Optical coherence and quantum optics / Leonard Mandel and Emil Wolf.

Includes bibliographical references and indexes.

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Cover; Half-title; Title; Copyright; Dedication; Contents; Preface; 1 Elements of probability theory; 1.1 Definitions; 1.2 Properties of probabilities; 1.2.1 Joint probabilities; 1.2.2 Conditional probabilities; 1.2.3 Bayes' theorem on inverse probabilities; 1.3 Random variables and probability distributions; 1.3.1 Transformations of variates; 1.3.2 Expectations and moments; 1.3.3 Chebyshev inequality; 1.4 Generating functions; 1.4.1 Moment generating function; 1.4.2 Characteristic function; 1.4.3 Cumulants; 1.5 Some examples of probability distributions.

1.5.1 Bernoulli or binomial distribution1.5.2 Poisson distribution; 1.5.3 Bose-Einstein distribution; 1.5.4 The weak law of large numbers; 1.5.5 Normal or Gaussian distribution; 1.5.6 The central limit theorem; 1.5.7 Gamma distribution; 1.6 Multivariate Gaussian distribution; 1.6.1 The Gaussian moment theorem; 1.6.2 Moment generating function and characteristic function; 1.6.3 Multiple complex Gaussian variates; Problems; 2 Random (or stochastic) processes; 2.1 Introduction to statistical ensembles; 2.1.1 The ensemble average; 2.1.2 Joint probabilities and correlations.

2.1.3 The probability functional2.2 Stationarity and ergodicity; 2.2.1 The time average of a stationary process; 2.2.2 Ergodicity; 2.2.3 Examples of random processes; 2.3 Properties of the autocorrelation function; 2.4 Spectral properties of a stationary random process; 2.4.1 Spectral density and the Wiener-Khintchine theorem; 2.4.2 Singularities of the spectral density; 2.4.3 Normalized correlations and normalized spectral densities; 2.4.4 Cross-correlations and cross-spectral densities; 2.5 Orthogonal representation of a random process; 2.5.1 The Karhunen-Loéve expansion.

2.5.2 The timeT-lnfinityan alternative approach to the Wiener-Khintchine theorem; 2.6 Time development and classification of random processes; 2.6.1 Conditional probability densities; 2.6.2 Completely random or separable process; 2.6.3 First-order Markov process; 2.6.4 Higher-order Markov process; 2.7 Master equations in integro-differential form; 2.8 Master equations in differential form; 2.8.1 The Kramers-Moyal differential equation; 2.8.2 Vector random process; 2.8.3 The order of the Kramers-Moyal differential equation; 2.9 Langevin equation and Fokker-Planck equation.

2.9.1 Transition moments for the Langevin process2.9.2 Steady-state solution of the Fokker-Planck equation; 2.9.3 Time-dependent solution of the Fokker-Planck equation; 2.10 The Wiener process (or one-dimensional random walk); 2.10.1 The random walk problem; 2.10.2 Joint probabilities and autocorrelation; 2.10.3 Equation of motion of the Wiener process; Problems; 3 Some useful mathematical techniques; 3.1 The complex analytic signal; 3.1.1 Definition and basic properties of analytic signals; 3.1.2 Quasi-monochromatic signals and their envelopes.

3.1.3 Relationships between correlation functions of real and associated complex analytic random processes.

This book presents a systematic account of optical coherence theory within the framework of classical optics, as applied to such topics as radiation from sources of different states of coherence, foundations of radiometry, effects of source coherence on the spectra of radiated fields, coherence theory of laser modes, and scattering of partially coherent light by random media. The book starts with a full mathematical introduction to the subject area and each chapter concludes with a set of exercises. The authors are renowned scientists and have made substantial contributions to many of the topi.

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