Page 9 - Phase Space Optics Fundamentals and Applications

viii Contents

3.7.3 Chirp Signal Analysis ........................... 94
3.7.4 Signal Encryption ............................... 94
3.7.5 Mode Converters ............................... 95
3.7.6 Beam Characterization .......................... 96
3.7.7 Gouy Phase Accumulation ..................... 100
3.8 Conclusions .......................................... 101
Acknowledgments ........................................ 102
References ................................................. 102

4 The Radon-Wigner Transform in Analysis, Design,
and Processing of Optical Signals .................. 107
4.1 Introduction .......................................... 107
4.2 Projections of the Wigner Distribution Function
in Phase Space: The Radon-Wigner
Transform (RWT) ..................................... 108
4.2.1 Definition and Basic Properties ................ 108
4.2.2 Optical Implementation of the RWT:
The Radon-Wigner Display .................... 117
4.3 Analysis of Optical Signals and Systems
by Means of the RWT ................................. 122
4.3.1 Analysis of Diffraction Phenomena ............ 122
4.3.1.1 Computation of Irradiance
Distribution along Different Paths
in Image Space ........................ 122
4.3.1.2 Parallel Optical Display
of Diffraction Patterns ................. 132
4.3.2 Inverting RWT: Phase-Space Tomographic
Reconstruction of Optical Fields ............... 134
4.3.3 Merit Functions of Imaging Systems
in Terms of the RWT ........................... 138
4.3.3.1 Axial Point-Spread Function (PSF)
and Optical Transfer Function (OTF) ... 138
4.3.3.2 Polychromatic OTF .................... 143
4.3.3.3 Polychromatic Axial PSF .............. 146
4.4 Design of Imaging Systems and Optical
Signal Processing by Means of RWT .................. 151
4.4.1 Optimization of Optical Systems:
Achromatic Design ............................ 151
4.4.2 Controlling the Axial Response: Synthesis
of Pupil Masks by RWT Inversion ............. 156
4.4.3 Signal Processing through RWT ................ 157
Acknowledgments ........................................ 162
References ................................................. 162