Linear Canonical Transforms

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 onquantum states of light.

John J. Healy was born in Dublin. He was awarded the BE and PhD degrees in electronic engineering by University College Dublin in 2005 and 2010. He worked as a Postdoctoral Fellow in Universidad Nacional Autónoma de México (UNAM) and Maynooth University. Healy is a member of IEEE, OSA and SPIE. He was a finalist in the European Community "Best PhD thesis in Computational Methods in Applied Sciences and Engineering 2010", and was awarded a Postdoctoral Fellowship from Irish Research Council for Science, Engineering and Technology (IRCSET) in 2010, and a NUI Fellowship in the Sciences in 2012. Since January 2015, he has been a Lecturer in Electronic Engineering at University College Dublin and Beijing Dublin International College at BJUT. His research interests span computational and applied optics, including the linear canonical transform, sampling theory, digital holography and 3D imaging, and time-frequency representations.

M. Alper Kutay received his BS, MS and PhD degrees in Electrical and Electronics Engineering from Bilkent University, Ankara in 1993, 1995 and 1999 respectively. Between March 1999 and July 2000 he was at the Communications and Signal Processing Laboratory, Drexel University, Philadelphia as a Postdoctoral Research Associate. He has been with The Scientific and Technological Research Council of Turkey (TUBITAK) since 2000. Positions he held include Acting Vice President of TUBITAK, Acting Director of the Advanced Technologies Research Institute, Project Leader, and Systems Engineer. He is currently Advisor to the President. He has been the technical leader of numerous research and development projects. He has published 25 refereed journal articles and 3 book chapters, and is the coauthor of The Fractional Fourier Transform (Wiley 2001). His publications have received more than 1500 citations. His research interests include signal detection, parameter estimation, radar signal processing, and time-frequency analysis.

Haldun M.

"It gives an up-to-date overview of the many aspects of the LCT. ... This book is a most welcome addition to the literature. ... This is a collection of survey papers written by renowned specialists that give a state-of-the-art of the many aspects of the linear canonical transform with an emphasis on the optical interpretation and applications." (Adhemar Bultheel, European Mathematical Society, euro-math-soc.eu, February, 2016)