Page 6 - Phase Space Optics Fundamentals and Applications

Contents

Preface ....................................................... xiii

1 Wigner Distribution in Optics ........................ 1
1.1 Introduction ............................................ 1
1.2 Elementary Description of Optical Signals
and Systems ............................................ 2
1.2.1 Impulse Response and Coherent
Point-Spread Function ........................... 3
1.2.2 Mutual Coherence Function
and Cross-Spectral Density ...................... 3
1.2.3 Some Basic Examples of Optical Signals .......... 4
1.3 Wigner Distribution and Ambiguity Function ........... 5
1.3.1 Definitions ....................................... 5
1.3.2 Some Basic Examples Again ...................... 7
1.3.3 Gaussian Light ................................... 9
1.3.4 Local Frequency Spectrum ...................... 11
1.4 Some Properties of the Wigner Distribution ............ 12
1.4.1 Inversion Formula .............................. 12
1.4.2 Shift Covariance ................................ 12
1.4.3 Radiometric Quantities ......................... 12
1.4.4 Instantaneous Frequency ....................... 14
1.4.5 Moyal’s Relationship ........................... 15
1.5 One-Dimensional Case and the Fractional
Fourier Transformation ................................ 15
1.5.1 Fractional Fourier Transformation ............... 15
1.5.2 Rotation in Phase Space ......................... 16
1.5.3 Generalized Marginals—Radon Transform ...... 16
1.6 Propagation of the Wigner Distribution ................ 18
1.6.1 First-Order Optical Systems—Ray
Transformation Matrix .......................... 18
1.6.2 Phase-Space Rotators—More Rotations
in Phase Space .................................. 19

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