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