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UC Berkeley UC Berkeley Electronic Theses and Dissertations UC Berkeley UC Berkeley Electronic Theses and Dissertations Title Imaging the foveal cone mosaic with a MEMS-based adaptive optics scanning laser ophthalmoscope Permalink https://escholarship.org/uc/item/9th5r171 Author Li, Yiang Publication Date 2010 Peer reviewed|Thesis/dissertation eScholarship.org Powered by the California Digital Library University of California Imaging the Foveal Cone Mosaic with a MEMS-based Adaptive Optics Scanning Laser Ophthalmoscope By Yiang Li A dissertation submitted in partial satisfaction of the requirements for the degree of Doctor of Philosophy in Vision Science in the Graduate Divisions of the University of California, Berkeley Committee in charge: Professor Austin J. Roorda Professor Masayoshi Tomizuka Professor Martin S. Banks Fall 2010 Imaging the Foveal Cone Mosaic with a MEMS-based Adaptive Optics Scanning Laser Ophthalmoscope Copyright 2010 By Yiang Li University of California, Berkeley Abstract Imaging the foveal cone mosaic with a MEMS-based adaptive optics scanning laser ophthalmoscope By Yiang Li Doctor of Philosophy in Vision Science University of California, Berkeley Professor Austin J. Roorda, Chair Our knowledge of the structure of the human photoreceptor mosaic is mostly based on histological data. Imaging microscopic structure in intact eyes has traditionally been difficult due to structural imperfections in the eye’s optics called aberrations. The introduction of adaptive optics (AO) into vision science has allowed us to access the living human retina at microscopic levels, opening up new possibilities for both basic and clinical research. This dissertation concerns the advancement of AO technology for retinal imaging while emphasizing its application to imaging the foveal cone photoreceptor mosaic in living human eyes. Foveal cones provide a fundamental challenge for today’s AO systems due to their small size (2 µm diameter). As a result, much of my effort has been put towards improving AO system performance to resolve these small cells consistently. I have improved the wavefront correction capabilities of an adaptive optics scanning laser ophthalmoscope (AOSLO) using a single MEMS deformable mirror, so that the smallest foveal cones in some eyes can now be resolved. Specifically, many of the nonlinear characteristics of the particular MEMS device used have been negated in the new wavefront controller, and the wavefront reconstructor has been optimized by incorporating measurement noise and aberration (Kolmogorov) statistics. This contribution is significant because, prior to this research, the capability to image the entire foveal cone mosaic in vivo had never been demonstrated using this imaging modality. Some basic scientific investigations were carried in parallel with the technical developments. Specifically, I used this MEMS-based AOSLO to investigate how foveal fixation is related to the cone density distribution and to determine the inter-subject variability of foveal cone density in relation to eye length. The foveae of 18 healthy eyes (18 subjects) with axial lengths from 22.86 mm to 28.31 mm were imaged and analyzed. The entire foveal cone mosaic was resolved in four eyes, but cones within 0.03 mm ( ≈ 0.1°) from the foveal center remained unresolved in most eyes. The preferred retinal 1 locus of fixation deviated significantly ( P < 0.001) from the location of peak cone density for all but one eye. Retinal cone density decreased significantly ( P < 0.05) with increasing axial length 0.30 mm away from the foveal center but not closer, so we can conclude that the axial myopia progression causes retinal stretch. However, how axial length affects cone density within the central fovea, or foveola, is swamped by other factors besides just cone density due to high levels of inter-subject variability observed there. 2 I dedicate this work to my family, my three best friends, and my teachers “The one who doesn’t fall never stands up” The Last Emperor i Table of contents Dedication i Table of contents ii List of figures iv List of tables vi List of symbols vii List of abbreviations ix Acknowledgements x Curriculum Vitae xii 1. Introduction 1 1.1 Challenges 3 1.1.1 Visual and adaptive optics 4 1.1.2 Foveal cone photoreceptors 7 1.2 Adaptive optics scanning laser ophthalmoscopy 9 1.3 Purpose and structure of dissertation 10 Acknowledgements 11 2. Measuring monochromatic ocular aberrations 12 2.1 Introduction 12 2.1.1 Shack-Hartmann sensor design 13 2.1.2 Pupil function 15 2.1.3 Point spread function 19 2.2 Wavefront sensing 23 2.2.1 Zernike polynomials 24 2.2.2 Wavefront gradient 27 2.2.3 Shack-Hartmann image processing 30 2.3 Wavefront reconstruction (estimation) 33 2.3.1 The classic Cubalchini method 34 2.3.2 Zonal reconstruction 37 2.3.3 Fourier methods 41 2.4 Discussion 43 2.4.1 Direct and indirect routes to fitting Zernike polynomials 43 2.4.2 Zonal Reconstruction 47 2.5 Conclusions 48 Acknowledgements 49 3. Controlling monochromatic ocular aberrations 50 3.1 Introduction 50 3.1.1 Background 53 3.1.2 AO control loop 55 3.2 Calibration and modeling 57 3.2.1 Interferometer 58 3.2.2 Input linearization 62 3.2.3 Interaction matrix model 64 3.3 Wavefront reconstruction (control) 65 ii 3.3.1 Pseudoinverse 66 3.3.2 Statistical weighting 67 3.3.3 Local waffle penalty 72 3.3.4 Zernike polynomials 73 3.4 Discussion 74 3.3.1 Interferometry concerns 74 3.3.2 AO loop stability 75 3.3.3 Performance comparison 77 3.5 Conclusions 79 Acknowledgements 80 4. Retinal imaging applications: cone density, foveal fixation and eye length 82 4.1 Introduction 82 4.1.1 Fixation 82 4.1.2 Myopia 83 4.1.3 Acuity 84 4.2 Methods 84 4.2.1 Retinal imaging 84 4.2.2 Image processing and analysis 85 4.2.3 Retinal feature size estimation 86 4.2.4 Cone density estimation 88 4.3 Results 90 4.3.1 Foveal fixation and cone density topography 91 4.3.2 Inter-subject cone density variability 94 4.3.3 Foveal cone density and visual acuity 97 4.4 Discussion 97 4.4.1 Peak cone density and fixation 98 4.4.2 Cone density and axial length 98 4.5 Conclusions 99 Acknowledgements 99 Bibliography 101 A. Proof of Equation 3.3.4 111 B. MATLAB code 112 B.1 Zonal reconstruction matrices for circular pupils 112 B.1.1 Main script 112 B.1.2 Supplementary functions 113 B.2 Automated cone photoreceptor identification 114 B.3 Retinal magnification factor 116 iii List of figures Figure 1.1 Schematic diagram of an AO flood illuminated ophthalmoscope 1 Figure 1.2 Image acquired with an AO flood illuminated ophthalmoscope 2 Figure 1.3 Microscope image of the surface of a BMC MEMS device 3 Figure 1.4 Image of a foveal cone mosaic acquired with AOSLOII 4 Figure 1.5 Schematic diagram of a four-surface eye model 6 Figure 1.6 Resolution limit as a function of the RMS wavefront error 7 Figure 1.7 Images acquired using differential interference contrast microscopy 8 Figure 1.8 Foveal cross section image acquired using AO OCT 9 Figure 1.9 AOSLOII photo and schematic diagram 10 Figure 2.1 Schematic diagram of a Shack-Hartmann wavefront sensor 13 Figure 2.2 Methods for counter reflections from the corneal front surface 14 Figure 2.3 Plane waves exiting out of a perfect (diffraction limited) eye 16 Figure 2.4 Distribution of field amplitude across the pupil 19 Figure 2.5 Image formation for a perfect eye 22 Figure 2.6 A wavefront contour map and its corresponding PSF 23 Figure 2.7 Zernike polynomial pyramid up to the 4 th radial order 26 Figure 2.8 Principle of Shack-Hartmann wavefront sensing 29 Figure 2.9 Shack-Hartmann sensor image processing procedure 31 Figure 2.10 Total execution time for wavefront related calculations 33 Figure 2.11 Southwell and Hudgin wavefront sensor geometries 38 Figure 2.12 Piston and global waffle wavefront modes 40 Figure 2.13 Zonal reconstructions of circular pupils with 4, 5 and 6 mm diameters 41 Figure 2.14 Same wavefront but reconstructed with three different algorithms 42 Figure 2.15 Two routes for estimating Zernike polynomial coefficients 43 Figure 3.1 General block diagram for a closed loop AO system 50 Figure 3.2 Different types of deformable mirrors available commercially 51 Figure 3.3 Schematic cross-sectional view of a BMC MEMS device 53 Figure 3.4 Schematic diagram and block diagram of AO control loop 56 Figure 3.5 Phase shifting interferometer used for DM characterization 59 Figure 3.6 Raw interferogram and the corresponding surface profile 62 Figure 3.7 Single actuator deflection plotted as a function of the squared voltage 64 Figure 3.8 Closed loop performance of the statistically weighted reconstructor 69 Figure 3.9 Frequency response of two different Laplacian filters designs 71 Figure 3.10 Piston, tilt and tip modes 72 Figure 3.11 Examples of localized waffle modes 73 Figure 3.12 Performance of reconstructors based on RMS wavefront error 77 Figure 3.13 Two images of the same location but using different reconstructors 78 Figure 3.14 Performance of reconstructors based on mean pixel values 79 Figure 3.15 Image of the cone mosaic at the very center of the fovea 81 Figure 4.1 Fixation stimulus appearance to the observer and to the subject 83 Figure 4.2 Visual angle and retinal image size 87 Figure 4.3 Calculating Voronois from cone coordinates 88 Figure 4.4 Axial length and retinal magnification as a function of refractive error 90 iv Figure 4.5 1° by 2° (320 µm by 640 µm) foveal cone mosaic of a healthy eye 91 Figure 4.6 Distribution of fixation events oriented at about 143° 92 Figure 4.7 Examples of cone density topography maps 94 Figure 4.8 Retinal cone density as a function of retinal eccentricity
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