Phase-space optics: fundamentals and applications
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
New York [u.a.]
McGraw-Hill
2010
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 393 S. Ill., graph. Darst. |
| ISBN: | 9780071597982 |
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MARC
| LEADER | 00000nam a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV035765137 | ||
| 003 | DE-604 | ||
| 005 | 20101108 | ||
| 007 | t | ||
| 008 | 091012s2010 xxuad|| |||| 00||| eng d | ||
| 010 | |a 2009026369 | ||
| 020 | |a 9780071597982 |9 978-0-07-159798-2 | ||
| 035 | |a (OCoLC)277205896 | ||
| 035 | |a (DE-599)BVBBV035765137 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
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| 049 | |a DE-703 |a DE-83 | ||
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| 084 | |a ZN 6280 |0 (DE-625)157542: |2 rvk | ||
| 245 | 1 | 0 | |a Phase-space optics |b fundamentals and applications |c Markus E. Testorf ; Bryan M. Hennelly ; Jorge Ojeda-Castañeda |
| 246 | 1 | 3 | |a Phase space optics |
| 264 | 1 | |a New York [u.a.] |b McGraw-Hill |c 2010 | |
| 300 | |a XV, 393 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Light |x Transmission | |
| 650 | 4 | |a Optics |x Statistical methods | |
| 650 | 4 | |a Wigner distribution | |
| 650 | 4 | |a Phase space (Statistical physics) | |
| 650 | 0 | 7 | |a Statistische Optik |0 (DE-588)4182960-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Phasenraum |0 (DE-588)4139912-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Phasenraum |0 (DE-588)4139912-2 |D s |
| 689 | 0 | 1 | |a Statistische Optik |0 (DE-588)4182960-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Testorf, Markus E. |e Sonstige |4 oth | |
| 700 | 1 | |a Hennelly, Bryan M. |e Sonstige |4 oth | |
| 700 | 1 | |a Ojeda-Castañeda, Jorge |e Sonstige |4 oth | |
| 856 | 4 | 2 | |m Digitalisierung UB Bayreuth |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018624940&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018624940 | ||
Record in the Search Index
| _version_ | 1804140691463340032 |
|---|---|
| adam_text | Contents
Preface
....................................................... xüi
Wigner Distribution in
Optics
........................ 1
1.1
Introduction
............................................ 1
1.2
Elementary Description of Optical
Signals
and Systems
............................................ 2
1.2.1
Impulse Response and Coherent
Point-Spread Function
........................... 3
1.2.2
Mutual Coherence Function
and Cross-Spectral Density
...................... 3
1.2.3
Some Basic Examples of Optical Signals
.......... 4
1.3
Wigner Distribution and Ambiguity Function
........... 5
1.3.1
Definitions
....................................... 5
1.3.2
Some Basic Examples Again
...................... 7
1.3.3
Gaussian Light
................................... 9
1.3.4
Local Frequency Spectrum
...................... 11
1.4
Some Properties of the Wigner Distribution
............ 12
1.4.1
Inversion Formula
.............................. 12
1.4.2
Shift Covariance
................................ 12
1.4.3 Radiometrie
Quantities
......................... 12
1.4.4
Instantaneous Frequency
....................... 14
1.4.5
Moyal s Relationship
........................... 15
1.5
One-Dimensional Case and the Fractional
Fourier Transformation
................................ 15
1.5.1
Fractional Fourier Transformation
............... 15
1.5.2
Rotation in Phase Space
......................... 16
1.5.3
Generalized Marginals
—
Radon Transform
...... 16
1.6
Propagation of the Wigner Distribution
................ 18
1.6.1
First-Order Optical Systems—Ray
Transformation Matrix
.......................... 18
1.6.2
Phase-Space Rotators
—
More Rotations
in Phase Space
.................................. 19
VI Contents
1.6.3
More General Systems
—
Ray-Spread Function
... 21
1.6.4
Geometric-Optical
Systems
..................... 22
1.6.5
Transport Equations
............................ 23
1.7
Wigner
Distribution Moments in First-Order
Optical Systems
....................................... 24
1.7.1
Moment Invariants
............................. 25
1.7.2
Moment Invariants for Phase-Space Rotators
— 26
1.7.3
Symplectic Moment Matrix
—
The Bilinear
ABCD Law
..................................... 28
1.7.4
Measurement of Moments
...................... 29
1.8
Coherent Signals and the Cohen Class
................. 29
1.8.1
Multicomponent Signals
—
Auto-Terms
and Cross-Terms
............................... 30
1.8.2
One-Dimensional Case and Some Basic
Cohen Kernels
................................. 32
1.8.3
Rotation of the Kernel
........................... 33
1.8.4
Rotated Version of the Smoothed
Interferogram
.................................. 35
1.9
Conclusion
............................................ 40
References
.................................................. 40
Ambiguity Function in Optical Imaging
............ 45
2.1
Introduction
........................................... 45
2.2
Intensity Spectrum of a Fresnel Diffraction
Pattern Under Coherent Illumination
.................. 47
2.2.1
General Formulation
............................ 47
2.2.2
Application to Simple Objects
................... 48
2.2.3
Contrast Transfer Functions
..................... 49
2.3
Propagation through a Paraxial Optical System
in Terms of AF
......................................... 49
2.3.1
Propagation in Free Space
....................... 49
2.3.2
Transmission through a Thin Object
............. 50
2.3.3
Propagation in a Paraxial Optical System
........ 51
2.4
The AF in Isoplanatic (Space-Invariant) Imaging
....... 52
2.5
The AF of the Image of an Incoherent Source
........... 53
2.5.1
Derivation of the Zernike-Van Cittert
Theorem from the Propagation of the AF
....... 53
2.5.2
Partial Coherence Properties in the Image
of an Incoherent Source
......................... 54
2.5.3
The Pupil-AF as a Generalization of the OTF
.... 54
2.6
Phase-Space Tomography
.............................. 55
2.7
Another Possible Approach to AF Reconstruction
...... 56
Contents
VII
2.8
Propagation-Based Holographic Phase Retrieval
from Several Images
................................... 58
2.8.1
Fresnel Diffraction Images
as In-Line Holograms
.......................... 58
2.8.2
Application to Phase Retrieval
and
Х
-Ray Holotomography
.................... 59
2.9
Conclusion
............................................ 60
References
.................................................. 60
Rotations in Phase Space
............................ 63
3.1
Introduction
........................................... 63
3.2
First-Order Optical Systems and Canonical
Integral Transforms
.................................... 64
3.2.1
Canonical Integral Transforms and Ray
Transformation Matrix Formalism
.............. 64
3.2.2
Modified Iwasawa Decomposition of Ray
Transformation Matrix
.......................... 66
3.3
Canonical Transformations Producing
Phase-Space Rotations
................................. 67
3.3.1
Matrix and Operator Description
................ 67
3.3.2
Signal Rotator
.................................. 69
3.3.3
Fractional Fourier Transform
.................... 69
3.3.4
Gyrator
......................................... 73
3.3.5
Other Phase-Space Rotators
..................... 74
3.4
Properties of the Phase-Space Rotators
................. 74
3.4.1
Some Useful Relations for Phase-Space
Rotators
........................................ 75
3.4.2
Similarity to the Fractional Fourier Transform
... 76
3.4.3
Shift Theorem
.................................. 77
3.4.4
Convolution Theorem
.......................... 77
3.4.5
Scaling Theorem
................................ 77
3.4.6
Phase-Space Rotations of Selected Functions
___ 78
3.5
Eigenfunctions for Phase-Space Rotators
............... 80
3.5.1
Some Relations for the Eigenfunctions
.......... 80
3.5.2
Mode Presentation on Orbital
Poincaré
Sphere
.. 82
3.6
Optical Setups for Basic Phase-Space Rotators
.......... 84
3.6.1
Flexible Optical Setups for Fractional FT
and Gyrator
.................................... 85
3.6.2
Flexible Optical Setup for Image Rotator
........ 87
3.7
Applications of Phase-Space Rotators
.................. 88
3.7.1
Generalized Convolution
....................... 88
3.7.2
Pattern Recognition
............................. 90
VHI
Contents
3.7.3
Chirp
Signal
Analysis
........................... 94
3.7.4
Signal Encryption
............................... 94
3.7.5
Mode Converters
............................... 95
3.7.6
Beam Characterization
.......................... 96
3.7.7
Gouy Phase Accumulation
..................... 100
3.8
Conclusions
.......................................... 101
Acknowledgments
........................................ 102
References
................................................. 102
The Radon-Wigner Transf
orni in
Analysis, Design,
and Processing of Optical Signals
.................. 107
4.1
Introduction
.......................................... 107
4.2
Projections of the Wigner Distribution Function
in Phase Space: The Radon-Wigner
Transform (RWT)
..................................... 108
4.2.1
Definition and Basic Properties
................ 108
4.2.2
Optical Implementation of the RWT:
The Radon-Wigner Display
.................... 117
4.3
Analysis of Optical Signals and Systems
by Means of the RWT
................................. 122
4.3.1
Analysis of Diffraction Phenomena
............ 122
4.3.1.1
Computation of Irradiance
Distribution along Different Paths
in Image Space
........................ 122
4.3.1.2
Parallel Optical Display
of Diffraction Patterns
................. 132
4.3.2
Inverting RWT: Phase-Space
Tomographie
Reconstruction of Optical Fields
............... 134
4.3.3
Merit Functions of Imaging Systems
in Terms of the RWT
........................... 138
4.3.3.1
Axial Point-Spread Function
(PSF)
and Optical Transfer Function (OTF)
... 138
4.3.3.2
Polychromatic OTF
.................... 143
4.3.3.3
Polychromatic Axial
PSF .............. 146
4.4
Design of Imaging Systems and Optical
Signal Processing by Means of RWT
.................. 151
4.4.1
Optimization of Optical Systems:
Achromatic Design
............................ 151
4.4.2
Controlling the Axial Response: Synthesis
of Pupil Masks by RWT Inversion
............. 156
4.4.3
Signal Processing through RWT
................ 157
Acknowledgments
........................................ 162
References
................................................. 162
Contents
IX
5
Imaging
Systems: Phase-Space
Representations .
.. 165
5.1
Introduction
.......................................... 165
5.2
The Product-Space Representation and Product
Spectrum Representation
............................. 166
5.3
Optical Imaging Systems
............................. 170
5.4
Bilinear Optical Systems
.............................. 173
5.5
Noncoherent Imaging Systems
....................... 176
5.6
Tolerance to Focus Errors and
to Spherical Aberration
............................... 178
5.7
Phase Conjugate Plates
............................... 183
References
................................................. 189
6
Super Resolved Imaging in Wigner-Based
Phase Space
........................................ 193
6.1
Introduction
.......................................... 193
6.2
General Definitions
................................... 195
6.3
Description of SR
.................................... 197
6.3.1
Code Division Multiplexing
................... 200
6.3.2
Time Multiplexing
............................. 201
6.3.3
Polarization Multiplexing
...................... 202
6.3.4
Wavelength Multiplexing
...................... 203
6.3.5
Gray-Level Multiplexing
....................... 203
6.3.6
Description in the Phase-Space Domain
........ 205
6.4
Conclusions
.......................................... 213
References
................................................. 214
7
Radiometry,
Wave Optics, and Spatial
Coherence
......................................... 217
7.1
Introduction
.......................................... 217
7.2
Conventional
Radiometry
............................ 218
7.3
Lambertian Sources
.................................. 221
7.4
Mutual Coherence Function
.......................... 221
7.5
Stationary Phase Approximation
..................... 224
7.6
Radiometry
and Wave Optics
......................... 226
7.7
Examples
............................................ 231
7.7.1
Blackbody
Radiation
........................... 231
7.7.2
Noncoherent Source
........................... 232
7.7.3
Coherent Wave Fields
.......................... 233
7.7.4
Quasi-Homogeneous Wave Field
.............. 234
Acknowledgments
........................................ 235
References
................................................. 235
X
Contents
8
Rays and Waves
.................................... 237
8.1
Introduction
.......................................... 237
8.2
Small-Wavelength Limit in the Position
Representation I: Geometrical Optics
................. 238
8.2.1
The Eikonal and Geometrical Optics
........... 239
8.2.2
Choosing
ζ
as the Parameter
................... 242
8.2.3
Ray-Optical Phase Space
and the
Lagrange
Manifold
.................... 243
8.3
Small-Wavelength Limit in the Position
Representation
Π:
The Transport Equation
and the Field Estimate
................................ 245
8.3.1
The Debye Series Expansion
................... 245
8.3.2
The Transport Equation and Its Solution
....... 245
8.3.3
The Field Estimate and Its Problems
at Caustics
.................................... 247
8.4
Flux Lines versus Rays
............................... 249
8.5
Analogy with Quantum Mechanics
................... 250
8.5.1
Semiclassical Mechanics
....................... 251
8.5.2
Bohmian Mechanics and the Hydrodynamic
Model
......................................... 253
8.6
Small-Wavelength Limit in the Momentum
Representation
....................................... 254
8.6.1
The Helmholtz Equation in the Momentum
Representation
................................ 254
8.6.2
Asymptotic Treatment and Ray Equations
...... 256
8.6.3
Transport Equation in the Momentum
Representation
................................ 258
8.6.4
Field Estimate
................................. 259
8.7
Maslov s Canonical Operator Method
................ 260
8.8
Gaussian Beams and Their Sums
..................... 261
8.8.1
Parabasal Gaussian Beams
..................... 261
8.8.2
Sums of Gaussian Beams
...................... 264
8.9
Stable Aggregates of Flexible Elements
............... 266
8.9.1
Derivation of the Estimate
..................... 266
8.9.2
Insensitivity to
y
............................... 269
8.9.3
Phase-Space Interpretation
..................... 270
8.10
A Simple Example
.................................... 271
8.11
Concluding Remarks
................................. 275
References
................................................. 275
9
Self-Imaging in Phase Space
....................... 279
9.1
Introduction
.......................................... 279
9.2
Phase-Space Optics Minimum Tool Kit
................ 280
9.3
Self-Imaging of Paraxial Wavefronts
.................. 284
Contents XI
9.4
The
Talbot
Effect
................................... 285
9.5
The Walk-off
Effect
.............................. 289
9.6
The Fractional
Talbot
Effect
......................... 290
9.7
Matrix Formulation of the Fractional
Talbot
Effect
.. 295
9.8
Point Source Illumination
.......................... 298
9.9
Another Path to Self-Imaging
....................... 301
9.10
Self-Imaging and Incoherent Illumination
.......... 302
9.11
Summary
.......................................... 305
References
............................................... 306
10
Sampling and Phase Space
........................ 309
10.1
Introduction
....................................... 309
10.2
Notation and Some Initial Concepts
................ 312
10.2.1
The Wigner Distribution Function
and Properties
............................. 312
10.2.2
The Linear Canonical Transform
and the WDF
............................... 314
10.2.3
The Phase-Space Diagram
.................. 314
10.2.4
Harmonics and Chirps
and Convolutions
.......................... 316
10.2.5
The Comb Function and
Rect
Function
..... 318
10.2.5.1
Comb Functions
.................. 318
10.2.5.2
Rect
Functions
................... 320
10.3
Finite Supports
.................................... 321
10.3.1
Band-limitedness in Fourier Domain
....... 321
10.3.2
Band-limitedness and the LCT
............. 322
10.3.3
Finite Space-Bandwidth
Product
—
Compact Support in
χ
and
к
...... 324
10.4
Sampling a Signal
.................................. 325
10.4.1
Nyquist-Shannon Sampling
................ 325
10.4.2
Generalized Sampling
...................... 328
10.5
Simulating an Optical System: Sampling
at the Input and Output
............................ 329
10.6
Conclusion
........................................ 332
References
............................................... 332
11
Phase Space in Ultrafast Optics
................... 337
11.1
Introduction
....................................... 337
11.2
Phase-Space Representations for Short
Optical Pulses
..................................... 338
11.2.1
Representation of Pulsed Fields
............ 338
11.2.2
Pulse Ensembles and Correlation
Functions
.................................. 340
XII Contents
11.2.3
The Time-Frequency Phase Space
........... 343
11.2.4
Phase-Space Representation of Paraxial
Optical Systems
............................ 349
11.2.5
Temporal Paraxiality and the Chronocyclic
Phase Space
................................ 353
11.3
Metrology of Short Optical Pulses
.................. 357
11.3.1
Measurement Strategies
.................... 357
11.3.2
Pulse Characterization Apparatuses
as Linear Systems
.......................... 358
11.3.3
Phase-Space Methods
...................... 361
11.3.3.1
Spectrographic Techniques
....... 362
11.3.3.2 Tomographie
Techniques
......... 366
11.3.4
Interferometrie
or Direct Techniques
........ 369
11.3.4.1
Two-Pulse Double-Slit
Interferometry
.................... 370
11.3.4.2
Shearing
Interferometry
.......... 374
11.4
Conclusions
........................................ 378
References
............................................... 379
Index
................................................... 385
|
| any_adam_object | 1 |
| building | Verbundindex |
| bvnumber | BV035765137 |
| callnumber-first | Q - Science |
| callnumber-label | QC389 |
| callnumber-raw | QC389 |
| callnumber-search | QC389 |
| callnumber-sort | QC 3389 |
| callnumber-subject | QC - Physics |
| classification_rvk | UH 5695 ZN 6280 |
| ctrlnum | (OCoLC)277205896 (DE-599)BVBBV035765137 |
| dewey-full | 535/.13 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 535 - Light and related radiation |
| dewey-raw | 535/.13 |
| dewey-search | 535/.13 |
| dewey-sort | 3535 213 |
| dewey-tens | 530 - Physics |
| discipline | Physik Elektrotechnik / Elektronik / Nachrichtentechnik |
| format | Book |
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| id | DE-604.BV035765137 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:04:00Z |
| institution | BVB |
| isbn | 9780071597982 |
| language | English |
| lccn | 2009026369 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018624940 |
| oclc_num | 277205896 |
| open_access_boolean | |
| owner | DE-703 DE-83 |
| owner_facet | DE-703 DE-83 |
| physical | XV, 393 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | McGraw-Hill |
| record_format | marc |
| spelling | Phase-space optics fundamentals and applications Markus E. Testorf ; Bryan M. Hennelly ; Jorge Ojeda-Castañeda Phase space optics New York [u.a.] McGraw-Hill 2010 XV, 393 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Light Transmission Optics Statistical methods Wigner distribution Phase space (Statistical physics) Statistische Optik (DE-588)4182960-8 gnd rswk-swf Phasenraum (DE-588)4139912-2 gnd rswk-swf Phasenraum (DE-588)4139912-2 s Statistische Optik (DE-588)4182960-8 s DE-604 Testorf, Markus E. Sonstige oth Hennelly, Bryan M. Sonstige oth Ojeda-Castañeda, Jorge Sonstige oth Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018624940&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Phase-space optics fundamentals and applications Light Transmission Optics Statistical methods Wigner distribution Phase space (Statistical physics) Statistische Optik (DE-588)4182960-8 gnd Phasenraum (DE-588)4139912-2 gnd |
| subject_GND | (DE-588)4182960-8 (DE-588)4139912-2 |
| title | Phase-space optics fundamentals and applications |
| title_alt | Phase space optics |
| title_auth | Phase-space optics fundamentals and applications |
| title_exact_search | Phase-space optics fundamentals and applications |
| title_full | Phase-space optics fundamentals and applications Markus E. Testorf ; Bryan M. Hennelly ; Jorge Ojeda-Castañeda |
| title_fullStr | Phase-space optics fundamentals and applications Markus E. Testorf ; Bryan M. Hennelly ; Jorge Ojeda-Castañeda |
| title_full_unstemmed | Phase-space optics fundamentals and applications Markus E. Testorf ; Bryan M. Hennelly ; Jorge Ojeda-Castañeda |
| title_short | Phase-space optics |
| title_sort | phase space optics fundamentals and applications |
| title_sub | fundamentals and applications |
| topic | Light Transmission Optics Statistical methods Wigner distribution Phase space (Statistical physics) Statistische Optik (DE-588)4182960-8 gnd Phasenraum (DE-588)4139912-2 gnd |
| topic_facet | Light Transmission Optics Statistical methods Wigner distribution Phase space (Statistical physics) Statistische Optik Phasenraum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018624940&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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