Diffraction, Fourier Optics and Imaging

Learn Fourier and diffractive optics through examples and computer simulation
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, and micro/nano systems. The author demonstrates how these theories become the foundation for a number of practical applications, including:TomographyMagnetic resonance imagingSynthetic aperture radar (SAR) and interferometric SAROptical communications and networking devices, such as directional couplers in fiber and integrated optics, dense wavelength division multiplexing and demimultiplexing systemsComputer–generated holograms and analog hologramsWireless systems using EM wavesMicro/nano systems requiring rigorous diffraction analysis
Diffraction, Fourier Optics and Imaging takes an innovative approach that focuses on the use of examples and computer simulations. This approach emerged from the author′s course notes and has been refined during his many years of classroom experience. Readers are given clear and concise explanations of theory, and examples that demonstrate the practical applications of theory are provided. Finally, readers are given exercises, ranging from simple to complex, to apply their knowledge to solving real–world problems. Many of the exercises and examples are solved using MATLAB®, enabling readers to perform highly complex computational tasks through software simulation.
This book is ideal for upper–level undergraduate and graduate courses in electrical engineering and physics. Its many examples and topics with computer simulation show students how an understanding of Fourier analysis can be applied in a broad range of fields in science and technology. Engineers and scientists particularly related to optical engineering, micro /nano systems and fiber optic communications/networking will find this an excellent resource that sheds new light on how to resolve key problems in imaging.

Spis treści:
Preface.
1. Diffraction, Fourier Optics and Imaging.
1.1 Introduction.
1.2 Examples of Emerging Applications with Growing Significance.
2. Linear Systems and Transforms.
2.1 Introduction.
2.2 Linear Systems and Shift Invariance.
2.3 Continuous–Space Fourier Transform.
2.4 Existence of Fourier Transform.
2.5 Properties of the Fourier Transform.
2.6 Real Fourier Transform.
2.7 Amplitude and Phase Spectra.
2.8 Hankel Transforms.
3. Fundamentals of Wave Propagation.
3.1 Introduction.
3.2 Waves.
3.3 Electromagnetic Waves.
3.4 Phasor Representation.
3.5 Wave Equations in a Charge–Free Medium.
3.6 Wave Equations in Phasor Representation in a Charge–Free Medium.
3.7 Plane EM Waves.
4. Scalar Diffraction Theory.
4.1 Introduction.
4.2 Helmholtz Equation.
4.3 Angular Spectrum of Plane Waves.
4.4 Fast Fourier Transform (FFT) Implementation of the Angular Spectrum of Plane Waves.
4.5 The Kirchoff Theory of Diffraction.
4.6 The Rayleigh–Sommerfeld Theory of Diffraction.
4.7 Another Derivation of the First Rayleigh–Sommerfeld Diffraction Integral.
4.8 The Rayleigh–Sommerfeld Diffraction Integral For Nonmonochromatic Waves.
5. Fresnel and Fraunhofer Approximations.
5.1 Introduction.
5.2 Diffraction in the Fresnel Region.
5.3 FFT Implementation of Fresnel Diffraction.
5.4 Paraxial Wave Equation.
5.5 Diffraction in the Fraunhofer Region.
5.6 Diffraction Gratings.
5.7 Fraunhofer Diffraction By a Sinusoidal Amplitude Grating.
5.8 Fresnel Diffraction By a Sinusoidal Amplitude Grating.
5.9 Fraunhofer Diffraction with a Sinusoidal Phase Grating.
5.10 Diffraction Gratings Made of Slits.
6. Inverse Diffracti on.
6.1 Introduction.
6.2 Inversion of the Fresnel and Fraunhofer Representations.
6.3 Inversion of the Angular Spectrum Representation.
6.4 Analysis.
7. Wide–Angle Near and Far Field Approximations for Scalar Diffraction.
7.1 Introduction.
7.2 A Review of Fresnel and Fraunhofer Approximations.
7.3 The Radial Set of Approximations.
7.4 Higher Order Improvements and Analysis.
7.5 Inverse Diffraction and Iterative Optimization.
7.6 Numerical Examples.
7.7 More Accurate Approximations.
7.8 Conclusions.
8. Geometrical Optics.
8.1 Introduction.
8.2 Propagation of Rays.
8.3 The Ray Equations.
8.4 The Eikonal Equation.
8.5 Local Spatial Frequencies and Rays.
8.6 Matrix Representation of Meridional Rays.
8.7 Thick Lenses.
8.8 Entrance and Exit Pupils of an Optical System.
9. Fourier Transforms and Imaging with Coherent Optical Systems.
9.1 Introduction.
9.2 Phase Transformation With a Thin Lens.
9.3 Fourier Transforms With Lenses.
9.4 Image Formation As 2–D Linear Filtering.
9.5 Phase Contrast Microscopy.
9.6 Scanning Confocal Microscopy.
9.7 Operator Algebra for Complex Optical Systems.
10. Imaging with Quasi–Monochromatic Waves.
10.1 Introduction.
10.2 Hilbert Transform.
10.3 Analytic Signal.
10.4 Analytic Signal Representation of a Nonmonochromatic Wave Field.
10.5 Quasi–Monochromatic, Coherent, and Incoherent Waves.
10.6 Diffraction Effects in a General Imaging System.
10.7 Imaging With Quasi–Monochromatic Waves.
10.8 Frequency Response of a Diffraction–Limited Imaging System.
10.9 Computer Computation of the Optical Transfer Function.
10.10 Aberrations.
11. Optical Devices Based on Wave Modulation.
11.1 Introduction.
11.2 Photographic Films and Plates.
11.3 Transmittance of Light by Film.
11.4 Modulation Transfer Function.
11.5 Bleaching.
11.6 Diffracti ve Optics, Binary Optics, and Digital Optics.
11.7 E–Beam Lithography.
12. Wave Propagation in Inhomogeneous Media.
12.1 Introduction.
12.4 Beam Propagation Method.
12.5 Wave Propagation in a Directional Coupler.
13. Holography.
13.1 Introduction.
13.2 Coherent Wave Front Recording.
13.3 Types of Holograms.
13.4 Computer Simulation of Holographic Reconstruction.
13.5 Analysis of Holographic Imaging and Magnification.
13.6 Aberrations.
14. Apodization, Superresolution, and Recovery of Missing Information.
14.1 Introduction.
14.2 Apodization.
14.2.1 Discrete–Time Windows.
14.3 Two–Point Resolution and Recovery of Signals.
14.4 Contractions.
14.5 An Iterative Method of Contractions for Signal Recovery.
14.6 Iterative Constrained Deconvolution.
14.7 Method of Projections.
14.8 Method of Projections onto Convex Sets.
14.9 Gerchberg–Papoulis (GP) Algorithm.
14.10 Other POCS Algorithms.
14.11 Restoration From Phase.
14.12 Reconstruction From a Discretized Phase Function by Using the DFT.
14.13 Generalized Projections.
14.14 Restoration From Magnitude.
14.15 Image Recovery By Least Squares and the Generalized Inverse.
14.16 Computation of Hþ By Singular Value Decomposition (SVD).
14.17 The Steepest Descent Algorithm.
14.18 The Conjugate Gradient Method.
15. Diffractive Optics I.
15.1 Introduction.
15.2 Lohmann Method.
15.3 Approximations in the Lohmann Method.
15.4 Constant Amplitude Lohmann Method.
15.5 Quantized Lohmann Method.
15.6 Computer Simulations with the Lohmann Method.
15.7 A Fourier Method Based on Hard–Clipping.
15.8 A Simple Algorithm for Construction of 3–D Point Images.
15.9 The Fast Weighted Zero–Crossing Algorithm.
15.10 One–Image–Only Holography.
15.11 Fresnel Zone Plates.
16. Diffractive Optics II.
16.1 Introduction.
16.2