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Optical Modeling of Schematic Eyes and the Ophthalmic Applications University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Doctoral Dissertations Graduate School 8-2009 Optical Modeling of Schematic Eyes and the Ophthalmic Applications Bo Tan University of Tennessee - Knoxville Follow this and additional works at: https://trace.tennessee.edu/utk_graddiss Part of the Atomic, Molecular and Optical Physics Commons Recommended Citation Tan, Bo, "Optical Modeling of Schematic Eyes and the Ophthalmic Applications. " PhD diss., University of Tennessee, 2009. https://trace.tennessee.edu/utk_graddiss/63 This Dissertation is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Doctoral Dissertations by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a dissertation written by Bo Tan entitled "Optical Modeling of Schematic Eyes and the Ophthalmic Applications." I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Doctor of Philosophy, with a major in Physics. James W. L. Lewis, Major Professor We have read this dissertation and recommend its acceptance: Ying-Ling Chen, Horace W. Crater, Christian Parigger, Ming Wang Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) To the Graduate Council: I am submitting herewith a dissertation written by Bo Tan entitled ―Optical modeling of schematic eyes and the ophthalmic applications.‖ I have examined the final electronic copy of this dissertation for form and content and recommend that it be accepted in partial fulfillment of requirements for the degree of Doctor of Philosophy, with a major in Physics. James W. L. Lewis, Major Professor We have read this dissertation and recommend its acceptance: Ying-Ling Chen Horace W. Crater Christian Parigger Ming Wang Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with original student records.) OPTICAL MODELING OF SCHEMATIC EYES AND THE OPHTHALMIC APPLICATIONS A Dissertation Presented for the Doctor of Philosophy Degree The University of Tennessee, Knoxville Bo Tan August 2009 Acknowledgements I would like to take this opportunity to thank all those who help me make this dissertation possible. First, thank goes to Dr. James W.L. Lewis and Dr. Ying-Ling Chen for their guidance and patience all the time in the research and the course work. What I have learned from them is not only the knowledge, the scientific research skills, and the logical thoughts, but also the rigorous scientific approach and the unremitting efforts. I would also like to express my appreciation to my committee members, Dr. Christian Parigger, Dr. Horace W. Crater, and Dr. Ming Wang for their assistance in getting this dissertation in its final form. Here I especially want to express my thankfulness to them for their help and care in my study and life since I came to UTSI. I would also like to thank my parents, my wife, all my family, and friends for their moral support through the years. ii Abstract The objectives of this dissertation are to advance and broaden the traditional average eye modeling technique by two extensions: 1) population-based and personalized eye modeling for both normal and diseased conditions, and 2) demonstration of applications of this pioneering eye modeling. The first type of representative eye modeling can be established using traditional eye modeling techniques with statistical biometric information of the targeted population. Ocular biometry parameters can be mathematically assigned according to the distribution functions and correlations between parameters. For example, the axial dimension of the eye relates to age, gender, and body height factors. With the investigation results from the studies of different population groups, population-based eye modeling can be established. The second type of eye model includes the optical components of the detailed corneal structure. Many of these structures, especially the corneal topography and wavefront aberration, are measured directly from the human eye. Therefore, the personalized eye models render the exact clinical measure and optical performance of the eye. In a sense, the whole eye, other than the identity of the individual, is quantified and stored in digital form for unlimited use for future research and industrial applications. The presentation of this dissertation is: Chapter 1 describes the background of the research in this area, the introduction of eye anatomy, and the motivation of this dissertation work. In Chapter 2, a comprehensive review of the contemporary techniques of measuring ocular parameters is presented and is followed by the review of literature and then the statistical analysis of the ocular biometry parameters. The goal of this chapter is to build a statistical base for population-based schematic eye modeling research. The analysis includes the investigation of the correlations between ocular parameters and ocular refraction, subject age, gender, ethnicity, and accommodation conditions. In Chapter 3, the tools and methods that are used in our optical eye modeling are introduced. The operation of the optical program ZEMAX is discussed. The detail of the optical eye modeling procedure and method of optical optimization, which is utilized to reproduce desired clinical measurement results, are described. The validation functions, which will be used to evaluate the optimization results, are also addressed. Chapter 4 includes the discussion of the population-based eye modeling and the personalized eye modeling. With the statistical information and the clinical measurements presented in Chapter 2 and the computation method described in Chapter 3, the two types of eye modeling technologies are demonstrated. The procedure, difficulty, and validation of eye modeling are included. The considerations of optical opacities, irregular optical surface, multiple reflection, scattering, and tear film breakup effects are discussed and the possible solutions in ZEMAX are suggested. Chapter 5 presents eye modeling applications of the simulations of ophthalmic instrument measurements. The demonstrated simulation results are retinoscopy and photorefraction. The simulation includes both normal eye model and diseased eye model. The close conformity between the simulation results with the actual clinical measurements further validates the eye modeling technique. The ophthalmic simulation application provides the potential for medical training and instrument development. The summary of the dissertation is given in Chapter 6. iii Contents 1 Introduction to eye modeling 1 2 Ocular Biometry Measurements and Population Based Statistics 5 2.1 MEASUREMENTS OF OCULAR BIOMETRY………………………………………...………5 2.1.1 Techniques for Measuring Curvature, Dimension, Thickness, or Distance of Ocular Elements...………………………………………………………………………………………….5 2.1.2 Techniques for Measuring Three-Dimensional Corneal Topography………….…………..12 2.1.3 Techniques for Measuring Crystalline Lens Parameters (Purkinje Images Method)……...15 2.2 REVIEW OF OPTICAL PARAMETERS OF CORNEA..…......................................................16 2.2.1 Anterior Corneal Radius of Curvature (CR1)………………………………………………16 2.2.2 Asphericity of Anterior Cornea Surface (Q1)...…………………..…………………………25 2.2.3 Central Corneal Thickness (CCT)………………………………………………………….35 2.2.4 Index of Refraction of Cornea (n1)...………………………………………………….…….41 2.2.5 Posterior Corneal Radius of Curvature (CR2).….………………………………………….41 2.2.6 Asphericity of Posterior Cornea Surface (Q2)...……………………………………………45 2.3 REVIEW OF PARAMETERS IN ANTERIOR, IRIS, AND POSTERIOR CHAMBERS…….47 2.3.1 Anterior Chamber Depth (ACD) Measured from the Cornea Vertex…………………........47 2.3.2 Index of Refraction of Aqueous Humor (n2)………………………………………………...58 2.3.3 Iris Stop……………………………………………………………………………………..58 2.4 REVIEW OF OPTICAL PARAMETERS OF LENS…………………………………………...58 2.4.1 Anterior Lens Radius (LR1)…………………………………………………………………59 2.4.2 Anterior Lens Asphericity (Q3)……………………………………………………………..59 2.4.3 Lens Thickness (LT)………………………………………………………………………...63 2.4.4 Refractive Index of Crystalline Lens (n3)…………………………………………………...72 2.4.5 Posterior Lens Radius of Curvature (LR2)………………………………………………….73 2.4.6 Posterior Lens Asphericity (Q4)………………………………………………………….....78 2.4.7 Tilt of Lens..……………………………...…………………………………………………….79 2.4.8 Decenter of Lens……..……………………………………………………………………...79 2.4.9 Diameter of Lens………………………………………………….………………………...79 2.5 REVIEW OF OCULAR AXIAL LENGTH (AL)…………………………………………........79 2.6 VITREOUS CHAMBER AND RETINA……………………………………………………….95 2.6.1 Vitreous Chamber Depth (VCD)……………………………………………………………95 2.6.2 Refractive Index of Vitreous Humor (nVC)…..…………………………………………….104 2.6.3 Retina……………………………………………………………………………...............104 2.7 CHALLENGE AND POTENTIAL POPULATION-BASED EYE MODELNG……………..105 3 Optical Eye Modeling 106 3.1 EYE MODELING USING CONTEMPORARY OPTICAL DESIGN SOFTWARE………...106 3.2 OPTICAL OPTIMIZATION…………………………………………………………………..109 3.2.1 Wavefront Aberration (WFA), Zernike Polynomials, and Root Mean Square (RMS) WFA……………………………………………………………………………………...……...110 3.2.2 Refractive Errors and Sphero-Cylindrical Refraction Prescription....................................114
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