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目录：
1. Introduction
1.1 Deterministic versus Statistical Phenomena and Models
1.2 Statistical Phenomena in Optics
1.3 An Outline of the Book
2. Random Variables
Definitions of Probability and Random Variables
Distribution Functions and Density Functions
Extension to Two or More Joint Random Variables
St at is tical Averages
2.4.1 Moments of a Random Variable
2.4.2 Joint Moments of Random Variables
2.4.3 Characteristic Functions
Transformations of Random Variables
2.5.1 General Transformation
2.5.2 Monotonic Functions
2.5.3 Multivariate Probability Transformations
Sums of Real Random Variables
2.6.1 Two Methods for Finding p,(z)
2.6.2 Independent Random Variables
2.6.3 The Central Limit Theorem
Gaussian Random Variables
2.7.1 Definitions
2.7.2 Special Properties of Gaussian Random Variables
Complex-Valued Random Variables
2.8.1 General Descriptions
2.8.2 Complex Gaussian Random Variables
xii CONTENTS
2.9 Random Phasor Sums
2.9.1 Initial Assumptions
2.9.2 Calculations of Means, Variances, and the
Correlation Coefficient
2.9.3 Statistics of the Length and Phase
2.9.4 A Constant Phasor Plus a Random Phasor Sum
2.9.5 Strong Constant Phasor Plus a Weak
Random Phasor Sum
3. Random Processes
Definition and Description of a Random Process
Stationarity and Ergodicity
Spectral Analysis of Random Processes
3.3.1 Spectral Densities of Known Functions
3.3.2 Spectral Density of a Random Process
3.3.3 Energy and Power Spectral Densities for
Linearly Filtered Random Processes
Autocorrelation Functions and the
Wiener- Khinchin Theorem
Cross-Correlation Functions and Cross-Spectral Densities
The Gaussian Random Process
3.6.1 Definition
3.6.2 Linearly Filtered Gaussian Random Processes
3.6.3 Wide-Sense Stationarity and Strict Stationarity
3.6.4 Fourth-Order Moments
The Poisson Impulse Process
3.7.1 Definitions
3.7.2 Derivation of Poisson Statistics from
Fundamental Hypotheses
3.7.3 Derivation of Poisson Statistics from Random
Event Times
3.7.4 Energy and Power Spectral Densities
of Poisson Processes
3.7.5 Doubly Stochastic Poisson Processes
3.7.6 Linearly Filtered Poisson Processes
Random Processes Derived from Analytic Signals
3.8.1 Representation of a Monochromatic Signal
by a Complex Signal
3.8 -2 Representation of a Nonmonochromatic Signal
by a Complex Signal
3.8.3 Complex Envelopes or Time-Varying Phasors
3.8.4 The Analytic Signal as a Complex-Valued
Random Process
. . . CONTENTS Xlll
3.9 The Complex Gaussian Random Process
3.10 The Karhunen-Loeve Expansion
4. Some First-Order Properties of Light Waves 116
4.1 Propagation of Light Waves 117
4.1.1 Monochromatic Light 117
4.1.2 Nonmonochromatic Light 118
4.1.3 Narrowband Light 120
4.2 Polarized and Unpolarized Thermal Light 120
4.2.1 Polarized Thermal Light 121
4.2.2 Unpolarized Thermal Light 124
4.3 Partially Polarized Thermal Light 127
4.3.1 Passage of Narrowband Light Through
Polarization-Sensitive Instruments 127
4.3.2 The Coherency Matrix 130
4.3.3 The Degree of Polarization 134
4.3.4 First-Order Statistics of the Instantaneous Intensity 136
4.4 Laser Light 138
4.4.1 Single-Mode Oscillation 139
4.4.2 Multimode Laser Light 145
4.4.3 Pseudothermal Light Produced by Passing Laser
Light Through a Moving Diffuser 151
5. Coherence of Optical Waves 157
5.1 Temporal Coherence
5.1 .I The Michelson Interferometer
5.1.2 Mathematical Description of the Experiment
5.1.3 Relationship of the Interferogram to the
Power Spectral Density of the Light Beam
5.1.4 Fourier Spectroscopy
5.2 Spatial Coherence
5.2.1 Young's Experiment
5.2.2 Mathematical Description of Young's Experiment
5.2.3 Some Geometric Considerations
5.2.4 Interference Under Quasimonochromatic
Conditions
5.2.5 Effects of Finite Pinhole Size
5.3 Cross-Spectral Purity
5.3.1 Power Spectrum of the Superposition of
Two Light Beams
5.3.2 Cross-Spectral Purity and Reducibility
CONTENTS
5.3.3 Laser Light Scattered by a Moving Diffuser
5.4 Propagation of Mutual Coherence
5.4.1 Solution Based on the Huygens-Fresnel Principle
5.4.2 Wave Equations Governing Propagation
of Mutual Coherence
5.4.3 Propagation of Cross-Spectral Density
5.5 Limiting Forms of the Mutual Coherence Function
5.5.1 A Coherent Field
5.5.2 An Incoherent Field
5.6 The Van Cittert-Zernike Theorem
5.6.1 Mathematical Derivation
5.6.2 Discussion
5.6.3 An Example
5.6.4 A Generalized Van Cittert-Zernike Theorem
5.7 Diffraction of Partially Coherent Light by an Aperture
5.7.1 Effect of a Thin Transmitting Structure
on Mutual Intensity
5.7.2 Calculation of the Observed Intensity Pattern
5.7.3 Discussion
6. Some Problems Involving High-Order Coherence
6.1 Statistical Properties of the Integrated Intensity
of Thermal or Pseudothermal Light
6.1.1 Mean and Variance of the Integrated Intensity
6.1.2 Approximate Form for the Probability
Density Function of Integrated Intensity
6.1.3 Exact Solution for the Probability Density
Function of Integrated Intensity
6.2 Statistical Properties of Mutual Intensity
with Finite Measurement Time
6.2.1 Moments of the Real and Imaginary Parts of J,,(T)
6.2.2 Statistics of the Modulus and Phase of J,,(T) for
Long Integration Time and Small p12
6.2.3 Statistics of the Modulus and Phase of J12(T) Under
the Condition of High Signal-to-Noise Ratio
6.3 Classical Analysis of the Intensity Interferometer
6.3.1 Amplitude versus Intensity Interferometry
6.3.2 Ideal Output of the Intensity Interferometer
6.3.3 "Classical" or "Self' Noise at the
Interferometer Output
CONTENTS xv
7. Effects of Partial Coherence on Imaging Systems 286
7.1 Some Preliminary Considerations 287
7.1.1 Effects of a Thin Transmitting Object on
Mutual Coherence 287
7.1.2 Time Delays Introduced by a Thin Lens 290
7.1.3 Focal-Plane- to-Focal-Plane Coherence Relationships 292
7.1.4 Object-Image Coherence Relations for
a Single Thin Lens 296
7.1.5 Relationship Between Mutual Intensities
in the Exit Pupil and the Image 300
7.2 Methods for Calculating Image Intensity 303
7.2.1 Integration over the Source 303
7.2.2 Representation of the Source by an Incident
Mutual Intensity Function 307
7.2.3 The Four-Dimensional Linear Systems Approach 312
7.2.4 The Incoherent and Coherent Limits 320
7.3 Some Examples 324
7.3.1 The Image of Two Closely Spaced Points 324
7.3.2 The Image of a Sinusoidal Amplitude Object 328
7.4 Image Formation as an Interferometric Process 331
7.4.1 An Imaging System as an Interferometer 331
7.4.2 Gathering Image Information with Interferometers 335
7.4.3 The Importance of Phase Information 340
7.4.4 Phase Retrieval 343
7.5 The Speckle Effect in Coherent Imaging 347
7.5.1 The Origin and First-Order Statistics of Speckle 348
7.5.2 Ensemble Average Coherence 351
8. Imaging in the Presence of Randomly Inhomogeneous Media 361
8.1 Effects of Thin Random Screens on Image Quality
8.1.1 Assumptions and Simplifications
8.1.2 The Average Optical Transfer Function
8.1.3 The Average Point-Spread Function
8.2 Random Absorbing Screens
8.2.1 General Forms of the Average OTF
and the Average PSF
8.2.2 A Specific Example
8.3 Random-Phase Screens
8.3.1 General Formulation
xvi CONTENTS
8.3.2 The Gaussian Random-Phase Screen
8.3.3 Limiting Forms for Average OTF and
Average PSF for Large Phase Variance
8.4 Effects of an Extended Randomly Inhomogeneous
Medium on Wave Propagation
8.4.1 Notation and Definitions
8.4.2 Atmospheric Model
8.4.3 Electromagnetic Wave Propagation Through
the Inhomogeneous Atmosphere
8.4.4 The Log-Normal Distribution
8.5 The Long-Exposure OTF
8.5.1 Long-Exposure OTF in Terms of the Wave
Structure Function
8.5.2 N ear-Field Calculation of the Wave Structure
Function
8.6 Generalizations of the Theory
8.6.1 Extension to Longer Propagation
Paths-Amplitude and Phase Filter Functions
8.6.2 Effects of Smooth Variations of the Structure
Constant C:
8.6.3 The Atmospheric Coherence Diameter r,
8.6.4 Structure Function for a Spherical Wave
8.7 The Short-Exposure OTF
8.7.1 Long versus Short Exposures
8.7.2 Calculation of the Average Short-Exposure OTF
8.8 Stellar Speckle Interferometry
8.8.1 Principle of the Method
8.8.2 Heuristic Analysis of the Method
8.8.3 A More Complete Analysis of Stellar Speckle
Interferometry
8.8.4 Extensions
8.9 Generality of the Theoretical Results
9. Fundamental Limits in Photoelectric Detection of Light
9.1 The Semiclassical Model for Photoelectric Detection
9.2 Effects of Stochastic Fluctuations of the Classical Intensity
9.2.1 Photocount Statistics for Well-Stabilized,
Single-Mode Laser Radiation
9.2.2 Photocount Statistics for Polarized Thermal
Radiation with a Counting Time Much
Shorter Than the Coherence Time
9.2.3 Photocount Statistics for Polarized Thermal
Light and an Arbitrary Counting Interval
CONTENTS xvii
9.2.4 Polarization Effects 477
9.2.5 Effects of Incomplete Spatial Coherence 479
9.3 The Degeneracy Parameter 481
9.3.1 Fluctuations of Photocounts 481
9.3.2 The Degeneracy Parameter for Blackbody Radiation 486
9.4 Noise Limitations of the Amplitude Interferometer
at Low Light Levels 490
9.4.1 The Measurement System and the Quantities to
Be Measured 491
9.4.2 Statistical Properties of the Count Vector 493
9.4.3 The Discrete Fourier Transform as an
Estimation Tool 494
9.4.4 Accuracy of the Visibility and Phase Estimates 496
9.5 Noise Limitations of the Intensity Interferometer at
Low Light Levels 501
9.5.1 The Counting Version of the Intensity
Interferometer 502
9.5.2 The Expected Value of the Count-Fluctuation
Product and Its Relationship to Fringe Visibility 503
9.5.3 The Signal-to-Noise Ratio Associated with
the Visibility Estimate 506
9.6 Noise Limitations in Speckle Interferometry 510
9.6.1 A Continuous Model for the Detection Process 511
9.6.2 The Spectral Density of the Detected Imagery 512
9.6.3 Fluctuations of the Estimate of Image
Spectral Density 517
9.6.4 Signal-to-Noise Ratio for Stellar
Speckle Interferometry 519
9.6.5 Discussion of the Results 521
Appendix A. The Fourier Transform 528
A.l Fourier Transform Definitions 528
A.2 Basic Properties of the Fourier Transform 529
A.3 Table of One-Dimensional Fourier Transforms 531
A.4 Table of Two-Dimensional Fourier
Transform Pairs 532
Appendix B. Random Phasor Sums 533
Appendix C. Fourth-Order Moment of the Spectrum
of a Detected Speckle Image
Index
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发表于 2022-5-30 15:59
