Advanced functional and intraoperative ophthalmic optical coherence tomography imaging

Advanced Functional and Intraoperative Ophthalmic Optical

Coherence Tomography Imaging

by

Chen David Lu

B.S., Electrical Engineering and Computer Science

U.C. Berkeley, 2010 MASSACHUSM!5 1NSTTUTE OF TECHNOLOGY MA R

2

P

LIBRARIES

ARCHIVES

S.M. Electrical Engineering and Computer Science

Massachusetts Institute of Technology, 2013

Submitted to the

DEPARTMENT OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE DOCTOR OF

in partial fulfillment of the requirements for the degree of

PHILOSOPHY in ELECTRICAL ENGINEERING AND COMPUTER SCIENCE At the

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

February 2018

C 2017 Massachusetts Institute of Technology All rights reserved

Signature of Author: 4

Certified by:

Department of Electrical Engineering and Computer Science September 13, 2017

Professor James G. Fujimoto Professor of Electrical Engineering and Computer Science Thesis Supervisor

Accepted by:

U 'Professor Leslie A. Kolodziej ski

Advanced Functional and Intraoperative Ophthalmic Optical

Coherence Imaging Tomography

by

Chen David Lu

Submitted to the Department of Electrical Engineering and Computer Science

on September 13, 2017 in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in Electrical Engineering and Computer Science

Abstract

Optical coherence tomography (OCT) is a non-contact, non-invasive imaging technique that uses optical interferometry to generate high-resolution, depth-resolved images of tissue in vivo. Ophthalmologists now use commercial OCT systems as a standard diagnostic instrument for imaging the retina to detect or monitor pathologies. However, prototype OCT research instruments exceed commercial systems in terms of faster imaging speeds and higher resolutions. Finding applications for these improvements will improve clinical utility for future OCT systems.

This thesis describes the design and use of an ultrahigh resolution spectral domain OCT system for detecting the photoreceptor changes during flash stimulus and an ultrahigh resolution swept source OCT system for use in eye surgery. The ultrahigh axial resolution of our system enabled visualization of thickness changes in the outer retinal layers after flash stimulus and subsequent dark adaptation. This finding could be used as a marker for photoreceptor health in retinal diseases that influence dark adaptation such as age-related macular degeneration. In the operating room, the ultrahigh speed system attaches to the operating microscope to share the surgeon's view and provide depth-resolved information that is not possible with the standard surgeon's stereoscopic view. This allows for imaging during surgical procedures and the ultrahigh speed enables acquisition of dense, widefield data sets as well as rapid volume acquisition to generate 3D visualizations in time. These data sets will enable 3D planning of procedures, assessment of outcomes before leaving the operating room, and feedback for surgical procedures.

Thesis Supervisor: James G. Fujimoto

Acknowledgements

I would like to thank my professor James Fujimoto for his guidance and support while obtaining

my Ph.D.

To the former and current members of the ophthalmic OCT team, Dr. Benjamin Potsaid, Dr. Ireneusz Grulkowski, Dr. Bernhard Baumann, Dr. Zhao Wang, Dr. Jonathan Liu, Dr. WooJhon Choi, ByungKun Lee, Eric Moult, and Patrick Yiu, I thank you all for your insights in OCT system building, image processing, and experience in conducting scientific studies. To our visiting students from University Erlangen-Nuremberg, Dr. Martin F. Kraus, Lennart Husvogt, Kathrin J. Mohler, Julia Schottenhamml, and Stefan Ploner, I thank you all for the computer science expertise to enable new forms of imaging technologies and techniques. I would also like to thank Dr. Hsiang-Chieh Lee and Dr. Michael Giacomelli for their mentorship during my Ph.D. studies.

Furthermore, I would like to thank my research collaborators Dr. Nadia Waheed, Dr. Andre Witkin, Dr. Caroline Baumal for their clinical knowledge throughout my time in the group and surgical assistance in our intraoperative studies. I would also like to thank Dr. Edward Pugh for our close collaboration in our back and forth discussions about study design and the origins of the effect we observed during our OCT dark adaption study.

Lastly, I would like to thank my wife, family, and friends for their unconditional love, understanding, and support throughout my long time in the laboratory.

Table of Contents

A bstract ... 3

A cknow ledgem ents ... 4

Table of C ontents...5

C hapter 1 Introduction and O verview ... 8

1.1 Introduction ... 8

1.2 Scope of Thesis...10

1.3 Sum m ary of C ontributions... 11

R eferences...15

Chapter 2 Spectral / Fourier Domain Optical Coherence Tomography...22

2.1 O verview ... 22

2.2 Spectral Domain Optical Coherence Tomography System Design...22

Light Source C hoice ... 23

C oupler C hoice ... 25

Sam ple A rm D esign...26

R eference A rm D esign...34

Spectrom eter D esign... 35

2.3 SD -O C T Processing... 38

Linear W avenum ber R esam pling ... 38

D ispersion C om pensation ... 41

W indow ing by Spectral Shaping... 45

2.4 O C T System Characterization ... 47

A xial R esolution... 47

Transverse R esolution... 49

Im aging R ange and Sensitivity R olloff... 50

O C T Sensitivity... 51

R eferences...52

Chapter 3 Ultrahigh Resolution OCT for Dark Adaptation...54

3.2 D ark A daptation Background ... . 55

H istory of D ark A daptation... 55

Retinal Diseases Inhibiting Dark Adaptation ... 59

3.3 R etinal Bleaching Instrum ent D esigns ... 60

3.4 D ark A daptom eter D esign... 66

3.5 U ltrahigh R esolution O CT... 68

3.6 Photoreceptor Band A nalysis ... 69

First Iteration... 69

Second Iteration... 73

Final Iteration ... 75

3.7 Preliminary Dark Adaptation OCT Results ... 78

Initial Dark Adaptation Experiment with Camera Flash...78

First Experiments with the Retinal Bleaching Instrument...80

High Power Retinal Bleaching Instrument with Finer Temporal Sampling.83 3.7 O C T D ark A daptation Study ... 87

M ethods ... 87

R esults...94

D iscussion ... 102

C onclusion...109

R eferences...110

Chapter 4 Swept Source Optical Coherence Tomography...117

4.1 O verview ... 117

4.2 Sw ept Source O CT System D esign...118

Light Sources...118

Interferom eter...120

Sam ple A rm D esign...121

R eference A rm D esign...121

Signal D etection and A cquisition ... 123

O ptical Clocking ... 126

4.3 Sw ept Source O CT Processing ... 133

Windowina cocoa

References ... 135

Chapter 5 Intraoperative SS-OCT Attachment for Retinal and Anterior Eye Imaging.. 138

5.1 Introduction ... 138 5.2 M ethods ... 141 5.3 Results ... 145 5.4 Discussion ... 151 5.5 Conclusions ... 155 References ... 155 Biography ... 165

Chapter 1

Introduction and Overview

1.1 Introduction

Optical coherence tomography (OCT) is an optical imaging technique for non-invasive, non-contact depth imaging based on the interference of coherent light. OCT was first developed in 1991 by our group with collaborators.1 OCT functions similarly to ultrasound but uses light

instead of sound. The light backscattered or back-reflected from a sample is interfered with a known reference light, generating an interference pattern. Processing the interference pattern or

fringe reveals the 1-dimensional encoded signals at various depths at a single position, known as

an A-scan. Sweeping this light beam in a line to acquire multiple A-scans produces a 2-dimensional

cross-sectional image known as a B-scan. Stepping the B-scan sweeps in a raster scan acquires a 3-dimensional volumetric OCT data.

Two critical OCT system specifications are the axial resolution and imaging speed. OCT's

imaging resolution lies between optical microscopy and ultrasound. Unlike traditional optical microscopy, the axial resolution and transverse resolution are decoupled. The optical spectral bandwidth determines the axial resolution while the imaging optics limit the transverse resolution.

The TD-OCT in the original publication achieved an axial resolution of 17 Pm in air using a

super-luminescent diode (SLD). Later TD-OCT systems could achieve ultrahigh resolutions of 2-3 Pm

differentiation of closely spaced retinal layers that previously blurred together. Spectral domain OCT (SD-OCT), developed in the early 2000s, offered increased sensitivity and speed compared

to previous TD-OCT systems.3'4 SD-OCT recorded the interference fringe with a spectrometer

built with a line scan camera. Since SD-OCT systems can operate using the same light sources as

TD-OCT, wide bandwidth light sources allow for ultrahigh resolution SD-OCT.5 Currently, the majority of commercial systems are SD-OCT systems. However, as of this thesis, most

commercial OCT systems operate at about 6 pm axial resolution in tissue while ultrahigh

resolution SD-OCT systems operate with <3 pm axial resolution. However, UHR-OCT systems

offer additional design challenges which will be described in the subsequent chapters.

The imaging speed, often given as A-scans per second, is critical for in vivo imaging

applications as the acquisition time is often limited. For example, the subject's eye can be held

open only for a limited amount of time. The first generation of OCT, known as time domain OCT

(TD-OCT), was limited in imaging speed because acquiring each A-scan required a physical

translation of the reference length. This limited the imaging speed to around single digit kHz. As

mentioned previously, SD-OCT increased the imaging speed by an order of magnitude compared

to traditional TD-OCT methods. SD-OCT systems operate from 10s of kHz to 100s of kHz.6 The

only limitation for SD-OCT is the imaging speed of the line scan camera in the spectrometer.

Another type of OCT system, swept source OCT (SS-OCT) samples a narrow wavelength laser

sweeping through wavelengths or frequencies in time instead of a light source emitting all

wavelengths at once. Both SD-OCT and SS-OCT detect light in the Fourier domain by measuring

the interference fringe and then Fourier transforming to extract the A-scan information. Since the

imaging speed is based on the laser sweep speed rather than on detection speed, recent advances

of kilohertz to megahertz.7_-0 _{These advances allowed SS-OCT to be an ideal system to construct}

an ultrahigh speed OCT system. Currently, the maximum commercial OCT system imaging speed

is 100 kHz. Research into ultrahigh speed OCT will provide applications for the next generation

of commercial OCT systems.

1.2 Scope of Thesis

This thesis focuses on the development of two advanced prototype OCT systems that

exceed the current commercial systems in terms of ultrahigh resolution and ultrahigh speed. The

ultrahigh resolution SD-OCT system was capable of imaging the micron-scale changes in the outer

retina after flash stimulus and subsequent dark adaptation. The unique thickness changes vary with

time and resemble the sensitivity recovery curves measured with a dark adaptometer. These results

may be used as a marker of photoreceptor health in diseases that affect sensitivity recovery in

darkness such as age-related macular degeneration. The other ultrahigh speed SS-OCT system

utilized a 400 kHz swept laser to acquire images during retinal and anterior eye surgery. The

ultrahigh speed enabled acquisition of widefield data and rapidly acquired volumes in time.

Analyzing the widefield data before the procedure provides surgical planning information while

widefield volumes after the procedure can analyze if the procedure was successful before the

patient leaves the operating room. The rapidly acquired volumes allow for 3D visualization of

surgical techniques while the surgeon is operating. In the future, this can be used to provide

real-time feedback for the surgeon to give them better accuracy to improve surgical outcomes. These

two systems will be described in the following chapters.

Chapter 2 describes the design of a SD-OCT system by using the ultrahigh resolution

Chanter first analyzes the nhvsical components of the system and then follows with the processing

necessary to recover an image with the best point spread function. The later part of the Chapter

analyzes how to characterize the specifications for an OCT system.

Chapter 3 introduces the OCT dark adaptation study using UHR-OCT. The Chapter starts

with background information about previous research into dark adaptation and some of the

diseases that impair sensitivity recovery in darkness. The next sections describe the bleaching

instrument and prototype dark adaptometer. The last portion of the Chapter describes the

preliminary studies followed by the final published dark adaptation study.

Chapter 4 parallels the structure of Chapter 2 by outlining the design considerations for a

SS-OCT system while focusing on the specifications of the intraoperative SS-OCT system. The

physical design is discussed followed by focusing on the processing necessary to generate the best

quality images.

Chapter 5 details the study using the intraoperative SS-OCT system to image patients in the operating room. The Chapter details the background behind prototype and commercial

integrated OCT systems used for ophthalmic surgery. The section will describe our system in

further detail and present the results from imaging 22 patients at the Tufts Medical Center.

1.3 Summary of Contributions

This section will summarize my contributions to the field of OCT during my time at MIT, including my Masters and Ph.D. work. From the start of my graduate program in 2010, our group

was one of the pioneers of high-speed SS-OCT research with our publication on the 100 kHz

commercial Axsun system by Dr. Benjamin Potsaid." With industrial support from Thorlabs Inc,

and Praevium Research, we had access to the vertical cavity surface-emitting laser (VCSEL) light

modifications on the initial laboratory results from the VCSEL light source.12 _{With knowledge of}

the VCSEL light source, I constructed and imaged with a 350 kHz VCSEL SS-OCT system with a handheld OCT scanner for my Masters thesis. This included building the optical components of

the SS-OCT system, programming the sinusoidal scan pattern, and modelling with SolidWorks the

3D printed enclosure for the handheld instrument. Before the publication, handheld OCT systems

were limited to commercial SD-OCT systems operating at 26-32 kHz and research prototypes at

70 kHz.13 _{The publication showed that a combination of ultrahigh speed, motion correction,}

reduced weight/size, and improved imaging range could overcome many of the prior limitations

of handheld OCT.14 Despite the current high cost of SS-OCT, technological advancements with

time will reduce the cost and size of OCT systems. This will enable portable OCT imaging in

settings beyond the ophthalmology setting, potentially enabling regular OCT screening of retinal

diseases at yearly doctor visits to detect and treat the diseases before they cause irreversible vision

loss.

Following the handheld OCT, I had two main directions to continue developing handheld

OCT devices. Dr. David Huang from Oregon Health and Science University (OHSU) proposed a

combination vitrectomy illuminator with OCT scanning using a gradient-index (GRIN) lens relay.

This would provide retinal surgeons with OCT depth information since they were limited to a

stereoscopic view on the retina. The OHSU group filed a patent on the device15 and I began

simulations to test the viability of such a scanner. However, after many simulations, I found that

the use of a GRIN lens to relay the scanning position causes the accumulation of aberrations with

increased pitch. Higher scan angles and smaller diameter GRIN lenses amplify this effect. While

limit the OCT scanning device to larger diameter needles (<20 gauge). Because of these reasons, the project was not continued.

The second direction was to develop a handheld OCT scanner that would scan patients during retinal surgery. Previous work at that time has used a commercial handheld SD-OCT scanner operating at ~20 kHz for imaging of the eye in the operating room.16_{'17 However, handheld}

intraoperative OCT imaging requires pauses in the operation to move the surgical microscope away from the eye before imaging alignment. This prevents imaging while the surgeon is operating and potentially extends the surgery time due to the pauses. Previous groups at that time had integrated OCT scanning inside of the surgical microscope before the objective lens so that OCT imaging can occur concurrently with the surgeon looking through the eyepieces. These systems were limited to SD-OCT with speeds of 20 kHz18 _{and 36 kHz.1}9 _{Rather than integrate the OCT}

scanning inside the microscope, we went another direction with an OCT scanning attachment after the objective lens in the surgical microscope. With assistance from Topcon Medical Systems, we received one of their commercial surgical microscopes and a prototype OCT scanner that attaches to the bottom of the microscope. I built the imaging engine consisting of a SS-OCT powered by a

1050 nn wavelength VCSEL system operating at 400 kHz. With this ultrahigh-speed SS-OCT

system, we were able to acquire dense widefield volumes, rapidly-acquired volumes over time for 4D imaging, and functional OCT angiography volumes in the operating room. Overall, we imaged 22 patients from 2015 to 2016. As of this thesis, we have submitted this work for publication.20

Since we began this project, the Duke University group have published their 100 kHz SS-OCT intraoperative system integrated into the surgical microscope.2 1_'

22 The group has also recently

demonstrated an effective 800 kHz imaging speed by buffering a 200 kHz Axsun to 400 kHz and

nrogress in intraonerative A 47 -- -- -- - --r-- - - -- -. -- -- -- OCT will -- -- -- --~0- --_ _ _ _ __ -,focus on lltili7ing higher imaging sneed to give more information to surgeons in the operating room.

Along with the ultrahigh speed intraoperative OCT project, I was assigned to investigate photoreceptor thickness changes after flash stimulus following a 2013 paper describing photoreceptor thickness changes seen in normal and Best disease patients under dark and light adaptation.2 4 _{This project was related to an aim in our National Institutes of Health (NIH)}

ophthalmic grant renewal where we specified that we would find possible disease markers using ultrahigh-resolution OCT (UHR-OCT). However, our group had not published any major ophthalmic UHR-OCT publications since 2009.25, 26 After many iterations of different flash

stimulus instruments, processing methods, and UHR-OCT systems, I completed the study for normal subjects and the manuscript has been accepted for publication for September 2017.27 In this paper, I detailed how there are three unique photorresponse waveforms that scale in amplitude and duration with bleaching intensity. These findings will need to be verified in patients with disease compared to normal subjects to analyze if the findings can be used as markers for disease progression. Discovering disease progression markers will be very important for clinical drug trials targeting dry age-related macular degeneration (AMD) to determine if treatment methods halt or reverse the disease.

In addition to these projects, I also contributed to deployment of OCT systems to our collaborators. One of my first tasks as a graduate student was to build a triggering circuit to synchronize the SS-OCT sweep trigger to the scanning mirrors and the acquisition card. This

triggering circuit was also integrated into an electrical enclosure that housed many of the electrical

connections and the galvanometer driver boards. I replicated this enclosure for a 100 kHz Axsun

split-spectrum amplitude-decorrelation angiography (SSADA 28_{, 29 now commerciali7ed as the}

Optovue Angiovue OCT angiography algorithm. I constructed the electrical enclosure for another

100 kHz Axsun SS-OCT system deployed to University of Pittsburg Medical Center (UPMC). I

also took charge of the C++ acquisition software and updated the graphics interface to make the acquisition procedure more intuitive for the operators. The UPMC system focused on studies of the lambina cribrosa in the optic nerve head of the eye.30-32 I also constructed the electrical

enclosure and optical components for the 100 kHz Axsun and 400 kHz VCSEL system deployed at New England Eye Center. The Axsun system generated studies on the vitreous33 and the VCSEL

system generated important studies with OCT angiography of retinal diseases.34-37 Lastly, I took

charge of the deployment of a second 100 kHz Axsun system for anterior eye imaging for OHSU. In addition to developing the electrical components, I programmed additional scan patterns and rebuilt the sample arm during the deployment at OHSU. The group at OHSU are currently using the system for preliminary studies for an anterior eye National Institutes of Health grant proposal.3 8

References

1. Huang D, Swanson EA, Lin CP, Schuman JS, Stinson WG, Chang W, Hee MR, Flotte T,

Gregory K, Puliafito CA, Fujimoto JG. Optical Coherence Tomography. Science

1991;254:1178-1181.

2. Drexler W, Morgner U, Ghanta RK, Kartner FX, Schuman JS, Fujimoto JG. Ultrahigh-resolution ophthalmic optical coherence tomography. Nature medicine 2001;7:502-507.

3. Leitgeb R, Hitzenberger CK, Fercher AF. Performance of fourier domain vs. time domain

4. Wojtkowski M, Leitgeb R, KowalczVk A Bairszewski T Fe-rcher AF. In vivo human retinal

imaging by Fourier domain optical coherence tomography. Journal of Biomedical Optics

2002;7:457-463.

5. Srinivasan VJ, Adler DC, Chen Y, Gorczynska I, Huber R, Duker JS, Schuman JS, Fujimoto

JG. Ultrahigh-Speed Optical Coherence Tomography for Three-Dimensional and En Face

Imaging of the Retina and Optic Nerve Head. Invest Ophth Vis Sci 2008;49:5103-5110.

6. Potsaid B, Gorczynska I, Srinivasan VJ, Chen Y, Jiang J, Cable A, Fujimoto JG. Ultrahigh

speed spectral / Fourier domain OCT ophthalmic imaging at 70,000 to 312,500 axial scans per second. Optics express 2008;16:15149-15169.

7. Jayaraman V, Jiang J, Li H, Heim PJS, Cole GD, Potsaid B, Fujimoto JG, Cable A. OCT

Imaging up to 760 kHz Axial Scan Rate Using Single-Mode 131 Onm MEMS-Tunable

VCSELs with > 1 00nm Tuning Range. 2011 Conference on Lasers and Electro-Optics (Cleo) 2011.

8. Potsaid B, Jayaraman V, Fujimoto JG, Jiang J, Heim PJS, Cable AE. MEMS tunable VCSEL

light source for ultrahigh speed 60kHz - 1 MHz axial scan rate and long range centimeter class OCT imaging. In: Joseph Al, James GF, Valery VT (eds): SPIE; 2012:82130M.

9. Wieser W, Biedermann BR, Klein T, Eigenwillig CM, Huber R. Multi-Megahertz OCT:

High quality 3D imaging at 20 million A-scans and 4.5 GVoxels per second. Optics Express 2010;18:14685-14704.

10. Klein T, Wieser W, Eigenwillig CM, Biedermann BR, Huber R. Megahertz OCT for

ultrawide-field retinal imaging with a 1050nm Fourier domain mode-locked laser. Optics Express 2011;19:3044-3062.

11. Potsaid B, Baumann B, Huang D, Barry S, Cable AE, Schuman JS, Duker JS. Fujimoto JG.

Ultrahigh speed 1050nm swept source/Fourier domain OCT retinal and anterior segment imaging at 100,000 to 400,000 axial scans per second. Optics express 2010;18:20029-20048. 12. Grulkowski I, Liu JJ, Potsaid B, Jayaraman V, Lu CD, Jiang J, Cable AE, Duker JS,

Fujimoto JG. Retinal, anterior segment and full eye imaging using ultrahigh speed swept source OCT with vertical-cavity surface emitting lasers. Biomedical optics express

2012;3:2733-2751.

13. Shelton RL, Jung W, Sayegh SI, McCormick DT, Kim J, Boppart SA. Optical coherence

tomography for advanced screening in the primary care office. Journal of biophotonics

2014;7:525-533.

14. Lu CD, Kraus MF, Potsaid B, Liu JJ, Choi W, Jayaraman V, Cable AE, Hornegger J, Duker

JS, Fujimoto JG. Handheld ultrahigh speed swept source optical coherence tomography

instrument using a MEMS scanning mirror. Biomedical optics express 2013;5:293-311.

15. Huang D, Wang Y, Wilson D, Stout JT, Fujimoto J, Lu C. Oct vitrectomy probe. US Patent

App. 14/890,035; 2014.

16. Dayani PN, Maldonado R, Farsiu S, Toth CA. Intraoperative use of handheld spectral

domain optical coherence tomography imaging in macular surgery. Retina 2009;29:1457-1468.

17. Ehlers JP, Dupps WJ, Kaiser PK, Goshe J, Singh RP, Petkovsek D, Srivastava SK. The

Prospective Intraoperative and Perioperative Ophthalmic ImagiNg with Optical CoherEncE TomogRaphy (PIONEER) Study: 2-year results. American journal of ophthalmology

1 Tao YK, Ehlers JP, Toth CA, lzatt JA. Intraoperative spectral domain ontical coherence

tomography for vitreoretinal surgery. Optics letters 2010;35:3315-3317.

19. Tao YK, Srivastava SK, Ehlers JP. Microscope-integrated intraoperative OCT with

electrically tunable focus and heads-up display for imaging of ophthalmic surgical maneuvers. Biomedical optics express 2014;5:1877-1885.

20. Lu CD, Waheed NK, Witkin AJ, Baumal CR, Liu JJ, Potsaid B, Joseph A, Jayaraman V, Cable A, Chan K, Duker JS, Fujimoto JG. Intraoperative Ultrahigh Speed Swept Source Optical Coherence Tomography with a Microscope Attachment for Widefield Retinal and

Anterior Segment Imaging. Ophthalmic surgery, lasers & imaging retina 2017.

21. Carrasco-Zevallos 0, Keller B, Viehland C, Shen L, Todorich B, Shieh C, Kuo A, Toth C, Izatt JA. 4D microscope-integrated OCT improves accuracy of ophthalmic surgical

maneuvers. Proc Spie; 2016:969306-969306-969307.

22. Carrasco-Zevallos OM, Keller B, Viehland C, Shen L, Waterman G, Todorich B, Shieh C, Hahn P, Farsiu S, Kuo AN, Toth CA, Izatt JA. Live volumetric (4D) visualization and guidance of in vivo human ophthalmic surgery with intraoperative optical coherence tomography. Scientific reports 2016;6:31689.

23. Carrasco-Zevallos 0, Viehland C, Keller B, N. Kuo A, Toth C, Izatt J. High-speed 4D

intrasurgical OCT at 800 kHz line rate using temporal spectral splitting and spiral scanning (Conference Presentation); 2017:100530E.

24. Abramoff MD, Mullins RF, Lee K, Hoffmann JM, Sonka M, Critser DB, Stasheff SF, Stone

EM. Human photoreceptor outer segments shorten during light adaptation. Invest Ophthalmol Vis Sci 2013;54:3721-3728.

25. Srinivasan VJ, Chen Y Duker JS, Fujimoto JCT In Vivo Functional Imaging of Intrinsic

Scattering Changes in the Human Retina with High-speed Ultrahigh Resolution OCT. Optics

express 2009;17:3861-3877.

26. Witkin AJ, Vuong LN, Srinivasan VJ, Gorczynska I, Reichel E, Baumal CR, Rogers AH,

Schuman JS, Fujimoto JG, Duker JS. High-speed ultrahigh resolution optical coherence

tomography before and after ranibizumab for age-related macular degeneration.

Ophthalmology 2009; 116:956-963.

27. Lu CD, Lee B, Schottenhamml J, Maier A, Pugh EN, Fujimoto JG. Photoreceptor Length

Thickness Changes During Dark Adaptation Observed with Ultrahigh Resolution Optical

Coherence Tomography. Invest Ophthalmol Vis Sci 2017.

28. Jia Y, Bailey ST, Wilson DJ, Tan 0, Klein ML, Flaxel CJ, Potsaid B, Liu JJ, Lu CD, Kraus

MF, Fujimoto JG, Huang D. Quantitative optical coherence tomography angiography of

choroidal neovascularization in age-related macular degeneration. Ophthalmology

2014;121:1435-1444.

29. Jia Y, Morrison JC, Tokayer J, Tan 0, Lombardi L, Baumann B, Lu CD, Choi W, Fujimoto JG, Huang D. Quantitative OCT angiography of optic nerve head blood flow. Biomedical

optics express 2012;3:3127-3137.

30. Nadler Z, Wang B, Wollstein G, Nevins JE, Ishikawa H, Kagemann L, Sigal IA, Ferguson

RD, Hammer DX, Grulkowski I. Automated lamina cribrosa microstructural segmentation in

optical coherence tomography scans of healthy and glaucomatous eyes. Biomedical optics

express 2013;4:2596-2608.

31. Wang B, Nevins JE, Nadler Z, Wollstein G, Ishikawa H, Bilonick RA, Kagemann L, Sigal IA, Grulkowski I, Liu JJ. In Vivo Lamina Cribrosa Micro-Architecture in Healthy and

Glaucomatous Eyes as Assessed by Optical Coherence Tomographyln Vivo Assessment of

3D LC Micro-Architecture. Invest Ophth Vis Sci 2013;54:8270-8274.

32. Wang B, Nevins JE, Nadler Z, Wollstein G, Ishikawa H, Bilonick RA, Kagemann L, Sigal IA, Grulkowski I, Liu JJ. Reproducibility of in-vivo OCT measured three-dimensional

human lamina cribrosa microarchitecture. PloS one 2014;9:e95526.

33. Liu JJ, Witkin AJ, Adhi M, Grulkowski I, Kraus MF, Dhalla A-H, Lu CD, Hornegger J,

Duker JS, Fujimoto JG. Enhanced vitreous imaging in healthy eyes using swept source

optical coherence tomography. PloS one 2014;9:e102950.

34. Choi W, Moult EM, Waheed NK, Adhi M, Lee B, Lu CD, De Carlo T, Jayaraman V,

Rosenfeld PJ, Duker JS. Ultrahigh Speed Swept Source OCT Angiography in Non-Exudative

Age-Related Macular Degeneration with Geographic Atrophy. Ophthalmology

2015; 122:2532.

35. Choi W, Moult EM, Waheed NK, Adhi M, Lee B, Lu CD, de Carlo TE, Jayaraman V,

Rosenfeld PJ, Duker JS, Fujimoto JG. Ultrahigh-Speed, Swept-Source Optical Coherence

Tomography Angiography in Nonexudative Age-Related Macular Degeneration with

Geographic Atrophy. Ophthalmology 2015;122:2532-2544.

36. Moult E, Choi W, Waheed NK, Adhi M, Lee B, Lu CD, Jayaraman V, Potsaid B, Rosenfeld PJ, Duker JS, Fujimoto JG. Ultrahigh-speed swept-source OCT angiography in exudative

AMD. Ophthalmic surgery, lasers & imaging retina 2014;45:496-505.

37. Moult EM, Waheed NK, Novais EA, Choi W, Lee B, Ploner SB, Cole ED, Louzada RN, Lu CD, Rosenfeld PJ. Swept-source optical coherence tomography angiography reveals

choriocapillaris alterations in eyes with nascent geographic atrophy and drusen-associated

38. Skalet AH, Li Y, Lu CD, Jia Y, Lee B, Husvogt L, Maier A, Fujimoto JG, Thomas CR,

Huang D. Optical coherence tomography angiography characteristics of iris melanocytic tumors. Ophthalmology 2017;124:197-204.

Chapter 2

Spectral / Fourier Domain Optical Coherence Tomography

2.1 Overview

Spectral / Fourier domain optical coherence tomography relies on accurately sampling wavenumbers to determine depth information encoded in sinusoidal interference fringes. One method of sampling wavenumbers is to detect continuously a broadband coherent light source with a spectrometer. This method of OCT is commonly known as spectral domain optical coherence tomography (OCT). Currently, most commercial ophthalmic OCT systems operate using

SD-OCT. The following sections will detail the various parts of the SD-OCT system assuming the

reader has background knowledge in Michaelson interferometry. These sections will characterize the SD-OCT system used for the OCT dark adaptation experiments described in Chapter 3.

Much of the SD-OCT knowledge listed in this Chapter was obtained from helpful discussions with Dr. Benjamin Potsaid, Dr. Jonathan Liu, and Dr. WooJhon Choi while planning and constructing SD-OCT systems. Additionally, I would like to acknowledge Dr. Jonathan Liu for programming the LabView acquisition software that interfaced with the SD-OCT system.

2.2 Spectral Domain Optical Coherence Tomography System Design

A SD-OCT system can be divided up into individual components. Figure 2.1 shows an

example of a fiber-based SD-OCT system with the major components labelled. The interferometer fiber coupler connects all the different parts of the SD-OCT system.

Light Source

Dichroic Telescope lenses

Mirror Isolator

SuperRuminescent

Diode (SLD) _{80/20 Scanning}

Coupler Mirrors

Line Scan Transmission Water/Glass Cat's Eye

Camera Grating AdJustable ND CompensationRef. Mirror

Light Atenuator Focusing Lens

Spectrometer Reference Arm

Figure 2.1. Fiber-based SD-OCT system schematic. Light Source Choice

In general, an OCT system is designed around its light source. The type of fibers used, fiber coupling ratio, lens coatings, and spectrometer components all depend on the wavelengths and output power of the light source. SD-OCT light sources need to continuously output a wide wavelength of light so that the spectrometer can sample the interference spectrum that encodes the depths as sinusoidal frequencies. Currently, most SD-OCT light sources multiplex one or more

superluminescent diodes (SLDs) to output a broad wavelength band of coherent laser light. In the past, femtosecond lasers have also been used to provide a wide optical bandwidth for OCT.'

The bandwidth of the light source determines the axial resolution of the system. To illustrate the relationship between optical bandwidth and axial resolution in OCT, assume that the input laser power follows a Gaussian distribution as a function of k

A 2(k)=exp -4i(2)(kk) 2 (2.2.1)

Ak2

where k is the mean wavenumber and A k is the full width half maximum (FWHM) of the

F IA22_{(k)} = Ak exp(jkz) exp -Z}

J2.

7r4 ln(2) 4 4ln(2) (2.2.2)

Gaussian

This is known as the point spread function (PSF). The PSF is the depth response from a single

reflector in the sample arm. The resulting A-scan image in depth of a complex tissue with

multiple reflectors is simply the convolution of PSF with those reflectors. However, due to non-uniform sampling and dispersion mismatches, the Fourier transform of the immediate data obtained from an SD-OCT system will not result in the best PSF. Section 2.3 will detail these

effects and methods of recovering the maximum resolution for the PSF. Section 2.4 will further

explain how to characterize the axial resolution from the PSF.

The previous analysis assumes that the spectrum has a Gaussian distribution. In reality, multiplexing multiple SLD modules results in a spectrum with intensity ripples over the band of

output wavelengths. Figure 2.2 shows the optical spectrum of the Superlum Broadlighter

T870-HP (Superlum Diodes Ltd, Carrigtwohill, Ireland) used in the SD-OCT system for the dark adaptation experiment. This light source multiplexes three SLD modules to generate a spectrum centered at 870 nm wavelength with a FWHM of 170 nm. These ripples will cause increased sidelobes in the PSF after the Fourier transformation. Section 2.4 will describe spectral shaping as a way of minimizing the effects of these ripples.

1 0.9 --- --- - - -- --- ---0.8 ..--- --- --- -- ---- --- -- -- -- -- - - - -0.6 --- -- --- -- -- -- .-- --- --- -- ---- - ---0.4 --- -- --- --- --- ---... ---- --- ---0.3 --- -- .. ... .--- --- -- --- --- -- ---0 z 0.2 --- --- --- --- --- --- -- ---950 800 850 900 950 1000 1050 Wavelengt (nm)

Figure 2.2. Optical spectrum of the Superlum Broadlighter T870-HP.

Lastly, an optical isolator placed after the output of the SLD prevents backcoupling of any

optical power into the SLD, which may result in degradation of the SLD light source with use. The

isolator must be selected with an appropriate passband to prevent the loss of optical bandwidth and

optical power for the OCT system.

Coupler Choice

To reduce power losses and save space, most OCT systems use a fiber-based

interferometer rather than a free-space interferometer. The 80/20 fiber coupler used in the

SD-OCT system connecting the four portions of the system acts as the beamsplitter in a standard

Michaelson interferometer. This coupling ratio varies from the 50/50 in a normal Michaelson

interferometer for two reasons. First, the SLD usually provides an excess of power, so the 20%

coupling to the sample arm ensures that the retinal exposure is below established limits.2 Second,

after the sample arm collects the returning back-scattered/back-reflected signal, 80% of that

power will couple to the spectrometer path. This higher coupling ratio ensures a higher collection

Sample Arm Design

The sample arm is designed with a telescopic arrangement of lenses to image the scanning

beam pivot plane onto the pupil plane of the eye. This pivot point allows the collimated beam to

focus down to scan the retina. As a double pass system, the sample arm collects the back-reflected

and back-scattered light from the retina through same path as the illumination. Shown in Figure

2.3, the choice of optical components determines key optical specifications for scanning the retina.

f1 1T2 T2 Fiber dc Connector G, fc de Scanner Dichroic f1 T2 Plane Mirror

Figure 2.3. Unfolded sample arm with indicated variables used to describe the optical scanning

of the eye.

From the fiber connector with a known numerical aperture NAf, the diameter of the beam

after the collimator is determined by

d, = 2f, tan(arcsin(NAf)) (2.2.3)

where

f,

relay the scanning plane on to the pupil of the eye. The focal lengths fj and

f

sets the magnification factor M.

M = -f2 / Ai (2.2.4)

'd -IAd

L4e - I I VAI 4C

and the input angle into the eye is

t,

= t-

(fI

f

Usually,

f2

A first order approximation of the scanning angle on the retina 0. can be determined by

the differences in the index of refraction between air and within the eye

6 Or e

- (2.2.7)

neye

where neye =1.336 is the refractive index of the eye. A more thorough calculation for the angle

on the retina requires an optical simulation using a model eye that includes the refractive effects

of the curved cornea and varying refractive index within the crystalline lens. The field of view

(FOV) in length units requires determination of the scanned arc on the retina assuming the pivot

position is at the pupil. This requires determination of the chord angle on the eye assuming as

1POSt

6.

_...

_...

_...

_...

_..

:E

F V

FOV

D

Figure 2.4. Diagram of scanning the retina to determine the field of view. The retinal scanning angle has been exaggerated to accentuate the angle relations. Point A lies on the pupil pivot plane for the beams. Point C is the center given by the radius of curvature for the back of the eye. The right triangle ABC forms from the relationship between the pupil pivot point and the center of the eye. Point D lies on the scanning point of the retina. Point E lies on the chord formed by scan angle.

To determine the chord angle 0, the length BC must be determined first

BC = sin,(Or )(lpost -r) (2.2.8)

Where 1post 20 mm is the posterior eye distance equal to the distance between the pupil to the

retina and r =12 mm is the retinal radius of curvature. Determination of BC allows for the computation of angle ZBCD

ZBCD= cos(BC-I /r)= cos-'(sin(r)(lpost -r)/r) (2.2.9)

The chord angle can then be determined through angle relationships

This produces the arc length equal to the FOV

20 4rr (90 -O,-cos-'( sin(Or }{ post -r)/ r 2

FOV = 2rr C _ s (2.2.11)

3600 3600

The transverse resolution or spot size depends on the imaging performance of the eye.

Assuming a Gaussian beam, the transverse resolution or spot size dr on the retina is dependent on

the diameter of the beam entering the eye.

dr = 44fe (2.2.12)

;neyed,

Where )4 is the wavelength of light in vacuum, and feye = 16.6 mm is the effective focal length

of the cornea and crystalline lens of the eye.

Since the spot size and field of view scale inversely, an invariant parameter describing the imaging performance is useful to compare sample arm designs. The number of resolvable spot

NRS measures the number of unique scan points along the entire field of view. The number of

resolvable spots can be determined by dividing the length of the field of view by the spot size.

NRS =FOV _(2.2.13)

dR

With this invariant parameter, increases in the magnification of the 4F telescope will reduce the

field of view at the same rate as narrowing the spot size, resulting in an invariant NRS. The number

of resolvable spots can only increase by increasing the input diameter into the scanner and/or the initial scanning angles.

The depth of field (DOF) or confocal parameter in the OCT system determines a range of depths where the system is in focus. Assuming the laser outputs a Gaussian beam, the depth of field is

27 2d

2

ZDOF - 2n edv (2.2.14)

Ideally, the depth of focus should be longer than the thickness of the retina (-300 pim) so that the

entirety of the retina can be in focus to maximize the signal from the layers and to prevent

transverse blurring.

The second lens translates axially to correct for myopic and hyperopic eyes as shown in

Figure 2.5. Because the beams at various scan angles are parallel in the infinity space before the

second lens, the overall scan angle into the cornea and the working distance from the surface of

the lens and the eye is unchanged. However, because the second lens is moving towards or away

from the subject's eye, the system must also move to maintain the working distance.

First Lens Second Lens

Position Position

Normal

Az2cor

Hyperopia

Myopia

Figure 2.5. Translation of the second lens in the 4F telescope accommodates for refractive errors in the subject without changing the working distance or scanning angle into the eye.

The axial translation of the second lens Az, corresponds to a refractive error correction measured

in diopters by the following relationship

(2.2.15)

D= I I

f2

f2

Typically, the correction should be at least 12 diopters to account for a diverse range of refractive

errors.

The previous analysis assumed that the X and Y galvanometer scanners are at the same

plane. In reality, because each scanning direction requires a mirror attached to a separate servo,

the scanning axes are displaced by some distance. This displacement contributes to axial shifts in

the pivot positions and in the scan angle for the X and Y scanning directions. Figure 2.6 shows

the effects of the scanning pivot displacement if the scanner is closer to the first lens by Az,.

I

Z

_1~

_I2

hOjhi3

II

Figure 2.6. Diagram for a scan displacement towards the first lens.

The resulting shift in the pupil pivot away from the second lens Az is equal to

&iW =&CsIM2 (2.2.16)

Determining the angle change AzW requires the lens equation. The focal position for the diverging beam is given by

I

Z2 = .j1J dISj (2.2.17)

AdJs

The scan height on the first lens can be written in terms of the original, non-displaced scan height

I% =f tan'I(9,). The displaced scan height at the first lens is given by

A~k

,

_k(1_

The height at the second lens is proportional to increase in distance between the first and second lens

h=Z2+f +f2 (2.2.19)

Z2

The angle incident on the cornea from the displaced scan point can then be calculated

O&, = tan - + j (2.2.20)

For the case where the scanning shift is away from the first lens, the calculations can be repeated with a negative Azds. _{Ideally, the scanning position should be set between the two galvanometer} scanners to minimize jAzds I for both the X and Y scanning directions. From this analysis, we can see that the pivot point can change the axial pivot position between the X and Y scanning, causing increased vignetting on one axis versus the other. The angle variations also may require slightly different mapping of scan angle to imaging area for X and Y directions.

The folded sample arm optics used in the SD-OCT system are shown in Figure 2.7. With

the listed optical components and specifications from the light source, the parameters derived from

f =80 mmf

=

Figure 2.7. Optical components used in the SD-OCT sample arm for OCT imaging.

Specification Variable Value Units

ight Source Center Wavelength AO 870 nm

780HP Fiber Numberical Aperture N44 0.13 Unitless

-ollimator Focal Length fr 20 mm

3eam Diameter After Collimator de 5.24 mm

ican Angle 09S 20 0

irst Telescope Lens Focal Length A 80 mm

)econd Telescope Lens Focal Length A 30.8 mm

F Telescope Magnification M -0.385 Unitless

3eam Diameter Before Eye d, 2.02 mm

3eam Angle into Eye _, 43.4 0

3eam Angle from Pupil On Retina 9. 32.5 1 *_

:hord Angle on Retina OG 53.5 0

Oaximum Field of View FOV 22.4 mm

7ransverse Resolution/Spot Size d, 6.88 pm

4umber of Resolvable Spots NRS 3255 Spots

)epth of Field DOF 457 pm

ial Translation of Second Lens ACor 25.4 mm

ositive Diopter Correction 153 D

egative Diopter Correction D -14.7 D

canning Pivot Displacement 5 mm

hift in Pupil Pivot 0.741 mm

ositive Shift in Pupil Pivot Beam Angle dis 43.4

egative Shift in Pupil Pivot Beam Angle dis 44.6 *

Table 2.1. Sample arm parameters from the SD-OCT system used in the final OCT dark adaptation study.

A few particular specifications require additional discussion. First, these specifications are

the zeroth order classification of the specifications for the sample arm. This means that the values may vary for measured data based on the assumptions used for the zeroth order calculations. The zeroth order specifications allow for quick comparison between different configurations but optical simulation testing would reveal the specifications that are closer to real world performance. Second, the scan angle listed is the absolute maximum optical scanning angle for the galvanometers. In reality, the full scanning range is not used for acquisition because the scanning mirrors need additional area during flyback to overshoot in order to steer the beam to the next scanning position. This effectively reduces the overall raster acquisition field of view of the retina. Furthermore, the complete field of view cannot be used if the axial imaging range cannot encompass the retina. The axial imaging range characterization is further explored in Section 2.4. Reference Arm Design

Shown in Figure 2.1, the other portion of light from the sample arm enters the reference arm. The reference arm requires an optical path distance that matches the sample arm for interference. Due to differences in the optics between the sample and reference arm, glass compensation elements help match the dispersive elements within the sample arm. The water cell compensates the beam imaging through the vitreous of the eye when imaging the retina. The dispersion compensation elements must be selected considering the reference arm is double-pass where the output beam is reflected and is collected by the same collimator. The reference arm path may contain an additional attenuator such as an adjustable neutral density filter or iris to prevent spectrometer light saturation. The reference beam should transmit through the dispersion compensation and attenuation elements at a non-normal angle to prevent back-coupling of reference arm signal which may manifest as interference artifacts. The collimated light focuses

waist lies at the mirror surface to improve light coupling on the return path. Furthermore, increasing optical delay by translating the entire cat's eye unit or transverse vibrations would have

minor effects on the beam focused on the mirror.

Spectrometer Design

The spectrometer detects and samples the interfered light from the sample and reference arms. The spectrometer listed in this system consists of a collimator, a transmission grating, a scan

lens, and a line scan camera shown in Figure 2.8. This section will describe parameters of interest

as a zeroth order way of modeling the spectrometer performance for a given light source. These

parameters will then be evaluated for the eventual SD-OCT system used in the OCT dark

adaptation study outlined in Chapter 3.

a (Ipmm) dpcfo

da,

fco

...---Figure 2.8. SD-OCT spectrometer with indicated parameters that characterize the spectrometer performance. The insert shows a zoomed view on the center wavelength angle of incidence of the first principle order.

The collimator with focal length

fco,

dspec =2JCol LakNtsi-l kIVAf)) (2-.2.21)

The collimated beam strikes a transmission grating which deflects the light based on the number of grating per length a. The angle of incidence 69 for the center wavelength 4 of the first principle order is given by

61 =sin-, a, (2.2.22)

2

The diameter of the beam after the grating dg also increases by d

d = _(2.2.23)

g _{cos(6 )}

Based on the lower Amn and upper Ama wavelengths of the spectrum, the angle span Os after the grating can be calculated

Ospec = sin-I - Amin -sin-' aK -- Ama (2.2.24)

The fan of wavelengths focuses through a focusing lens of focal length

ffoc

cam = 2

_ffoc

(2.2.25)

This line is detected with a line scan camera with horizontal pixels that sample the spectrum. For

a given wavelength, the focusing lens focuses the beam down to a spot size of dcm detected by

the line scan camera.

d am = (2.2.26)

This spot should be smaller than the pixel sampling in the vertical direction to ensure the maximum

collection of signal by the system. The spot should also be narrow in the horizontal direction to

prevent blurring of neighboring wavelengths that would reduce the overall wavelength resolution

of the spectrometer. This is one of the factors that would cause sensitivity rolloff, which is further

explained in Section 2.4.

The spacing of spectral sampling by the line scan camera determines the axial imaging

range after Fourier transform of the interference fringe. The bit-range of the camera determines

the quantization noise present in the signal. The speed of the line scan camera in sampling the

entire line, known as the line rate, determines the A-scan rate of the overall SD-OCT system.

The parameters described above used to design the SD-OCT spectrometer used in the OCT

dark adaptation study are shown in Table 2.2.

Spectrometer specification Variable Value Units

ight Source Upper Wavelength Al 960 nm

ight Source Center Wavelength /3 870 nm

ight Source Lower Wavelength Alnin 780 nm

80HP Fiber Numberical Aperture N -f 0.13 Unitless

ollimator Focal Length fco _ 82 mm

'earn Diameter After Collimator d 13.11 mm

ransmission Grating per length 7 1200 Lines per mm

ngle of Incidence 31.47 *

iameter After Grating d 15.37 mm

Angle Span After Grating 16.54 0

ocusing Lens Focal Length 100 mm

ine Width on Camera Wcan 29.07 mm

pot Size (Upper Wavelength) da 8 pm

pot Size (Center Wavelength) can 7.2 pm

pot Size (Lower Wavelength) d 6.4 pm

ine Scan Camera Model _____ spL4096 140km N/A

ine Scan Camera Pixel Size 10 pm

/aximum Camera Pixels 4096 Pixels

-amera Line Scan Width 40.96 mm

Jsed Number of Pixels 2907 Pixels

ixel Bit Depth 12 bits

maging Speed 70000 Lines per second

maging Speed Lowered Pixels 98630 Lines per second

Table 2.2. Zeroth order calculations for the design of the SD-OCT spectrometer used in the OCT

Of narticular note, the sn4096-140km (Basler AG Ahrensburg Germny) line scan camera can trade off the number of acquisition pixels to achieve more imaging speed. Our group has previously achieved imaging speeds of up to 312.5 Hz using this camera.3 _{In the SD-OCT system used for} the dark adaptation experiment, the specified spectrum in Table 2.2 covers 2907 pixels of the line scan camera. Sampling only those pixels proportionally boosts the imaging speed to 98.6 kHz. In reality, the number of sampled pixels is increased from 2907 to sample both ends of the spectrum. In the end, the number of acquired pixels is 3072 for an imaging speed of 91 kHz.

2.3 SD-OCT Processing

After the spectrometer acquires the interference fringe, each acquisition requires additional processing to recover the maximum possible axial resolution for each A-scan. The three major processing steps are the resampling to linear wavenumber, dispersion compensation, and spectral shaping.

Linear Wavenumber Resampling

While the spectrometer in the previous section can resolve the spectrum, the grating displaces the spectrum linearly in wavelength rather than in wavenumber. Directly Fourier transforming the linear wavelength acquisition will result in a phase mismatch from improperly sampling the interference fringe. This spectrum will require resampling to linear wavenumber before the Fourier transformation to recover the depth-encoded elements. There are two methods to determine the wavelength to wavenumber conversion.

The first method of recovering the absolute wavelength values for resampling is to illuminate the spectrometer with a mercury-argon light source with known emission bands (Figure

1~~

Figure 2.9. (A) Mercury-argon calibration light source. (B) Calibration spectrum seen on the pixels of the line scan camera in the spectrometer. Certain wavelength peaks indicated on the mercury-argon source manifest as double peaks due to the high spectral resolution of the spectrometer. Online resources can provide a more accurate listing of the additional emission peaks. 2500 2000. 1500-1000~ 500 . i00 750o 8000 8S0 9000 Wavelength (angstrom)

B

Figure 2.10. (A) The mercury-argon emission peaks plotted against line-scan camera pixel. The spectrometer shows high linearity in wavelength. (B) Conversion of wavelength to wavenumber

with a 51 order fitted curve. This curve provides the conversion from wavelength to linear

wavenumber.

The second method does not require a known light source. This method determines the

resampling parameters for a spectrometer by imaging a single reflector at two different depths.

I

B

Explaining this technique will require examination of the phase obtained from a single reflector. In a Michaelson interferometer, the current at the detector will have a DC autocorrelation term and an oscillating cross-correlation term. The phase of the cross-correlation term of a single reflector at two separate displacements L, and 4 from the reference arm are

Zicross, (k) = 2kL₁ + (D(k)

Zicross,2 (k) 2kL2 + I?(k)

where (D(k) includes additional phase effects such as dispersion mismatch. Since the dispersion effects from the displacement between L, and L2 are small, they are ignored and both depths experience the same phase effects. By subtracting the two phases, the additional phase effects cancel out and what remains is a linear phase with a slope dependent on the separation between the two depths

Zicross,2 - cross,1(k) = 2k(L2 -L) (2.3.2)

If the wavenumber is sampled with equal periods between samples, the phase difference of the two

reflectors will appear linear. However, as mentioned in Section 2.2, the standard spectrometer samples linearly in wavelength, resulting in a curved phase difference between the two reflectors.

By interpolating the points such that the curvature is linear, it is possible to resample the spectrum

to linear wavenumbers so that the data can be directly Fourier transformed.

A comparison between the two methods is shown in Figure 2.11. Since both methods yield

similar results, the two-depth displacement method is preferable since it only requires back-coupling of a single reflector in the sample arm and two measurements.

Ar C C A Calibration o 9 - Displacement Calibration 08. 07 ) 6) .4

Displacement Calibration i _E03

0 Z 02

0 1

0355 036 0365 037 0375 038

Axial Depth (mm in air)

Figure 2.11. Retinal images with linear wavenumber resampling from (A) mercury argon calibration and (B) two-depth displacement calibration. (C) Point spread function for both methods.

Dispersion Compensation

Dispersion occurs because the propagation velocity depends on the wavelength or frequency of light passing through the material. This produces a wavelength dependent phase delay

determined by the type and length of material. As seen from the SD-OCT system schematic, the

sample and reference arms in the system have distinct optical elements that can create dispersion

mismatch between the two arms. Excessive dispersion mismatch in OCT can cause a broadening

of the point spread function, reducing axial resolution and image quality. In general, the sample

arm contains more dispersive elements due to the telescopic arrangement of lenses and from

imaging through the vitreous of the eye. While a portion of this dispersion can be compensated

physically with the use of added glass and a water cell in the reference arm shown in Section 2.2, numerical dispersion compensation is required to completely recover the point spread function.

To illustrate the effects of dispersion, a phase delay cD (k) dependent on the wavenumber

in vacuum k = 27rc/! where c is the speed of light in vacuum and

Z