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1．Elementary coherence phenomena 1

1.1 Interference and statistical similarity 1

1.2 Temporal coherence and the coherence time 4

1.3 Spatial coherence and the coherence area 5

1.4 The coherence volume 8

Problems 10

2．Mathematical preliminaries 11

2.1 Elementary concepts of the theory of random processes 11

2.2 Ergodicity 17

2.3 Complex representation of a real signal and the envelope of a narrow-band signal 19

2.4 The autocorrelation and the cross-correlation functions 22

2.4.1 The autocorrelation function of a finite sum of periodic components with random amplitudes 24

2.5 The spectral density and the Wiener-Khintchine theorem 25

Problems 29

3．Second-order coherence phenomena in the space-time domain 31

3.1 Interference law for stationary optical fields.The mutual coherence function and the complex degree of coherence 31

3.2 Generation of spatial coherence from an incoherent source.The van Cittert-Zernike theorem 37

3.3 Illustrative examples 46

3.3.1 Michelson's method for measuring stellar diameters 46

3.3.2 Michelson's method for determining energy distribution in spectral lines 51

3.4 Propagation of the mutual intensity 54

3.5 Wave equations for the propagation of mutual coherence in free space 56

Problems 58

4．Second-order coherence phenomena in the space-frequency domain 60

4.1 Coherent-mode representation and the cross-spectral density as a correlation function 60

4.2 The spectral interference law and the spectral degree of coherence 63

4.3 An illustrative example:spectral changes on interference 69

4.4 Interference of narrow-band light 73

Problems 76

5．Radiation from sources of different states of coherence 79

5.1 Fields generated by sources with different coherence properties 79

5.2 Correlations and the spectral density in the far field 81

5.3 Radiation from some model sources 88

5.3.1 Schell-model sources 88

5.3.2 Quasi-homogeneous sources 90

5.4 Sources of different states of spatial coherence which generate identical distributions of the radiant intensity 95

5.5 Coherence properties of Lambertian sources 97

5.6 Spectral changes on propagation.The scaling law 102

Problems 108

6．Coherence effects in scattering 111

6.1 Scattering of a monochromatic plane wave on a deterministic medium 111

6.2 Scattering of partially coherent waves on a deterministic medium 115

6.3 Scattering on random media 118

6.3.1 General formulas 118

6.3.2 Examples 121

6.3.3 Scattering on a quasi-homogeneous medium 123

Problems 127

7．Higher-order coherence effects 129

7.1 Introduction 129

7.2 Intensity interferometry with radio waves 131

7.3 The Hanbury Brown-Twiss effect and intensity interferometry with light 134

7.4 Einstein's formula for energy fluctuations in blackbody radiation and the wave-particle duality 140

7.5 Mandel's theory of photoelectric detection of light fluctuations 143

7.5.1 Mandel's formula for photocount statistics 143

7.5.2 The variance of counts from a single photodetector 145

7.5.3 Correlation between count fluctuations from two detectors 147

7.6 Determination of statistical properties of light from photocount measurements 149

Problems 151

8．Elementary theory of polarization of stochastic electromagnetic beams 154

8.1 The 2×2 equal-time correlation matrix of a quasi-monochromatic electromagnetic beam 154

8.2 Polarized,unpolarized and partially polarized light.The degree of polarization 158

8.2.1 Completely polarized light 158

8.2.2 Natural(unpolarized) light 160

8.2.3 Partially polarized light and the degree of polarization 161

8.2.4 The geometrical significance of complete polarization.The Stokes parameters of completely polarized light.The Poincaré sphere 165

Problems 171

9．Unified theory of polarization and coherence 174

9.1 The 2×2 cross-spectral density matrix of a stochastic electromagnetic beam 174

9.2 The spectral interference law,the spectral degree of coherence and the spectral degree of polarization of stochastic electromagnetic beams 175

9.3 Determination of the cross-spectral density matrix from experiments 179

9.4 Changes in random electromagnetic beams on propagation 181

9.4.1 Propagation of the cross-spectral density matrix of a stochastic electromagnetic beam--general formulas 181

9.4.2 Propagation of the cross-spectral density matrix of an electromagnetic Gaussian Schell-model beam 183

9.4.3 Examples of correlation-induced changes in stochastic electromagnetic beams on propagation 186

9.4.4 Coherence-induced changes of the degree of polarization in Young's interference experiment 191

9.5 Generalized Stokes parameters 194

Problems 197

Appendices 202

Ⅰ Cells of phase space and the degeneracy parameter 202

（a）Cells of phase space of a quasi-monochromatic light wave(Section 1.4) 202

（b） Cells of phase space of radiation in a cavity(Sections 7.4 and 7.5) 204

（c）The degeneracy parameter 206

Ⅱ Derivation of Mandel's formula for photocount statistics [Eq.(2)of Section 7.5.1] 208

Ⅲ The degree of polarization of an electromagnetic Gaussian Schell-model source 210

Ⅳ Some important probability distributions 212

（a） The binomial(or Bernoulli)distribution and some of its limiting cases 212

（b）The Bose-Einstein distribution 214

Author index 216

Subject index 220