Linear canonical transforms : theory and applications
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Bibliographic Information
Linear canonical transforms : theory and applications
（Springer series in optical sciences, v. 198）
Springer, c2016
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Includes bibliographical references
Description and Table of Contents
Description
This book provides a clear and accessible introduction to the essential mathematical foundations of linear canonical transforms from a signals and systems perspective. Substantial attention is devoted to how these transforms relate to optical systems and wave propagation. There is extensive coverage of sampling theory and fast algorithms for numerically approximating the family of transforms. Chapters on topics ranging from digital holography to speckle metrology provide a window on the wide range of applications.
This volume will serve as a reference for researchers in the fields of image and signal processing, wave propagation, optical information processing and holography, optical system design and modeling, and quantum optics. It will be of use to graduate students in physics and engineering, as well as for scientists in other areas seeking to learn more about this important yet relatively unfamiliar class of integral transformations.
Table of Contents
Foreward.- PART I : Fundamentals.- Development of linear canonical transforms - a historical sketch.- The linear canonical transformation: definition and properties.- Eigenfunctions of the linear canonical transform.- Uncertainty principles and the linear canonical transform.- The linear canonical transformations in classical optics.- Optical Implementation of Linear Canonical Transforms.- PART II : Discretization and Computation.- Linear canonical domains and degrees of freedom of signals and systems.- Sampling and discrete linear canonical transforms.- Self-imaging and discrete paraxial optics.- Fast algorithms for digital computation of linear canonical transforms.- PART III : Applications.- Deterministic phase retrieval using the LCT.- Analyzing digital holographic systems with the LCT.- Double random phase encoding based optical encryption systems using some linear canonical transforms: weaknesses and countermeasures.- Complex valued ABCD Matrices.- Linear canonical transforms on quantum states of light.
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