Page 7 - Phase Space Optics Fundamentals and Applications

vi Contents

1.6.3 More General Systems—Ray-Spread Function ... 21
1.6.4 Geometric-Optical Systems ..................... 22
1.6.5 Transport Equations ............................ 23
1.7 Wigner Distribution Moments in First-Order
Optical Systems ....................................... 24
1.7.1 Moment Invariants ............................. 25
1.7.2 Moment Invariants for Phase-Space Rotators .... 26
1.7.3 Symplectic Moment Matrix—The Bilinear
ABCD Law ..................................... 28
1.7.4 Measurement of Moments ...................... 29
1.8 Coherent Signals and the Cohen Class ................. 29
1.8.1 Multicomponent Signals—Auto-Terms
and Cross-Terms ............................... 30
1.8.2 One-Dimensional Case and Some Basic
Cohen Kernels ................................. 32
1.8.3 Rotation of the Kernel ........................... 33
1.8.4 Rotated Version of the Smoothed
Interferogram .................................. 35
1.9 Conclusion ............................................ 40
References .................................................. 40

2 Ambiguity Function in Optical Imaging ............ 45
2.1 Introduction ........................................... 45
2.2 Intensity Spectrum of a Fresnel Diffraction
Pattern Under Coherent Illumination .................. 47
2.2.1 General Formulation ............................ 47
2.2.2 Application to Simple Objects ................... 48
2.2.3 Contrast Transfer Functions ..................... 49
2.3 Propagation through a Paraxial Optical System
in Terms of AF ......................................... 49
2.3.1 Propagation in Free Space ....................... 49
2.3.2 Transmission through a Thin Object ............. 50
2.3.3 Propagation in a Paraxial Optical System ........ 51
2.4 The AF in Isoplanatic (Space-Invariant) Imaging ....... 52
2.5 The AF of the Image of an Incoherent Source ........... 53
2.5.1 Derivation of the Zernike-Van Cittert
Theorem from the Propagation of the AF ....... 53
2.5.2 Partial Coherence Properties in the Image
of an Incoherent Source ......................... 54
2.5.3 The Pupil-AF as a Generalization of the OTF .... 54
2.6 Phase-Space Tomography .............................. 55
2.7 Another Possible Approach to AF Reconstruction ...... 56