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1.2.1.2 Image Quality Metrics Assessed with Adaptive Optics The effec- tive use of wavefront sensing to refract the eye depends on the ability to transform the wave aberration, which is usually defined by several dozen Zernike coefficients, into the values of sphere, cylinder, and axis that generate the best subjective image quality. This transformation is not as trivial as it might first appear because the amounts of defocus and astigmatism required to optimize image quality depend on higher order aberrations as well as neural factors [43]. Adaptive optics has played a useful role in this effort because it can be used not only to correct aberrations but also to generate them (see also Section 5.4.3). This has allowed Li Chen at Rochester to measure the effect of aberrations on vision with psychophysical methods and helped to generate plausible metrics for image quality [44]. 1.2.1.3 Blur Adaptation The use of adaptive optics to generate aberrations has also been used in clever experiments by Pablo Artal to reveal the eye’s adaptation to its own point spread function (PSF) [45]. Artal measured the subjective blur when subjects viewed a scene through their normal wave aber- ration, as well as through rotated versions of their normal wave aberration. Li Chen and Ben Singer developed the method to rotate the wave aberration using the deformable mirror in the adaptive optics system. Despite the fact that the amount of aberration in all conditions was constant, the subjective blur varied significantly, with the least blur occurring when the subject was seeing the world through his or her own wave aberration. These experiments reveal the neural mechanisms that influence subjective image quality and show that the nervous system has learned to at least partially discount the blur produced by the particular pattern of aberrations through which it must view the world. 1.2.2 Retinal Imaging The use of adaptive optics to increase the resolution of retinal imaging prom- ises to greatly extend the information that can be obtained from the living retina. Adaptive optics now allows the routine examination of single cells in the eye, such as photoreceptors and leukocytes, providing a microscopic view of the retina that could previously only be obtained in excised tissue. The ability to see these structures in vivo provides the opportunity to noninvasively monitor normal retinal function, the progression of retinal disease, and the efficacy of therapies for disease at a microscopic spatial scale. 1.2.2.1 Photoreceptor Optics Revealed with Adaptive Optics Retinal Imaging The benefit of adaptive optics for photoreceptor imaging can be seen in Figure 15.7. Adaptive optics has also proved useful in studying the optical properties of single cones in vivo, properties that are difficult if not impossible to study in excised retina. Cone photoreceptors appear bright in high-resolution images because they act as waveguides radiating the light APPLICATIONS OF OCULAR ADAPTIVE OPTICS 11 12 DEVELOPMENT OF ADAPTIVE OPTICS IN VISION SCIENCE incident on them back toward the pupil in a relatively narrow beam with a roughly Gaussian profile. Images of the cone mosaic have high contrast over a wide range of wavelengths [46] as shown in Figure 1.4. The angular dependence of the light radiated from the cones is closely related to the Stiles–Crawford effect measured psychophysically. The Stiles– Crawford effect describes the loss in sensitivity of the eye to light incident on the mosaic with increasing obliquity from the optical axes of the receptors, which point roughly toward the pupil center [47]. This tuning function is measured with a relatively large number of cones and is therefore the combi- nation of the waveguide properties of single photoreceptors and the disarray in individual cone pointing direction. Though psychophysical methods have suggested that the disarray is likely to be small [48], it has not been possible to disentangle these factors with direct measurements in the human eye. With adaptive optics we have succeeded in measuring the angular tuning proper- ties of individual human cones for the first time, and the disarray in individual cone axes that contributes to the angular tuning properties of the retina as a whole [49]. Figure 1.5 shows images of the same patch of cones when they are illuminated with light entering different locations of the pupil

viii CONTENTS 6.3 Measuring Wavefront Slope 142 6.3.1 Setting Regions of Interest 142 6.3.2 Issues Related to Image Coordinates 143 6.3.3 Adjusting for Image Quality 143 6.3.4 Measurement Pupils 143 6.3.5 Preparing the Image 143 6.3.6 Centroiding 144 6.4 Aberration Recovery 144 6.4.1 Principles 144 6.4.2 Implementation 145 6.4.3 Recording Aberration 147 6.4.4 Displaying a Running History of RMS 147 6.4.5 Displaying an Image of the Reconstructed 148 Wavefront 6.5 Correcting Aberrations 149 6.5.1 Recording Influence Functions 149 6.5.2 Applying Actuator Voltages 150 6.6 Application-Dependent Considerations 150 6.6.1 One-Shot Retinal Imaging 150 6.6.2 Synchronizing to Display Stimuli 150 6.6.3 Selective Correction 151 6.7 Conclusion 151 6.7.1 Making Programmers Happy 151 6.7.2 Making Operators Happy 151 6.7.3 Making Researchers Happy 152 6.7.4 Making Subjects Happy 152 6.7.5 Flexibility in the Middle 153 7 Adaptive Optics System Assembly and Integration 155 Brian J. Bauman and Stephen K. Eisenbies 7.1 Introduction 155 7.2 First-Order Optics of the AO System 156 7.3 Optical Alignment 157 7.3.1 Understanding Penalties for Misalignments 158 7.3.2 Optomechanics 159 7.3.3 Common Alignment Practices 163 7.3.4 Sample Procedure for Offline Alignment 170 7.4 AO System Integration 174 7.4.1 Overview 174 7.4.2 Measure the Wavefront Error of Optical Components 175 7.4.3 Qualify the DM 175 CONTENTS ix 7.4.4 Qualify the Wavefront Sensor 177 7.4.5 Check Wavefront Reconstruction 180 7.4.6 Assemble the AO System 181 7.4.7 Boresight FOVs 182 7.4.8 Perform DM-to-WS Registration 183 7.4.9 Measure the Slope Influence Matrix and Generate Control Matrices 184 7.4.10 Close the Loop and Check the System Gain 184 7.4.11 Calibrate the Reference Centroids 185 8 System Performance Characterization 189 Marcos A. van Dam 8.1 Introduction 189 8.2 Strehl Ratio 189 8.3 Calibration Error 191 8.4 Fitting Error 192 8.5 Measurement and Bandwidth Error 194 8.5.1 Modeling the Dynamic Behavior of the AO System 194 8.5.2 Computing Temporal Power Spectra from the Diagnostics 196 8.5.3 Measurement Noise Errors 198 8.5.4 Bandwidth Error 199 8.5.5 Discussion 200 8.6 Addition of Wavefront Error Terms 200 PART THREE RETINAL IMAGING APPLICATIONS 203 9 Fundamental Properties of the Retina 205 Ann E. Elsner 9.1 Shape of the Retina 206 9.2 Two Blood Supplies 209 9.3 Layers of the Fundus 210 9.4 Spectra 218 9.5 Light Scattering 220 9.6 Polarization 225 9.7 Contrast from Directly Backscattered or Multiply Scattered Light 228 9.8 Summary 230 10 Strategies for High-Resolution Retinal Imaging 235 Austin Roorda, Donald T. Miller, and Julian Christou 10.1 Introduction 235 x CONTENTS 10.2 Conventional Imaging 236 10.2.1 Resolution Limits of Conventional Imaging Systems 237 10.2.2 Basic System Design 237 10.2.3 Optical Components 239 10.2.4 Wavefront Sensing 240 10.2.5 Imaging Light Source 242 10.2.6 Field Size 244 10.2.7 Science Camera 246 10.2.8 System Operation 246 10.3 Scanning Laser Imaging 247 10.3.1 Resolution Limits of Confocal Scanning Laser Imaging Systems 249 10.3.2 Basic Layout of an AOSLO 249 10.3.3 Light Path 249 10.3.4 Light Delivery 251 10.3.5 Wavefront Sensing and Compensation 252 10.3.6 Raster Scanning 253 10.3.7 Light Detection 254 10.3.8 Frame Grabbing 255 10.3.9 SLO System Operation 255 10.4 OCT Ophthalmoscope 256 10.4.1 OCT Principle of Operation 257 10.4.2 Resolution Limits of OCT 259 10.4.3 Light Detection 262 10.4.4 Basic Layout of AO-OCT Ophthalmoscopes 264 10.4.5 Optical Components 266 10.4.6 Wavefront Sensing 266 10.4.7 Imaging Light Source 267 10.4.8 Field Size 267 10.4.9 Impact of Speckle and Chromatic Aberrations 268 10.5 Common Issues for all AO Imaging Systems 271 10.5.1 Light Budget 271 10.5.2 Human Factors 272 10.5.3 Refraction 272 10.5.4 Imaging Time 276 10.6 Image Postprocessing 276 10.6.1 Introduction 276 10.6.2 Convolution 276 10.6.3 Linear Deconvolution 278 10.6.4 Nonlinear Deconvolution 279 10.6.5 Uses of Deconvolution 283 10.6.6 Summary 283 CONTENTS xi PART FOUR VISION CORRECTION APPLICATIONS 289 11 Customized Vision Correction Devices 291 Ian Cox 11.1 Contact Lenses 291 11.1.1 Rigid or Soft Contact Lenses for Customized Correction? 293 11.1.2 Design Considerations—More Than Just Optics 295 11.1.3 Measurement—The Eye, the Lens, or the System? 297 11.1.4 Customized Contact Lenses in a Disposable World 298 11.1.5 Manufacturing Issues—Can the Correct Surfaces Be Made? 300 11.1.6 Who Will Benefit? 301 11.1.7 Summary 304 11.2 Intraocular Lenses 304 11.2.1 Which Aberrations—The Cornea, the Lens, or the Eye? 305 11.2.2 Correcting Higher Order Aberrations— Individual Versus Population Average 306 11.2.3 Summary 308 12 Customized Corneal Ablation 311 Scott M. MacRae 12.1 Introduction 311 12.2 Basics of Laser Refractive Surgery 312 12.3 Forms of Customization 317 12.3.1 Functional Customization 317 12.3.2 Anatomical Customization 319 12.3.3 Optical Customization 320 12.4 The Excimer Laser Treatment 321 12.5 Biomechanics and Variable Ablation Rate 322 12.6 Effect of the LASIK Flap 324 12.7 Wavefront Technology and Higher Order Aberration Correction 325 12.8 Clinical Results of Excimer Laser Ablation 325 12.9 Summary 326 13 From Wavefronts To Refractions 331 Larry N. Thibos 13.1 Basic Terminology 331 13.1.1 Refractive Error and Refractive Correction 331 13.1.2 Lens Prescriptions 332 xii CONTENTS 13.2 Goal of Refraction 334 13.2.1 Definition of the Far Point 334 13.2.2 Refraction by Successive Elimination 335 13.2.3 Using Depth of Focus to Expand the Range of Clear Vision 336 13.3 Methods for Estimating the Monochromatic Refraction from an Aberration Map 337 13.3.1 Refraction Based on Equivalent Quadratic 339 13.3.2 Virtual Refraction Based on Maximizing Optical Quality 339 13.3.3 Numerical Example 353 13.4 Ocular Chromatic Aberration and the Polychromatic Refraction 354 13.4.1 Polychromatic Wavefront Metrics 356 13.4.2 Polychromatic Point Image Metrics 357 13.4.3 Polychromatic Grating Image Metrics 357 13.5 Experimental Evaluation of Proposed Refraction Methods 358 13.5.1 Monochromatic Predictions 358 13.5.2 Polychromatic Predictions 359 13.5.3 Conclusions 360 14 Visual Psychophysics With Adaptive Optics 363 Joseph L. Hardy, Peter B. Delahunt, and John S. Werner 14.1 Psychophysical Functions 364 14.1.1 Contrast Sensitivity Functions 364 14.1.2 Spectral Efficiency Functions 368 14.2 Psychophysical Methods 370 14.2.1 Threshold 370 14.2.2 Signal Detection Theory 371 14.2.3 Detection, Discrimination, and Identification Thresholds 374 14.2.4 Procedures for Estimating a Threshold 375 14.2.5 Psychometric Functions 377 14.2.6 Selecting Stimulus Values 378 14.3 Generating the Visual Stimulus 380 14.3.1 General Issues Concerning Computer-Controlled Displays 381 14.3.2 Types of Computer-Controlled Displays 384 14.3.3 Accurate Stimulus Generation 386 14.3.4 Display Characterization 388 CONTENTS xiii 14.3.5 Maxwellian-View Optical Systems 390 14.3.6 Other Display Options 390 14.4 Conclusions 391 PART FIVE DESIGN EXAMPLES 395 15 Rochester Adaptive Optics Ophthalmoscope 397 Heidi Hofer, Jason Porter, Geunyoung Yoon, Li Chen, Ben Singer, and David R. Williams 15.1 Introduction 397 15.2 Optical Layout 398 15.2.1 Wavefront Measurement and Correction 398 15.2.2 Retinal Imaging: Light Delivery and Image Acquisition 403 15.2.3 Visual Psychophysics Stimulus Display 404 15.3 Control Algorithm 405 15.4 Wavefront Correction Performance 406 15.4.1 Residual RMS Errors, Wavefronts, and Point Spread Functions 406 15.4.2 Temporal Performance: RMS Wavefront Error 407 15.5 Improvement in Retinal Image Quality 409 15.6 Improvement in Visual Performance 410 15.7 Current System Limitations 412 15.8 Conclusion 414 16 Design of an Adaptive Optics Scanning Laser Ophthalmoscope 417 Krishnakumar Venkateswaran, Fernando Romero-Borja, and Austin Roorda 16.1 Introduction 417 16.2 Light Delivery 419 16.3 Raster Scanning 419 16.4 Adaptive Optics in the SLO 420 16.4.1 Wavefront Sensing 420 16.4.2 Wavefront Compensation Using the Deformable Mirror 421 16.4.3 Mirror Control Algorithm 421 16.4.4 Nonnulling Operation for Axial Sectioning in a Closed-Loop AO System 423 16.5 Optical Layout for the AOSLO 425 16.6 Image Acquisition 426 xiv CONTENTS 16.7 Software Interface for the AOSLO 429 16.8 Calibration and Testing 431 16.8.1 Defocus Calibration 431 16.8.2 Linearity of the Detection Path 432 16.8.3 Field Size Calibration 432 16.9 AO Performance Results 432 16.9.1 AO Compensation 432 16.9.2 Axial Resolution of the Theoretically Modeled AOSLO and Experimental Results 434 16.10 Imaging Results 438 16.10.1 Hard Exudates and Microaneurysms in a Diabetic’s Retina 438 16.10.2 Blood Flow Measurements 439 16.10.3 Solar Retinopathy 440 16.11 Discussions on Improving Performance of the AOSLO 441 16.11.1 Size of the Confocal Pinhole 441 16.11.2 Pupil and Retinal Stabilization 443 16.11.3 Improvements to Contrast 443 17 Indiana University AO-OCT System 447 Yan Zhang, Jungtae Rha, Ravi S. Jonnal, and Donald T. Miller 17.1 Introduction 447 17.2 Description of the System 448 17.3 Experimental Procedures 453 17.3.1 Preparation of Subjects 453 17.3.2 Collection of Retinal Images 454 17.4 AO Performance 455 17.4.1 Image Sharpening 457 17.4.2 Temporal Power Spectra 458 17.4.3 Power Rejection Curve of the Closed-Loop AO System 459 17.4.4 Time Stamping of SHWS Measurements 460 17.4.5 Extensive Logging Capabilities 461 17.4.6 Improving Corrector Stability 461 17.5 Example Results with AO Conventional Flood- Illuminated Imaging 461 17.6 Example Results With AO Parallel SD-OCT Imaging 463 17.6.1 Parallel SD-OCT Sensitivity and Axial Resolution 463 17.6.2 AO Parallel SD-OCT Imaging 466 17.7 Conclusion 474 CONTENTS xv 18 Design and Testing of A Liquid Crystal Adaptive Optics Phoropter 477 Abdul Awwal and Scot Olivier 18.1 Introduction 477 18.2 Wavefront Sensor Selection 478 18.2.1 Wavefront Sensor: Shack–Hartmann Sensor 478 18.2.2 Shack–Hartmann Noise 483 18.3 Beacon Selection: Size and Power, SLD versus Laser Diode 484 18.4 Wavefront Corrector Selection 485 18.5 Wavefront Reconstruction and Control 486 18.5.1 Closed-Loop Algorithm 487 18.5.2 Centroid Calculation 488 18.6 Software Interface 489 18.7 AO Assembly, Integration, and Troubleshooting 491 18.8 System Performance, Testing Procedures, and Calibration 492 18.8.1 Nonlinear Characterization of the Spatial Light Modulator (SLM) Response 493 18.8.2 Phase Wrapping 493 18.8.3 Biased Operation of SLM 495 18.8.4 Wavefront Sensor Verification 495 18.8.5 Registration 496 18.8.6 Closed-Loop Operation 499 18.9 Results from Human Subjects 502 18.10 Discussion 506 18.11 Summary 508 APPENDIX A: OPTICAL SOCIETY OF AMERICA’S STANDARDS FOR REPORTING OPTICAL ABERRATIONS 511 GLOSSARY 529 SYMBOL TABLE 553 INDEX 565

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