Adaptive Optics for Vision Science: Principles, Practices, Design, and Applications

FOREWORD xvii

ACKNOWLEDGMENTS xxi

CONTRIBUTORS xxiii

PART ONE INTRODUCTION 1

1 Development of Adaptive Optics in Vision Science and Ophthalmology 3
David R. Williams and Jason Porter

1.1 Brief History of Aberration Correction in the Human Eye 3

1.1.1 Vision Correction 3

1.1.2 Retinal Imaging 5

1.2 Applications of Ocular Adaptive Optics 9

1.2.1 Vision Correction 9

1.2.2 Retinal Imaging 11

PART TWO WAVEFRONT MEASUREMENT AND CORRECTION 31

2 Aberration Structure of the Human Eye 33
Pablo Artal, Juan M. Bueno, Antonio Guirao, and Pedro M. Prieto

2.1 Introduction 33

2.2 Location of Monochromatic Aberrations Within the Eye 34

2.3 Temporal Properties of Aberrations: Accommodation and Aging 40

2.3.1 Effect of Accommodation on Aberrations and Their Correction 40

2.3.2 Aging and Aberrations 42

2.4 Chromatic Aberrations 43

2.4.1 Longitudinal Chromatic Aberration 44

2.4.2 Transverse Chromatic Aberration 45

2.4.3 Interaction Between Monochromatic and Chromatic Aberrations 45

2.5 Off-Axis Aberrations 46

2.5.1 Peripheral Refraction 47

2.5.2 Monochromatic and Chromatic Off-Axis Aberrations 48

2.5.3 Monochromatic Image Quality and Correction of Off-Axis Aberrations 51

2.6 Statistics of Aberrations in Normal Populations 52

2.7 Effects of Polarization and Scatter 53

2.7.1 Impact of Polarization on the Ocular Aberrations 53

2.7.2 Intraocular Scatter 55

3 Wavefront Sensing and Diagnostic Uses 63
Geunyoung Yoon

3.1 Wavefront Sensors for the Eye 63

3.1.1 Spatially Resolved Refractometer 65

3.1.2 Laser Ray Tracing 65

3.1.3 Shack–Hartmann Wavefront Sensor 66

3.2 Optimizing a Shack–Hartmann Wavefront Sensor 68

3.2.1 Number of Lenslets Versus Number of Zernike Coefficients 68

3.2.2 Trade-off Between Dynamic Range and Measurement Sensitivity 71

3.2.3 Focal Length of the Lenslet Array 73

3.2.4 Increasing the Dynamic Range of a Wavefront Sensor Without Losing Measurement Sensitivity 74

3.3 Calibration of a Wavefront Sensor 75

3.3.1 Reconstruction Algorithm 76

3.3.2 System Aberrations 77

3.4 Summary 79

4 Wavefront Correctors for Vision Science 83
Nathan Doble and Donald T. Miller

4.1 Introduction 83

4.2 Principal Components of an AO System 84

4.3 Wavefront Correctors 86

4.4 Wavefront Correctors Used in Vision Science 88

4.4.1 Macroscopic Discrete Actuator Deformable Mirrors 89

4.4.2 Liquid Crystal Spatial Light Modulators 90

4.4.3 Bimorph Mirrors 91

4.4.4 Microelectromechanical Systems 92

4.5 Performance Predictions for Various Types of Wavefront Correctors 95

4.5.1 Description of Two Large Populations 98

4.5.2 Required Corrector Stroke 99

4.5.3 Discrete Actuator Deformable Mirrors 101

4.5.4 Piston-Only Segmented Mirrors 106

4.5.5 Piston/Tip/Tilt Segmented Mirrors 107

4.5.6 Membrane and Bimorph Mirrors 109

4.6 Summary and Conclusion 111

5 Control Algorithms 119
Li Chen

5.1 Introduction 119

5.2 Configuration of Lenslets and Actuators 119

5.3 Influence Function Measurement 122

5.4 Spatial Control Command of the Wavefront Corrector 124

5.4.1 Control Matrix for the Direct Slope Algorithm 124

5.4.2 Modal Wavefront Correction 127

5.4.3 Wave Aberration Generator 127

5.5 Temporal Control Command of the Wavefront Corrector 128

5.5.1 Open-Loop Control 128

5.5.2 Closed-Loop Control 129

5.5.3 Transfer Function of an Adaptive Optics System 130

6 Adaptive Optics Software for Vision Research 139
Ben Singer

6.1 Introduction 139

6.2 Image Acquisition 140

6.2.1 Frame Rate 140

6.2.2 Synchronization 140

6.2.3 Pupil Imaging 141

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 Wavefront 148

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 Offl ine 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

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 Infl uence 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

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

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

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

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

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

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