Diffraction, Fourier Optics and Imaging

$Diffraction, Fourier Optics and Imaging by Ersoy, Okan K., 9780471238164$

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ISBN: 9780471238164 | 0471238163
Cover: Hardcover
Copyright: 12/1/2006

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This book presents current theories of diffraction, imaging, and related topics based on Fourier analysis and synthesis techniques, which are essential for understanding, analyzing, and synthesizing modern imaging, optical communications and networking, as well as micro/nano systems. Applications covered include tomography; magnetic resonance imaging; synthetic aperture radar (SAR) and interferometric SAR; optical communications and networking devices; computer-generated holograms and analog holograms; and wireless systems using EM waves.

Preface

xiii

1. Diffraction, Fourier Optics and Imaging

(5)

1.1 Introduction

(1)

1.2 Examples of Emerging Applications with Growing Significance

(4)

1.2.1 Dense Wavelength Division Multiplexing/Demultiplexing (DWDM)

(1)

1.2.2 Optical and Microwave DWDM Systems

(1)

1.2.3 Diffractive and Subwavelength Optical Elements

(1)

1.2.4 Nanodiffractive Devices and Rigorous Diffraction Theory

(1)

1.2.5 Modern Imaging Techniques

(2)

2. Linear Systems and Transforms

(19)

2.1 Introduction

(1)

2.2 Linear Systems and Shift Invariance

(3)

2.3 Continuous-Space Fourier Transform

(1)

2.4 Existence of Fourier Transform

(1)

2.5 Properties of the Fourier Transform

(6)

2.6 Real Fourier Transform

(2)

2.7 Amplitude and Phase Spectra

(1)

2.8 Hankel Transforms

(4)

3. Fundamentals of Wave Propagation

(16)

3.1 Introduction

(1)

3.2 Waves

(5)

3.3 Electromagnetic Waves

(2)

3.4 Phasor Representation

(1)

3.5 Wave Equations in a Charge-Free Medium

(2)

3.6 Wave Equations in Phasor Representation in a Charge-Free Medium

(1)

3.7 Plane EM Waves

(4)

4. Scalar Diffraction Theory

(22)

4.1 Introduction

(1)

4.2 Helmholtz Equation

(2)

4.3 Angular Spectrum of Plane Waves

(3)

4.4 Fast Fourier Transform (FFT) Implementation of the Angular Spectrum of Plane Waves

(6)

4.5 The Kirchoff Theory of Diffraction

(4)

4.5.1 Kirchoff Theory of Diffraction

(1)

4.5.2 Fresnel-Kirchoff Diffraction Formula

(1)

4.6 The Rayleigh-Sommerfeld Theory of Diffraction

(2)

4.6.1 The Kirchhoff Approximation

(1)

4.6.2 The Second Rayleigh-Sommerfeld Diffraction Formula

(1)

4.7 Another Derivation of the First Rayleigh-Sommerfeld Diffraction Integral

(2)

4.8 The Rayleigh-Sommerfeld Diffraction Integral For Nonmonochromatic Waves

(2)

5. Fresnel and Fraunhofer Approximations

(21)

5.1 Introduction

(1)

5.2 Diffraction in the Fresnel Region

(8)

5.3 FFT Implementation of Fresnel Diffraction

(1)

5.4 Paraxial Wave Equation

(1)

5.5 Diffraction in the Fraunhofer Region

(2)

5.6 Diffraction Gratings

(2)

5.7 Fraunhofer Diffraction By a Sinusoidal Amplitude Grating

(1)

5.8 Fresnel Diffraction By a Sinusoidal Amplitude Grating

(2)

5.9 Fraunhofer Diffraction with a Sinusoidal Phase Grating

(1)

5.10 Diffraction Gratings Made of Slits

(2)

6. Inverse Diffraction

(6)

6.1 Introduction

(1)

6.2 Inversion of the Fresnel and Fraunhofer Representations

(1)

6.3 Inversion of the Angular Spectrum Representation

(1)

6.4 Analysis

(4)

7. Wide-Angle Near and Far Field Approximations for Scalar Diffraction

(22)

7.1 Introduction

(1)

7.2 A Review of Fresnel and Fraunhofer Approximations

(2)

7.3 The Radial Set of Approximations

(2)

7.4 Higher Order Improvements and Analysis

(1)

7.5 Inverse Diffraction and Iterative Optimization

(1)

7.6 Numerical Examples

(13)

7.7 More Accurate Approximations

110

(1)

7.8 Conclusions

111

(1)

8. Geometrical Optics

112

(22)

8.1 Introduction

112

(1)

8.2 Propagation of Rays

112

(5)

8.3 The Ray Equations

117

(1)

8.4 The Eikonal Equation

118

(2)

8.5 Local Spatial Frequencies and Rays

120

(3)

8.6 Matrix Representation of Meridional Rays

123

(7)

8.7 Thick Lenses

130

(2)

8.8 Entrance and Exit Pupils of an Optical System

132

(2)

9. Fourier Transforms and Imaging with Coherent Optical Systems

134

(19)

9.1 Introduction

134

(1)

9.2 Phase Transformation With a Thin Lens

134

(2)

9.3 Fourier Transforms With Lenses

136

(3)

9.3.1 Wave Field Incident on the Lens

136

(1)

9.3.2 Wave Field to the Left of the Lens

137

(1)

9.3.3 Wave Field to the Right of the Lens

138

(1)

9.4 Image Formation As 2-D Linear Filtering

139

(3)

9.4.1 The Effect of Finite Lens Aperture

141

(1)

9.5 Phase Contrast Microscopy

142

(2)

9.6 Scanning Confocal Microscopy

144

(3)

9.6.1 Image Formation

144

(3)

9.7 Operator Algebra for Complex Optical Systems

147

(6)

10. Imaging with Quasi-Monochromatic Waves

153

(24)

10.1 Introduction

153

(1)

10.2 Hilbert Transform

154

(3)

10.3 Analytic Signal

157

(4)

10.4 Analytic Signal Representation of a Nonmonochromatic Wave Field

161

(1)

10.5 Quasi-Monochromatic, Coherent, and Incoherent Waves

162

(1)

10.6 Diffraction Effects in a General Imaging System

162

(2)

10.7 Imaging With Quasi-Monochromatic Waves

164

(2)

10.7.1 Coherent Imaging

165

(1)

10.7.2 Incoherent Imaging

166

(1)

10.8 Frequency Response of a Diffraction-Limited Imaging System

166

(5)

10.8.1 Coherent Imaging System

166

(1)

10.8.2 Incoherent Imaging System

167

(4)

10.9 Computer Computation of the Optical Transfer Function

171

(2)

10.9.1 Practical Considerations

172

(1)

10.10 Aberrations

173

(4)

10.10.1 Zernike Polynomials

174

(3)

11. Optical Devices Based on Wave Modulation

177

(11)

11.1 Introduction

177

(1)

11.2 Photographic Films and Plates

177

(2)

11.3 Transmittance of Light by Film

179

(3)

11.4 Modulation Transfer Function

182

(1)

11.5 Bleaching

183

(1)

11.6 Diffractive Optics, Binary Optics, and Digital Optics

184

(1)

11.7 E-Beam Lithography

185

(3)

11.7.1 DOE Implementation

187

(1)

12. Wave Propagation in Inhomogeneous Media

188

(10)

12.1 Introduction

188

(1)

12.2 Helmholtz Equation For Inhomogeneous Media

189

(1)

12.3 Paraxial Wave Equation For Inhomogeneous Media

189

(1)

12.4 Beam Propagation Method

190

(3)

12.4.1 Wave Propagation in Homogeneous Medium with Index n

191

(1)

12.4.2 The Virtual Lens Effect

192

(1)

12.5 Wave Propagation in a Directional Coupler

193

(5)

12.5.1 A Summary of Coupled Mode Theory

193

(1)

12.5.2 Comparison of Coupled Mode Theory and BPM Computations

194

(4)

13. Holography

198

(14)

13.1 Introduction

198

(1)

13.2 Coherent Wave Front Recording

199

(3)

13.2.1 Leith–Upatnieks Hologram

201

(1)

13.3 Types of Holograms

202

(3)

13.3.1 Fresnel and Fraunhofer Holograms

203

(1)

13.3.2 Image and Fourier Holograms

203

(1)

13.3.3 Volume Holograms

203

(2)

13.3.4 Embossed Holograms

205

(1)

13.4 Computer Simulation of Holographic Reconstruction

205

(1)

13.5 Analysis of Holographic Imaging and Magnification

206

(4)

13.6 Aberrations

210

(2)

14. Apodization, Superresolution, and Recovery of Missing Information

212

(32)

14.1 Introduction

212

(1)

14.2 Apodization

213

(4)

14.2.1 Discrete-Time Windows

215

(2)

14.3 Two-Point Resolution and Recovery of Signals

217

(2)

14.4 Contractions

219

(2)

14.4.1 Contraction Mapping Theorem

220

(1)

14.5 An Iterative Method of Contractions for Signal Recovery

221

(2)

14.6 Iterative Constrained Deconvolution

223

(2)

14.7 Method of Projections

225

(2)

14.8 Method of Projections onto Convex Sets

227

(2)

14.9 Gerchberg–Papoulis (GP) Algorithm

229

(1)

14.10 Other POCS Algorithms

229

(1)

14.11 Restoration From Phase

230

(2)

14.12 Reconstruction From a Discretized Phase Function by Using the DFT

232

(2)

14.13 Generalized Projections

234

(1)

14.14 Restoration From Magnitude

235

(2)

14.14.1 Traps and Tunnels

237

(1)

14.15 Image Recovery By Least Squares and the Generalized Inverse

237

(1)

14.16 Computation of H+ By Singular Value Decomposition (SVD)

238

(2)

14.17 The Steepest Descent Algorithm

240

(2)

14.18 The Conjugate Gradient Method

242

(2)

15. Diffractive Optics I

244

(31)

15.1 Introduction

244

(2)

15.2 Lohmann Method

246

(1)

15.3 Approximations in the Lohmann Method

247

(1)

15.4 Constant Amplitude Lohmann Method

248

(1)

15.5 Quantized Lohmann Method

249

(1)

15.6 Computer Simulations with the Lohmann Method

250

(4)

15.7 A Fourier Method Based on Hard-Clipping

254

(3)

15.8 A Simple Algorithm for Construction of 3-D Point Images

257

(4)

15.8.1 Experiments

259

(2)

15.9 The Fast Weighted Zero-Crossing Algorithm

261

(4)

15.9.1 Off-Axis Plane Reference Wave

264

(1)

15.9.2 Experiments

264

(1)

15.10 One-Image-Only Holography

265

(7)

15.10.1 Analysis of Image Formation

268

(2)

15.10.2 Experiments

270

(2)

15.11 Fresnel Zone Plates

272

(3)

16. Diffractive Optics II

275

(31)

16.1 Introduction

275

(1)

16.2 Virtual Holography

275

(12)

16.2.1 Determination of Phase

276

(2)

16.2.2 Aperture Effects

278

(1)

16.2.3 Analysis of Image Formation

279

(3)

16.2.4 Information Capacity, Resolution, Bandwidth, and Redundancy

282

(1)

16.2.5 Volume Effects

283

(1)

16.2.6 Distortions Due to Change of Wavelength and/or Hologram Size Between Construction and Reconstruction

284

(1)

16.2.7 Experiments

285

(2)

16.3 The Method of POCS for the Design of Binary DOE

287

(2)

16.4 Iterative Interlacing Technique (IIT)

289

(4)

16.4.1 Experiments with the IIT

291

(2)

16.5 Optimal Decimation-in-Frequency Iterative Interlacing Technique (ODIFIIT)

293

(7)

16.5.1 Experiments with ODIFIIT

297

(3)

16.6 Combined Lohmann-ODIFIIT Method

300

(6)

16.6.1 Computer Experiments with the Lohmann-ODIFIIT Method

301

(5)

17. Computerized Imaging Techniques I: Synthetic Aperture Radar

306

(20)

17.1 Introduction

306

(1)

17.2 Synthetic Aperture Radar

306

(2)

17.3 Range Resolution

308

(1)

17.4 Choice of Pulse Waveform

309

(2)

17.5 The Matched Filter

311

(2)

17.6 Pulse Compression by Matched Filtering

313

(3)

17.7 Cross-Range Resolution

316

(1)

17.8 A Simplified Theory of SAR Imaging

317

(3)

17.9 Image Reconstruction with Fresnel Approximation

320

(2)

17.10 Algorithms for Digital Image Reconstruction

322

(4)

17.10.1 Spatial Frequency Interpolation

322

(4)

18. Computerized Imaging II: Image Reconstruction from Projections

326

(12)

18.1 Introduction

326

(1)

18.2 The Radon Transform

326

(2)

18.3 The Projection Slice Theorem

328

(2)

18.4 The Inverse Radon Transform

330

(1)

18.5 Properties of the Radon Transform

331

(1)

18.6 Reconstruction of a Signal From its Projections

332

(1)

18.7 The Fourier Reconstruction Method

333

(2)

18.8 The Filtered-Backprojection Algorithm

335

(3)

19. Dense Wavelength Division Multiplexing

338

(23)

19.1 Introduction

338

(1)

19.2 Array Waveguide Grating

339

(2)

19.3 Method of Irregularly Sampled Zero-Crossings (MISZC)

341

(6)

19.3.1 Computational Method for Calculating the Correction Terms

345

(1)

19.3.2 Extension of MISZC to 3-D Geometry

346

(1)

19.4 Analysis of MISZC

347

(4)

19.4.1 Dispersion Analysis

349

(1)

19.4.2 Finite-Sized Apertures

350

(1)

19.5 Computer Experiments

351

(8)

19.5.1 Point-Source Apertures

351

(2)

19.5.2 Large Number of Channels

353

(2)

19.5.3 Finite-Sized Apertures

355

(1)

19.5.4 The Method of Creating the Negative Phase

355

(1)

19.5.5 Error Tolerances

356

(1)

19.5.6 3-D Simulations

356

(2)

19.5.7 Phase Quantization

358

(1)

19.6 Implementational Issues

359

(2)

20. Numerical Methods for Rigorous Diffraction Theory

361

(16)

20.1 Introduction

361

(1)

20.2 BPM Based on Finite Differences

362

(2)

20.3 Wide Angle BPM

364

(3)

20.4 Finite Differences

367

(1)

20.5 Finite Difference Time Domain Method

368

(3)

20.5.1 Yee's Algorithm

368

(3)

20.6 Computer Experiments

371

(3)

20.7 Fourier Modal Methods

374

(3)

Appendix A: The Impulse Function

377

(5)

Appendix B: Linear Vector Spaces

382

(9)

Appendix C: The Discrete-Time Fourier Transform, The Discrete Fourier Transform and The Fast Fourier Transform

391

(6)

References

397

(6)

Index

403

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Diffraction, Fourier Optics and Imaging

Summary

Author Biography

Table of Contents

Supplemental Materials