Part I Fundamentals
1 Development of Linear Canonical Transforms: A Historical
Sketch ....................................................... 3
Kurt Bernardo Wolf
2 The Linear Canonical Transformation: Definition and
Properties .................................................. 29
Martin J. Bastiaans and Tatiana Alieva
3 Eigenfunctions of the Linear Canonical Transform ............ 81
Soo-Chang Pei and Jian-Jiun Ding
4 Uncertainty Principles and the Linear Canonical Transform ... 97
Ran Tao and Juan Zhao
5 The Linear Canonical Transformations in Classical Optics ... 113
Tatiana Alieva, José A. Rodrigo, Alejandro Cámara, and
Martin J. Bastiaans
6 Optical Implementation of Linear Canonical Transforms ...... 179
M. Alper Kutay, Haldun M. Ozaktas, and Jose A. Rodrigo
Part II Discretization and Computation
7 Linear Canonical Domains and Degrees of Freedom of
Signals and Systems ........................................ 197
Figen S. Oktem and Haldun M. Ozaktas
8 Sampling and Discrete Linear Canonical Transforms .......... 241
John J. Healy and Haldun M. Ozaktas
9 Self-imaging and Discrete Paraxial Optics .................. 257
Markus Testorf and Bryan Hennelly
10 Fast Algorithms for Digital Computation of Linear
Canonical Transforms ....................................... 293
Aykut Koç, Figen S. Oktem, Haldun M. Ozaktas, and
M. Alper Kutay
Part III Applications
11 Deterministic Phase Retrieval Using the LCT ................ 331
Unnikrishnan Gopinathan, John Healy, Damien P. Kelly, and
John T. Sheridan
12 Analyzing Digital Holographic Systems with the LCT ......... 347
Damien P. Kelly and John T. Sheridan
13 Double Random Phase Encoding Based Optical Encryption
Systems Using Some Linear Canonical Transforms:
Weaknesses and Countermeasures ............................. 367
Pramod Kumar, Joby Joseph, and Kehar Singh
14 Complex-Valued ABCD Matrices and Speckle Metrology ......... 397
Steen G. Hanson, Michael L. Jakobsen, and Harold T. Yura
15 Linear Canonical Transforms on Quantum States of Light ..... 429
Gabriel F. Calvo and Antonio Picón
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