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Phase-Space Optics: Fundamentals and Applications [Kõva köide]

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  • Formaat: Hardback, 416 pages, kõrgus x laius x paksus: 236x160x30 mm, kaal: 724 g, 0 Illustrations
  • Ilmumisaeg: 16-Aug-2009
  • Kirjastus: McGraw-Hill Professional
  • ISBN-10: 0071597980
  • ISBN-13: 9780071597982
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Phase-Space Optics: Fundamentals and ApplicationsSuurem pilt
  • Formaat: Hardback, 416 pages, kõrgus x laius x paksus: 236x160x30 mm, kaal: 724 g, 0 Illustrations
  • Ilmumisaeg: 16-Aug-2009
  • Kirjastus: McGraw-Hill Professional
  • ISBN-10: 0071597980
  • ISBN-13: 9780071597982
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A comprehensive cross section of phase-space optics

This definitive volume highlights an elegant, unified approach to optical rays, waves, and system design using cutting-edge phase-space techniques. Phase-Space Optics: Fundamentals and Applications details theoretical concepts of phase space as well as novel engineering applications in specific disciplines. This authoritative guide includes full coverage of sampling, superresolution imaging, and the phase-space interpretation of ultrafast optics. Work with Wigner optics, analyze phase-space equations, develop wave propagation models, and gain a new understanding of optical sources and systems. Discover how to:





Describe optical phenomena using Wigner and ambiguity functions

Perform phase-space rotations using ray transformation matrices

Influence the trade-off between pupil size and depth of field

Analyze and design optical signals using the Radon-Wigner transform

Accomplish superresolution by squeezing phase space

Interpret the intimate relationship between radiometry and coherence

Use basic algebra to discover self-imaging, Fresnel diffraction, and the Talbot effect

Develop discrete models, sampling criteria, and interpolation formulae

Work with ultrafast processes and complex space-time structures
Preface xiii
Wigner Distribution in Optics
1(44)
Introduction
1(1)
Elementary Description of Optical Signals and Systems
2(3)
Impulse Response and Coherent Point-Spread Function
3(1)
Mutual Coherence Function and Cross-Spectral Density
3(1)
Some Basic Examples of Optical Signals
4(1)
Wigner Distribution and ambiguity Function
5(7)
Definitions
5(2)
Some Basic Examples Again
7(2)
Gaussian Light
9(2)
Local Frequency Spectrum
11(1)
Some Properties of the Wigner Distribution
12(3)
Inversion Formula
12(1)
Shift Covariance
12(1)
Radiometric Quantities
12(2)
Instantaneous Frequency
14(1)
Moyal's Relationship
15(1)
One-Dimensional Case and the Fractional Fourier Transformation
15(3)
Fractional Fourier Transformation
15(1)
Rotation in Phase Space
16(1)
Generalized Marginals---Radon Transform
16(2)
Propagation of the Wigner Distribution
18(6)
First-Order Optical Systems---Ray Transformation Matrix
18(1)
Phase-Space Rotators---More Rotations in Phase Space
19(2)
More General Systems---Ray-Spread Function
21(1)
Geometric-Optical Systems
22(1)
Transport Equations
23(1)
Wigner Distribution Moments in First-Order Optical Systems
24(5)
Moment Invariants
25(1)
Moment Invariants for Phase-Space Rotators
26(2)
Symplectic Moment Matrix---The Bilinear ABCD Law
28(1)
Measurement of Moments
29(1)
Coherent Signals and the Cohen Class
29(11)
Multicomponent Signals---Auto-Terms and Cross-Terms
30(2)
One-Dimensional Case and Some Basic Cohen Kernels
32(1)
Rotation of the Kernel
33(2)
Rotated Version of the Smoothed Interferogram
35(5)
Conclusion
40(1)
References
40(5)
Ambiguity Function in Optical Imaging
45(18)
Introduction
45(2)
Intensity Spectrum of a Fresnel Diffraction Pattern Under Coherent Illumination
47(2)
General Formulation
47(1)
Application to Simple Objects
48(1)
Contrast Transfer Functions
49(1)
Propagation through a Paraxial Optical System in Terms of AF
49(3)
Propagation in Free Space
49(1)
Transmission through a Thin Object
50(1)
Propagation in a Paraxial Optical System
51(1)
The AF in Isoplanatic (Space-Invariant) Imaging
52(1)
The AF of the Image of an Incoherent Source
53(2)
Derivation of the Zernike-Van Cittert Theorem fromthe Propagation of the AF
53(1)
Partial Coherence Properties in the Image of an Incoherent Source
54(1)
The Pupil-AF as a Generalization of the OTF
54(1)
Phase-Space Tomography
55(1)
Another Possible Approach to AF Reconstruction
56(2)
Propagation-Based Holographic Phase Retrieval from Several Images
58(2)
Fresnel Diffraction Images as In-Line Holograms
58(1)
Application to Phase Retrieval and X-Ray Holotomography
59(1)
Conclusion
60(1)
References
60(3)
Rotations in Phase Space
63(44)
Introduction
63(1)
First-Order Optical Systems and Canonical Integral Transforms
64(3)
Canonical Integral Transforms and Ray Transformation Matrix Formalism
64(2)
Modified Iwasawa Decomposition of Ray Transformation Matrix
66(1)
Canonical Transformations Producing Phase-Space Rotations
67(7)
Matrix and Operator Description
67(2)
Signal Rotator
69(1)
Fractional Fourier Transform
69(4)
Gyrator
73(1)
Other Phase-Space Rotators
74(1)
Properties of the Phase-Space Rotators
74(6)
Some Useful Relations for Phase-Space Rotators
75(1)
Similarity to the Fractional Fourier Transform
76(1)
Shift Theorem
77(1)
Convolution Theorem
77(1)
Scaling Theorem
77(1)
Phase-Space Rotations of Selected Functions
78(2)
Eigenfunctions for Phase-Space Rotators
80(4)
Some Relations for the Eigenfunctions
80(2)
Mode Presentation on Orbital Poincare Sphere
82(2)
Optical Setups for Basic Phase-Space Rotators
84(4)
Flexible Optical Setups for Fractional FT and Gyrator
85(2)
Flexible Optical Setup for Image Rotator
87(1)
Applications of Phase-Space Rotators
88(13)
Generalized Convolution
88(2)
Pattern Recognition
90(4)
Chirp Signal Analysis
94(1)
Signal Encryption
94(1)
Mode Converters
95(1)
Beam Characterization
96(4)
Gouy Phase Accumulation
100(1)
Conclusions
101(1)
Acknowledgments
102(1)
References
102(5)
The Radon-Wigner Transform in Analysis, Design, and Processing of Optical Signals
107(58)
Introduction
107(1)
Projections of the Wigner Distribution Function in Phase Space: The Radon-Wigner Transform (RWT)
108(14)
Definition and Basic Properties
108(9)
Optical Implementation of the RWT: The Radon-Wigner Display
117(5)
Analysis of Optical Signals and Systems by Means of the RWT
122(29)
Analysis of Diffraction Phenomena
122(1)
Computation of Irradiance Distribution along Different paths in Image Space
122(10)
Parallel Optical Display of Diffraction Patterns
132(2)
Inverting RWT: Phase-Space Tomographic Reconstruction of Optical Fields
134(4)
Merit Functions of Imaging Systems in Terms of the RWT
138(1)
Axial Point-Spread Function (PSF) and Optical Transfer Function (OTF)
138(5)
Polychromatic OTF
143(3)
Polychromatic Axial PSF
146(5)
Design of Imaging Systems and Optical Signal Processing by Means of RWT
151(11)
Optimization of Optical Systems: Achromatic Design
151(5)
Controlling the Axial Response: Synthesis of Pupil Masks by RWT Inversion
156(1)
Signal Processing through RWT
157(5)
Acknowledgments
162(1)
References
162(3)
Imaging Systems: Phase-Space Representations
165(28)
Introduction
165(1)
The Product-Space Representation and Product Spectrum Representation
166(4)
Optical Imaging Systems
170(3)
Bilinear Optical Systems
173(3)
Noncoherent Imaging Systems
176(2)
Tolerance to Focus Errors and to Spherical Aberration
178(5)
Phase Conjugate Plates
183(6)
References
189(4)
Super Resolved Imaging in Wigner-Based Phase Space
193(24)
Introduction
193(2)
General Definitions
195(2)
Description of SR
197(16)
Code Division Multiplexing
200(1)
Time Multiplexing
201(1)
Polarization Multiplexing
202(1)
Wavelength Multiplexing
203(1)
Gray-Level Multiplexing
203(2)
Description in the Phase-Space Domain
205(8)
Conclusions
213(1)
References
214(3)
Radiometry, Wave Optics, and Spatial Coherence
217(20)
Introduction
217(1)
Conventional Radiometry
218(3)
Lambertian Sources
221(1)
Mutual Coherence Function
221(3)
Stationary Phase Approximation
224(2)
Radiometry and Wave Optics
226(5)
Examples
231(4)
Blackbody Radiation
231(1)
Noncoherent Source
232(1)
Coherent Wave Fields
233(1)
Quasi-Homogeneous Wave Field
234(1)
Acknowledgments
235(1)
References
235(2)
Rays and Waves
237(42)
Introduction
237(1)
Small-Wavelength Limit in the Position Representation I: Geometrical Optics
238(7)
The Eikonal and Geometrical Optics
239(3)
Choosing z as the Parameter
242(1)
Ray-Optical Phase Space and the Lagrange Manifold
243(2)
Small-Wavelength Limit in the Position Representation II: The Transport Equation and the Field Estimate
245(4)
The Debye Series Expansion
245(1)
The Transport Equation and Its Solution
245(2)
The Field Estimate and Its Problems at Caustics
247(2)
Flux Lines versus Rays
249(1)
Analogy with Quantum Mechanics
250(4)
Semiclassical Mechanics
251(2)
Bohmian Mechanics and the Hydrodynamic Model
253(1)
Small-Wavelength Limit in the Momentum Representation
254(6)
The Helmholtz Equation in the Momentum Representation
254(2)
Asymptotic Treatment and Ray Equations
256(2)
Transport Equation in the Momentum Representation
258(1)
Field Estimate
259(1)
Maslov's Canonical Operator Method
260(1)
Gaussian Beams and Their Sums
261(5)
Parabasal Gaussian Beams
261(3)
Sums of Gaussian Beams
264(2)
Stable Aggregates of Flexible Elements
266(5)
Derivation of the Estimate
266(3)
Insensitivity to γ
269(1)
Phase-Space Interpretation
270(1)
A Simple Example
271(4)
Concluding Remarks
275(1)
References
275(4)
Self-Imaging in Phase Space
279(30)
Introduction
279(1)
Phase-Space Optics Minimum Tool Kit
280(4)
Self-Imaging of Paraxial Wavefronts
284(1)
The Talbot Effect
285(4)
The ``Walk-Off'' Effect
289(1)
The Fractional Talbot Effect
290(5)
Matrix Formulation of the Fractional Talbot Effect
295(3)
Point Source Illumination
298(3)
Another Path to Self-Imaging
301(1)
Self-Imaging and Incoherent Illumination
302(3)
Summary
305(1)
References
306(3)
Sampling and Phase Space
309(28)
Introduction
309(3)
Notation and Some Initial Concepts
312(9)
The Wigner Distribution Function and Properties
312(2)
The Linear Canonical Transform and the WDF
314(1)
The Phase-Space Diagram
314(2)
Harmonics and Chirps and Convolutions
316(2)
The Comb Function and Rect Function
318(1)
Comb Functions
318(2)
Rect Functions
320(1)
Finite Supports
321(4)
Band-limitedness in Fourier Domain
321(1)
Band-limitedness and the LCT
322(2)
Finite Space-Bandwidth Product---Compact Support in x and k
324(1)
Sampling a Signal
325(4)
Nyquist-Shannon Sampling
325(3)
Generalized Sampling
328(1)
Simulating an Optical System: Sampling at the Input and Output
329(3)
Conclusion
332(1)
References
332(5)
Phase Space in Ultrafast Optics
337(48)
Introduction
337(1)
Phase-Space Representations for Short Optical Pulses
338(19)
Representation of Pulsed Fields
338(2)
Pulse Ensembles and Correlation Functions
340(3)
The Time-Frequency Phase Space
343(6)
Phase-Space Representation of Paraxial Optical Systems
349(4)
Temporal Paraxiality and the Chronocyclic Phase Space
353(4)
Metrology of Short Optical Pulses
357(21)
Measurement Strategies
357(1)
Pulse Characterization Apparatuses as Linear Systems
358(3)
Phase-Space Methods
361(1)
Spectrographic Techniques
362(4)
Tomographic Techniques
366(3)
Interferometric or Direct Techniques
369(1)
Two-Pulse Double-Slit Interferometry
370(4)
Shearing Interferometry
374(4)
Conclusions
378(1)
References
379(6)
Index 385
Markus Testorf is currently an assistant professor at the Thayer School of Engineering at Dartmouth College. He has written numerous articles on the use of phase-space optics and has taught optics courses throughout his professional career.



Bryan Hennelly is currently a research fellow at the National University of Ireland, Maynooth. He has written or coauthored numerous articles based on Wigner or phase-space optics relating to optical metrology systems and the sampling and numerical simulation of optical systems.



Jorge Ojeda-Castañeda has been a visiting professor at the Institute of Optics in Madrid, the University of Valencia, the Autonomous University of Barcelona, and the University James I in Spain. He is currently professor of applied optics, in the University of Guanajuato, México. Dr. Ojeda-Castañeda is a fellow of the SPIE and the OSA.