of retinal layers as shown in figure 4-1.
The
r
T~
- `_f.
F2x
-_
··
ii
'""':'
r::
~.·~·:":
_·iP'
~'-
-i*-·
.·kt·.:1·r
Figure 4-1.
OCT images from a normal Long-Evans rat.
·-3s-i·
·'
n-~ s::~P
(A) An OCT fundus
image created by axial summation of a 3D-OCT dataset consisting of 180 images
of 512 axial scans.
(B-D) 512-axial-scan cross-sectional OCT images at
corresponding positions.
(E) High-definition OCT image cropped from a
8196-axial-scan cross-sectional image.
layers is shown.
Clear visualization of major retinal
3D rendering of OCT dataset.
Visualization of 3D-OCT dataset,
including 180 images with 512 axial scans.
A projected OCT fundus photo is
Figure 4-2.
also shown.
layers. 2
It is possible to quantitatively measure thickness between retinal
4.4 Diabetic Macular Edema Study
Diabetic retinopathy is the most common diabetic eye disease and a leading cause of blindness in
American adults caused by changes in the blood vessels of the retina.
Currently, diabetic
macular edema, which can occur at any stage of diabetic retinopathy, lacks effective treatment
for preventing further vision loss. One limitation in the development of treatments for macular
edema is the lack of appropriate animal models. In evaluating anti-vascular permeability agents
for treatment of diabetic macular edema in humans, an animal model that exhibits quantifiable
edema is desired."9 OCT is the clinical standard for quantifying diabetic macular edema in
humans, and is therefore the preferred method for characterization of retinal edema in animal
models.
OCT imaging of normal Sprague-Dawley rat retinas was performed before and 48
hours after intavitreal injection of kallikrein.
The OCT imaging procedure and protocol is same
as described in section 4.3 for normal Long-Evans rats.
Work in this section is done in
collaboration with Allen C. Clermont of the Joslin Diabetes Center, and is a product of an
ongoing collaboration between the laboratories of James G Fujimoto of the Massachusetts
Institute of Technology and Edward P. Feener of the Joslin Diabetes Center.
Figure 4-3 shows pre-injection and 48-hours post-injection images of the rat retina. The fundus
images are acquired with a visible-light camera. The OCT cross-sectional images and OCT
fundus images are obtain from the 3D-OCT dataset consisting of 180 images with 512 axial
scans. Only one representative OCT cross-sectional image is selected and shown for each time
point. The ripples in the OCT fundus images are due to motion artifacts caused by breathing
and heartbeat.
There are no observable changes from examining the fundus photo, OCT
cross-sectional image, and OCT fundus image in the saline injected eye before and 48 hours after
injection.
The bubbles on the sides of the fundus photos are due to gaps between the coverslip
and the cornea. This causes blurring on the sides of the OCT image since the curvature of the
cornea is not corrected and additional aberrations are introduced.
severe response is observed 48 hours after injection.
In the kallikrein injected eye,
Severe morphological changes including
macular edema and possible hemorrhage in the retina are observed after intavitreal injection of
kallikrein.
This study demonstrates the ability of spectral / Fourier domain OCT to monitor
morphological retinal changes in an individual animal.
Fundus Photo
OCT Cross-sectional
OCT Fundus
i
P
e
sl
Po tijcio ,s ln
Figure 4-3.
Comparison of pre- and 48-hours post-injection of saline and
kallikrein in normal Sprague-Dawley rat retina.
Severe edema occurred after
kallikrein injection, while no obvious changes occurred after saline injection.
vivo OCT imaging was performed in the same eyes before and after injection.
In
4.5 Doppler Flow Calculation
Retinal hemodynamics is important for investigating diseases such as glaucoma, 20 diabetic
retinopathy,21 and age-related macular degeneration.22 Doppler OCT is a robust noninvasive in
vivo technique for retinal blood flow measurement.
Spectral / Fourier domain OCT systems
achieve high acquisition speeds 100 times faster than conventional OCT systems, enabling
Doppler OCT techniques to quantitatively measure blood flow. In addition to the intensity
information, phase information is directly accessible after inverse Fourier transforming the
interference spectrum in spectral / Fourier domain OCT.
OCT provides micron-scale,
three-dimensional intensity images of retinal structure along with the ability to extract vessel
structure and blood flow measurements from Doppler OCT data. Therefore, Doppler OCT has
the potential to become a useful tool for noninvasive in vivo retinal perfusion measurement in
ocular disease research using animal models. In this section, a normal Long-Evans rat is
imaged with the same procedure as described in section 4.3, but with different OCT scan
protocols. A 3D-OCT dataset was acquired over a 750x750gm area, with sequential axial scans
1.5gjm apart, corresponding to a -85% overlap of the transverse spot size.
Additionally, 150Atm
cross-sectional images with 150 axial scans scanned over a single blood vessel were taken
continuously over time at -32 frames per second.
Doppler OCT images are formed by subtracting the phase information between adjacent axial
scans as displayed in figure 4-4. A positive phase difference is caused by motion towards the
output of the scanning OCT beam or the objective lens, while a negative phase difference
indicates motion away from the objective lens beam output. Since phase stability is related to
signal strength as shown in section 2.4.6, Doppler OCT images are thresholded according to the
OCT intensity image signal strength.2 3
Bulk motion from movement of the retina and
galvanometer scanning can be corrected using an average-shifted histogram method for each
axial scan.24 Due to the limited Doppler OCT data points in each axial scan, a single histogram
with large bins does not provide precise estimation of bulk motion, while a single histogram with
small bins provide erroneous estimation of bulk motion. The average-shifted histogram method
uses multiple histograms with different origin of bins with identical bin width to obtain a smooth
phase difference distribution. The bin width used is determined by the Freedman & Diaconis
rule, which takes into account the interquartile range of the data as well as the number of data
points.
After motion correction, only the movement of blood flow in retinal vessels is visible.
i.n
rl
-2
Figure 4-4.
-1
0
Doppler OCT processing.
structural information.
1
2
3 radians
(A) OCT intensity image showing
(B) Phase information directly obtained from spectral /
Fourier domain OCT processing.
(C) Differential phase data between adjacent
axial scans thresholded according to OCT intensity.
Bulk motion is visible in the
retinal structures as a red band on the left side of the image and a blue band on the
right. (D) Doppler OCT image of retinal blood flow after bulk motion
correction.
A vessel in an OCT cross-sectional image is selected for further analysis. phase
wrapping occurs when the absolute phase deference between adjacent axial scan pixels
exceeds 7r. This creates a 2r ambiguity in the Doppler OCT information. By
unwrapping the differential phase values higher than the phase noise floor, a more
realistic Doppler OCT profile is obtained. The parabolic profile of blood flow within a
retinal blood vessel is shown in figure 4-5.
An average filter is applied to reduce noise.
The 3D profile of the blood flow obtained by Doppler OCT shows a parabolic flow
distribution in the retinal vessel.
T_
C
U,
CL
a,
U,
U,
0a
8
150
100
50
0
Position (um)
'a
(U
C
Uo
1*g
g/j
S0
o
0
Co
M 0
IU
0
8
0
100
Position (urn)
-3
-1
-2
Figure 4-5.
0
1
2
Doppler OCT processing of a single retinal vessel.
OCT image of a single retinal vessel.
Position (um)
3 radians
(A) Doppler
(B) Parabolic profile of blood flow in
retinal vessel shown with Doppler OCT. Data corresponds to position indicated
as white line.
The blue data points are values corrected for phase wrapping.
The red curve is a
2 nd
order polynomial fit of the Doppler data.
Average-filtered Doppler OCT image.
flow.
(C)
(D) 3D profile of Doppler OCT blood
Rlnnd
L·VVY Flnw
IV···Yvi Timi
IIIIU
n~
".4
0.45
A
0.4
0.35
-
S0.3
0
LL 0.25
o
.
0.2
0.15
0.1
0.05
0
B
Time (sec)
Blood Flow vs Time
0.5
0.45
" 0.4
0
U-
0.35
0.3
0.25
o 0.2
0.15
0.1
0.05
0, 29
Time (sec)
I
I
ilI I I I
I
III i I I II
C
-
0
Figure 4-6.
1
2
3
4
6
7
8
9mm/sec
Quantitative Doppler OCT measurement in the axial direction
showing pulsatile blood flow. (A) Pulsatile blood flow showing
a heart rate of
-270 beats/min. The abnormal pulse occurring roughly every
second is possibly
due to respiratory motion. The vessel moves out of the region
of interest,
resulting in a decrease of measured blood flow. (B, C) Doppler
OCT images and
blood flow measurements showing pulsatility during two cardiac
cycles.
Finally, quantitative measurement of blood flow in the axial direction in retinal blood vessel is
demonstrated in figure 4-6. By continuously acquiring 150gm cross-sectional images with 150
axial scans and -32 images per second, quantitative Doppler OCT measurements of blood flow
in the axial direction show pulsatility in the rat retinal vessel.
Sequential OCT scans are 1•m
apart, corresponding to a -90% overlap in transverse spot size. Total Doppler differential phase
shift is obtained by summing the Doppler OCT phase difference of all pixels within the region of
interest. Blood flow in the axial direction is calculated by the corresponding speed multiplied
with the pixel area. The pulsatile blood flow shows a heart rate -270 beats per minute.
The
normal heart rate of the rat is -300 beats per minute.25 A significant drop of blood flow occurs
every second because the vessel shifts outside of the imaging region possibly due to breathing.
The respiratory rate calculated from such movement of the blood vessel is -60 per minutes,
while the normal rat respiratory rate is 70-115 per minute.26 It is also known that both heart rate
and respiratory rate in animals decrease under anesthesia.
The results demonstrate the potential
in measuring rodent retinal perfusion using spectral / Fourier domain OCT.
References
1.
Q. Li, A.M. Timmers, K. Hunter, C. Gonzalez-Pola, A.S. Lewin, D.H. Reitze, and W.W.
Hauswirth, "Noninvasive imaging by optical coherence tomography to monitor retinal
degeneration in the mouse," Investigative ophthalmology & visual science, vol. 42, pp.
2981-9,2001.
2.
V.J. Srinivasan, T.H. Ko, M. Wojtkowski, M. Carvalho, A. Clermont, S.E. Bursell, Q.H.
Song, J. Lem, J.S. Duker, J.S. Schuman, and J.G. Fujimoto, "Noninvasive volumetric
Imaging and morphometry of the rodent retina with high-speed, ultrahigh-resolution
3.
optical coherence tomography," Investigative Ophthalmology & Visual Science, vol. 47,
pp. 5522-5528,2006.
M. Ruggeri, H. Webbe, S.L. Jiao, G Gregori, M.E. Jockovich, A. Hackam, Y.L. Duan,
and C.A. Puliafito, "In vivo three-dimensional high-resolution imaging of rodent retina
4.
5.
6.
7.
with spectral-domain optical coherence tomography," Investigative Ophthalmology &
Visual Science, vol. 48, pp. 1808-1814,2007.
K.H. Kim, M. Puoris'haag, GN. Maguluri, Y. Umino, K. Cusato, R.B. Barlow, and J.F. de
Boer, "Monitoring mouse retinal degeneration with high-resolution spectral-domain
optical coherence tomography," J Vis, vol. 8, pp. 17 1-11,2008.
X.J. Wang, T.E. Milner, and J.S. Nelson, "Characterization of Fluid-Flow Velocity by
Optical Doppler Tomography," Optics Letters, vol. 20, pp. 1337-1339,1995.
Z. Chen, T.E. Milner, D. Dave, and J.S. Nelson, "Optical Doppler tomographic imaging
of fluid flow velocity in highly scattering media," Optics Letters, vol. 22, pp. 64-6,1997.
Z. Chen, T.E. Milner, S. Srinivas, X. Wang, A. Malekafzali, M.J.C. van Gemert, and J.S.
8.
9.
10.
Nelson, "Noninvasive imaging of in vivo blood flow velocity using optical Doppler
tomography," Optics Letters, vol. 22, pp. 1119-21,1997.
J.A. Izatt, M.D. Kulkami, S. Yazdanfar, J.K. Barton, and A.J. Welch, "In vivo
bidirectional color Doppler flow imaging of picoliter blood volumes using optical
coherence tomography," Optics Letters, vol. 22, pp. 1439-41,1997.
S. Yazdanfar, M.D. Kulkarni, and J.A. Izatt, "High resolution imaging of in vivo cardiac
dynamics using color Doppler optical coherence tomography," Optics Express, vol.
1,1997.
Z. Chen, Y.Zhao, S.M. Srinivas, J.S. Nelson, N. Prakash, and R.D. Frostig, "Optical
Doppler tomography," IEEE Journalof Selected Topics in Quantum Electronics, vol. 5,
11.
pp. 1134-42,1999.
Z. Chen, Y.Zhao, and J.S. Nelson, "Phase-resolved functional optical coherence
tomography," Optics & PhotonicsNews, vol. 12, pp. 29,2001.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
R.A. Leitgeb, L. Schmetterer, W. Drexler, A.F. Fercher, R.J. Zawadzki, and T.
Bajraszewski, "Real-time assessment of retinal blood flow with ultrafast acquisition by
color Doppler Fourier domain optical coherence tomography," Optics Express, vol. 11, pp.
3116-3121,2003.
R.A. Leitgeb, W. Drexler, A. Unterhuber, B. Hermann, T. Bajraszewski, T. Le, A. Stingl,
and A.F. Fercher, "Ultrahigh resolution Fourier domain optical coherence tomography,"
Optics Express, vol. 12, pp. 2156-2165,2004.
J. Zhang and Z.P. Chen, "In vivo blood flow imaging by a swept laser source based
Fourier domain optical Doppler tomography," Optics Express, vol. 13, pp.
7449-7457,2005.
A.H. Bachmann, M.L. Villiger, C. Blatter, T. Lasser, and R.A. Leitgeb, "Resonant
Doppler flow imaging and optical vivisection of retinal blood vessels," Optics Express,
vol. 15, pp. 408-422,2007.
R.K. Wang, S.L. Jacques, Z. Ma, S. Hurst, S.R. Hanson, and A. Gruber, "Three
dimensional optical angiography," Optics Express, vol. 15, pp. 4083-4097,2007.
R. Michaely, A.H. Bachmann, M.L. Villiger, C. Blatter, T. Lasser, and R.A. Leitgeb,
"Vectorial reconstruction of retinal blood flow in three dimensions measured with high
resolution resonant Doppler Fourier domain optical coherence tomography," JBiomed
Opt, vol. 12, pp. 041213,2007.
Y.Wang, B.A. Bower, J.A. Izatt, O.Tan, and D. Huang, "In vivo total retinal blood flow
measurement by Fourier domain Doppler optical coherence tomography," JBiomed Opt,
vol. 12, pp. 041215,2007.
B.B. Gao, A. Clermont, S. Rook, S.J. Fonda, V.J. Srinivasan, M. Wojtkowski, J.G
Fujimoto, R.L. Avery, P.G. Arrigg, S.E. Bursell, L.P. Aiello, and E.P. Feener,
"Extracellular carbonic anhydrase mediates hemorrhagic retinal and cerebral vascular
permeability through prekallikrein activation," Nature Medicine, vol. 13, pp.
181-188,2007.
J. Flammer, S. Orgul, V.P. Costa, N. Orzalesi, GK. Krieglstein, L.M. Serra, J.P. Renard,
and E. Stefansson, "The impact of ocular blood flow in glaucoma," Prog Retin Eye Res,
vol. 21, pp. 359-93,2002.
V.Patel, S. Rassam, R. Newsom, J. Wiek, and E. Kohner, "Retinal blood flow in diabetic
retinopathy," Bmj,vol. 305, pp. 678-83,1992.
E. Friedman, "A hemodynamic model of the pathogenesis of age-related macular
25.
degeneration," Am J Ophthalmol,vol. 124, pp. 677-82,1997.
B.R. White, M.C. Pierce, N. Nassif, B. Cense, B.H. Park, GJ. Tearney, B.E. Bouma, T.C.
Chen, and J.F. de Boer, "In vivo dynamic human retinal blood flow imaging using
ultra-high-speed spectral domain optical Doppler tomography," Optics Express, vol. 11,
pp. 3490-3497,2003.
S. Makita, Y.Hong, M. Yamanari, T. Yatagai, and Y.Yasuno, "Optical coherence
angiography," Optics Express, vol. 14, pp. 7821-7840,2006.
R.G Hoskins, M.O. Lee, and E.P. Durrant, "The Pulse Rate of The Normal Rat," The
26.
American JournalofPhysiology, vol. 82, pp. 621-629,1927.
J.E. Harkness and J.E. Wagner, The Biology and Medicine of Rabbits andRodents. 4 Sub
23.
24.
ed. 1995: Williams & Wilkins. 372.