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9780471238164

Diffraction, Fourier Optics and Imaging

by
  • ISBN13:

    9780471238164

  • ISBN10:

    0471238163

  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2006-12-01
  • Publisher: Wiley-Interscience
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Summary

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.

Author Biography

OKAN K. ERSOY, PhD, is Professor of Electrical and Computer Engineering at Purdue University. He is also an adjunct professor at Bogazici University. His research interests include optical information processing, digital signal/image processing, statistical and computer intelligence, Fourier-related transforms and time- frequency methods.

Table of Contents

Preface xiii
1. Diffraction, Fourier Optics and Imaging
1(5)
1.1 Introduction
1(1)
1.2 Examples of Emerging Applications with Growing Significance
2(4)
1.2.1 Dense Wavelength Division Multiplexing/Demultiplexing (DWDM)
3(1)
1.2.2 Optical and Microwave DWDM Systems
3(1)
1.2.3 Diffractive and Subwavelength Optical Elements
3(1)
1.2.4 Nanodiffractive Devices and Rigorous Diffraction Theory
4(1)
1.2.5 Modern Imaging Techniques
4(2)
2. Linear Systems and Transforms
6(19)
2.1 Introduction
6(1)
2.2 Linear Systems and Shift Invariance
7(3)
2.3 Continuous-Space Fourier Transform
10(1)
2.4 Existence of Fourier Transform
11(1)
2.5 Properties of the Fourier Transform
12(6)
2.6 Real Fourier Transform
18(2)
2.7 Amplitude and Phase Spectra
20(1)
2.8 Hankel Transforms
21(4)
3. Fundamentals of Wave Propagation
25(16)
3.1 Introduction
25(1)
3.2 Waves
26(5)
3.3 Electromagnetic Waves
31(2)
3.4 Phasor Representation
33(1)
3.5 Wave Equations in a Charge-Free Medium
34(2)
3.6 Wave Equations in Phasor Representation in a Charge-Free Medium
36(1)
3.7 Plane EM Waves
37(4)
4. Scalar Diffraction Theory
41(22)
4.1 Introduction
41(1)
4.2 Helmholtz Equation
42(2)
4.3 Angular Spectrum of Plane Waves
44(3)
4.4 Fast Fourier Transform (FFT) Implementation of the Angular Spectrum of Plane Waves
47(6)
4.5 The Kirchoff Theory of Diffraction
53(4)
4.5.1 Kirchoff Theory of Diffraction
55(1)
4.5.2 Fresnel-Kirchoff Diffraction Formula
56(1)
4.6 The Rayleigh-Sommerfeld Theory of Diffraction
57(2)
4.6.1 The Kirchhoff Approximation
59(1)
4.6.2 The Second Rayleigh-Sommerfeld Diffraction Formula
59(1)
4.7 Another Derivation of the First Rayleigh-Sommerfeld Diffraction Integral
59(2)
4.8 The Rayleigh-Sommerfeld Diffraction Integral For Nonmonochromatic Waves
61(2)
5. Fresnel and Fraunhofer Approximations
63(21)
5.1 Introduction
63(1)
5.2 Diffraction in the Fresnel Region
64(8)
5.3 FFT Implementation of Fresnel Diffraction
72(1)
5.4 Paraxial Wave Equation
73(1)
5.5 Diffraction in the Fraunhofer Region
74(2)
5.6 Diffraction Gratings
76(2)
5.7 Fraunhofer Diffraction By a Sinusoidal Amplitude Grating
78(1)
5.8 Fresnel Diffraction By a Sinusoidal Amplitude Grating
79(2)
5.9 Fraunhofer Diffraction with a Sinusoidal Phase Grating
81(1)
5.10 Diffraction Gratings Made of Slits
82(2)
6. Inverse Diffraction
84(6)
6.1 Introduction
84(1)
6.2 Inversion of the Fresnel and Fraunhofer Representations
84(1)
6.3 Inversion of the Angular Spectrum Representation
85(1)
6.4 Analysis
86(4)
7. Wide-Angle Near and Far Field Approximations for Scalar Diffraction
90(22)
7.1 Introduction
90(1)
7.2 A Review of Fresnel and Fraunhofer Approximations
91(2)
7.3 The Radial Set of Approximations
93(2)
7.4 Higher Order Improvements and Analysis
95(1)
7.5 Inverse Diffraction and Iterative Optimization
96(1)
7.6 Numerical Examples
97(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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