9780471399162

Statistical Optics

by
  • ISBN13:

    9780471399162

  • ISBN10:

    0471399167

  • Edition: 1st
  • Format: Paperback
  • Copyright: 2000-08-14
  • Publisher: Wiley-Interscience

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Summary

The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Robert G. Bartle The Elements of Integration and Lebesgue Measure George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Finite Groups of Lie Type: Conjugacy Classes and Complex Characters R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I Richard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold M. S. Coxeter Introduction to Modern Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Bruno de Finetti Theory of Probability, Volume 1 Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research Amos de Shalit & Herman Feshbach Theoretical Nuclear Physics, Volume 1 - Nuclear Structure J. L. Doob Stochastic Processes Nelson Dunford & Jacob T. Schwartz Linear Operators, Part One, General Theory Nelson Dunford & Jacob T. Schwartz Linear Operators, Part Two, Spectral Theory-Self Adjoint Operators in Hilbert Space Nelson Dunford & Jacob T. Schwartz Linear Operators, Part Three, Spectral Operators Herman Feshbach Theoretical Nuclear Physics: Nuclear Reactions Bernard Friedman Lectures on Applications-Oriented Mathematics Phillip Griffiths & Joseph Harris Principles of Algebraic Geometry Gerald J. Hahn & Samuel S. Shapiro Statistical Models in Engineering Morris H. Hansen, William N. Hurwitz & William G. Madow Sample Survey Methods and Theory, Volume I-Methods and Applications Morris H. Hansen, William N. Hurwitz & William G. Madow Sample Survey Methods and Theory, Volume II-Theory Peter Henrici Applied and Computational Complex Analysis, Volume 1-Power Series-Integration-Conformal Mapping-Location of Zeros Peter Henrici Applied and Computational Complex Analysis, Volume 2-Special Functions-Integral Transforms-Asymptotics-Continued Fractions Peter Henrici Applied and Computational Complex Analysis, Volume 3-Discrete Fourier Analysis- Cauchy Integrals-Construction of Conformal Maps-Univalent Functions Peter Hilton & Yel-Chiang Wu A Course in Modern Algebra Harry Hochstadt Integral Equations Leslie Kish Survey Sampling Shoshichi Kobayashi & Katsumi Nomizu Foundations of Differential Geometry Erwin O. Kreyszig Introductory Functional Analysis with Applications William H. Louisell Quantum Statistical Properties of Radiation Ali Hasan Nayfeh Introduction to Perturbation Techniques Ali Hasan Nayfeh and Dean T. Mook Nonlinear Oscillations Emanuel Parzen Modern Probability Theory and Its Applications P. M. Prenter Splines and Variational Methods Walter Rudin Fourier Analysis on Groups I. H. Segel Enzyme Kinetics: Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems C. L. Siegel Topics in Complex Fu

Table of Contents

Introduction
1(6)
Deterministic versus Statistical Phenomena and Models
2(1)
Statistical Phenomena in Optics
3(2)
An Outline of the Book
5(2)
Random Variables
7(53)
Definitions of Probability and Random Variables
7(2)
Distribution Functions and Density Functions
9(3)
Extension to Two or More Joint Random Variables
12(3)
Statistical Averages
15(6)
Moments of a Random Variable
16(1)
Joint Moments of Random Variables
17(2)
Characteristic Functions
19(2)
Transformations of Random Variables
21(8)
General Transformation
21(2)
Monotonic Functions
23(4)
Multivariate Probability Transformations
27(2)
Sums of Real Random Variables
29(4)
Two Methods for Finding pz(z)
29(2)
Independent Random Variables
31(1)
The Central Limit Theorem
31(2)
Gaussian Random Variables
33(7)
Definitions
34(3)
Special Properties of Gaussian Random Variables
37(3)
Complex-Valued Random Variables
40(4)
General Descriptions
40(1)
Complex Gaussian Random Variables
41(3)
Random Phasor Sums
44(16)
Initial Assumptions
44(2)
Calculations of Means, Variances, and the Correlation Coefficient
46(2)
Statistics of the Length and Phase
48(2)
A Constant Phasor Plus a Random Phasor Sum
50(4)
Strong Constant Phasor Plus a Weak Random Phasor Sum
54(6)
Random Processes
60(56)
Definition and Description of a Random Process
60(3)
Stationarity and Ergodicity
63(5)
Spectral Analysis of Random Processes
68(5)
Spectral Densities of Known Functions
68(2)
Spectral Density of a Random Processes
70(1)
Energy and Power Spectral Densities for Linearly Filtered Random Processes
71(2)
Autocorrelation Functions and the Wiener--Khinchin Theorem
73(6)
Cross-Correlation Functions and Cross-Spectral Densities
79(3)
The Gaussian Random Process
82(3)
Definition
82(1)
Linearly Filtered Gaussian Random Processes
83(1)
Wide-Sense Stationarity and Strict Stationarity
84(1)
Fourth-Order Moments
84(1)
The Poisson Impulse Process
85(14)
Definitions
85(3)
Derivation of Poisson Statistics from Fundamental Hypotheses
88(2)
Derivation of Poisson Statistics from Random Event Times
90(1)
Energy and Power Spectral Densities of Poisson Processes
91(4)
Doubly Stochastic Poisson Processes
95(2)
Linearly Filtered Poisson Processes
97(2)
Random Processes Derived from Analytic Signals
99(9)
Representation of a Monochromatic Signal by a Complex Signal
99(2)
Representation of a Nonmonochromatic Signal by a Complex Signal
101(2)
Complex Envelopes or Time-Varying Phasors
103(1)
The Analytic Signal as a Complex-Valued Random Process
104(4)
The Complex Gaussian Random Process
108(1)
The Karhunen--Loeve Expansion
109(7)
Some First-Order Properties of Light Waves
116(41)
Propagation of Light Waves
117(3)
Monochromatic Light
117(1)
Nonmonochromatic Light
118(2)
Narrowband Light
120(1)
Polarized and Unpolarized Thermal Light
120(7)
Polarized Thermal Light
121(3)
Unpolarized Thermal Light
124(3)
Partially Polarized Thermal Light
127(11)
Passage of Narrowband Light Through Polarization-Sensitive Instruments
127(3)
The Coherency Matrix
130(4)
The Degree of Polarization
134(2)
First-Order Statistics of the Instantaneous Intensity
136(2)
Laser Light
138(19)
Single-Mode Oscillation
139(6)
Multimode Laser Light
145(6)
Pseudothermal Light Produced by Passing Laser Light Through a Moving Diffuser
151(6)
Coherence of Optical Waves
157(80)
Temporal Coherence
158(12)
The Michelson Interferometer
158(3)
Mathematical Description of the Experiment
161(3)
Relationship of the Interferogram to the Power Spectral Density of the Light Beam
164(5)
Fourier Spectroscopy
169(1)
Spatial Coherence
170(17)
Young's Experiment
170(3)
Mathematical Description of Young's Experiment
173(4)
Some Geometric Considerations
177(3)
Interference Under Quasimonochromatic Conditions
180(3)
Effects of Finite Pinhole Size
183(4)
Cross-Spectral Purity
187(8)
Power Spectrum of the Superposition of Two Light Beams
187(2)
Cross-Spectral Purity and Reducibility
189(4)
Laser Light Scattered by a Moving Diffuser
193(2)
Propagation of Mutual Coherence
195(7)
Solution Based on the Huygens-Fresnel Principle
196(3)
Wave Equations Governing Propagation of Mutual Coherence
199(2)
Propagation of Cross-Spectral Density
201(1)
Limiting Forms of the Mutual Coherence Function
202(5)
A Coherent Field
202(3)
An Incoherent Field
205(2)
The Van Cittert-Zernike Theorem
207(15)
Mathematical Derivation
207(3)
Discussion
210(1)
An Example
211(7)
A Generalized Van Cittert-Zernike Theorem
218(4)
Diffraction of Partially Coherent Light by an Aperture
222(15)
Effect of a Thin Transmitting Structure on Mutual Intensity
222(1)
Calculation of the Observed Intensity Pattern
223(3)
Discussion
226(11)
Some Problems Involving High-Order Coherence
237(49)
Statistical Properties of the Integrated Intensity of Thermal or Pseudothermal Light
238(18)
Mean and Variance of the Integrated Intensity
239(5)
Approximate Form for the Probability Density Function of Integrated Intensity
244(6)
Exact Solution for the Probability Density Function of Integrated Intensity
250(6)
Statistical Properties of Mutual Intensity with Finite Measurement Time
256(15)
Moments of the Real and Imaginary Parts of J12(T)
258(5)
Statistics of the Modulus and Phase of J12(T) for Long Integration Time and Small μ12
263(6)
Statistics of the Modulus and Phase of J12(T) Under the Condition of High Signal-to-Noise Ratio
269(2)
Classical Analysis of the Intensity Interferometer
271(15)
Amplitude versus Intensity Interferometry
272(2)
Ideal Output of the Intensity Interferometer
274(3)
``Classical'' or ``Self'' Noise at the Interferometer Output
277(9)
Effects of Partial Coherence on Imaging Systems
286(75)
Some Preliminary Considerations
287(16)
Effects of a Thin Transmitting Object on Mutual Coherence
287(3)
Time Delays Introduced by a Thin Lens
290(2)
Focal-Plane-to-Focal-Plane Coherence Relationships
292(4)
Object-Image Coherence Relations for a Single Thin Lens
296(4)
Relationship Between Mutual Intensities in the Exit Pupil and the Image
300(3)
Methods for Calculating Image Intensity
303(21)
Integration over the Source
303(4)
Representation of the Source by an Incident Mutual Intensity Function
307(5)
The Four-Dimensional Linear Systems Approach
312(8)
The Incoherent and Coherent Limits
320(4)
Some Examples
324(7)
The Image of Two Closely Spaced Points
324(4)
The Image of a Sinusoidal Amplitude Object
328(3)
Image Formation as an Interferometric Process
331(16)
An Imaging System as an Interferometer
331(4)
Gathering Image Information with Interferometers
335(5)
The Importance of Phase Information
340(3)
Phase Retrieval
343(4)
The Speckle Effect in Coherent Imaging
347(14)
The Origin and First-Order Statistics of Speckle
348(3)
Ensemble Average Coherence
351(10)
Imaging in the Presence of Randomly Inhomogeneous Media
361(104)
Effects of Thin Random Screens on Image Quality
362(5)
Assumptions and Simplifications
362(2)
The Average Optical Transfer Function
364(2)
The Average Point-Spread Function
366(1)
Random Absorbing Screens
367(7)
General Forms of the Average OTF and the Average PSF
367(4)
A Specific Example
371(3)
Random-Phase Screens
374(10)
General Formulation
375(1)
The Gaussian Random-Phase Screen
376(5)
Limiting Forms for Average OTF and Average PSF for Large Phase Variance
381(3)
Effects of an Extended Randomly Inhomogeneous Medium on Wave Propagation
384(18)
Notation and Definitions
385(3)
Atmospheric Model
388(5)
Electromagnetic Wave Propagation Through the Inhomogeneous Atmosphere
393(6)
The Log-Normal Distribution
399(3)
The Long-Exposure OTF
402(12)
Long-Exposure OTF in Terms of the Wave Structure Function
402(5)
Near-Field Calculation of the Wave Structure Function
407(7)
Generalizations of the Theory
414(19)
Extension to Longer Propagation Paths---Amplitude and Phase Filter Functions
415(12)
Effects of Smooth Variations of the Structure Constant C2n
427(2)
The Atmospheric Coherence Diameter r0
429(3)
Structure Function for a Spherical Wave
432(1)
The Short-Exposure OTF
433(8)
Long versus Short Exposures
433(3)
Calculation of the Average Short-Exposure OTF
436(5)
Stellar Speckle Interferometry
441(16)
Principle of the Method
442(4)
Heuristic Analysis of the Method
446(4)
A More Complete Analysis of Stellar Speckle Interferometry
450(5)
Extensions
455(2)
Generality of the Theoretical Results
457(8)
Fundamental Limits in Photoelectric Detection of Light
465(63)
The Semiclassical Model for Photoelectric Detection
466(2)
Effects of Stochastic Fluctuations of the Classical Intensity
468(13)
Photocount Statistics for Well-Stabilized, Single-Mode Laser Radiation
470(2)
Photocount Statistics for Polarized Thermal Radiation with a Counting Time Much Shorter Than the Coherence Time
472(3)
Photocount Statistics for Polarized Thermal Light and an Arbitrary Counting Interval
475(2)
Polarization Effects
477(2)
Effects of Incomplete Spatial Coherence
479(2)
The Degeneracy Parameter
481(9)
Fluctuations of Photocounts
481(5)
The Degeneracy Parameter for Blackbody Radiation
486(4)
Noise Limitations of the Amplitude Interferometer at Low Light Levels
490(11)
The Measurement System and the Quantities to Be Measured
491(2)
Statistical Properties of the Count Vector
493(1)
The Discrete Fourier Transform as an Estimation Tool
494(2)
Accuracy of the Visibility and Phase Estimates
496(5)
Noise Limitations of the Intensity Interferometer at Low Light Levels
501(9)
The Counting Version of the Intensity Interferometer
502(1)
The Expected Value of the Count-Fluctuation Product and Its Relationship to Fringe Visibility
503(3)
The Signal-to-Noise Ratio Associated with the Visibility Estimate
506(4)
Noise Limitations in Speckle Interferometry
510(18)
A Continuous Model for the Detection Process
511(1)
The Spectral Density of the Detected Imagery
512(5)
Fluctuations of the Estimate of Image Spectral Density
517(2)
Signal-to-Noise Ratio for Stellar Speckle Interferometry
519(2)
Discussion of the Results
521(7)
Appendix A. The Fourier Transform 528(5)
A.1 Fourier Transform Definitions
528(1)
A.2 Basic Properties of the Fourier Transform
529(2)
A.3 Table of One-Dimensional Fourier Transforms
531(1)
A.4 Table of Two-Dimensional Fourier Transform Pairs
532(1)
Appendix B. Random Phasor Sums 533(6)
Appendix C. Fourth-Order Moment of the Spectrum of a Detected Speckle Image 539(4)
Index 543

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