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Development of Jones matrix tomography for functional ophthalmic imaging Ju, Myeong Jin 2015

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Development of Jones Matrix Tomographyfor Functional Ophthalmic ImagingbyMyeong Jin JuM.Sc., GIST (Gwangju Institute of Science and Technology) 2011A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDoctor of PhilosophyinTHE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES(Electrical and Computer Engineering)The University of British Columbia(Vancouver)August 2015c© Myeong Jin Ju, 2015AbstractOptical coherence tomography (OCT) provides the axial profile of back-scatteredlight from biological tissues and enables non-invasive, three-dimensional structureimaging. Since the introduction of OCT technique, OCT has shown its powerfulutility especially in the field of ophthalmology. However its capability is still limitedto the structural investigation. Because many eye diseases are tightly associatedwith tissue functions such as blood circulation and tissue microstructure, develop-ment of functional OCT is important. Since the necessity of functional extension ofOCT technique got more attention, Doppler OCT and polarization-sensitive OCT(PS-OCT) have been developed for blood flow and birefringence measurements, re-spectively, and have been widely utilized for ophthalmic imaging for clinical andpathological research purposes. Jones-matrix-based OCT, also named as Jones ma-trix tomography (JMT), was originally designed as one type of PS-OCTs capableof measuring the polarization properties of biological tissue. In this dissertation, anadvance version of JMT system is developed and also novel applications of JMT inophthalmology is introduced.New JMT algorithms are developed, which make JMT system being capa-ble of multi-contrast imaging including scattering, localized flow, and polarizationcontrasts. Novel spectral shift compensation and adaptive averaging methods areiidevised for achieving sensitivity-enhanced scattering OCT and polarization prop-erty measurements. Especially, by stabilizing the phase of the system, Doppler flowmeasurement is achieved with a high sensitivity.As a new clinical application, JMT is utilized for three-dimensional volumet-ric in vivo imaging of human eyelid. With the degree of polarization uniformitycontrast (DOPU), one of the polarization contrasts produced by JMT, meibomianglands (MGs) are exclusively segmented from OCT volumetric image. With MGsegmentation, its age-dependent morphological characteristics are further investi-gated.As another clinical application, JMT is also utilized for investigating cornealcollagen cross-linking (CXL) effect on cornea stroma. Fresh bovine corneas aretreated by two different CXL protocols (standard and accelerated CXL) and mea-sured ex vivo. Morphological changes on the cornea after the two different protocolsare cross-examined to evaluate their treatment outcomes in terms of the cross-linkingeffectiveness and progression.Through this study, JMT is shown to have great potential to monitor anddiagnose many different ocular diseases non-invasively.iiiPrefaceChapter 3. A version of these materials have been published in the following papers:• M. J. Ju , Y.-J. Hong, S. Makita, Y. Lim, K. Kurokawa, L. Duan, M. Miura,S. Tang, and Y. Yasuno, ”Advanced multi-contrast Jones matrix optical co-herence tomography for Doppler and polarization sensitive imaging,” Opt.Express 21, 19412-19436 (2013).• M. J. Ju , Y.-Joo. Hong, Y. Lim, L. Duan, S. Makita, S. Tang, M. Miura, andY. Yasuno, ”Multi-functional optical coherence tomography for polarizationand Doppler investigation of posterior eye,” SPIE proc. (Photonics west 2013)8571-14 (2013).• M. J. Ju , Y. -J. Hong, S. Makita, M. Masahiro, S. Tang, and Y. Yasuno,”Simultaneous birefringence and flow imaging with Multifunctional Jones ma-trix optical coherence tomography,” Association for Research in Vision andOphthalmology (ARVO) 1611656 (2013).I was the lead investigator, responsible for all major areas of concept formation,data collection and analysis, as well as manuscript composition. Y. Lim and Y.-J.Hong were involved in the early stage of system implementation and contributed todata collection and analysis. M. Miura arranged patient experiment and providedivthe patient’s medical history. Y. Yasuno was the supervisory author on this projectand was involved throughout the project in concept formation and manuscript com-position.A version of Chapter 4 has been published in the following papers:• M. J. Ju , J. G. Shin, S. Hoshi, Y. Yasuno, B. H. Lee, S. Tang, and T. J.Eom, ”Three-dimensional volumetric human meibomian gland investigationusing polarization-sensitive optical coherence tomography,” J. Biomed. Opt.19, 030503 (2014).• M. J. Ju , J. G. Shin, D. K. Kasaragod, S. Hoshi, B. H. Lee, S. Tang,T. J. Eom, and Y. Yasuno, ”Volumetric Meibomian glands visualization usingOffice-based Multifunctional optical coherence tomography,” European Con-ferences on Biomedical Optics (ECBO) 1648552 (2013).I was the lead investigator, responsible for all major areas of concept formation,data collection and analysis, as well as manuscript composition. S. Hoshi arrangedpatient experiments and provided the patients’ medical history. T. J. Eom wasthe supervisory author on this project and was involved throughout the project inconcept formation and manuscript composition.The project located in Chapter 5 was conducted in the Biophotonics Lab-oratory at the University of British Columbia (Vancouver campus), and has beenreported in the following papers:• M. J. Ju , and S. Tang, Usage of polarization-sensitive optical coherencetomography for investigation of collagen cross-linking,” J. Biomed. Opt. 20,046001 (2015).v• M. J. Ju , and S. Tang, ”Investigation of corneal collagen cross-linking usingpolarization-sensitive optical coherence tomography,” SPIE proc. (Photonicswest 2015) 9307-18 (2015).I was the lead investigator, responsible for all major areas of concept formation, datacollection and analysis, as well as manuscript composition. S. Tang was the super-visory author on this project and was involved throughout the project in conceptformation and manuscript composition.The works described in Chapter 3 and Chapter 4 were conducted undersupervision of S. Tang, Y. Yasuno and T. J. Eom at the University of Tsukubain Japan. All protocols for the measurement in Chapter 3 and Chapter 4 wereapproved by the Institution Review Board of University of Tsukuba. The workshown in Chapter 5, was performed under supervision of S. Tang at the Universityof British Columbia in Canada.viTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of Abbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xviiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Optical coherence tomography . . . . . . . . . . . . . . . . . . . . . 11.2 OCT & ophthalmology . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 Developments of OCT technology . . . . . . . . . . . . . . . . . . . . 71.4 Functional extensions of OCT . . . . . . . . . . . . . . . . . . . . . . 111.4.1 Doppler OCT . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.4.2 Polarization-sensitive OCT . . . . . . . . . . . . . . . . . . . 14vii1.5 Objectives & contributions . . . . . . . . . . . . . . . . . . . . . . . 181.6 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202 Jones matrix tomography . . . . . . . . . . . . . . . . . . . . . . . 222.1 Principle of Jones matrix measurement . . . . . . . . . . . . . . . . . 232.2 Multiplexing of incident polarization states . . . . . . . . . . . . . . 262.3 Polarization-diversity detection . . . . . . . . . . . . . . . . . . . . . 312.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 Advanced Jones matrix tomography . . . . . . . . . . . . . . . . . 343.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.2.1 System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.2.1.1 System configuration . . . . . . . . . . . . . . . . . 353.2.1.2 Incident polarization multiplexing by polarization de-lay unit . . . . . . . . . . . . . . . . . . . . . . . . . 393.2.1.3 Polarization diversity detection . . . . . . . . . . . . 403.2.1.4 Phase calibration reflector . . . . . . . . . . . . . . 413.2.2 Post-processing . . . . . . . . . . . . . . . . . . . . . . . . . . 423.2.2.1 Monitoring and correction of spectral shift . . . . . 423.2.2.2 Phase retardation and relative attenuation calculation 453.2.2.3 Adaptive Jones matrix averaging . . . . . . . . . . . 453.2.2.4 Degree of polarization uniformity calculation . . . . 473.2.2.5 Coherent composition of matrix entries . . . . . . . 483.2.2.6 Doppler phase shift calculation . . . . . . . . . . . . 503.2.2.7 Sensitivity-enhanced scattering OCT . . . . . . . . 52viii3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.3.1 Jones matrix imaging of normal retina . . . . . . . . . . . . . 543.3.2 Geographic atrophy . . . . . . . . . . . . . . . . . . . . . . . 583.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613.4.1 Phase stability analysis . . . . . . . . . . . . . . . . . . . . . 613.4.2 Advantages of the phase stabilization process . . . . . . . . . 653.4.3 Global-phase-corrected and bulk-phase-corrected sensitivity-enhanced scattering OCT . . . . . . . . . . . . . . . . . . . . 663.4.4 Effect of practical factors in JMT measurement . . . . . . . . 693.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 704 Volumetric human meibomian gland investigation . . . . . . . . . 724.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 724.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744.2.1 System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 744.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 774.3.1 Meibomian gland segmentation . . . . . . . . . . . . . . . . . 774.3.2 3-D volumetric MG visualization . . . . . . . . . . . . . . . . 814.3.3 Acinar atrophy with advancing age . . . . . . . . . . . . . . . 824.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 834.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845 Corneal collagen cross-linking investigation . . . . . . . . . . . . . 855.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855.2 Materials & methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 885.2.1 System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88ix5.2.2 Specimen preparation . . . . . . . . . . . . . . . . . . . . . . 915.2.3 Measurement and post-processing protocol . . . . . . . . . . 925.2.4 Corneal thickness calculation . . . . . . . . . . . . . . . . . . 935.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 945.3.1 Cross-linking effect on cornea . . . . . . . . . . . . . . . . . . 945.3.2 Corneal thickness change . . . . . . . . . . . . . . . . . . . . 965.3.3 Time-series investigation of CXL effect . . . . . . . . . . . . . 995.3.4 Time-series investigation of ACXL effect . . . . . . . . . . . . 1015.3.5 Standard CXL vs. accelerated CXL (ACXL) . . . . . . . . . 1045.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1055.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1086 Conclusion & future directions . . . . . . . . . . . . . . . . . . . . 1096.1 Development of advanced Jones matrix tomography system and reti-nal imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1106.2 Human meibomian gland imaging . . . . . . . . . . . . . . . . . . . . 1116.3 Corneal imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1116.4 Future directions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115xList of TablesTable 1.1 Summary of various PS-OCT system designs . . . . . . . . 17Table 2.1 Summary of incident polarization multiplexing methods . . 30Table 3.1 Summary of advanced JMT specification. . . . . . . . . . . 53Table 4.1 Summary of EOM-based JMT specification. . . . . . . . . . 76Table 5.1 Summary of the specifications of the JMT for cornea imaging. 91xiList of FiguresFigure 1.1 Schematic of a typical Michelson interferometer based OCTsystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Figure 1.2 OCT signal and image formation process. . . . . . . . . . . 3Figure 1.3 Comparison of resolution and imaging depth for OCT andother tomographic modalities. . . . . . . . . . . . . . . . . . 4Figure 1.4 In vivo retina OCT imaging in the fovea region of healthyhuman eye with OCT. . . . . . . . . . . . . . . . . . . . . . 6Figure 1.5 In vivo anterior segment OCT image. . . . . . . . . . . . . . 7Figure 1.6 Time- and Fourier-domain OCT systems and interferencesignals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Figure 1.7 3D volume OCT and OCA images of human optic nerve head(ONH). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13Figure 1.8 Volumetric PS-OCT imaging in the human retina. . . . . . 15Figure 2.1 A conceptual scheme of polarization properties of Jones ma-trix tomography. . . . . . . . . . . . . . . . . . . . . . . . . 23Figure 2.2 Example of the optical scheme for polarization modulationalong the transversal scan. . . . . . . . . . . . . . . . . . . . 28Figure 2.3 Schematics of delay based input polarization multiplexingand demultiplexing. . . . . . . . . . . . . . . . . . . . . . . . 29xiiFigure 2.4 Polarization-diversity detection unit. . . . . . . . . . . . . . 31Figure 3.1 Schematic diagram of advanced JMT system. . . . . . . . . 36Figure 3.2 Diagram of the Fourier transformed interference signals. . . 40Figure 3.3 Jones matrix cross-sectional images of a normal macular. . . 55Figure 3.4 Jones matrix cross-sections of a normal ONH. . . . . . . . . 56Figure 3.5 En face projection images of an ONH. . . . . . . . . . . . . 57Figure 3.6 In vivo measurement images of a GA patient. . . . . . . . . 59Figure 3.7 Multi-contrast Jones matrix cross-section images of geographicatrophy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60Figure 3.8 Measured phase noise with (◦) and without () the spectralshift correction. . . . . . . . . . . . . . . . . . . . . . . . . . 62Figure 3.9 OCT images of the macular of a healthy volunteer. . . . . . 64Figure 3.10 The comparison between global- and bulk- phase-correctedsensitivity-enhanced scattering OCTs. . . . . . . . . . . . . 67Figure 4.1 Schematic diagram of EOM-based JMT system. . . . . . . . 74Figure 4.2 Meibography and Jones matrix tomography cross-sectionalimages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78Figure 4.3 Histograms of retardation and degree of polarization unifor-mity (DOPU). . . . . . . . . . . . . . . . . . . . . . . . . . 80Figure 4.4 En face MG segmentation result. . . . . . . . . . . . . . . . 81Figure 4.5 3D volume MG segmentation result. . . . . . . . . . . . . . 81Figure 4.6 Extracted MG volume structure images from the subjectswith different ages. . . . . . . . . . . . . . . . . . . . . . . . 83Figure 5.1 Schematic and photograph of JMT system for cornea imaging. 89xiiiFigure 5.2 Graph theory-based cornea segmentation procedure. . . . . 93Figure 5.3 Representative B-scan images of the bovine cornea. . . . . . 95Figure 5.4 Histograms of the phase retardation of control A (red bars)and CXL group (blue bars). . . . . . . . . . . . . . . . . . . 96Figure 5.5 Representative OCT intensity B-scan time-series images ofcontrol A (upper row), control B (middle row), and CXLgroup (bottom row) with time intervals of 1 hour. . . . . . . 97Figure 5.6 Corneal thickness change with time of three different mea-surement groups. . . . . . . . . . . . . . . . . . . . . . . . . 98Figure 5.7 Time-series measurement result of CXL Group. . . . . . . . 100Figure 5.8 Time-series measurement result of ACXL Group. . . . . . . 103Figure 5.9 Comparison of collagen cross-linking effect of CXL and ACXLprocedures. . . . . . . . . . . . . . . . . . . . . . . . . . . . 105xivList of AbbreviationsA-line Axial line of an image.ACXL Accelerated collagen cross-linking.AMD Age-related macular degeneration.ANSI American national standard institute.AOM Acousto-optic modulator.AS-OCT Anterior segment optical coherence tomography.BPD Balanced photo-detector.BS Non-polarizing beam splitter.CCD Charge-coupled device.CH choroid.CLSM Confocal laser scanning microscopy.CXL Collagen cross-linking.DOPU Degree of polarization uniformity.ELM External limiting membrane.EOM Electro-optic modulator.FA Fluorescence angiography.xvFAF Fundus auto-fluorescence.FPN Fixed-pattern noise.FWHM Full width at half maximum.GA Geographic atrophy.GCL ganglion cell layer.ICGA Indocyanine green angiography.INL inner nuclear layer.IPL internal plexiform layer.IS/OS inner and outer segments of the photoreceptor.ISO International organization for standardization.JMT Jones matrix tomography.LC Lamina cribrosa.MEMS Microelectromechanical systems.MG Meibomian gland.MGD Meibomian gland dysfunction.NIR Near-infrared.OCA Optical coherence angiography.OCE Optical coherence elastography.OCT Optical coherence tomography.ODT Optical Doppler tomography.ONH Optic nerve head.ONL Outer nuclear layer.xviOPL outer plexiform layer.OPLD Optical path length difference.PBS Polarization beam splitter.PD Polarization diversity.PS-OCT Polarization-sensitive optical coherence tomography.PT posterior tip of the outer segment.QWP Quarter wavelength plate.RNFL retinal nerve fibers layer.RPE retinal pigment epithelium.SD Standard deviation.SD-OCT Spectral-domain optical coherence tomography.SHG second harmonic generation.SNR Signal to noise ratio.SS-OCT Swept-source based optical coherence tomography.TPEF Two-photon excitation fluorescence.UV-A Ultraviolet-A : (315 nm – 400 nm wavelength).xviiAcknowledgementsFour years has passed since I joined Biophotonics group as a graduate student inthe University of British Columbia. I would like to thank all of the lab membersand ex-members for their help. Especially, Leo Pan, Tom Lai, and Mengzhe Shenhelp me a lot to get used to living in Vancouver and studying in UBC.I would like to express my gratitude to Prof. Shuo Tang for guding me tofocus on the research. She always trusts me, and at the same time encouragesme to learn how to do my own research and become independent. Without herkindness, instruction, and support, I was not able to continue my research. I finallyunderstood that I am lucky to have such a grateful mentor.I am grateful to Prof. Yoshiaki Yasuno, who is an outstanding engineer,researcher, and leader of Computational Optics Group (COG) in the Universityof Tsukuba. He gave me a chance to work in his group as visiting scholar for 10months. During the time, I had learned much more about polarization-sensitiveoptical coherence tomography and Doppler angiography systems. I also would liketo thank every COG members. Dr. Shuichi Makita, Dr. Kazuhiro Kurokawa, andDr. Youngjoo Hong gave me enormously helpful and practical advices. Withouttheir instructions, it would be very difficult to finalize my research project.I would like to thank all the committee members and external reviewer, Prof.xviiiCalum MacAulay, Prof. Alireza Nojeh, Prof. Jeff Young and Prof. Jennifer KehletBarton (University of Arizona). Thanks to their helpful advices and suggestions, Icould successfully finalize my dissertation.I would like to thank anonymous reviewers and excellent researcher some-where in the world for having a discussion, question, suggestion, and encouragement.They pointed out very accurately and suggested me a lot of valuable experiments.I thank my parent and parent-in-low. They encouraged me to go to graduateschool, and they gave me emotional support and financial assistance. I also give aspecial feeling of gratitude to my farther, Il-Chang Ju whose word encourages meto keep pursuing my path as a researcher.I also dedicate this dissertation to my friends, Myung-Hoo Park and Jung-Mi Kim who have supported our family and helped me to focus on my work. I willalways appreciate all they have done to me and my family.Finally, I would like to give a special thanks to my lovely and beautiful wife,Hyo-Jin Hwang who has never left my side and are very special means to me morethan anything in the world.Myeong Jin JuThe University of British Columbia(Vancouver)August 2015xixDedicated to Lord, Jesus Christ.xxChapter 1Introduction1.1 Optical coherence tomographyOptical coherence tomography (OCT) is an interferometric imaging modality thatprovides tomography of human tissues non-invasively and in vivo [1]. OCT is ascanning low-coherence interferometer utilizing coherence gating to resolve the depthstructure of a sample.Figure 1.1 shows a typical OCT system schematic. A low coherence lightsource is directed to a Michelson interferometer and is then split into referenceand sample beams. In the reference arm, the light exiting from the reference portof a beam splitter in the interferometer is reflected from a reference mirror, andredirected into the beam splitter. In the sample arm, the light exiting from thesample port of the beam splitter is focused on the sample after a lateral scanningdevice and an objective lens. The light backscattered from the sample, Esamp(t),is redirected to the beam splitter and combined with the returning reference light,Eref (t), in the beam splitter. The electric field at the output of the interferometer1Low- Coherence Sample Detector Reference Lateral  scanning Mirror Objective lens Collimation lens Eref (t) Esamp (t) Eref (t) + Esamp (t) Beam splitter Figure 1.1: Schematic of a typical Michelson interferometer based OCT the sum of the sample and reference electric fields, Eref (t) + Esamp(t) that isdetected by a detector. The detector measures the intensity of of the output, whichis proportional to the square of the output electric field:Iout (t) ∝ |Eref (t)|2 + |Esamp (t)|2 + 2Eref (t)Esamp (t) cos (2k∆L) , (1.1)where k is a wavenumber and ∆L is the path length difference between the sampleand reference arms of the interferometer. In Eq. 1.1, the factor of 2 in the cosineterm accounts for the round-trip path length of the sample beam. The electricsignals from the detector are then processed into A-scan (or A-line) representingthe depth-resolved reflectivity profile of the sample around the focal spot [1].The depth-resolved cross-sectional structure images are generated by scan-ning the probe beam transversely and performing multiple axial measurement ofecho time delay (axial scans), as shown in Fig. 1.2. In the case of one-dimensionaltransverse scanning (X), a two-dimensional cross-section image (XZ), which rep-2resents the optical backscattering in a cross-sectional plane through the tissue, isobtained. Three-dimensional, volumetric data sets can be generated by acquiringsequential cross-sectional images by scanning the incident optical beam in a rasterpattern (XY).Axial Position [depth] Backscattered Intensity Axial (Z) scan Axial (Z) & Transverse (X) scans Axial (Z) & Raster (XY) scans Figure 1.2: OCT signal and image formation process. OCT provides cross-sectionaland three-dimensional volumetric images by detecting the backscattered magnitudecorresponding echo time delay of light. Axial scans measure the backscatteringversus depth. Cross-sectional images are generated by performing a series of axialscans at different transverse positions. Three-dimensional volume image can beacquired from sequential cross-sectional images by raster scanning.Among different medical tomography modalities, OCT is characterized bythe following properties. First, OCT is non-invasive since OCT uses a low powernear-infrared (NIR) light as a probe which keeps the sample remaining free of pho-tochemical and photothermal damage. Second, OCT has higher resolution (a mi-crometer resolution of around 2 to 15 µm) than other clinical tomographic methodssuch as X-ray computed tomography, magnetic resonance imaging, and ultrasoundtomography [2]. Third, the measurement speed of OCT is fast. The first generationof OCT, known as time-domain OCT (TD-OCT), had an imaging speed betweenseveral hundreds to several thousands of A-lines per second [2]. A more recent3Image penetration [mm] Resolution [µm] 0.1 1 10 100 1 10 100 1000 Optical coherence tomography Ultrasound High frequency Standard clinical Confocal microscopy Figure 1.3: Comparison of resolution and imaging depth for OCT and other tomo-graphic modalities.OCT method, Fourier-domain OCT (FD-OCT) provides an even faster speed ofaround several hundred-thousand A-lines per second [3,4]. This high speed enables3-D investigation of organs in vivo within a realistic measurement time. Anothercharacteristic property of OCT is its measurement depth or penetration depth. Asmentioned, OCT uses light as probe beam which is relatively highly scattered bythe sample to be measured compared to ultrasound and X-ray. This high scatteringunfortunately limits the penetration depth of OCT to within a few millimeters. Asshown in Fig. 1.3, OCT fills a gap between ultrasound and microscopy in termsof imaging resolution and depth. The resolution of clinical ultrasound imaging isaround 0.1 – 1 mm. Since sound waves at the standard wave frequencies (3 – 40MHz) has relatively low absorption in biological tissue, it is possible to image deepin the body. Although high resolution of 15 – 20 µm has been achieved with highultrasound frequencies (∼ 100 MHz), these high frequencies have strong attenuation4in the biological tissue so that imaging depths are limited to only a few millime-ters. Confocal microscopy, one of the optical microscopic imaging techniques, hasextremely high resolution of 1 µm. However, its imaging depth range is limited to afew hundred micrometers. Considering all of these OCT properties, it is clear thatOCT is not an all-purpose tomography modality. However, there are some organsthat are extremely suitable for OCT such as the eye.1.2 OCT & ophthalmologyOCT has been utilized in a variety of clinical fields such as ophthalmology [5–10],dermatology [11–18], dentistry [19–22], gastroenterology [23–27], and cardiology [28–33]. Among these clinical fields, ophthalmology is especially suited to OCT. Theeye itself is an optical instrument and perfect organ for investigation by opticalmodalities. Because the eye is an imaging system that images an object onto theretina, it is also convenient to build an optical system that images the retina ontoan arbitrary imaging plane using the eye optics.Another important characteristic of the eye is transparency. As shown in Fig.1.3, OCT penetration is limited to a few millimeters, mainly because of scatteringin tissue. However, the scattering within the optical media of the eye including thecornea, aqueous humor (that fills the anterior eye chamber), crystalline lens, andvitreous is negligible. Hence, several-millimeter penetration of retinal OCT imagingis defined not from the surface of the eye but from the surface of the retina, locatedaround 24 mm under the eye surface. Because the thickness of the retina is about afew hundred micrometers, the limited penetration of OCT is not a serious issue forretinal imaging.The direction of the tomographic cross-sectional imaging also enhances the5value of OCT. While most other eye imaging modalities such as ophthalmoscope,color fundus photography, and angiographies are en face imaging modalities, OCTis the only one that is an in vivo modality that provides a depth-oriented cross-sectional imaging of the retina. Because the retina has a fine multi-layered structureand its destruction is highly associated with eye diseases, the in vivo cross-sectionaltomography provided by OCT is extremely important for ophthalmic diagnosis.Figure 1.4 depicts cross-sectional and volumetric retina OCT images in the fovearegion of a healthy human eye as an example.(a) (b) (c) (d) Figure 1.4: In vivo retina OCT imaging in the fovea region of healthy human eyewith OCT: (a) Cross-sectional tomography image; (b) 3D rendering of the volumet-ric image; (c) En face projection image; (d) OCT fundus tomogram near the centerof fovea.The non-invasiveness of OCT is also particularly important in ophthalmology.This is because the eye is one of a few organs that we cannot biopsy. Since allportions of the retina are associated with visual function, it is impossible to excise6even a small portion of its tissue for diagnosis purposes. Considering these propertiesof the eye and OCT, it is natural to conclude that the eye is a perfect organ forinvestigation by OCT. It is also natural that the eye was selected as the first targetfor OCT.(a) (b) Figure 1.5: In vivo anterior segment OCT image. (a) Cross-sectional tomographyimage; (b) 3D rendering of the volume image.It should be noted that the application of OCT in ophthalmology is notlimited to retina. OCT can also be used to image the anterior segment that is thefront of the eyeball. Figure 1.5 shows an example of the anterior chamber OCTimage from which the anterior angle and detailed cross-sectional corneal structureare observed.1.3 Developments of OCT technologyMeasurement speed of OCT is particularly important for in vivo eye imaging becauseof the involuntary eye motion. Therefore, the OCT measurement speed needs to7be fast enough to make eye motion negligible. Another important requirement forophthalmic OCT is high sensitivity. Because the reflectivity of retina can be as lowas 10−5 – 10−6, a high system sensitivity and the corresponding high signal-to-noiseratio (SNR) are required. In general, the SNR of OCT is roughly proportionalto the measurement time and optical power of the probe beam. Since the OCTmeasurement time should be short for avoiding the eye motion, it is not an optionto increase measurement time for enhancing the SNR. Increasing the probe poweris also not a practical solution. Because the eye is a photosensitive organ, it isalso very sensitive to photodamage. Even though OCT uses NIR light as the probebeam, the probe beam power for ophthalmic imaging is strictly limited by safetystandards such as ANSI [34] and ISO [35]. For example, the maximum allowableprobe power for retinal OCT is around 700 µW for a probe wavelength of 840 nmand around 1.2 – 1.7 mW for 1060 nm probe wavelength.The first generation of OCT, TD-OCT (Fig. 1.6(a)), is a relatively slowimaging modality. In TD-OCT, the optical path-length in reference arm is translatedlongitudinally in time for depth scanning. Because of the property of low coherenceinterferometry, interference is only occurred when the path-length difference betweenthe reference and sample arms lies within the coherence length of the light source.Here, the coherence length equivalent to the theoretical axial resolution of OCT isdescribed bylc =2 ln (2)piλ2c∆λ, (1.2)where λc and ∆λ are the center wavelength and wavelength bandwidth of the lightsource, respectively. As shown in Fig. 1.6(d), the envelope of the modulation causedby the interference changes as the path length difference is varied, in which the peakposition of the envelope corresponds to the path-length matching. In practice, the8(a) TD-OCT Low-Coherence Source Fiber Coupler Lateral Beam Scanning Sample Photodiode detector Mirror Axial scanning (b) SD-OCT (c) SS-OCT Line CCD Lens Grating Low-Coherence Source Fiber Coupler Lateral Beam Scanning Mirror Sample Swept Source Fiber Coupler Lateral Beam Scanning Photodiode detector Mirror Sample FD-OCT Interference signal in TD vs. FD-OCT (d) Interference signal in TD-OCT (e) Interference signal in FD-OCT I z FWHM I λ I λ I λ Fourier  Transform I z FWHM Figure 1.6: Time- and Fourier domain OCT systems and interference signals. (a)TD-OCT; (b) SD-OCT; (c) SS-OCT; (d)–(e) interference signals in TD-OCT andFD-OCT, respectively.axial resolution of TD-OCT system is defined as the full width at half maximum(FWHM) of the envelope. In the case of TD-OCT, two scannings are required fora single cross-sectional imaging, and a third scanning is necessary for construct-ing volumetric tomography. This multi-dimensional mechanical scanning limits themeasurement speed, and causes poor sensitivity as well.These limitations have driven researchers to develop a new OCT technologynamed as FD-OCT. There are two representative FD-OCT techniques: spectral-domain OCT (SD-OCT; Fig. 1.6(b)) and swept-source based OCT (SS-OCT; Fig.1.6(c)). In SD-OCT, the interference fringe is spectrally decomposed by a diffractiongrating and then detected by a charge-coupled device (CCD) array. In SS-OCT, by9means of a wavelength-swept laser source, interference fringe is mapped to the timecorresponding to each scanned wavelength and is measured with a photodetector asa function of time. In both SD-OCT and SS-OCT, each data point of the spectralfringe corresponds to a spatial frequency component of the depth profile of thesample. Therefore, the axial profile of an image (A-line) is obtained by performinga discrete Fourier transform of the acquired spectral encoded interference fringe.Similar to TD-OCT, the axial resolution of FD-OCT is also given by measuring theFWHM of the interference peak after the Fourier transform (shown in Fig. 1.6(e)).FD-OCT first attracted the attention because of its fast measurement speed.Soon it was recognized that it also had a higher sensitivity than TD-OCT [36–38].This higher sensitivity can be seen as a result of the higher throughput of the probebeam to the image formation. In TD-OCT, the reference and probe beams generatean interference signal only when the optical path length difference (OPLD) is lessthan the coherence length. Although this is the origin of the depth resolution ofTD-OCT, it also means that the probe beam that is outside of the coherence lengthcannot contribute to image formation. On the other hand, FD-OCT is consideredto be a bundle of monochromatic interferometers. As an example, in the case of SD-OCT, the signal output at each wavelength channel of the spectrometer providesmonochromatic interference between the reference and probe beams. Hence, thebeams generate an interference signal even when the OPLD is several millimeterslong. The broadband interference, i.e., low-coherence interference, which providesthe depth resolution, is then numerically performed later in a computer. Becauseof this interference scheme, almost all portions of the probe beam power contributeto image formation.Because of these two major advantages of FD-OCT, i.e., high speed and high10sensitivity, it has quickly become the standard for tomographic investigation of theeye. Especially, SS-OCT at 1 µm wavelength becomes a common option for posterioreye investigation these days because of the lower absorption of melanin [39], longimaging depth (due to the short instantaneous line-width) [3], and high imagingspeed [4, 40,41].1.4 Functional extensions of OCTOne of the greatest challenges for extending clinical applications of OCT is to findmore contrast mechanisms for providing physiological information beyond the mor-phological structure obtained by general OCT. Therefore, several functional OCTshave been developed, including Doppler OCT and polarization-sensitive OCT.1.4.1 Doppler OCTDoppler OCT which is also denoted as optical Doppler tomography (ODT) is oneof the extensions of OCT, and is actively applied for the ophthalmic investigation[42–45]. Doppler OCT has been mainly utilized in blood flow measurement [46,47].Doppler OCT combines the Doppler principle with OCT to measure the Dopplershift of probe beam of OCT and to enable depth-resolved cross-sectional flow imag-ing of eye in vivo.In general, Doppler frequency shift (∆fDoppler) of a moving scatter is de-scribed as∆fDoppler = 2vaxial/λc, (1.3)where vaxial is the axial velocity of the moving scatters parallel to the direction ofthe incident light with a center wavelength of λc. In order to obtain the Doppler11frequency shift using OCT, several scans of complex OCT signals are obtained at thesame region of interest, and the phase-differences among the complex OCT signalsare calculated. Since the complex OCT signals are recorded separately at fixed timeintervals ∆t, the axial velocity of moving scatters for each coherent volume is nowdescribed asvaxial,i =λc4npiT∆φi, (1.4)where ∆φi is given by ∆φi(z,∆t) = Arg[Γi(z, t)Γ∗i+1(z, t+ ∆t)]. Here, Γi(z, t) isthe i-th complex OCT signal given time of t and at a depth of z. The sensitivityof the Doppler flow measurment is mainly limited by the time interval ∆t, Dopplerangle, and phase noise. Here, the time interval can be altered by modifying thescanning protocols [48–51] or implementing dual-beam scan techniques [52,53].Among several variations of Doppler OCT, phase-resolved Fourier domainDoppler OCT [42, 43] has become the most popular Doppler OCT technique be-cause of the recent success of FD-OCT. In terms of the vasculature mapping, OCT-based angiography named as optical coherence angiography (OCA) [54] has beendeveloped as an alternative to the standard ophthalmic angiography such as fluo-rescein angiography (FA) and indocyanine green angiography (ICGA), and utilizedfor visualizing retinal and choroidal vasculatures as shown in Fig. 1.7.12(a) (b) (c) Low High Figure 1.7: 3D volume OCT and OCA images of human optic nerve head (ONH).(a) 3D volume-rendered OCT image; (b) En face projection of OCT image of humanONH; (c) En face projection of retinal and choroidal vasculature.131.4.2 Polarization-sensitive OCTPolarization-sensitive OCT (PS-OCT) is another representative extension of theOCT techniques. PS-OCT is capable of measuring the polarization properties ofbiological tissues and visualizing their properties with different contrast mechanismsas shown in Fig. 1.8. It is known that several types of biological tissues possessmicroscopic fibrous structures such as collagen fibers and nerve fibers. Since thesemicroscopic structures are smaller than the resolution of OCT, standard OCT is notcapable of assessing them. However, the microscopic structures are known to possessbirefringence, and PS-OCT is capable of assessing these microscopic tissue propertiesby measuring its polarization property. PS-OCT has been also applied to severalclinical investigations in ophthalmology such as corneal integrity [55, 56], retinaldisorders including macular diseases [57–59], glaucoma surgery [60], quantificationof the retinal nerve fiber layer [61,62,64–68] and choroidal thickness [69,70], contrastenhancement of fibrous tissue [58, 60, 71–73] and retinal pigment epithelium (RPE)[57,74].PS-OCT systems are classified into several sub-types. One of the most widelyutilized methods is the circular-polarization-based method (also known as Hee-Hitzenberger method), which was first demonstrated by Hee et al. [75] and laterinvestigated by Hizenberger and his associates [55, 57, 72]. The Hee-Hitzenbergermethod determines the phase-retardation and the optics-axis orientation of a sam-ple by using a circularly polarized probe beam. Since this method uses only theintensity of OCT and does not use its phase to determine the phase-retardation,this method is robust and stable. On the other hand, since the probe beam shouldbe circularly polarized, the interferometer should be implemented by bulk optics orbuilt with a polarization maintaining fiber. Another property of this method is its14(a) (b) (c) (d) Low High 0 π Figure 1.8: Volumetric PS-OCT imaging in the human retina. (a) 3D renderingof the volumetric OCT image of human macular; (b) Volumetric phase retardationimage corresponding to (a); (c) 3D rendering of the volumetric OCT image of humanoptic nerve head; (b) Volumetric phase retardation image corresponding to (c).15insensitivity to diattenuation. Here, diattenuation is the property of a material inwhich the transmittance depends on the incident polarization states of light.Stokes parameter-based PS-OCT has also been widely investigated [76]. Thismethod is capable of determining the phase-retardation and optic-axis orientationof a sample. As with the Hee-Hitzenberger method, the Stokes method is also notcapable of measuring the diattenuation of the sample. One of the advantages ofthis method is its ability to be implemented with single-mode fiber, which is widelyutilized for OCT [68,77,78]. The optic-axis orientation measured by this method isan absolute orientation if the system is implemented with a bulk interferometer ora relative axis orientation if it is implemented with a flexible single-mode fiber. Onedrawback of this method is its requirement for an active optical device that altersthe polarization state of the probe beam, typically an electro-optic modulator.Mueller matrix-based PS-OCT has been also demonstrated [79, 80]. Thismethod determines the Mueller matrix of a sample, and hence it provides all of thepolarization properties of the sample including the phase retardation, axis orien-tation, and the diattenuation except depolarization. The depolarization cannot bemeasured because of a fundamental limitation of a coherent imaging modality suchas OCT [81]. Mueller matrix PS-OCT uses only the intensity of OCT signal, andhence it could be robust in principle. However this method requires relatively largenumbers of measurements, so that the measurement time is relatively long. Thislong measurement time would deteriorate the accuracy of the polarization propertiesin an in vivo measurement.Among the several sub-types of PS-OCT, Jones-matrix-based OCT, or Jonesmatrix tomography (JMT) in short, is a method that determines the polarizationproperties of a sample by measuring the double-pass Jones matrix of the sample16or its similar matrix [82–85]. This method can be implemented both with a bulkinterferometer or a single-mode-fiber based interferometer. With the bulk interfer-ometer, this method can provide a round-trip Jones matrix of the sample, directly.On the other hand, with the single-mode fiber interferometer, a similar matrix of theround-trip Jones matrix of the sample is obtained. From the round-trip Jones ma-trix or its similar matrix, the phase retardation, the diattenuation, and the relativeoptic-axis orientation could be obtained.Table 1.1 shows the summary of different PS-OCT configurations and theircharacteristics.Table 1.1: Summary of various PS-OCT system designsTypeIncidentpolarizationMeasurementprotocolRequiredsignalsPolarizationcontrastsHee-HitzenbergerSingle circularpolarizationSinglemeasurementIntensityRetardationOrientationStokesparameterSingle circularpolarizationSinglemeasurementIntensity+ PhaseRetardationOrientationMuellermatrixTwo or morelinearpolarizationsMultiplemeasurementsIntensityRetardationOrientationDiattenuationJonesmatrixTwolinearpolarizationsSinglemeasurementIntensity+ PhaseRetardationOrientationDiattenuationNote: The systems requiring circular polarization incident should be implemented based on eitherbulk optic or polarization maintaining fiber optic components.171.5 Objectives & contributionsRecent technology advances of wavelength sweeping laser have led to a significantpopularity increase in SS-OCT. As a result, several swept-source based JMT sys-tems have been published and utilized in ophthalmology [82, 83, 85]. In addition,because of the advantages of optical fibers, such as convenient system alignment andhandling, many JMT systems have been developed with fiber optics. However, thefiber causes a transformation of the polarization state due to its birefringence, whichcauses alternation into the input polarization state on the sample. Therefore, twodifferent input polarization states with known relation are typically required. Thisrequirement could be achieved by either sequential probing with two polarizationstates or multiplexing the two polarization states in one simultaneous axial scanacquisition. The former approach involves two or more sequential measurements,which results in slow acquisition rate and high phase noise. In the multiplexing case,for simultaneous detection of the signal from two incident polarization states, theimaging range is significantly reduced because of the limited detection bandwidth.Since high measurement speed is crucial for clinical usage of OCT in ophthalmologyas described in Sect. 1.3, most of the current JMT systems have been built with themultiplexing scheme even with sacrifice of imaging range. The multiplexing of theincident polarization state is usually achieved with an active modulation device suchas electro-optic modulator (EOM) or acousto-optic modulator (AOM), where properencoding of the polarization states is important. Here, these polarization modula-tors give arise to high cost and complexity in handling the system with sophisticatedsynchronization controls.The main objectives of this thesis are to implement a JMT system with highstability, to develop novel JMT algorithms for the enhancement of JMT imaging18capability, and to develop new clinical applications of JMT in the field of ophthal-mology. The following contributions have been made in the course of achieving theobjectives:I implemented a JMT system for multi-functional ophthalmic imaging. Ialso designed a phase compensation unit based on the general characteristic of apolarization optical component, and integrated it with the JMT system. Fromthe phase compensation unit, a static calibration signal was detected and used forestimating the spectral shift caused by jittering of wavelength scanning of the sweptsource.I devised a phase stabilization process that is based on the cross-correlationof the calibration signal. A coherent composition algorithm was also developed inorder to overcome the inherent sensitivity disadvantage of Jones matrix OCT imagecompared to conventional scattering OCT image. Based on the relationship betweenJones vector and Stokes parameters, the degree of polarization uniformity (DOPU)quantity was extracted from the Jones matrix measurement. I also demonstratedthe robustness and the effectiveness of the Jones matrix measurement.Retinas of healthy and pathological subjects were measured in vivo using theJMT system, which demonstrated the functionality and clinical utility of the JMTsystem for posterior eye imaging. In vivo human eyelid imaging was also performedas a novel clinical application of JMT. For the first time, UV-A/riboflavin inducedcorneal collagen cross-linking (CXL) treatment effect on cornea was also investigatedwith the JMT system.191.6 OutlineIn Chapter 2, the general principle of Jones matrix measurement and typical imple-mentation approaches of JMT are described.In Chapter 3, an advance version of JMT system is introduced. This JMT is acombination of Doppler and PS-OCT, and enables simultaneously detection of tissuestructure, tissue birefringence properties and flow in the tissue. Especially, thisadvanced JMT system is capable to measure full Jones matrix of the sample withoutany active modulation device that is typically applied for polarization modulation[82,83]. With advanced signal processing, the phase stability of the OCT detectionis enhanced, and high-sensitive Doppler imaging is performed. Owing to the highimage quality and stability, the system is capable of investigating clinical subject.In Chapter 4, an application of JMT system is demonstrated, where three-dimensional volumetric meibomian glands (MGs) visualization is presented. Fromthe polarization contrasts provided by JMT such as phase retardation and degreeof polarization uniformity (DOPU), distinctive features of the MGs and adjacenttissues are investigated. Segmentation of the conjunctiva layer located above theMGs is achieved with a DOPU threshold. Furthermore, investigation of the MGsvariation with advancing age is also demonstrated by in vivo measurements of severalsubjects with different ages. Based on this investigation result, we introduce novelclinical utility of JMT for diagnosis of MG-related dry eye disease.In Chapter 5, another application of JMT system is introduced, where theclinical outcome of riboflavin/UV-A induced collagen cross-linking treatment (CXL)is evaluated. Ex vivo measurement of fresh bovine eye is performed using JMT. Fromcomparative study of the cross-linking effect with control groups, it is revealed thatthe main cause of corneal thinning followed by CXL is dehydration effect from20riboflavin solution. In addition, the effective cross-linking region is qualitativelydifferentiated by multi-contrast images created by JMT such as scattering, phaseretardation, and DOPU images. Particularly, the effective cross-linking depth isestimated by applying empirical DOPU threshold. Two different CXL protocols(standard and accelerated CXL) are applied and their treatment outcomes are cross-examined in terms of the treatment effectiveness and progression.Chapter 6 concludes this dissertation.21Chapter 2Jones matrix tomographyThe general principles of Jones matrix measurement and implementation conceptsof various conventional JMT systems are provided in this chapter.The primary objective of Jones matrix tomography (JMT) is to obtain the to-mographies of the round-trip phase retardation, diattenuation, relative optic-axisorientation, and back-scattering intensity of a sample. To obtain these polarizationparameters, JMT determines the Jones matrix or its similar matrix at each locationin the sample. Since a matrix and its similar matrix have the same eigenvalues, thephase retardation, namely the phase difference between two eigenvalues, are derivedfrom the similar matrix. The axis orientation is determined as the direction of theeigenvectors of the round-trip Jones matrix of the sample. Here it is noted that theabsolute axis orientation cannot be obtained from the similar matrix because a ma-trix and its similar matrix do not always possess the identical eigenvectors. However,JMT still provides a relative optic-axis orientation from the similar matrix.22( )out zE( ) ( )1 2( ) ( )out outE z E z ≡   ( )s z′J( )Ts z′JFigure 2.1: A conceptual scheme of polarization properties of Jones matrix tomog-raphy.2.1 Principle of Jones matrix measurementJMT determines a Jones matrix by measuring Jones vectors of two back-scatteredprobe beams. More precisely, by employing two incident polarization states andpolarization diversity (PD) detection, JMT determines the polarization property ofa sample through Jones matrix analysis [85, 86]. To mathematically describe thisprocess, a simplified model of Jones matrix measurement done by JMT is introducedand its schematic is shown in Fig. 2.1.In Fig. 2.1, Jin and Jout represent Jones matrices of the illumination andcollection optics that may include the optical fiber, and J′s(z) is a single-trip Jonesmatrix of a sample. By denoting the Jones vector of one of the incident polariza-tion states as ~E(1)in =[H(1)in V(1)in]T(H and V represent horizontal and verticalcomponents of polarization, respectively) and the corresponding OCT signals mea-sured by the two detectors in the PD detection unit as E(1)outA(z), E(1)outB(z), and~E(1)out(z) ≡[E(1)outA(z) E(1)outB(z)]T, the relationship between ~E(1)in and ~E(1)out(z) be-comes23~E(1)out(z) = χ Jall(z) ~E(1)in (2.1)where Jall(z) is the Jones matrix representing the overall polarization property in-cluding the Jones matrix of JMT system and the depth-resolved round trip Jonesmatrix of the sample. Here, χ is a general transform matrix which transforms thehorizontal and vertical components of the Jones vector at the PD detection unit tothe two arbitrary polarization components detected by the two detectors in the PDdetection unit. In short, χ represents the imperfection of the PD detection. Thisincludes the imbalance in the reference power of OCT detection, the gain imbalanceof the photo-detectors, and the cross-talk between the two detectors. Similarly,the other incident polarization component and its corresponding OCT signals arerelated as~E(2)out(z) = χ Jall(z) ~E(2)in . (2.2)Note that, in a polarization multiplexing scheme based JMT, the OCT signalscorresponding to ~E(1)in (z) and ~E(2)in (z) appear at two different frequencies and/ordepths. Here, to avoid confusion, we define the variable z as the relative depth fromeach zero-delay point of each incident polarization component. Namely, equal valuesof z represent the same depth location in the sample.Equations (2.1) and (2.2) can be combined asEout(z) = χ Jall(z) Ein (2.3)where Ein ≡[H(1)in H(2)in ; V(1)in V(2)in]and Eout(z) is a matrix of measured OCTsignals24Eout(z) =E(1)outA(z) E(2)outA(z)E(1)outB(z) E(2)outB(z). (2.4)Note that, in Eq. (2.3), Eout(z) is a measured value, while Ein is a predefined butnot accurately known matrix.By considering the general configuration of JMT, Jall(z) can be decomposedinto three components asJall(z) = Jout Js(z) Jin (2.5)where Jin is the Jones matrix from the polarization delay unit to the sample surface,Jout is from the sample surface to the PD detection unit, and Js(z) = J′s(z)TJ′s(z)is the round trip Jones matrix of the sample with that of the single trip being J′s(z).The purpose of the Jones matrix measurement is to determine the polariza-tion properties of Js through its eigenvalues. To obtain the eigenvalues, a similarmatrix of Js is obtained by the following protocol. First, the surface of the sam-ple is segmented, and Eout is obtained at the sample surface as Eout(z0), where z0represents the depth position of the surface. Then, a similar matrix of the Js(z) ateach location in the sample is obtained asEout(z) Eout(z0)−1 = χ Jout Js(z) Jin Ein (χ Jout Jin Ein )−1= χ Jout Js(z) Jin Ein E−1in J−1in J−1out χ−1= χ Jout Js(z) J−1out χ−1(2.6)25This equation indicates that using the two measured matrices Eout(z) and Eout(z0),we can define the similar matrix of the round-trip Jones matrix of the sampleand hence its eigenvalues. Here, Eout(z0) (= χ Jout Jin Ein ) represents the system-oriented birefringence that can be cancelled after multiplying Eout(z) with the in-verse of Eout(z0). It is noteworthy that JMT provides the similar matrices regardlessof the combination of the input polarization states, except when the two states areparallel to each other [86].2.2 Multiplexing of incident polarization statesIn Jones matrix measurement, two polarization states are multiplexed by severalmeans including time-division multiplexing [85], polarization modulation along thetransversal scan (mainly for SD-OCT) [82] or along the wavelength scan (only forSS-OCT) [83], frequency shifting [87], and delay-based multiplexing [88,89].In the time-division multiplexing scheme [85], two polarization states of theincident beam are sequentially switched for A-line by A-line. This method is themost straightforward implementation of incident polarization multiplexing. Becauseof the sequential measurements with different polarization states, however, it is notsuitable for high-speed measurement.In the multiplexing scheme based on polarization modulation along the trans-verse scan, the phase of a polarization component of incident light is modulated bya sinusoidal function along the transversal scanning direction. By this modulation,two incident beams with two polarization states are multiplexed such that one ismodulated in phase and the other is not. After OCT detection, these two mul-tiplexed components are demultiplexed by spatial frequency filtering based on anumerical Fourier transform along the transversal direction [82]. The modulation is26typically performed by an electro-optic modulator (EOM) as shown in Fig. 2.2. TheEOM is configured to modulate the relative phase of the polarization component ofa probe beam that is oriented to one of the axes of the modulator (so denoted asEOM axis) in respect to the phase of the OCT reference beam, while the relativephase of the polarization component oriented to the other axis (non-EOM axis) isnot modulated. The frequency of the modulation is defined with respect to theA-line frequency of the OCT detection so that it is several fractions of the A-linefrequency. In this transversal modulation scheme, the probe locations on the samplecorresponding to the two incident polarizations are slightly displaced to each otherbecause the EOM alters the incident polarization states for each A-line. This smalldisplacement results in a structural decorrelation between the two OCT signals asso-ciated with the two incident polarization states and it finally degrades the sensitivityof the Jones matrix measurement. In order to minimize the sensitivity degradation,the A-line can be densely scanned in space so that the separation between the adja-cent A-lines is less than a fraction of the transversal optical resolution. As a result,however, the wide-range and high-speed measurement are in contradiction to eachother with the transversal modulation scheme.A variation of the above mentioned multiplexing method is the polarizationmodulation along the wavelength scan. In particular, this multiplexing scheme isonly applicable to SS-OCT. The phase modulation is performed by the EOM witha similar optical scheme to that in Fig. 2.2, but along the wavelength scan. Similarto the modulation along the transversal scan, the two incident polarization statesare demultiplexed by frequency filtering but based on a numerical Fourier trans-form along the wavelength scan [83]. Unlikely to the above mentioned transversalmodulation method, in this wavelength scan oriented modulation scheme, the OCT27SLD EOM LP PC PC PC PC LP DCP M G LSC LSC PBS Figure 2.2: Example of the optical scheme for polarization modulation along thetransversal scan. SLD is a superluminescent diode light source, PCs are polarizationcontrollers, LPs are linear polarizers, DCP is dispersion compensation prism, ND isneutral density filter, EOM is an electro-optic modulator. This example system isequipped with a polarization diversity spectrometer composed of a grating (G), apolarization beam splitter (PBS), and two line scan CCD cameras.signals associated with two incident polarization states are obtained at exactly thesame time and location. Hence the structural decorrelation does not occur. Thisproperty makes the wavelength oriented modulation scheme suitable for high-speedand wide-range measurements.There is also unique multiplexing method for SS-OCT named as frequencyshifting-based multiplexing [87]. In this scheme, the frequencies of the two incidentbeams with orthogonal polarization states are frequency-shifted by two frequencyshifter with different shifting frequencies. Namely, two incident polarization statesare multiplexed in its frequency. The multiplexed incident beams would have dif-ferent carrier frequency after interference with a reference beam, and these beamsare demultiplexed by numerical Fourier transform. To avoid unwanted interference,this scheme is equipped with an unpolarizer, which is a polarization dependent de-lay unit generating a path length difference more than the instantaneous coherencelength of the light source between the two polarization states.28PBS PBS DP DP PBS Light In Light Out (a) (b) Light In Light Out (1) EIn (2) EIn DC (1) EIn (2) EIn * OCT Intensity Depth (z) * (c) QWP QWP M M Figure 2.3: Schematics of delay based input polarization multiplexing and demul-tiplexing. (a) and (b) the optical schemes for delay based input polarization mul-tiplexing. PBSs are polarization beam splitter, DPs are Dove prisms, QWPs arequarter wavelength plates and Ms are mirrors. (c) A schematic figure of demulti-plexing two incident polarization components. The OCT images associated withtwo incident polarization states appear at different depths.Most recently developed multiplexing scheme is the delay-based incident po-larization multiplexing. If the coherence length of the light source in SS-OCT orspectral resolution of the spectrometer in SD-OCT is large and hence the depth mea-surement range of the OCT is sufficiently long, the two incident polarizations canalso be multiplexed at two different depths. This polarization dependent spectraldelay can be implemented, for example, by two polarization beam splitters (PBSs)and two Dove prisms as depicted in Fig. 2.3(a) [88] or by the combination of a PBS29and two quarter wave plates (QWPs) as depicted in Fig. 2.3(b) [89]. Since theOCT images associated with the two incident polarization states appear at differentdepths as depicted in Fig. 2.3(c), it can be easily demultiplexed by cropping thespecific portions of the OCT images. Since this scheme does not require any activeoptical components, such as the EOM, it is stable and the sequential control of thistype of JMT would be simpler than those of using polarization modulation schemes.Table 2.1 shows the summary of different incident polarization multiplexingmethods.Table 2.1: Summary of incident polarization multiplexing methodsTypeTimedivisionPolarizationmodulationFrequencyshiftingPath-lengthdelayMultiplexingdeviceElectro-optic orAcousto-opticmodulatorsElectro-optic orAcousto-opticmodulatorsPair ofFrequency shiftersOptical delay unitDemultiplexingcomplexitySimple Complex Complex SimpleUsage ofactive deviceYes Yes Yes NoMeasurementspeed(restiction)Slow(Modulatorfrequency)Moderate(Modulatorfrequency)Moderate(Shifterfrequency)Fast- CCD camera- sweeping rateMeasurabledepth rangeFull range Full range Half of full range Half of full range302.3 Polarization-diversity detectionIn JMT, the Jones vector of the back-scattered probe beam after the collection op-tics, i.e. ~E(1)out(z) and ~E(2)out(z) of Fig. 2.1, is measured by a polarization-diversity(PD) detection unit. In the PD detection unit, two orthogonal polarization compo-nents, typically horizontal and vertical, of the probe and reference beams are splitby a PBS or a Wollaston prism and detected by two detectors, except for somesophisticated PD detection units that use a single detector.(a) Probe  + Reference LSC L G LSC L G (c) Probe  + Reference LSC WP L G (b) Probe  + Reference LSC LSC LP L G PBS (d) Probe Reference BS PBS PBS LP BPD BPD V H Figure 2.4: Polarization-diversity detection unit. (a)-(c) examples of polarization-diversity spectrometer. (d) polarization-diversity balanced detection unit. L: lenses,G: grating, LS: line sensors grating, PBS: polarization beam splitter, LP: linear po-larizer, WP: Wollaston prism, BS: non-polarization beam splitter, and BPD: bal-anced photo-detector.31A PD spectrometer is a detection unit specifically utilized for SD-OCT. Al-though there are some variations, all of them split the two orthogonal polarizationcomponents after combining the reference and probe beams in an interferometer.Figure 2.4(a) is a straightforward implementation of PD spectrometer, which wasoriginally developed for a Hee-Hitzenberger type PS-OCT [72]. In this scheme, theprobe and reference beams are combined in an OCT interferometer and then in-troduced into the PD spectrometer unit. In this spectrometer unit, the horizontaland vertical polarization components of the probe beams are split by a fiber PBSand detected by two independent spectrometers. This PD spectrometer is a verystraightforward implementation and is hence easy to design. On the other hand,it requires two whole spectrometers and thus results in double the implementationcost. In addition, it is sometimes difficult to obtain a fiber PBS with sufficientquality for some wavelength bands.Figure 2.4(b) is the PD spectrometer using only one diffraction grating [82].The vertical and horizontal polarization components are resolved into its spectralcomponents by a single diffraction grating, and then split into two polarizationcomponents by PBS. The two polarization components are then detected by two linesensors. Since the purity of polarization of a reflected beam by PBS is relatively low,a polarizer after reflection (so-called clean-up polarizer) can be optionally utilizedin order to improve the purity and the accuracy of Jones vector measurement. Thistype of PD spectrometer is relatively easy to design, but it sometimes requires alarge PBS to cover the whole area of the line sensors.Figure 2.4(c) shows one of the sophisticated designs of PD spectrometersusing only one line sensor that was originally developed for Stokes parameter-basedPS-OCT [68]. In this scheme, the two polarization components are displaced relative32to each other by the Wollaston prism, and two spectra corresponding to the two po-larization components illuminate different areas of a single line sensor. This schemerequires fewer optical components than the other schemes and can be compactlyimplemented in size. On the other hand, it requires more careful optic design tosuppress aberrations to obtain high spectral resolution for both of the polarizationcomponents.Figure 2.4(d) shows a balanced PD detection unit for SS-OCT [83]. Theprobe and reference beams are introduced into this detection unit through two inde-pendent fiber ports. The two beams are combined by a non-polarization beam split-ter (BS) and then decomposed into its polarization components by two PBSs. Eachof the polarization components is then detected by two balanced photo-detectors(BPDs).Similar to the configuration shown in Fig. 2.4(b), the purity of the polariza-tion can be improved using clean-up polarizer. The polarizer at the input port ofthe reference beam is to balance the optical powers of the reference beam betweenthe two detection channels.2.4 SummaryThe principle of Jones matrix measurement and conventional implementations ofJMT is presented in this chapter. This chapter is organized to provide an introduc-tion and overview of JMT. An advanced version of JMT and more comprehensiveexplanations about system configuration and Jones matrix algorithm are introducedin Chapter 333Chapter 3Advanced Jones matrixtomography∗In this chapter, an advanced version of JMT system and newly developed algorithmsare introduced.3.1 IntroductionRecently, Lim et al. [88] and Baumann et al. [89] independently developed Jonesmatrix tomography (JMT) systems using passive optical components for the delay-based incident polarization multiplexing described in Sect. 2.2. These systems real-ized Jones matrix measurement without any active modulation devices, e.g. electro-optic or acousto-optic modulators. In particular, a fiber-based multi-contrast Jonesmatrix swept-source OCT [88] was used for simultaneous Doppler and polarization∗This chapter has been mainly adopted from the following publication:M. J. Ju, Y.-J. Hong, S. Makita, Y. Lim, K. Kurokawa, L. Duan, M. Miura, S. Tang, andY. Yasuno, ”Advanced multi-contrast Jones matrix optical coherence tomography for Doppler andpolarization sensitive imaging,” Opt. Express 21, 19412-19436 (2013)34imaging. As measuring both a standard wave plate and a retina of a healthy sub-ject in vivo, accuracy of the polarization detection and its functionality was verified.Because of the depth-encoded polarization multiplexing method, however, the mea-surable depth range was relatively shorter than that of a non-polarization OCTsystem. Furthermore, its phase instability and relatively low imaging quality limitthe system for clinical applications.In this chapter, an advanced version of JMT is demonstrated. In comparisonto previously reported JMT [88, 89], this new JMT is advanced in terms of phasestability, image quality, and imaging depth. In addition, this JMT is based on anew principle in which all of the measurements of scattering OCT, Doppler OCTand PS-OCT are integrated. Distinct features of the system and post-processingalgorithms are also concretely described. Furthermore, I show the measurementresults of a healthy and clinical case subject in order to demonstrate the clinicalutility of the system in ophthalmology.3.2 Methods3.2.1 System3.2.1.1 System configurationFigure 3.1 shows the schematic of the JMT system. An MEMS-based swept-source(Axsun Technology Inc., MA) with a center wavelength of 1.06 µm, FWHM of 111nm, and scanning width of 123 nm is used as a light source. The scanning rate ofthe light source is 100 kHz, and the average output power is 30 mW.35SweptSource IsolatorPCLPFC FCFCFCM MPCLPPC FCFC FCFCFCV-BPDH-BPDFCGalvanometerscannerLensPBS1PBS2Dove prismDove prismPBSPBSBS90/10Coupler80/20CouplerPolarization Delay UnitPolarization diversity detection unitMLensAFCP-polarizationS-polarizationPS + P (partial) BFigure 3.1: Schematic diagram of advanced JMT system. LP: linear polarizer,PC: polarization controller, FC: fiber collimator, M: mirror, PBS: polarizing beamsplitter, BS: beam splitter, H- and V-BPD: balanced photo-detector for horizontallyand vertically polarized signals, respectively. (Source: Ju et al. Advanced multi-contrast Jones matrix optical coherence tomography for Doppler and polarizationsensitive imaging [90])36The interferometer is built with single-mode optical fibers. The light is splitby a 90:10 single-mode optical fiber coupler after passing through an isolator usedfor the protection of the source from back-reflected lights. The 90 % port of thefiber coupler is connected to a probe arm consisting of a polarization controller anda passive polarization delay unit, described in Sect. The 10 % portion ofthe light from the coupler is coupled to a reference arm.The light from the polarization delay unit passes through an 80:20 fibercoupler. The 80% portion of the light is directed to a calibration reflector (box-A inFig. 3.1) composed of a fiber collimator, lens, and mirror, and the remaining 20%portion of the light illuminates the eye after passing through a collimator (F280APC-C, Thorlabs Inc., NJ), a two-axis galvanometer scanner, an objective lens (f= 60 mm), and an aspheric ophthalmic lens (40D, Volk Optical Inc., OH). Thebeam diameter (1/e2) incident on the cornea is around 1.4 mm, which provides atheoretical diffraction-limited spot size (1/e2) of 21 µm on the retina. The opticalpower on the cornea is configured to be around 1.15 mW in order to satisfy thesafety standard defined by ANSI [34]. The back-scattered light from the retina isrecoupled to the 80:20 coupler, and 80 % of the back-scattered light is directed to apolarization diversity (PD) detection unit.The PD detection unit consists of a linear polarizer, a non-polarizing beamsplitter (BS), two polarizing beam splitters (PBSs), and two 350 MHz balancedphoto-detectors (BPDs, PDB430C, Thorlabs Inc.). The reference light coupledthrough the 90:10 fiber coupler is also directed to the PD detection unit, in whicha linear polarizer is embedded for aligning the polarization state of the light to 45-degree angle. In the PD detection unit, the reference and back-scattered light fromthe eye is combined at the BS, then split into horizontal and vertical polarization37components by the two PBSs, and finally detected by the BPDs. The detected sig-nals from the BPDs are sampled by an ATS9350 digitizer (AlazarTech Inc., PointeClaire, QC, Canada) with 12-bit resolution and a sampling rate of 500 MHz afterpassing through a high-pass (1.5 MHz) and low-pass (250 MHz) filter (HP1CH3-0Sand LP250Ch3-0S, R&K Co. Ltd., Shizuoka, Japan). Here, the interference signalis sampled with 2560 sampling points for each A-line and the effective wavelengthrange being sampled is approximately 110 nm. The sampled interference signals arerescaled to the linear frequency domain using pre-defined rescaling parameters de-termined by a time-frequency calibration method [91]. The rescaling algorithm alsocancels the spectral shift among A-lines and stabilizes the phase of the OCT signalas described in Sect. After applying a Gaussian window, the interferencesignal is Fourier transformed to yield an OCT signal. For the retinal measurement,the chromatic dispersion of the eye as well as the residual dispersion of the inter-ferometer is canceled by a method described in Ref. [92]. The scanning property ofthe light source, the parameters for the sampling of the spectral interference signal,and the windowing finally define the measured depth-resolution to be 8.5 µm in air,corresponding to 6.2 µm in tissue.With an average probe power of 1.15 mW, the sensitivity is 91.05 dB and thesignal roll-off measured at 0.3 to 2.6-mm depth range is -0.65 dB/mm. According tothe literal definition of sensitivity, it is the maximum measurable attenuation of theprobe beam represented as a negative value in dB. In this thesis, the negative signis omitted by following the conventional notation. Because the signal energy is splitinto the four OCT images, the sensitivity of the system measured for a single image is6-dB lower than that of standard OCT. This fundamental sensitivity loss is overcomeby a method discussed in Sect. By accounting the inherent loss of the 80:2038coupler, the shot-noise-limited sensitivity of a single image becomes 99.4 dB. Thedeparture of the measured sensitivity from the shot-noise-limited sensitivity by -8.4dB is accounted by the double-pass transmittance of the posterior-eye-scanning unit,which is measured to be -3.8 dB, the fiber-coupling loss at the PD detection unit,which is measured to be -3.7 dB and possible recoupling loss at the fiber-tip in thescanning unit occurred by the misalignment of the mirror target for the sensitivitymeasurement. Incident polarization multiplexing by polarization delay unitA passive polarization delay unit is used to multiplex two incident polarizationstates by applying the optical path lengths difference (OPLD). As shown in Fig.3.1, the passive polarization delay unit consists of a linear polarizer, two PBSs, andtwo Dove prisms. In this delay unit, the collimated light passes through a linearpolarizer oriented at 45-degree angle and splits into two orthogonal polarizationcomponents by the PBS 1. After the internal reflection in the Dove prisms, the twoorthogonally polarized lights are combined by the PBS 2, then coupled to an opticalfiber connected to the 80:20 fiber coupler.The two incident polarization states are multiplexed in depth position, andthe OPLD is adjusted by moving one of the Dove prisms. In our particular setup,the OPLD is adjusted to zd = 3.1 mm, so the two OCT signals corresponding to thetwo multiplexed incident polarization states appear with a depth separation of 3.1mm. With this configuration, the measurable imaging depth range for each signalis determined to be around 2.95 mm, which is large enough for clinical imaging ofpathologic posterior eyes.Since this polarization delay unit is compact in size and consists only of bulk39optical components, the perturbation of the delay caused by temperature fluctu-ation is negligible. In addition, this polarization delay unit relies only on passivepolarization components. This results in high stability and easy operation of theJMT system. Polarization diversity detectionLike the other JMT systems, this JMT also relies on PD detection, by which twointerference signals corresponding to different polarization states are independentlydetected. It should be noted that the two polarization states are not necessarilyidentical to those of the polarization delay unit. By this detection scheme, twointerference signals of different polarization states are simultaneously detected bytwo balanced photo-detectors. Each interference signal generates two OCT imagesat different depth positions, which correspond to the two incident polarization statesmultiplexed by the polarization delay unit. Finally, owing to the PD detection andthe incident polarization multiplexing, four OCT images are simultaneously acquiredas schematically shown in Fig. 3.2.H-Detector V-DetectorDepthzd DepthzdIntensity Input state-1 Input state-2 Input state-1 Input state-2Figure 3.2: Diagram of the Fourier transformed interference signals from horizontal(H) and vertical (V) detection channels. (Source: Ju et al. Advanced multi-contrastJones matrix optical coherence tomography for Doppler and polarization sensitiveimaging [90])403.2.1.4 Phase calibration reflectorIn this JMT system, the fluctuations in spectral sampling timing among OCT A-lines are monitored and canceled using a stable spectral interference fringe denotedas a calibration signal. The generation of a calibration signal relies on the imper-fection of the PBSs in the polarization delay unit. Ideally, the PBS separates S-and P-polarization components by reflecting only the S-polarization component andtransmitting only the P-polarization component. However, with an off-the-shelfPBS, some portion of the P-polarization component is reflected and mixed withthe S-polarization component. At the 1.06-µm wavelength, according to the man-ufacturer’s specifications, the reflected beam of the PBS employed in the passivepolarization delay unit (NT49-870, Edmund Optics Inc., NJ, US) includes 4.4% ofP-polarization.Owing to this imperfection of the PBS, the polarization delay unit behavesas a Mach-Zehnder interferometer with an OPLD of zd for the P-polarization com-ponent and generates the calibration signal. The calibration signal is directed tothe BPDs in the PD detection unit through the 80:20 fiber coupler and a calibra-tion reflector (box-A in Fig. 3.1). Note that the calibration signal generated by thepolarization delay unit is a common-mode signal for the BPDs. However, the op-tical power of the calibration signal is significantly larger than that of OCT signal,and hence it can be detected even with the common-mode-rejection property of theBPD.As shown in the orange squares in Fig. 3.2, the calibration signal appearsat the depth location of zd that is exactly the axial displacement between the twodepth-multiplexed signals. This calibration signal is used to correct the fluctuationof spectral sampling as described in Sect. is noteworthy that the imperfection of PBS does not disturb the polar-ization sensitive measurement because of the inherent robustness of JMT, which ismore precisely discussed in Sect. Post-processing3.2.2.1 Monitoring and correction of spectral shiftFluctuations in the synchronization between the wavelength sweeping of the lightsource and the digitizer cause random shifts of the digitized spectrum among theA-lines, which result in phase instability. The phase instability could impose errorson the phase measurements and degrades the sensitivity of Doppler OCT measure-ments. In addition, phase instability results in reduced performance of numericalcancellation of fixed pattern noise. Hence, the spectral shift needs to be correctlyestimated and canceled. In previous systems, the spectral shift was corrected by sev-eral means [45,50,83,93,94]. In the current JMT, I utilize a new method specializedfor the JMT which is simple in its hardware configuration.To obtain phase-stabilized OCT, the spectral shift is estimated and canceledusing the calibration signal described in Sect. Since the same amount ofspectral shift occurs in both detection channels of the PD detection, the calibrationsignal with the higher signal-to-noise ratio is used to estimate the spectral shifts ofboth channels.The details of the estimation of the spectral shift are as follows. In thisestimation, the relative shift between the two spectra are obtained. One of thetwo spectra is denoted as a reference spectrum, and is typically the first A-lineof a B-scan. The other spectrum is the spectrum under shift correction and itsshift is corrected with respect to the reference spectrum. For the estimation, two42of the digitized spectra are first Fourier transformed without rescaling. After thisFourier transform, the calibration signals appear between the two OCT signals ofthe two incident polarization components as shown in Fig. 3.2 (green signals) andare selected by a binary window function.For an intuitive understanding of the method, I consider the inversely Fouriertransformed spectra of the windowed calibrated signals of the reference spectrum(Ir(j)) and the spectrum under shift-correction (Ic(j)). These spectra are describedasIr(j) = |Er(j) + Et(j)|2 (3.1)Ic(j) = |Er(j − βj) + Et(j − βj)|2 = Ir(j) ∗ δ(j − βj) (3.2)where Er(j) and Et(j) are the sampled spectra of the reflected and transmittedbeams of the polarization delay unit with a spectral sampling index of j. The ∗denotes the convolution operation, and βj indicates the relative shift of the spectrumin number of sampling points.In the spectral shift estimation process, the numerically Fourier transformedcalibration signal of the reference A-line is multiplied with the complex conjugateof the Fourier transformed calibration signal of the A-line under correction asF [Ir(j)]F [Ic(j)]∗ = F [Ir(j)]F [I∗r (−j)]F [δ(−j − βj)] (3.3)where F [ ] represents the Fourier transform and the superscript of ∗ represents thecomplex conjugate.The numerical inverse Fourier transform of the signal represented by Eq.(3.3) yields43F−1 [F [Ir(j)]F [Ic(j)]∗] = Ir(j) ∗ I∗r (−j) ∗ δ(−j − βj)= {Ir(j)⊗ Ir(j)} ∗ δ(−j − βj)(3.4)where ⊗ represents the correlation operation. Ir(j) ⊗ Ir(j) is the auto-correlationof Ir(j). It would have a maximum at j = 0, so the signal represented by Eq.(3.4) has its maximum at j = −βj . Finally, the amount of spectral shift βj isdetermined by detecting the peak of this signal. It is noteworthy that the accuracyof the spectral shift estimation can be enhanced by zero-padding the signal of Eq.(3.3). In our particular case the sampling number of the spectrum is zero-paddedto yield a sampling number 16-times larger than the original, thus the spectral shiftis determined with an accuracy of 1/16 of the original spectral sampling period.The estimated βj is then added to the predetermined rescaling table, whichis a vector of sub-fractional indexes of spectral sampling points for each rescaledsampling point. The A-line under correction is then rescaled using this modifiedrescaling table and a shift-corrected and rescaled spectrum is obtained.In the spectral estimation method described in this section, the sampled spec-tra are Fourier transformed without being rescaled into the linear frequency domain.And hence the calibration signal have a broad width after the Fourier transforma-tion, which is typically around 70 pixels width, and sometimes overlaps with aninterference signal originated from the sample. However, due to the significantlyhigher SNR of the calibration signal with respect to those of the sample signal, thecalibration signal still overwhelmingly dominates the spectral shift estimation. As aresult, this estimation method shows remarkable performance as discussed in Sect. Phase retardation and relative attenuation calculationThe round-trip phase retardation of the sample is obtained from the similar matrixobtained through Eq. (2.6). The eigenvalues of the round-trip sample Jones matrixcan be obtained through matrix diagonalization [82] or the following equation [95]λ1,2 = T/2±√T 2/4−D (3.5)where T and D are the trace and determinant of the similar matrix, and λ1,2 in-dicates the two eigenvalues of the matrix. Here I have utilized the fact that theeigenvalues of the similar matrix are identical to those of the round-trip Jones ma-trix of the sample.The phase retardation δ(z) is then obtained as the phase difference betweenthe two eigenvalues asδ(z) =Arg [λ1λ∗2] : 0 ≤ Arg [λ1λ∗2] ≤ piArg [λ∗1λ2] : otherwise. (3.6)Note that δ(z) is defined to be aliased into the range of [0, pi] because the assignmentof λ1 and λ2 is unspecified.In addition to the phase retardation, the relative attenuation between thetwo characteristic polarization states (z) is obtained as(z) =∣∣∣∣ln|λ1||λ2|∣∣∣∣ (3.7) Adaptive Jones matrix averagingTo obtain a high quality phase retardation image, adaptive Jones matrix averagingcan optionally be applied to the similar Jones matrices. Note that the basic con-45cept of adaptive Jones matrix averaging was firstly described in Ref. [56] and waspreviously called as complex Jones averaging.This method relies on a weighted least-square estimation of the relative globalphase of a Jones matrix in respect to an arbitrary reference Jones matrix. Considerseveral Jones matrices M(j) (or similarly several of Eout) obtained in a single ho-mogeneous birefringence domain of a sample but not within a coherence volume,i.e. the resolution of OCT. Under this condition, it would be rational to assumethe following relationship: M(0) ' exp(i∆ϕ(0,j))M(j). Here ∆ϕ(0,j) is the relativeglobal phase between M(0) and M(j). The basic concept of adaptive Jones matrixaveraging is averaging M(j) after canceling the global phase.In the adaptive Jones matrix averaging method, the global phase betweentwo Jones matrices is estimated as∆ϕ(0,j) ≡ Arg4∑l=1exp i(Arg[M (j)l /M(0)l])∣∣∣M(0)l∣∣∣−1+∣∣∣M(j)l∣∣∣−1 , (3.8)where M (j)l is the l-th entry of the j-th matrix under averaging.After determining the global phase, the averaged matrix is defined asM ≡∑jexp(−i∆ϕ(0,j))M(j). (3.9)Note that M(0) is a reference matrix for the determination of the global phase.Hence the phase noise of this matrix should be small. In practical processing, theJones matrix possessing the highest total signal energy among the matrices beingaveraged is utilized as M(0).In practical JMT measurement, this adaptive Jones matrix averaging is op-tionally applied to the similar matrices (Eout(z)Eout(z0)−1 in Eq. (2.6)) with an46averaging kernel smaller than the birefringence domain of the sample prior to cal-culating the eigenvalues. Degree of polarization uniformity calculationDegree of polarization uniformity (DOPU) is a parameter originally introduced byGo¨tzinger et al. [74] for representing the spatial uniformity of polarization. Sincesome important tissues such as retinal pigment epithelium (RPE) are selectivelyvisualized by DOPU contrast, DOPU imaging by JMT is of great interest.DOPU was first defined by using the Hee-Hitzenberger type PS-OCT [75]and recently applied for JMT [89]. In our JMT, DOPU is obtained directly fromEout(z) (in Eq. (2.4)) by the following method.Since DOPU is defined based on the Stokes parameters of back-scatteredlight, a virtual incident beam with an arbitrary state of polarization is defined.To simplify computation, a virtual incident polarization state of Eout(z0)[1 0]Tfrom Eq. (2.6) is assumed. When this virtual incident light illuminates the similarmatrix of the round-trip Jones matrix, Eout(z)Eout(z0)−1 in Eq. (2.6), the Jonesvector of the output light becomes Eout(z)[1 0]T =[E(1)outA(z) E(1)outB(z)]T. Thecorresponding Stokes parameters are then defined asS =IQUV=∣∣∣E(1)outA(z)∣∣∣2+∣∣∣E(1)outB(z)∣∣∣2∣∣∣E(1)outA(z)∣∣∣2−∣∣∣E(1)outB(z)∣∣∣2E(1)outA(z)E(1)outB(z)∗ + E(1)outA(z)∗E(1)outB(z)i(E(1)outA(z)E(1)outB(z)∗ − E(1)outA(z)∗E(1)outB(z)).(3.10)Note that these Stokes parameters are only calculated from two OCT signals ob-tained from the PD detection unit.47DOPU is then defined asDOPU =√Q2+ U2+ V2(3.11)with(Q,U, V)=(∑iQiIi,∑iUiIi,∑iViIi)(3.12)where i indicates the i-th pixel within a spatial kernel by which DOPU is defined.It should be noted that this DOPU is not directly determined from the polarizationproperty of the sample Js(z), but from Eout(z) = χJout Js(z) Jin Ein. However, itwould provide a reasonable measure of the sample’s DOPU, because χ, Jout, Jin,and Ein can be regarded as constant in space and time.In our particular implementation, the kernel size of 8 pixels (horizontal) ×3 pixels (vertical) (70 µm × 12 µm) is used, which is experimentally determined toprovide best result in RPE segmentation [74]. Coherent composition of matrix entriesIn previous multi-contrast OCT based on JMT, a scattering OCT image was ob-tained by averaging the four entries of a Jones matrix in squared intensity. Simi-larly, Doppler tomography was obtained by averaging the squared power of the fourDoppler phase shift signals of the four entries of the Jones matrix [88]. Althoughthis method provided satisfactory image quality, it still suffered fundamental sensi-tivity degradation of JMT, caused by splitting a probe beam power into four OCTimages, i.e. the four entries of the Jones matrices.To overcome this issue, I introduce a new advanced signal processing methodby which the four entries of a matrix are coherently combined. In the current JMT, asensitivity-enhanced scattering OCT and Doppler OCT are obtained from a coherentcomposite of the four entries.48The coherent composition of the matrix entries is based on the followingmathematical model of the depth resolved OCT matrix Eout(z).Eout(z) =E(1)outA(z) E(2)outA(z)E(1)outB(z) E(2)outB(z)'E(1)outA(z) eiθ1E(1)outA(z)eiθ2E(1)outA(z) eiθ3E(1)outA(z)(3.13)where θ1,2,3 are depth-independent relative phase offsets with respect to the firstentry, which account for spatial frequency difference, separate detection, and bothof the frequency difference and separate detection, respectively. In addition to therelative phase offset, there are still depth-dependent phase differences among thematrix entries caused by the birefringence of the sample. However, the amountof the phase differences are so small compared to the relative phase offsets that Ihave assumed that the birefringence of the sample is negligible, as is assumed inconventional non-polarization sensitive OCT.In our coherent composition method, θ1,2,3 are estimated asθ1 ≡ Arg[∑zE(2)outA(z) E(1)outA(z)∗](3.14)θ2 ≡ Arg[∑zE(1)outB(z) E(1)outA(z)∗](3.15)θ3 ≡ Arg[∑zE(2)outB(z) E(1)outA(z)∗](3.16)where∑z represents a summation of all pixels along the depth.Using θ1,2,3, the coherent composition is defined asEout(z) =14[E(1)outA(z) + e−iθ1E(2)outA(z) + e−iθ2E(1)outB(z) + e−iθ3E(2)outB(z)]. (3.17)49Since this composite signal is a coherent summation of four OCT signals, this methodprovides enhanced sensitivity and higher accuracy for Doppler phase shift measure-ment. Doppler phase shift calculationIn our measurement protocol, the Doppler phase shift is defined as the phase differ-ence between B-scans [54, 96], and for this purpose, a single location of a sample isscanned multiple times.In general, a raw Doppler phase shift obtained from a living sample is ex-pressed as∆φ(z) =4piτλcnνz(z) + φb (3.18)where λc is the center wavelength, n is the refractive index of the sample, νz is theaxial velocity of the flow of interest, and φb is a constant phase offset incurred by thebulk motion of the sample. τ is the time interval between two scans under Dopplercalculation, and, in our protocol, is equivalent to the time interval of B-scans.In the current JMT, the raw Doppler phase shift ∆φ(j) is, in principle,defined using the coherently composite signals as∆φ(z, j) = Arg[Eout(z, j + 1)Eout(z, j)∗] (3.19)where ∆φ(j) is the Doppler phase shift of an A-line in the j-th B-scan against thecorresponding A-line in the (j+1)-th B-scan. The bulk phase offset φb(j) is obtainedby averaging the complex part of Eq. (3.19) as [97]50φb(j) = Arg[∑zEout(z, j + 1)Eout(z, j)∗](3.20)where j denotes the index of the B-scan.In the current measurement protocol, multiple (m) B-scans are obtained atthe same location of a sample. Using these m B-scans and their bulk phase offsets,a sensitivity-enhanced Doppler signal is obtained as∆φ(z, j) = Argm0+m−2∑j=m0Eout(z, j + 1)Eout(z, j)∗ exp (−iφb(j))W (z, j) (3.21)where m0 is the starting B-scan index of the multiple B-scans, W (z, j) is an intensitymask defined asW (z, j) =1 : Eout(z, j + 1)Eout(z, j)∗ > 20 : otherwise(3.22)and 2 is the intensity of the noise floor of an OCT image.For the particular case of m = 1 in which only single B-scan is performed,the bulk-phase-offset-free Doppler phase shift can be defined as∆φ(z, j) = Arg[Eout(z, j + 1)Eout(z, j)∗ exp (−iφb(j))W (z, j)]. (3.23)For displaying optical coherence angiography, the squared intensity of the Dopplerphase shift∣∣∆φ(z, j)∣∣2 is used, and this image is denoted as a power-of-Doppler-shiftimage.513.2.2.7 Sensitivity-enhanced scattering OCTA sensitivity-enhanced scattering OCT can be defined using the coherent composi-tion of the matrix entries as I(z, j) =∣∣Eout(z, j)∣∣2.Furthermore, with our particular measurement protocol, high-quality scatter-ing OCT is obtained by complex-averaging m B-scans obtained at the same locationon the sample asI (z, j) =∣∣∣∣∣∣m0+m−1∑j=m0Eout(z, j) exp(−i∆ϕ(z)(m0,j))∣∣∣∣∣∣2(3.24)where m0 is the starting B-scan index of the multiple B-scans and ∆ϕ(z)(m0,j) is theglobal phase offset between matrices defined by Eq. (3.8) with substitutions of M(0)by Eout (z,m0) and M(j) by Eout (z, j). I denote the high-quality scattering OCTobtained by Eq. (3.24) as global-phase-corrected sensitivity-enhanced scatteringOCT.Yet another type of sensitivity-enhanced scattering OCT is defined asI′(z, j) =∣∣∣∣∣∣m0+m−1∑j=m0Eout(z, j) exp(−iφ′b (m0, j))∣∣∣∣∣∣2(3.25)where φ′b (m0, j) is the bulk phase offset between Eout(z,m0) and Eout(z, j) definedasφ′b(m0, j) = Arg[∑zEout(z, j)Eout(z,m0)∗]. (3.26)I denote this type of high-quality scattering OCT as bulk-phase-corrected sensitivity-enhanced scattering OCT.As discussed later in Sect. 3.4.3, the global-phase-corrected and bulk-phase-corrected sensitivity-enhanced scattering OCTs provide different scattering contrast.52For cases shown in Sect. 3.3, global-phase-corrected sensitivity-enhanced scatteringOCT is utilized.3.3 ResultsTable 3.1 shows specification summary of the current JMT system.Table 3.1: Summary of advanced JMT specification.CenterwavelengthWavelengthband widthWavelengthsweeping speedSampleprobing power1.06 µm 111 nm 100 kHz 1.15 mWSystemsensitivitySensitivityroll-offMeasurabledepth-rangeDepth resolution(in air)91.05 dB -0.65 dB/mm 2.95 mm 8.5 µmTo demonstrate the clinical potential of the JMT, a posterior eye of a healthysubject and a geographic atrophy patient are measured. A transversal area of 4.5mm (horizontal) × 4.5 mm (vertical) is scanned with 512 × 1024 A-scans in 6.6seconds. In this measurement protocol, 4 B-scans are taken at a single location andused to create a sensitivity-enhanced Doppler signal (Eq. (3.21)) and global-phase-corrected sensitivity-enhanced scattering OCT (Eq. 3.24), where the Doppler timeseparation is 6.4 ms. Hence, the final number of B-scans after processing is 256.For retardation imaging, the 4 B-scans are averaged by the adaptive Jonesmatrix averaging method described in Sect. prior to calculating the eigen-values. DOPU is also obtained from the averaged Jones matrix.All protocols for measurement were approved by the Institution ReviewBoard of University of Tsukuba. Written, informed consent was obtained prior53to measurement.3.3.1 Jones matrix imaging of normal retinaThe macular and optic nerve head (ONH) of the right eye of the healthy subject arescanned by the JMT. Figure 3.3(a) shows the OCT images taken by the two BPDsin the PD detection unit. An OCT signal obtained by a single BPD contains twoOCT images at different depths, which corresponds to the two incident polarizationstates. The calibration signal exists at approximately the center of the depth field.Figures 3.3(b)–3.3(e) represent the global-phase-corrected sensitivity-enhancedscattering OCT (b), phase retardation (c), DOPU images (d), and squared powerof the Doppler phase shift (e). In the sensitivity-enhanced scattering OCT (Fig.3.3(b)), retinal layers including the retinal nerve fibers layer (RNFL), ganglion celllayer (GCL), internal plexiform layer (IPL), inner nuclear layer (INL), outer plexi-form layer (OPL), outer nuclear layer (ONL), external limiting membrane (ELM),junction of the inner and outer segments of the photoreceptor (IS/OS) and posteriortip of the outer segment (PT), retinal pigment epithelium (RPE), and choroid (CH)are visualized despite the relatively low sensitivity of the raw OCT image at 91.05dB.Among the layers, the ELM, IS/OS and PT layers exhibit hyper-scatteringlines in the scattering OCT, while they show constant phase retardation in theretardation image (Fig. 3.3(c)). In the DOPU image (Fig. 3.3(d)), the RPE appearsas a low DOPU band. In the power-of-Doppler-phase-shift image (Fig. 3.3(e)), aretinal vessel is clearly visible. The choroid vascular layer below the RPE is alsodensely visualized as exhibiting random phase shift signals.Similar aspects also appear in the images of ONH as shown in Fig. 3.4. From54Detection channel A(horizontal polarization)Detection channel B(vertical polarization)Zero-delayCalibrationsignal(a)(b) (c)(d) (e)RPEINL ONLELMIS/OSPTRPEOPL IPLGCLNFLCHRetinal vesselRPE0 π0 1 0 π2Figure 3.3: Jones matrix cross-sectional images of a normal macular. (a) RawOCT intensity images detected by detection channels of A (horizontal polarization)and B (vertical polarization) of the PD detection unit. The lower and upper imagescorrespond to the first and second polarization state, respectively. (b) Global-phase-corrected sensitivity-enhanced scattering OCT obtained by coherent composition.(c) A phase retardation image, (d) A DOPU image, (e) power-of-Doppler-phase-shift image (e). The scale bar represents 500 µm × 500 µm. (Source: Ju et al.Advanced multi-contrast Jones matrix optical coherence tomography for Doppler andpolarization sensitive imaging [90])55NFLIPLOPLINLONLCh0 πScleral canal rimSclera Lamina cribrosa0 1RPERetinal vessel(a)(c) (d)(b)0 π2Figure 3.4: Jones matrix cross-sections of a normal ONH. (a) a global-phase-corrected sensitivity-enhanced scattering OCT, (b) phase retardation, (c) DOPU,and (d) power of Doppler phase shift. The scale bar represents 500 µm × 500µm. (Source: Ju et al. Advanced multi-contrast Jones matrix optical coherencetomography for Doppler and polarization sensitive imaging [90])56(a) (b) (c)Figure 3.5: En face projection images of an ONH. (a) global-phase-correctedsensitivity-enhanced scattering OCT, (b) power of Doppler shift and (c) ICGA. Thescale bar represents 1 mm × 1 mm. (Source: Ju et al. Advanced multi-contrastJones matrix optical coherence tomography for Doppler and polarization sensitiveimaging [90])the phase retardation image of the ONH (Fig. 3.4(b)), the birefringence of laminacribrosa and sclera are clearly visualized with rapidly varying phase retardationalong the depth while they are not identified in the scattering OCT or the DOPUimages. In particular, the scleral canal rim at the edge of the ONH exhibits strongbirefringence.In addition to the multi-contrast images, the en face projection of scatteringOCT and the power of Doppler phase shift are shown in Fig. 3.5. From the en facescattering OCT (Fig. 3.5(a)), general posterior eye structures such as a myopic conusand retinal vessels are visualized. The choroidal vessels which are located deeperthan the retinal vessels are not clearly visible. Conversely, the choroidal vessels areobserved with enhanced contrast in the en face projection of the power of Dopplerphase shift (Fig. 3.5(b)). The detail of blood vessels shown in the power-of-Doppler-phase-shift image is consistent with that of indocyanine green angiography (ICGA)shown in Fig. 3.5(c).573.3.2 Geographic atrophyAs a pathological subject study, an eye of a geographic atrophy (GA) patient (72-year-old Japanese male) is also examined to evaluate the clinical performance of theJMT system.GA is an advanced form of dry age-related macular degeneration (AMD), andhere atrophy refers to the degeneration of the RPE cells. GA is usually defined bya sharply circumscribed area of pigment epithelial atrophy through which choroidalvessels can be seen [98, 99]. The continent-shaped area appears different from thesurrounding retina because of the loss of the pigmented RPE in the color fundus andfundus auto-fluorescence (FAF) images as shown in Figs. 3.6(a) and 3.6(b). The areaof GA looks whiter than the surrounding area in the color fundus and appears darkin the FAF image. The enhanced visibility of the choroidal vasculature in the GAregion is found in the scattering OCT as shown in Fig. 3.6(c), while the choroidalvasculature in this region is more clearly visible in the power-of-Doppler-shift imageas shown in Fig. 3.6(d).58(a) (b)(c) (d)(1)(2)(3)Figure 3.6: In vivo measurement images of a GA patient; (a) fundus photograph,(b) fundus auto-fluorescence image, en face projection images of (c) global-phase-corrected sensitivity-enhanced scattering intensity, and (d) Doppler shift power.The scale bar indicates 1 mm × 1 mm. (Source: Ju et al. Advanced multi-contrastJones matrix optical coherence tomography for Doppler and polarization sensitiveimaging [90])59ScatteringPower of Doppler shiftPhase retardationDOPU(1) (2) (3)Figure 3.7: Multi-contrast Jones matrix cross-section images of geographic atrophy.The first to the fourth rows correspond to coherent composite scattering images,phase retardation images, DOPU images, and power-of-Doppler-shift images, re-spectively. Columns (1)–(3) were obtained at the location indicated in Fig. 3.6(a).Arrows indicate the atrophic region. The scale bar indicates 500 µm × 500 µm.(Source: Ju et al. Advanced multi-contrast Jones matrix optical coherence tomog-raphy for Doppler and polarization sensitive imaging [90])60Typically, a histopathologic section of GA shows the thinning or absence ofRPE, closure of the choriocapillaris, and degeneration of the overlying photorecep-tors [98]. For comparison between the areas with and without GA, three represen-tative multi-contrast B-scan images are shown in Fig. 3.7. Figures 3.7(1)–3.7(3)correspond to the horizontal lines (1)–(3) in Fig. 3.6(a), which represent cross sec-tions of the near-edge, middle, and area outside of the GA region, respectively.As indicated by the dashed lines, the atrophic regions appear in the scatteringOCT as regions without RPE. The absence of RPE is more clearly visualized byDOPU images.It is also noteworthy that some part of the choroid shows low DOPU values.Since melanin exists in the choroid [100], this appearance would be associated withchoroidal melanin concentration.3.4 Discussion3.4.1 Phase stability analysisIn this section, the performance of the spectral shift correction for enhancing phasestability is examined quantitatively and qualitatively. For the phase stability test,I measure a static mirror at different depths without transversal scanning and ana-lyzed the stability of the phase difference between adjacent A-lines. At each depth,1024 A-lines are measured.610 1 2 3 4 5 605101520253035σ ∆φ [degrees]Depth [mm] w/o spectral shift cancelation with spectral shift compensation Theoretical predictionFigure 3.8: Measured phase noise with (◦) and without () the spectral shift cor-rection. The green line indicates the theoretical prediction. (Source: Ju et al.Advanced multi-contrast Jones matrix optical coherence tomography for Doppler andpolarization sensitive imaging [90])Figure 3.8 shows the standard deviation of the phase differences with andwithout spectral shift cancellation. The green line in Fig. 3.8 is the theoretical phasenoise limit that represents the maximum phase stability (minimum phase noise) ofthe system and can be described by [93],σ∆φ =√(1SNRs)+(zszc)2( 1SNRc)(3.27)where σ∆φ is the standard deviation of the phase difference, SNRs and SNRc arethe SNRs of the sample, in this case a mirror, and the calibration signal. zs and zcare the depth positions of the sample and the calibration signal, respectively.The result verifies enhancement of phase stability after applying the spectralshift correction. Here SNRs is 42 dB, the roll-off measured at the depth rangeof 0.3 to 5.6 mm is -1.06 dB/mm, and SNRc is 38 dB. For SNRs of 42 dB, σ∆φis measured to be 0.47 degree (8.16 mrad), while its theoretical prediction is 0.4662degree (8.02 mrad). This phase stability is comparable to previously publishedswept-source OCT [94]. Although recognizable difference between measured phasenoise of 2.38 degree (41.58 mrad) and the theoretical prediction of 1.62 degree (28.34mrad) exists at a depth of 5.58 mm, where the SNRs is 36 dB, it is still better thanthe result reported by Baumann et al. [45] (97 mrad at 100 kHz for the SNRs of 35dB).In addition to the quantitative analysis, the impact of the spectral shift cor-rection on the fixed-pattern noise (FPN) elimination is investigated qualitatively.The FPN consists of interference signals from undesired reflection in the interferom-eter from the light source and cannot be removed unless the OCT signals becomestabilized in phase, and hence is a good indicator of the phase stability of the OCT.As shown in Fig. 3.9(a), severe FPN can be seen if an FPN elimination pro-cess is not applied. When a median estimator-based FPN elimination process [101] isapplied, significant FPN still exists if spectral shift cancellation is not simultaneouslyapplied, as shown in Fig. 3.9(b). The combination of the spectral shift correctionwith 1/16 pixel resolution and the median estimator-based FPN elimination showselimination of almost all of the FPN, as shown in Fig. 3.9(d).It is noteworthy that, without the zero-padding process required for the sub-pixel correction of the spectral shift, the FPN becomes even stronger than it iswithout spectral shift cancellation, as shown in Fig. 3.9(c). Particularly, spectralshift correction with single-pixel resolution worsenes the phase stability. Therefore,as mentioned in Sect., a proper amount of zero-padding is essential.63(a) (b)(c) (d)Figure 3.9: OCT images of the macular of a healthy volunteer. (a) A raw imagewithout FPN removal, (b) FPN removal without spectral shift cancellation, (c) withspectral shift cancellation and FPN removal, but no zero-padding applied. (d) FPNremoval was performed after spectral shift cancellation with 1/16 pixel resolution.(Source: Ju et al. Advanced multi-contrast Jones matrix optical coherence tomog-raphy for Doppler and polarization sensitive imaging [90])643.4.2 Advantages of the phase stabilization processThe proposed phase stabilization process is based on the cross-correlation of thecalibration signals that originated from general characteristics of the PBS and sys-tematic features of the current JMT system. Because of the origin and locationof the calibration signal, this method has several advantages over other methodsrecently reported [45,94].First, no specific optical component that extracts light from the interferom-eter, such as a coupler, is required. And hence there is no additional optical loss.This also makes the system simple and cost-efficient. Second, the calibration signaldoes not reduce the depth measurement range, because it appears at exactly thezero-delay point of the OCT image corresponding to the delayed polarization com-ponent. In addition, the depth location of the calibration signal does not dependon the path length of the calibration mirror arm. This further eases the opticaland mechanical design of the OCT scanner, especially for applications in which thereference path length frequently alters to adjust to that of a sample arm, such as inposterior eye imaging. It should be noted that the path length difference betweenthe 80:20 coupler to the calibration mirror and the coupler to the retina should bemore than the full depth measurement range that covers the depth ranges of inputstate-1 and -2. Otherwise the interference signal between the light from calibrationmirror and the reference appears as an FPN and overlaps with the OCT image.In comparison to a fully numerical method [50] used in the previous JMT [88],our overall processes are simplified and the performance is stable. In the previousnumerical process, OCT signal generated by a reference beam located at the regionclose to the zero delay was used for rough estimation of the spectral shift amount.In addition, a weighted linear iteration fitting algorithm, fully described in Sect. 2.365of Ref. [50], was additionally applied to correct the residual spectral shift. On theother hand, our current stabilization method only requires to calculate the cross-correlation between the reference and test calibration signals.It would be fair to declare the relatively long computational time of the phasestabilization process. The current implementation is in LabVIEW 2011 on a 64-bitWindows 7 PC with an Intel core i7 950 3.07GHz CPU, and it takes around 27minutes for a single volume consisting of 512 × 1024 A-scans. Since the phase sta-bilizations of each A-line are independent to each other, the process can be highlyparallelized by using a GPU or multiple CPU cores. So the possible parallel process-ing and/or further optimized algorithm would enable sufficiently high-speed phasestabilization.Finally, the high accuracy and effectiveness of the proposed method, as ver-ified in the previous sections, provides a high reliability to the system for clinicalapplications.3.4.3 Global-phase-corrected and bulk-phase-corrected sensitivity-enhanced scattering OCTThe global- and bulk- phase-corrected sensitivity-enhanced scattering OCTs definedin Sect. provide different scattering contrasts.Figures 3.10(a) and 3.10(b) are the examples of sensitivity-enhanced B-scansof the GA eye presented in Sect. 3.3.2. Figure 3.10(a) is obtained with a global-phase correction while Fig. 3.10(b) is obtained with a bulk-phase correction. Inthe global-phase-corrected image, the lumens of large choroidal vessels appear withmore-hyper-scattering than those in the bulk-phase-corrected image.This difference is explained by the difference in the phase estimation meth-66Global-phase-corrected Bulk-phase-corrected(a) (b)(c) (d)Figure 3.10: The comparison between global- and bulk- phase-corrected sensitivity-enhanced scattering OCTs. (a) and (c) are a B-scan and en face projection ofsensitivity-enhanced OCTs with global-phase correction, and (b) and (d) are thosewith bulk-phase correction. (Source: Ju et al. Advanced multi-contrast Jonesmatrix optical coherence tomography for Doppler and polarization sensitive imag-ing [90])67ods. Namely, the global phase is estimated in point-wise, while the bulk phase isestimated in A-line-wise. Therefore the bulk-phase correction corrects a constantphase offset of each A-line, where the constant phase offset, in general, is occurredby a bulk motion of the sample and is a phase offset at the region of a static tissue.And hence, the bulk-phase correction can enhance the OCT signal at the statictissue but cannot enhance the OCT signal at regions with a localized motion, suchas a region with blood flow.On the other hand, global-phase correction corrects any phase offset includingthose occurred by a bulk motion and also by a localized motion. As a result, theglobal-phase correction enhances the OCT signals both at the static tissue and at theregion with blood flow. This difference between the two phase correction methodsresult in the different contrasts of choroidal vessels.Similarly, the global-phase correction also corrects phase offset occurred byshadowing of Doppler shift of the blood flow. This results in more hyper scatteringsignals at the region beneath large choroidal vessels in the global-phase-correctedimage than the bulk-phase-corrected image as exemplified by an arrow in Figs.3.10(a) and 3.10(b).Because the signal degradation occurred by the blood flow is larger in thebulk-phase-corrected image, the choroidal vessels appear more clearly in the enface projection of bulk-phase-corrected sensitivity-enhanced scattering OCT thanthat of global-phase-corrected OCT. Figures 3.10(c) and 3.10(d) show an ONH ofthe subject presented in Sect. 3.3.1 obtained with a global-phase correction andbulk-phase correction, respectively. The bulk-phase-corrected image reveals finerdetails of the choroidal vessels with higher contrast than the global-phase-correctedimage. On the other hand, the scattering property of the tissue would be more68easily evaluated with the global-phase-corrected image. Note that Figs. 3.10(c) and3.10(d) are displayed with a gray-color-map while Figs. 3.10(a) and 3.10(b) aredisplayed with an inverted-gray-color-map.Since the phase-offset occurred by quick eye motion reduces the signal inten-sity of the sensitivity-enhanced OCT, the quick eye motion creates a dark horizontalline artifact in the en face projection as shown in Fig. 3.10(d). As exemplified by thevessel contrast, the global-phase correction has higher ability to correct the phase-offset than the bulk-phase correction. And hence the contrast of the dark horizontalline artifacts in the en face image created with the global-phase correction (Fig.3.10(c)) is significantly less than that with bulk-phase correction (Fig. 3.10(d)).3.4.4 Effect of practical factors in JMT measurementIn this discussion, fundamental robustness of the JMT method is provided. Asdiscussed in Sect. 2.1, the relationship between incident and output light in an idealJMT is described by Eq. (2.3).In a practical system, several additional factors should be considered. Byaccounting for these factors and by substituting Jall(z) = JoutJs(z)Jin, Eq. (2.3) ismodified toEout(z) = ηX′R ρJout Js(z) Jin X f (X Ein ) (3.28)where X is a matrix representing the imperfection of the PBS in the polarization de-lay unit. As it is used to generate the calibration signal, there is a significant amountof polarization cross-talk in the PBS. The off-diagonal entries of X account for thecross-talk and the diagonal entries represent the transmittance and reflectance of thehorizontally and vertically polarized light. Here, f( ) is a function which representsthe delay between two incident polarization states generated by the polarization69delay unit. In Eq. (3.28), R represents interference with the reference beams and isR =[H∗ref 0; 0 V∗ref]where H∗ref and V∗ref are the complex conjugates of the fieldamplitudes of the reference beam with horizontal and vertical polarization states.In addition, ρ is a rotation matrix representing the relative rotation between thepolarization delay unit and the PD detection unit. X′ represents the imperfectionof the PBS in the PD detection unit, similar to that of the polarization delay unitX. Finally, η represents the detection efficiency of the two BPDs in the polarizationdelay unit as η = [ηA 0; 0 ηB], where ηA and ηB are the detection efficiencies ofthe two BPDs.Although Eout(z) is affected, these practical factors do not affect the phaseretardation measurement. In JMT, a similar matrix of Js(z) is obtained by Eq.(2.6). By substituting Eq. (3.28) for Eq. (2.6), it is found thatEout(z)Eout(z0)−1 = ηX′R ρJout Js(z) J−1out ρ−1 R−1 X′−1 η−1. (3.29)It is evident that the right-hand side of this equation retains its similarity to Js(z).Hence all the practical factors discussed in this section do not significantly affectthe Jones matrix measurement.3.5 SummaryIn this chapter, an advance version of JMT system based on a passive polarizationdelay at 1-µm wavelength was presented. Because of the accurate spectral shiftcorrection method based on cross-correlation of the calibration signal originatedfrom the general characteristics of PBS, I achieved a highly phase-stabilized system.New JMT algorithms which integrated polarization measurement, Doppler70measurement, and scattering measurement were also presented. Owing to these newalgorithms and high phase stability, highly-sensitive Doppler OCT and sensitivity-enhanced scattering OCT were demonstrated.In vivo measurements of a healthy and pathologic eye were demonstrated.The Doppler image revealed small vessels invisible in the OCT intensity image, whilethe phase retardation and DOPU image demonstrated tissue-selective visualizationof the human retina and choroid. These results indicated the clinical utility of theJMT.71Chapter 4Volumetric human meibomiangland investigation∗As a new clinical application of JMT, human meibomian gland imaging is performedusing a conventional EOM-based JMT system. For Jones matrix analysis, the ad-vanced JMT algorithms introduced in Chapter 3 are employed.4.1 IntroductionHuman meibomian glands (MGs) are large secretory lipid-excreting glands embed-ded in the tarsal plate with approximately 31 and 26 individual glands in the upperand lower eyelid, respectively [102]. Each MG is comprised of multiple acini thatare circularly arranged around a common central duct and connected to it by shortductle. A single acinus that have an elongated or spherical shape of about 150 µm to∗This chapter has been mainly adopted from the following publication:M. J. Ju, J. G. Shin, S. Hoshi, Y. Yasuno, B. H. Lee, S. Tang, and T. J. Eom, ”Three-dimensional volumetric human meibomian gland investigation using polarization-sensitive opticalcoherence tomography,” J. Biomed. Opt. 19, 30503 (2014)72200 µm diameter is completely filled with secretory cells, termed meibocytes [103].The meibocytes, located more toward the center of the acinus, are found to pro-gressively accumulate lipids in the cytoplasm while it appears increasely foamy andpale in conventional histology processed after extracting lipid contents. Meibum isthe oily secretory product from whole cell contents in the acinus and the main com-ponent of the superficial layer of the tear film which as important functions such asformation of a hydrophobic barrier to prevent tear overflow onto the lids [103] andstabilization of tear film by lowering surface tension [104]. Importantly, the meibummay also provide a barrier function to prevent entry of bacteria into the tear filmand inhibit entry of undesirable sebum at the lid margin [103].As increasing interest of MG functions, several imaging modalities have beendeveloped in order to investigate and diagnose MG related diseases (e.g., meibo-mian gland dysfunction (MGD)) by visualizing MG structure. In recent study byWilliam Ngo et al. [105], functionalities and characteristics of several MG visual-ization methods such as lid transillumination, video and non-contact meibography,confocal microscopy, ultrasound, and OCT were provided. Among them, OCT,which is a well-known technique for creating a cross-sectional and three-dimensionalstructure of biological tissue in a non-invasive way and with high-contrast [1], hasbeen utilized to acquire volumetric MG structure with ultra-high resolution of 3 µmin axial and 10 µm in lateral [106]. By employing the ultrahigh resolution OCT sys-tem, a few ductles and acini were observed. However, because of the limited imagingrange due to such high resolution, it seems to be difficult to extract the general MGstructure consisting of multiple acini, and to assess MG dropout (disappearance ofthe glandular tissue inside the tarsal plate).In this chapter, Jones matrix tomography (JMT) [56, 83] based on polar-73ization modulation along the wavelength scan described in Sect. 2.2 is employedfor volumetric investigation of MG structure. By scanning the everted upper eye-lid using the JMT, internal structure of the inner lid is obtained with scatteringcontrast. In addition, with the help of the polarization contrast, MG structure isexclusively visualized after segmenting out the conjunctiva layer located above theMGs. Furthermore, I show the measurement results of different age subjects, whichdemonstrate the utility of the system for clinical ophthalmology.4.2 Methods4.2.1 SystemSwept source EOM LP PC 90/10 Coupler M C PC PC M GP BS PBS LP BPD BPD C A/D Computer PBS V H PeBS Galvos OL Figure 4.1: Schematic diagram of EOM-based JMT system. EOM: electro-opticmodulator, LP: linear polarizer, PC: polarization controller, M: mirror, C: circulator,GP: glass plate, OL: objective lens, BS: beam splitter, PBS: polarizing beam splitter,PeBS: pellicle beam splitter, BPD: balanced photo-detector.74The system has been previously developed by Lim et al. [56]. Here I brieflydescribe the system configuration. Figure 4.1 shows the schematic of JMT basedon polarization modulation along the wavelength scan, whose technical concept anddetail are described in Sect. 2.2 and Refs. [56, 83], respectively. This JMT, basedon a high speed wavelength sweeping laser with 30 kHz sweeping rate and a centerwavelength of 1.31 µm, consists of fiber based Mach-Zehnder interferometer, electro-optic modulator for continuous polarization modulation of the light source along thewavelength sweeping, and two balanced photo-detectors used for polarization diver-sity (PD) detection of both vertically polarized and horizontally polarized spectralinterferograms.An EOM (PC-B3-00-SFAP-SFA-130-UL; EOspace, WA) is employed for con-tinuous polarization modulation of the light source. After the modulation, the lightsource is split by a single mode fiber coupler (10202A-90-FC; Thorlabs, NJ), andthen directed to a sample arm and a reference arm with a ratio of 90:10. The refer-ence light is reflected by a mirror and directed to PD detection arm. In the samplearm, after splitting by a pellicle beam splitter (CM1-BP5; Thorlabs), 92 % of thelight illuminates the sample and 8 % of the light is directed to a phase reference glassplate for stabilizing the phase of OCT signal among A-scans. More detail about thestabilization process can be found from the Ref. [83]. The back-scattered light fromthe sample combines with the light reflected from the reference mirror at the non-polarization beam splitter in the PD detection. Finally, vertically and horizontallypolarized signals are separated by the two polarization beam splitters, and theninterference fringes are detected by the two balanced photo-detectors (BPD-200;Santec Corp.).The probing power is measured to be 2.8 mW, which is below the laser safety75limits defined by ANSI [34]. The imaging depth resolution and range are measuredto be around 12.7 µm (in air) and 5.3 mm, respectively. The sensitivity of thesystem is measured to be 98 dB at a depth of 141 µm from the zero-delay, and thesensitivity roll-off is -1.3 dB/mm.In this JMT system, by employing sinusoidal modulation on the incident po-larization and PD detection, interference signals of two different polarization statesare detected simultaneously. From the obtained interference signals, four OCT sig-nals corresponding to the Jones matrix elements are extracted as described in theRef. [83]. Finally, this JMT system provides the Jones matrix tomography in whicheach pixel represents a Jones matrix of the corresponding point of the sample. Table4.1 shows the specification summary of EOM-based JMT system employed in thischapter.Table 4.1: Summary of EOM-based JMT specification.CenterwavelengthWavelengthband widthWavelengthsweeping speedSampleprobing power1.31 µm 100 nm 30 kHz 2.8 mWSystemsensitivitySensitivityroll-offMeasurabledepth-rangeDepth resolution(in air)98 dB -1.3 dB/mm 5.3 mm 12.7 µm764.3 Results4.3.1 Meibomian gland segmentationFrom Jones matrix measurement, phase retardation and DOPU images are simul-taneously acquired as well as scattering OCT image. Among them, the retardationand DOPU derived by the methods described in Sect. 3.2.2 are utilized for inves-tigation of polarization properties of the MG and its surrounding tissue. In ourpractical implementation, a kernel size of 5 pixels (horizontal) × 3 pixels (vertical)(97.6 µm × 25.8 µm) is used for both of the Jones matrix averaging and DOPUcalculation.Figure 4.2 shows the representative cross-sectional JMT images (Figs. 4.2(b)–4.2(d)] obtained within the red window in the meibography image (Fig. 4.2(a)).The meibography image is captured by IR-CCD camera and exhibits a wide rangeof gland morphology. From the cross-sectional scattering OCT image (Fig. 4.2(b)),the conjunctiva layer and the MGs can be roughly identified by the difference in theintensity contrast. The conjunctiva layer appearing as hyperscattering in the OCTimage shows nearly a constant value in the phase retardation image (Fig. 4.2(c)) anda value close to 1 in the DOPU image (Fig. 4.2(d)). In contrast with the conjunctivalayer, nonconstant retardation and relatively lower DOPU quantities are observedfrom the MGs, as shown in Figs. 4.2(c) and 4.2(d).In this study, histogram-based polarization contrast analysis is performed foracquiring the criteria to make a discrimination between the conjunctiva layer and theMGs. Based on the criteria, it can be expected to achieve more reliable volumetricMG structure investigation. The representative regions within the conjunctiva layerand the acini (Rconj and Racini) are first selected as shown in Figs. 4.2(c) and 4.2(d).77Figure 4.2: Meibography and Jones matrix tomography cross-sectional images. (a)Meibography image and (b)–(d) Jones matrix tomography cross-sectional images:(b) scattering intensity OCT image, (c) phase retardation image, and (d) DOPU im-age. The scale bar represents 1 mm × 1 mm. (Source: Ju et al. Three-dimensionalvolumetric human meibomian gland investigation using polarization-sensitive opticalcoherence tomography [107])78The histograms of the phase retardation and the DOPU quantities within the givenareas are then obtained as shown in Fig. 4.3.In the Rconj, polarization-maintaining property of the layer is evident fromthe narrow width of the retardation histogram (Fig. 4.3(a)) with the standard de-viation (SD) of 0.07 (in radian). On the contrary, in the case of the Racini (Fig.4.3(b)), a broad-phase retardation distribution represented by the histogram withthe SD of 0.33 (in radian) is observed. Figures 4.3(c) and 4.3(d) show the DOPUhistograms of the Rconj and the Racini, in which the difference between the conjunc-tiva layer and the MGs is more clearly identified. Most pixels within the Rconj havethe DOPU quantities higher than 0.95, whereas the DOPU values from the Racinispread out over the DOPU range below the value of 0.95. This implies that the spa-tial uniformity of polarization within the conjunctiva layer is very high as comparedwith the one in the acini. As a result, the DOPU value of 0.95 is empirically set asthe threshold for MG structure extraction.In order to extract MG structure from the scattering OCT image, pixels withDOPU value over 0.95 are segmented as the conjunctiva layer from the DOPU imageand then the segmented layer is applied onto the OCT intensity image as a binarymask. Figure 4.4(a) shows a representative en face OCT intensity image selectedfrom the volume measurement result. In the en face image, the conjunctiva layeris revealed by a hyper-scattering band while MGs composed of several granular-shaped acini appear with relatively lower intensity. Figures 4.4(b) and 4.4(c) showthe segmented conjunctiva layer from the DOPU image and the extracted MG struc-ture from the intensity image after applying the binary mask corresponding to theconjunctiva layer.79Figure 4.3: Histograms of retardation and degree of polarization uniformity(DOPU). (a, c) Data from Rconj and (b, d) data from Racini in Figs. 4.2(c) and4.2(d). (Source: Ju et al. Three-dimensional volumetric human meibomian glandinvestigation using polarization-sensitive optical coherence tomography [107])80(a)(c)(b)MGConjunctivaConjunctivaMGsFigure 4.4: En face sliced MG segmentation result. (a) scattering intensity OCTimage, (b) segmented conjunctiva layer from DOPU image, and (c) extracted MGsimage from (a)4.3.2 3-D volumetric MG visualizationFigure 4.5: 3D volume MG segmentation result. (a) original scattering intensityimage, (b) classification-processed volume image, and (c) extracted MG volumeimage. In the processed volume image (b), red and green color regions represent theconjunctiva layer (CL) and the meibomian glands (MGs), respectively. (Source: Juet al. Three-dimensional volumetric human meibomian gland investigation usingpolarization-sensitive optical coherence tomography [107])Figure 4.5 illustrates the overall processing steps proposed in this research. Inthe 3-D volumetric OCT intensity image shown in Fig. 4.5(a), the conjunctiva layerand MGs appear with different intensities. On the other hand, the conjunctiva layerand MGs are displayed by red and green colors in Fig. 4.5(b), respectively. Here, redand green represent the regions over and below the DOPU threshold, respectively.81After differentiating each region based on the threshold, the conjunctiva layer issegmented and applied to the OCT image as a binary mask. As a result, exclusivevisualization of MG structure is achieved as shown in Fig. 4.5(c).4.3.3 Acinar atrophy with advancing ageTo demonstrate the clinical potential of the proposed method, age-dependent MGalteration is investigated as one of the clinical applications. For this purpose, sixupper eyelids without dry eye disease and MGD disorder from six subjects of dif-ferent ages are involved in this study. This in vivo measurements were approved bythe Institutional Review Board of the University of Tsukuba and conformed to theDeclaration of Helsinki.According to the several reports [108–110], MGs may undergo a degenerativeatrophic process with progressive destruction of the tissue inside the lid. In additionto increasing intraglandular pressure due to stasis of continuously produced meibum,advancing age is also able to affect such atrophic degeneration as in other organsof the human. [110, 111] A decreasing number of active glands indicated by glanddropout is considered as one of the evidence of a natural aging process occurredon the lid. Recently, high age-dependent dropout rate of MGs between the age of20 and 80 years was observed using the meibography technique. Obata et al. [110]who described acinar atrophy without distinct dilatation as one of the pathologicalfinding in MGs, suggest that acinar atrophy may lead to a decrease in the MGsecretion with aging. Unlike normal round-shaped acini, atrophic acini tend toshow small and irregular shape.Figure 4.6 shows the extracted 3-D volumetric MG structures obtained fromthe subjects: (a) 28 years, (b) 32 years, (c) 56 years, (d) 63 years, (e) 72 years, and82Figure 4.6: Extracted MG volume structure images from the subjects with differentages. (a) 28 years, (b) 32 years, (c) 56 years, (d) 63 years, (e) 72 years, and (f)82 years old. (Source: Ju et al. Three-dimensional volumetric human meibomiangland investigation using polarization-sensitive optical coherence tomography [107])(f) 82 years old. In Figs. 4.6(a) and 4.6(b), round-shaped and well-arranged multipleacini are clearly observed. However, in Fig. 4.6(c), noticeable gland dropout processstarts to appear at the bottom of the image, even though several MG branchs stillremain intact at the top. This decreasing number of active glands is consideredas one of the evidences of a natural aging process on the lid. In addition, theMG structure with small and irregular shape is also found in Fig. 4.6(d). Unlikethe other cases, most of the acini are not recognizable anymore in Figs. 4.6(e) and4.6(f), instead randomly distributed thread-shaped structures are observed.4.4 DiscussionUp to now, various imaging modalities have been developed and employed for grad-ing the scale of MG dropout that can be used as a parameter for diagnosis of83MG-related diseases. Although there are several studies using different gradingmethods [111–116], there are no agreed and established standards to grade MGdropout. JMT has been developed as one of the prototypes of polarization sensi-tive OCT (PS-OCT) systems. Currently, PS-OCT is not commercially available.However several prototypes of PS-OCT including JMT have been implemented andemployed to demonstrate its clinical application on posterior [57, 117] and anterioreye segments [56,118]. Once commercial PS-OCT is released because of its potentialclinical applications, it can be expected to be utilized as clinical routine like conven-tional ophthalmic OCT. In the future, with advanced quantitative analysis method,3-D volumetric MG visualization presented in this study will be possible to establishstandard criteria for grading MG dropout, and to be used as a routine measurementfor monitoring MG alteration and for diagnosis of MG-related diseases.4.5 SummaryIn summary, distinctive polarization features of the conjunctiva layer and the MGswere investigated by using JMT system. Especially, from the DOPU contrast, thediscrimination criteria were empirically determined as the DOPU threshold. Us-ing the threshold, segmentation of the conjunctiva layer and exclusive visualizationof the MG structure were successfully achieved. In addition, age-dependent MGstructure variation was also observed through in vivo measurements of several sub-jects with different ages, which demonstrated the clinical utility of the system formonitoring MG alteration and diagnosis of MG-related dry eye disease.84Chapter 5Corneal collagen cross-linkinginvestigation∗In this chapter, JMT is utilized for observing morphological change followed by CXLtreatment and evaluating cross-linking effect on cornea. For corneal imaging, theJMT system in Chapter 3 is slightly modified with a single objective lens and sim-plified polarization delay unit.5.1 IntroductionCorneal collagen cross-linking (CXL), a nearly non-invasive treatment method, hasbeen developed to slow down or halt the progression of keratoconus [119]. Theprocedure of CXL is based on application of combined ultraviolet-A (UV-A) lightand riboflavin (vitamin B2). Riboflavin injection followed by UV-A irradiationcauses photochemical reaction (photosensitized oxidation) [120] that gives rise to∗This chapter has been mainly adopted from the following publication:M. J. Ju, and S. Tang, ”Usage of polarization-sensitive optical coherence tomography forinvestigation of collagen cross-linking,” J. Biomed. Opt. 20, 046001 (2015)85cross-linking by forming intra- and inter- fibrillar covalent bond between collagenfibrils in the corneal stroma [121]. As a result, mechanical stiffness of the corneaand its biochemical resistance to enzymatic digestion are increased [122,123], whichimpedes the progression of keratoconus. Owing to its safety, positive clinical out-comes, and simple protocol, CXL treatment has become very common, [119], andits clinical sustaining effects have been demonstrated [124]. Since then, detectionand measurement of the treatment results have been getting a lot of attention.To date, several optical imaging techniques have been applied to investigatethe morphological changes and to identify the treatment effect on cornea after theCXL treatment. Mazzotta et al. [125] investigated the side-effects of CXL treatmentsuch as stromal edema, rarefaction, and stromal keratocyte reappearance with timeusing confocal laser scanning microscopy (CLSM) that enabled the observation andevaluation of corneal layers and nerves at the sub-cellular level [126–129]. Withimmunofluorescence confocal imaging system, Botto´s et al. [130] directly visualizedultrastructural stromal modification in porcine cornea after CXL procedure andquantitatively assessed the CXL treatment effect. However, staining with specificfluorescent dye and/or contrast agent for targeting cellular components requires ad-ditional sample preparation and can be toxic to tissues. Bueno et al. [131] identifiedmorphological changes in corneal stroma after CXL treatment in bovine and porcineeyes using nonlinear microscopy which provides two-photon excitation fluorescence(TPEF) and second harmonic generation (SHG) corneal images without any stain-ing process [132–135]. Although those microscopic imaging modalities can achievesubcellular spatial resolution, their imaging speed, penetration depth, and field ofview are limited. As an alternative imaging method, Doors et al. [136] used anteriorsegment optical coherence tomography (AS-OCT) to report short-term CXL treat-86ment result and its relationship with morphological characteristics appearing afterthe treatment. Although this method has high imaging speed, deep penetrationdepth and large field of view, it is only capable of providing scattering propertywithout other functional tissue properties such as birefringence.In human eye imaging, PS-OCT has been demonstrated to distinguish struc-tures with birefringent, polarization preserving, and depolarizing properties [58,62,71, 74, 83, 137, 138]. Due to the fact that cornea consists of highly organized col-lagen fibrils in the stroma, it is known to have birefringence, and abnormalities inthe cornea such as keratoconus causing the disruption in the organization of thecollagen fibrils appear with alternation of the birefringence [139].As one of the sub-types of PS-OCT, JMT has been also utilized to investigatethe birefringence property of keratoconus [118, 139]. Recently, Alonso-Canerio etal. [140] reported promising potential of JMT for identifying the changes occurredafter chemical agent (glutaraldehyde)-based CXL treatment on porcine cornea.The aim of this pilot study presented in this chapter is to assess the utilityof JMT to image and discriminate the morphological variation caused by more clin-ically relevant riboflavin/UV-A induced collagen cross-linking treatment on cornea.The riboflavin instillation followed by UV-A irradiation is applied on freshly enucle-ated bovine eyes in order to stimulate cross-linking. Using JMT, the cross-linkingeffect is observed in cross-sectional structure with standard scattering OCT image,and polarization contrast images such as phase retardation and degree of polar-ization uniformity (DOPU) [74]. With graph theory-based cornea segmentationalgorithm [141], the thickness variation caused by CXL is also quantitatively ana-lyzed. In particular, a global threshold is set from averaged DOPU depth-profileand applied for estimating the effective cross-linking depth. Furthermore, both87standard and accelerated CXL protocols are applied on the bovine cornea, and thecross-linking effectiveness following the different protocols are compared.5.2 Materials & methods5.2.1 SystemFigure 5.1 shows the schematic and photograph of the JMT system modified forcorneal imaging from the system presented in Fig. 3.1 . The system design andprocessing principle are very similar to the system described in Sect. 3.2.1. Thesystem is based on a MEMS-based swept-source (Axsun Technology Inc., MA) with100-kHz sweeping rate, a center wavelength of 1060 nm, and a spectral range around110 nm. These properties of the light source determine the depth resolution of thesystem, which is measured to be 8.1 µm in air. The light source is directed to a 90:10fiber coupler after passing through a fiber isolator that is inserted for protection ofthe light source from back-reflected light; 90% and 10% of the light is coupled to apassive polarization delay unit and a reference arm, respectively.The polarization delay unit composed of a linear polarizer, a polarizationbeam splitter (PBS), and two mirror-based retroreflectors is employed for multi-plexing two polarization states of the light source by splitting the beam into twoorthogonal linear polarization states, delaying one to the other by adjusting one ofthe retroreflectors, and recombining them. The light from the polarization delayunit is then directed to a 50:50 fiber coupler. The two ports of the fiber coupler areconnected to a sample arm and a phase stabilization unit, respectively. From thephase stabilization unit that consists of a fiber collimator, lens and mirror, phasecalibration signal is generated and utilized for stabilizing the phase of OCT signal88SweptSourceIsolator90/10Coupler50/50CouplerFCFCFCFCFCPolarization diversity detectionPC PCPCFCFCVHFC FCFCLPLPNPBSPBSPBSFCGalvo ScannerLOLL MM MMMMPBS Phase stabilizationPolarization delay[Schematic] [Photograph] Figure 5.1: Schematic and photograph of JMT system for cornea imaging. LP:linear polarizer, PC: polarization controller, FC: fiber collimator, M: mirror, PBS:polarizing beam splitter, NPBS: non-polarizing beam splitter, H and V: horizontaland vertical balanced photo-detectors. (Source: Ju et al. Usage of polarization-sensitive optical coherence tomography for investigation of collagen cross-linking[142])89among A-scans. The detailed description of the unit and data processing is preciselyillustrated in Sect. 3.2.2.The sample beam passes through a collimator (F280 APC-C, Thorlabs Inc.,NJ), a two-axis galvanometer scanner, and an objective lens (AC254-060-C-ML,Thorlabs Inc., NJ) and finally illuminates the eye. The reference beam, reflectedby a mirror and recoupled to the 90:10 coupler, is aligned to the linear polarizationstate of 45-degree angle by a linear polarizer in the polarization diversity (PD)detection unit that also consists of a non-polarization beam splitter (NPBS), twoPBSs, and two balanced photodetectors (BPDs, PDB430C, Thorlabs Inc.). In thePD detection unit, the reference light combines with the back-scattered samplelight from the eye at the NPBS. The combined light is then split into horizontaland vertical polarization components by the PBSs, and finally interference signal isdetected by the BPDs.In the sample arm, a collimated light with diameter of 3.4 mm is introducedinto the objective lens with a focal length of 60 mm. The lateral resolution isestimated to be around 14 µm. The measurable imaging depth range is determinedto be around 2.95 mm with the polarization delay displacement of about 3 mm thatis set by the polarization delay unit. With an optical probing power of 1.5 mWwhich is below the laser safety limit defined by ANSI [34], the sensitivity and signalroll-off are measured to be 93.5 dB and -0.64 dB/mm, respectively. Table 5.1 showsthe specification summary of the JMT system used in this chapter.90Table 5.1: Summary of the specifications of the JMT for cornea imaging.CenterwavelengthWavelengthband widthWavelengthsweeping speedSampleprobing power1.06 µm 111 nm 100 kHz 1.5 mWSystemsensitivitySensitivityroll-offMeasurabledepth-rangeDepth resolution(in air)93.5 dB -0.64 dB/mm 2.95 mm 8.1 µm5.2.2 Specimen preparationTo investigate cross-linking effect on corneal stroma in detail after CXL procedure,several bovine corneas with different preparation processes are measured ex vivo.Fresh bovine ocular globes (30 specimens) are obtained from a local abattoir (PittMeadows Meats Ltd., Canada). All eyes are from less than 8 months old animals,enucleated and transported within two hours post-mortem. During the transporta-tion, the samples are submerged in physiologic saline medium (0.9 % sodium chlo-ride irrigation, Baxter Corp.) and kept in a cool box. Without staining or fixation,the eyes are submerged under BSS sterile irrigation solution (Alcon Canada Inc.,Canada) in a container with the anterior side facing the probe beam, and imagedwithin 24 hours post-mortem. The bovine eyes are divided into 4 groups accordingto the different preparation processes.For the CXL group (10 eyes), conventional CXL procedure is performed asfollowing the standard protocol (Wollensak et al. [119]). In order to allow the pho-tosensitizer solution to diffuse into the stroma, after removing corneal epitheliumusing a scalpel, riboflavin solution (10 mg riboflavin-5-phosphaste 0.1 % in 10 mg91dextran-T-500 20 % solution, Macdonald’s prescriptions laboratory, Canada) is ad-ministrated every 5 minutes for 30 minutes. Next, UV-A light irradiance with 365nm wavelength and 3 mW/cm2 power is applied for 30 minutes (Energy dose of5.4 J/cm2). During the UV-A exposure time, instillation of riboflavin solution iscontinued every 5 minutes.For the accelerated CXL (ACXL) group (10 eyes), similar protocol as CXLprocedure except with a higher UV-A irradiation power of 9 mW/cm2 but a shorterexposure time of 10 minutes is applied where the same energy dose of 5.4 J/cm2 isused.Two control groups are designed. In control A (5 eyes), only mechanical ep-ithelial debridement are performed. In control B (5 eyes), instillation of riboflavinsolution at every 5 minutes is applied for 30 minutes additionally. No UV-A irradi-ation is applied to either control group.5.2.3 Measurement and post-processing protocolJones matrix images are acquired from the center of the cornea. A transversal areaof 4.5 mm is scanned with 512 A-lines to form a B-scan image and 10 B-scans aresuccessively taken at the same location. With the multiple B-scans, global-phase-corrected sensitivity-enhanced scattering OCT image is created. For phase retarda-tion image, adaptive Jones matrix averaging with a kernel size of 3 × 5 pixels (axial× lateral) is applied for improving the image quality of phase retardation. Finally,DOPU image is also produced from the averaged Jones matrix image. Here, sinceaccuracy of the polarization-dependent measurements can be drastically affected bythe signal-to-noise ratio (SNR) [86], data points whose effective SNR is lower than10 dB are discarded in the computation of the phase retardation and DOPU images.92Original Image Segmentation Result (a) (b) (c) (d) (e) (f) (g) Figure 5.2: Graph theory-based cornea segmentation procedure. Original OCT in-tensity image (a), positive and negative gradient images ((b) and (c)), top and bot-tom cornea boundaries ((d) and (e)) obtained from the gradient images, segmentedcornea layer (f), and final segmentation result with 2nd order polynomial fittingprocess (g). (Source: Ju et al. Usage of polarization-sensitive optical coherencetomography for investigation of collagen cross-linking [142])In order to identify the time-dependent morphological variation caused by the CXLprocedure, each eye sample is imaged every 10 minutes over a period of 2 hours.5.2.4 Corneal thickness calculationIn order to measure the corneal thickness, a simplified version of the graph theory-based cornea segmentation algorithm [141] is applied in this study. The segmen-tation process is illustrated with one eye of the control A group as shown in Fig.5.2.First, positive gradient (Fig. 5.2(b)) and negative gradient (Fig. 5.2(c)) im-93ages are obtained from the scattering OCT image (Fig. 5.2(a)). Second, from thegradient images, the surface (Fig. 5.2(d)) and the bottom (Fig. 5.2(e)) boundariescorresponding to Bowman’s membrane and corneal endothelium layers, are deter-mined and then overlapped with the original OCT image (Fig. 5.2(f)). Finally, thesegmented layers are fitted by second order polynomial fitting process and delineatedas shown in Fig. 5.2(g).With these fitted boundary information, the mean and standard deviation(SD) of the overall corneal thickness are calculated and used for quantitative anal-ysis of the time-dependent thickness variation described in Sect. 5.3.2. Here, arefractive index of bovine stroma (n = 1.376) [143] is used in this study for calcu-lating the corneal thickness because the dominant corneal layer component withinthe measurement range is stroma after removing the epithelium layer.5.3 Results5.3.1 Cross-linking effect on corneaFigure 5.3 shows the representative JMT measurement results of the control A(upper row; taken immediately after removing the corneal epithelium) and CXLgroup (bottom row; taken right after completing CXL procedure). In Fig. 5.3, eachcolumn represents scattering OCT ((a) and (d)), phase retardation ((b) and (e)),and DOPU images ((c) and (f)), respectively.In the case of control A, within the stromal layer, homogeneous intensitydistribution and random phase retardation are observed in the scattering OCT image(Fig. 5.3(a)) and the phase retardation image (Fig. 5.3(b)), respectively. In addition,as shown in Fig. 5.3(c), no remarkable feature is identified with the DOPU contrast.94High Low π 0 1 1 mm 0 1 mm (a) (d) (b) (e) (c) (f) Figure 5.3: Representative B-scan images of the bovine cornea. Upper and bottomrows represent control A and CXL group, respectively. Scattering OCT images ((a)and (d)), phase retardation images ((b) and (e)), and DOPU images ((c) and (f))are shown. scale bars show 1 mm. (Source: Ju et al. Usage of polarization-sensitiveoptical coherence tomography for investigation of collagen cross-linking [142])In the CXL group, on the other hand, the anterior part of the stroma appearswith a slightly higher contrast in the scattering OCT image (Fig. 5.3(d)). Unlikethe control case, a depth-oriented slow increase is observed in the phase retardationimage (Fig. 5.3(e)). Particularly, a distinctive zone is clearly identified at the anteriorstroma in the DOPU image (Fig. 5.3(f)) as exhibiting an increased DOPU contrast.In this study, this distinctive region observed within the anterior stroma after CXLprocedure is defined as an effective cross-linking region, which is more specificallydescribed in Sect. 5.4.The histograms of the phase retardation are further shown in Fig. 5.4. Be-cause of the depth-oriented phase retardation increase within the effective cross-linking area, asymmetrical shape known as right-skewed distribution pattern is ob-served in the histogram of the CXL group (blue bars), while a pattern very close tonormal distribution is found from the histogram of control A (red bars).95Figure 5.4: Histograms of the phase retardation of control A (red bars) and CXLgroup (blue bars). (Source: Ju et al. Usage of polarization-sensitive optical coher-ence tomography for investigation of collagen cross-linking [142])5.3.2 Corneal thickness changeDuring the time-series measurement, it is noticed that the CXL procedure causescorneal thinning. In order to identify the main factor of the corneal thinning, mea-surement results of three different groups with time intervals of 1 hour are comparedas shown in Fig. 5.5: control A (without riboflavin instillation and UV-A irradia-tion, upper row ((a)–(c))), control B (with riboflavin instillation but without UV-Airradiation, middle row ((d)–(f))), and CXL group (with riboflavin instillation andUV-A irradiation, bottom row ((g)–(i))). Each time-series measurement starts afterthe corneal epithelium abrasion (control A), riboflavin administration for 30 minutes(control B), and UV-A illumination for 30 minutes (CXL group), respectively.As shown in Fig. 5.5, the corneal thickness reduction could be observed fromall of the three groups listed above, even though the eyes are immersed in irrigating96(a) (d) (g) (b) (e) (h) (c) (f) (i) 1 mm × 1 mm  High Low Measurement time Figure 5.5: Representative OCT intensity B-scan time-series images of control A(upper row), control B (middle row), and CXL group (bottom row) with time inter-vals of 1 hour. (Source: Ju et al. Usage of polarization-sensitive optical coherencetomography for investigation of collagen cross-linking [142])97Figure 5.6: Corneal thickness change with time of three different measurementgroups. Control A (blue), Control B (green), and CXL Group (red) are plotted.(Source: Ju et al. Usage of polarization-sensitive optical coherence tomography forinvestigation of collagen cross-linking [142])solution to avoid dehydration effect. Nevertheless, more rapid progression of cornealthinning is found from both the control B and CXL group.Using the corneal thickness calculation method described in Sect. 5.2.4, themean corneal thickness of each group and its variation over 2 hours with time inter-vals of 10 minutes are measured and plotted in Fig. 5.6. From control A, dehydrationeffect on the corneal thickness given by the experiment condition is confirmed by itsmean thickness change rate of -3.33 µm/min (thickness from 2.19 ± 0.02 mm to 1.79± 0.03 mm). From CXL group, the mean thickness decrease rate of -4.75 µm/min(thickness from 1.95 ± 0.05 mm to 1.38 ± 0.07 mm) is found, which demonstratesthe corneal thinning followed by CXL procedure as showing more steep decreasein corneal thickness as comparing with control A. In addition, comparable cornealthickness change rate of -4.83 µm/min (thickness from 2.21 ± 0.03 mm to 1.63 ±0.04 mm) is also observed in control B. While dehydration in the ex vivo cornea is98unavoidable under the current experimental condition, the faster thinning rate inthe control B and CXL group indicates that additional corneal thinning happensdue to the riboflavin instillation that is the common process of these two groups (notin the control A). Accordingly, it seems that the main factor for the CXL-inducedcorneal thinning is the dehydration effect from the riboflavin solution instead of theUV-A irradiation.Here, it should be noted that the refractive index change caused by thedehydration effect is not considered in this cornea thickness calculation with theconstant refractive index of 1.376 (Sect. 5.2.4).5.3.3 Time-series investigation of CXL effectAfter completing CXL procedure, dynamical morphology change with time occursand is observed in scattering OCT, phase retardation, and DOPU images. Figure5.7 presents a series of tomographic Jones matrix images ((a)–(i)) of the cornea afterCXL procedure and the averaged depth-profiles of each contrast image ((j)–(l)).From the scattering OCT images (Figs. 5.7(a), (d) and (g)), it can be foundthat the effective cross-linking region defined in Sect. 5.3.1 becomes more and morehyper-scattering as time passes. From the phase retardation images (Figs. 5.7(b), (e)and (h)), the effective region starts to appear with slow phase retardation increase indepth, and exhibits a higher value of phase retardation increase as time progresses(shown more clearly in the averaged depth-profile of phase retardation (Fig. 5.7(k))).In the DOPU contrast images (Figs. 5.7(c), (f) and (i)), pixels with high DOPUvalues are observed within the effective cross-linking region, in which the density ofthe high DOPU value pixels increases as time progresses.Figures 5.7(j), (k) and (l) show the averaged depth-profiles of each contrast99High Low 1 mm 1 mm π 0 1 0 (e) (h) (f) (i) (b) (c) (j) (k) (l) (d) (g) (a) Figure 5.7: Time-series measurement result of CXL Group. Jones matrix tomogra-phy images in the first, second, and third rows were taken immediately, 1 hour, and2 hours after CXL procedure, respectively. Scattering OCT images ((a), (d) and(g)), phase retardation images ((b), (e) and (h)), and DOPU images ((c), (f) and(i)) are shown. scale bars show 1 mm. Bottom row represents depth-profile analysisof Jones matrix time-series measurement. Averaged depth-profiles of normalizedintensity (j), phase retardation (k), and DOPU (l) are shown. The effective cross-linking depth (2 hours after CXL procedure), determined by a DOPU threshold of0.4, is marked by the black dotted-lines. The estimated effective cross-linking depthsfor 0, 1 and 2 hours are displayed by red dashed-lines in the scattering OCT images((a), (d) and (g)), respectively. (Source: Ju et al. Usage of polarization-sensitiveoptical coherence tomography for investigation of collagen cross-linking [142])100image obtained by averaging the A-lines along the B-scan direction (after imageflattening with cornea layer segmentation (Sect. 5.2.4)). In this study, from theaveraged DOPU depth-profile (Fig. 5.7(l)), the DOPU quantity of 0.4 is empiricallydetermined as a global threshold for estimating the effective cross-linking depth thatrepresents the transition between the cross-linking affected and non-affected regionsin the cornea. As an example, the effective cross-linking depth corresponding to 2hours after CXL are estimated as the depth of intersection with the DOPU threshold,and its result is marked by black dotted-line in Figs. 5.7(j)–(l). At the estimatedeffective cross-linking depth, local minimum intensity and phase retardation increaseare observed in the averaged depth-profile of normalized intensity (Fig. 5.7(j)) andphase retardation (Fig. 5.7(k)), respectively. From the scattering OCT images (Figs.5.7(a), (d) and (g)) where the effective cross-linking depth is delineated by reddashed-line, it can be found that the estimation result closely matches with theboundary of the effective cross-linking region.5.3.4 Time-series investigation of ACXL effectIn the standard CXL procedure, it involves 30 minutes of UV-A irradiation at anintended irradiance of 3 mW/cm2 with total surface energy dose of 5.4 J/cm2 (Dres-den protocol [119]). Although the conventional CXL treatment has been demon-strated for its safety and long-term treatment effectiveness in different clinical tri-als [144–148], its long procedure time lasting from 40 minutes to 1 hour may leadto patient discomfort.According to the photochemical law of reciprocity (Bunsen-Roscoe law) [149],it is believed that the photochemical process behind cross-linking depends on theabsorbed UV-A energy and its following biological effect is proportional to the total101energy dose delivered to the biological tissue. Based on this physical theory, foraccelerating the cross-linking procedure so called accelerated corneal cross-linking(ACXL) [150, 151], it is possible in principle to achieve identical biological effectby delivering the same amount of energy dose with reduced illumination time butincreased irradiation UV-A intensity. In this study, ACXL procedure (10 min-utes UV-A illumination at 9 mW/cm2), with the same energy dose as standard 3mW/cm2 for 30 minutes, is carried out and its time-series effect is investigated.Figure 5.8 presents a series of tomographic Jones matrix images ((a)–(i))of the cornea after ACXL procedure and the averaged depth-profiles of each con-trast image ((j)–(l)). Similarly to the standard CXL case, in the scattering OCTimages (Figs. 5.8(a), (d) and (g)), the effective cross-linking area appears as hyper-scattering immediately after the ACXL procedure, and its intensity tends to increaseas time progresses. Within the effective cross-linking region, increase of phase retar-dation with depth is observed in the phase retardation images (Figs. 5.8(b), (e) and(h)), and distinctive feature in comparison to the rest of the cornea is more clearlyprovided from DOPU images (Figs. 5.8(c), (f) and (i)).Figures 5.8(j), (k) and (l) show the time-dependent change in the averageddepth-profiles of the normalized intensity, phase retardation, and DOPU images,respectively. Same as the standard CXL case, DOPU value of 0.4 in its depth-profile (Fig. 5.8(l)) is set as the threshold for estimating the effective cross-linkingdepth. The black dotted-line in the averaged depth-profile of Jones matrix images(Figs. 5.8(j), (k) and (l)) represents the effective cross-linking depth 2 hours afterthe ACXL procedure. In the scattering OCT images (Figs. 5.8(a), (d) and (g)), theeffective cross-linking depth at 0, 1 and 2 hours, respectively, determined by theDOPU threshold is also marked by red dashed-line.102High Low 1 mm 1 mm π 0 1 0 (e) (h) (f) (i) (b) (c) (j) (k) (l) (d) (g) (a) Figure 5.8: Time-series measurement result of ACXL Group. Jones matrix tomogra-phy images in the first, second, and third rows were taken immediately, 1 hour, and2 hours after ACXL procedure, respectively. Scattering OCT images ((a), (d) and(g)), phase retardation images ((b), (e) and (h)), and DOPU images ((c), (f) and(i)) are shown. scale bars show 1 mm. Bottom row represents depth-profile analysisof Jones matrix time-series measurement. Averaged depth-profiles of normalizedintensity (j), phase retardation (k), and DOPU (l) are shown. The effective cross-linking depth (2 hours after CXL procedure), determined by a DOPU threshold of0.4, is marked by the black dotted-lines. The estimated effective cross-linking depthsfor 0, 1 and 2 hours are displayed by red dashed-lines in the scattering OCT images((a), (d) and (g)), respectively. (Source: Ju et al. Usage of polarization-sensitiveoptical coherence tomography for investigation of collagen cross-linking [142])1035.3.5 Standard CXL vs. accelerated CXL (ACXL)According to the equal-dose principle, the same cross-linking effect is expected fromthe two different CXL procedures applied in this study: CXL (30 minutes UV-A illumination at 3 mW/cm2) and ACXL (10 minutes UV-A illumination at 9mW/cm2).Although very similar morphological variation aspects are found in both CXLand ACXL procedure results as shown in Sect. 5.3.3 and Sect. 5.3.4, there is alsoperceptible difference in terms of the cross-linking effectiveness between the twoCXL procedures. In this study, in order to evaluate the effectiveness, comparison ofthe effective cross-linking depth is firstly performed, and its result is shown in Fig.5.9(a). As mentioned in Sect. 5.3.3 and Sect. 5.3.4, the effective cross-linking depthis estimated from the DOPU depth-profile by setting the DOPU threshold of 0.4.With the standard CXL procedure, the cross-linking depth is 261.51 ± 20.76 µmimmediately after the procedure, and moderately increases to 313.52 ± 10.11 µmafter 2 hours. In the case of the ACXL protocol, the effective cross-linking depthis firstly observed at 197.93 ± 11.74 µm, and reaches to 235.50 ± 7.36 µm 2 hoursafter the ACXL procedure.In addition to the effective cross-linking depth, cross-linking effects followedby the two protocols are also examined with respect to the averaged mean DOPUvalue within the cross-linking region as shown in Fig. 5.9(b). From the ACXL group,as compared with the CXL group, higher mean DOPU values are observed at theinitial and final staged of the time-series measurement. Meanwhile, the CXL group(from 0.54 ± 0.03 to 0.71 ± 0.01) shows more progressive incline aspect than theACXL group (from 0.63 ± 0.02 to 0.74 ± 0.01).104Figure 5.9: Comparison of collagen cross-linking effect of CXL and ACXL proce-dures. Effective cross-linking depth (a) and mean DOPU value (b) variations withtime. (Source: Ju et al. Usage of polarization-sensitive optical coherence tomogra-phy for investigation of collagen cross-linking [142])5.4 DiscussionIn this project, the bovine cornea are measured ex vivo using JMT system in orderto investigate the CXL treatment effects on the cornea.Firstly, cornea thickness reduction followed by the treatment is observedand cross-examined with two different control groups. From the examination, it isfound that the dehydration of the riboflavin solution is the main cause of the corneathinning followed by the CXL treatment. Although the bovine cornea is used inthis study based on its similar biochemical property with a human cornea [152], itstill remains to be demonstrated that the results shown here extend to the humancornea. Especially, in the case of in vivo human cornea measurement, the thicknessreduction may be compensated by the human body functions such as tears and awatery fluid inside of the anterior chamber.The effective cross-linking region is also differentiated by JMT. It appears as105showing hyper-scattering, slow phase retardation change in depth, and high DOPUvalue. The effective cross-linking depth can be determined by empirical DOPUthreshold. This depth matches well with the stromal demarcation line reported inthe literatures [125,136,153–155].Currently, it is believed that the stromal demarcation line observed after theCXL treatment represents the activation of keratocyte followed by the keratocyterepopulation and new collagen synthesis [156]. Based on this hypothesis, in general,the stromal demarcation line is regarded as the transition zone between cross-linkedanterior corneal stroma and untreated posterior corneal stroma after CXL treatment.With slit-lamp examination, the stromal demarcation line could be detectable at adepth of about 300 µm as early as 2 weeks after the CXL procedure [153,154]. Usingconfocal microscopy and AS-OCT, the depth of cross-linking was also detected at adepth of 270 to 330 µm [125, 136, 155]. In this chapter, in the case of the standardCXL protocol, the effective cross-linking depth appears at 313.52 ± 10.11 µm, whichcorresponds well to the depth of the stromal demarcation line reported previously.Recently, by using confocal microscopy, Dhaliwal et al. [157] observed hyper-reflective spherical structures with diameter of 4–10 µm in the anterior of the humancornea immediately after the CXL treatment for up to a depth of 300 µm. Theyalso identified keratocyte damage (cell shrinking and apoptosis) by histology withinthe depth in which the spherical structures were visible. The authors stated thatthe spherical structures might represent damaged cells or cellular fragments. Thehyper-scattering observed in our scattering OCT image could be regarded as affectedby the hyper-reflective spherical structures.In addition, Botto´s et al. [130] directly visualized the cross-linking effect usingconfocal fluorescence imaging. After the CXL procedure, well organized and densely106packed collagen fiber distribution was pronouncedly observed within the limitedanterior stroma that was regarded as cross-linked zone. The change in the phaseretardation and DOPU contrasts observed in this study could be explained basedon the above reported morphological evidence appearing after the CXL treatment.After the CXL procedure, the organization pattern of the collagen fibers in theanterior stroma changes to more dense and compact, which gives rise to moderateincrease in the cumulative phase retardation image and high uniformity in the DOPUimage within the cross-linked region.In the presented experiments, different cross-linking progress aspects fromtwo different CXL procedures are observed. The effective cross-linking depth issignificantly deeper after after a 30 minutes CXL treatment than after a 10 minutesACXL procedure. The conventional CXL procedure provides more progressive cross-linking effect on the cornea than the ACXL procedure, which is implied by morerapid and lasting rise of mean DOPU value with time. Based on these results, itwould be possible to infer that photochemical reaction established by the Bunsen-Roscoe law cannot be directly corresponded to photo-biological effect on complexbiological systems.In this study, instead of the intensity threshold based method that is morestraightforward approach in general, empirical DOPU threshold quantity is usedfor determining the effective cross-linking depth because DOPU is less affected bySNR and provides high consistency among the samples. In the future, more robustautomatic segmentation and quantification of the cross-linking progress with polar-ization related parameters such as local birefringence should be devised in order tofind optimal condition for maximizing cross-linking effect with minimized proceduretime.1075.5 SummaryIn this chapter, I introduced JMT as a reliable imaging modality in terms of eval-uating the outcome of CXL treatment. Using JMT imaging, effective cross-linkingdepth and cross-linking progression as a function of time could be determined, whichwould be able to provide a direct clinical sign to detect effectiveness of CXL treat-ment. To date, specific criteria and/or guideline for achieving maximum cross-linking effect ensuring a long lasting outcome is still unknown. However, I believeit would be possible to find the optimal condition through mid-long term clinicalstudy with the proposed method using JMT system.108Chapter 6Conclusion & future directionsOCT is an interferometric based tomography technique for non-invasive measure-ment of biological tissue. Among the various clinical fields, in which OCT has beenutilized, ophthalmology is regarded as one of the most successful applications ofOCT technique. Recent developments in FD-OCT have dramatically improved theimaging speed and sensitivity, which make OCT become a standard tomographymodality in ophthalmology.In addition, functional extensions of OCT have been developed to acquirevarious physiological information for more comprehensive investigation. Most widelyutilized functional extensions of OCT are Doppler OCT and PS-OCT. Doppler OCThas been utilized for retinal blood flow measurement, or for retinal and choroidalvasculature visualization. PS-OCT, capable of measuring the depth-resolved bire-fringence, has been developed for identification of ocular tissue properties, and forexamination of ocular diseases.Jones matrix tomography (JMT), developed as one of PS-OCT schemes, de-termines the polarization properties of ocular tissues. Conventional swept-source109based JMT employed EOM or AOM for modulating the incident polarization state.Usage of these active modulation devices causes extra expense in system configu-ration, instability in system performance, and complexity in data acquisition andprocessing.In this dissertation, I have developed an advanced version of JMT and newJMT algorithms, which integrated sensitivity-enhanced scattering, Doppler phaseshift, and polarization measurements. Using the JMT system, I successfully achievedmulti-contrast ophthalmic imaging with high stability and sensitivity. In addition,several applications of JMT in ophthalmology are also demonstrated.6.1 Development of advanced Jones matrix tomographysystem and retinal imagingThe advanced JMT system was developed by employing passive polarization delayscheme. Based on the inherent property of the delay unit, novel phase stabilizationmethod was devised, which increased the overall system stability. Furthermore,advanced Jones matrix analysis algorithms have been developed, which enabled thesystem to perform multi-contrast Jones matrix imaging.In vivo measurements of a healthy and pathologic posterior eyes were per-formed using the JMT in order to demonstrate its stability and functionality. Clearmorphological features of macular and ONH were revealed with enhanced sensitiv-ity after compensating the inherent sensitivity loss occurred in conventional JMTthrough processing of the coherent composition of matrix entry. Polarization prop-erty imaging such as phase retardation and DOPU provided additional tissue proper-ties of retina structure which was not revealed from scattering contrast. In addition,110detailed vasculature of retina (macular and optic nerve head) which was invisible inthe conventional scattering OCT were resolved by Doppler contrast.6.2 Human meibomian gland imagingAs a promising clinical application of JMT, in vivo upper eyelid imaging was per-formed in order to visualizing meibomian gland (MG) located within a tarsal platein the eyelid. From the Jones matrix measurement, distinctive features of the con-junctiva layer and the MGs were identified. Particularly, the discrimination criteriawas empirically set from histogram-based DOPU contrast analysis. With the DOPUthreshold, exclusive visualization of MG structure was achieved after segmenting theconjunctiva layer. Furthermore, in vivo measurements of several subjects with dif-ferent ages were performed for investigation of acinar atrophy with advancing age.These results demonstrated the clinical utility of JMT system in ophthalmology.6.3 Corneal imagingI also demonstrated the utilization of JMT for investigating the morphological varia-tions followed by corneal collagen cross-linking (CXL) treatment and for determiningthe effectiveness of the cross-linking. For this purpose, ex vivo bovine cornea imagingwas performed after applying the CXL treatment. From the comparative study ofcross-linking effect with two different control groups, the main factor for the cornealthickness reduction caused by CXL was identified. The effective cross-linking regionwas differentiated from different contrast images created by JMT, and its boundarywas also determined from averaged DOPU depth-profile. In addition, acceleratedversion of CXL procedure, which needed shorter procedure time with higher UV-A111irradiation power, was also performed, and its outcomes were compared with thoseof the standard CXL procedure in terms of the effectiveness and progression of cross-linking. Based on these results, JMT would be useful for finding optimal conditionfor maximizing cross-linking effect with minimized procedure time.6.4 Future directionsIn this dissertation, I introduced a newly developed JMT system with improvedstability and expanded functionality, and also demonstrated various clinical utiliza-tions of JMT system. Some future developments and investigations can be carriedout to further improve the system capability and applications.Recently, optical coherence elastography (OCE), capable of determining biome-chanical properties of tissues such as strain and elasticity, was utilized for quantifyinglocal spatial variations in corneal tissue properties induced by CXL treatment [158].Because of the high phase sensitivity of JMT, it is possible to adopt OCE techniqueinto the current JMT system. With the combination of JMT and OCE, it can beexpected to perform more comprehensive analysis of CXL induced mechanical andpolarization property changes in cornea as well as its morphological variation.Omodaka et al. [159] reported volumetric evaluation of the lamina cribrosa(LC) using SS-OCT. LC is the primary site of axonal damage in glaucoma that is thesecond most common cause of blindness [160]. For the purpose of glaucoma diag-nosis, the authors developed LC segmentation algorithm and measured the averagethickness of LC from healthy, early, and late stage glaucoma subjects. From themeasurement results, they found significant correlation between glaucoma severityand LC thickness. For measuring LC thickness, the upper and lower borders of theLC and the flank of the LC were all identified only based on scattering contrast. As112a result, their segmentation algorithm tended to overestimate the LC thickness, es-pecially when measuring tilted optic head disc. As shown in Fig. 3.4, JMT providesadditional contrast to the LC. Since LC has strong birefringence property, LC canbe clearly visualized with rapid change of phase retardation as shown in Fig. 3.4(b).Therefore, based on various contrast mechanisms provided by JMT, it is possibleto quantify the LC thickness more precisely and robustly. Furthermore, throughextensive pathological subject study using JMT, a clearer correlation between theLC thickness and status of the glaucoma can be found.Novel clinical investigation of JMT is very important for expanding its fea-sibility in ophthalmology. However, as mentioned in Sect. 1.3, measurement speedis also important for in vivo ophthalmic imaging because of involuntary eye motionand its related artifacts. Therefore, improving of Jones matrix acquisition speed isquite natural and also necessary. In any swept-source based OCT, the sweeping rateof the source is key for determining measurement speed. Choi et al. [161] used 1050nm vertical-cavity surface-emitting laser (VCSEL) source with 400 kHz wavelengthsweeping rate for phase-sensitive Doppler OCT. Employing the VCSEL source intothe current JMT system will be a robust, straightforward, and computationally ef-ficient way to achieve high speed Jones matrix measurement. However, 1050 nmVCSEL source with over 400 kHz is not commercially available yet, and it will bevery expensive to customize the VCSEL source for JMT system. As a result, thisapproach is not practical and not cost-efficient. As an alternative approach, opti-cal switch based buffering technique [162] could be adopted into the current JMTsystem for reducing measurement time. With this strategy, the current 100 kHzsweeping rate with 50 % duty cycle could be doubled by maximizing the duty cycleof swept-laser close to 100 %. Although this method could not provide compara-113ble measurement speed as the VCSEL swept-source, it can be implemented withthe current swept-source, and also can provide better performance in measurementspeed.With continuous improvement in JMT, this technique can find more andmore applications in ophthalmology and other clinical fields.114Bibliography[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. 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