Linear Canonical Transforms

Theory and Applications

  • John J. Healy
  • M. Alper Kutay
  • Haldun M. Ozaktas
  • John T. Sheridan

Part of the Springer Series in Optical Sciences book series (SSOS, volume 198)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Fundamentals

    1. Front Matter
      Pages 1-1
    2. Martin J. Bastiaans, Tatiana Alieva
      Pages 29-80
    3. Soo-Chang Pei, Jian-Jiun Ding
      Pages 81-96
    4. Tatiana Alieva, José A. Rodrigo, Alejandro Cámara, Martin J. Bastiaans
      Pages 113-178
    5. M. Alper Kutay, Haldun M. Ozaktas, José A. Rodrigo
      Pages 179-194
  3. Discretization and Computation

    1. Front Matter
      Pages 195-195
    2. Figen S. Oktem, Haldun M. Ozaktas
      Pages 197-239
    3. John J. Healy, Haldun M. Ozaktas
      Pages 241-256
    4. Markus Testorf, Bryan Hennelly
      Pages 257-292
    5. Aykut Koç, Figen S. Oktem, Haldun M. Ozaktas, M. Alper Kutay
      Pages 293-327
  4. Applications

    1. Front Matter
      Pages 329-329
    2. Unnikrishnan Gopinathan, John J. Healy, Damien P. Kelly, John T. Sheridan
      Pages 331-346
    3. Damien P. Kelly, John T. Sheridan
      Pages 347-365
    4. Steen G. Hanson, Michael L. Jakobsen, Harold T. Yura
      Pages 397-428
    5. Gabriel F. Calvo, Antonio Picón
      Pages 429-453

About this book


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.


Linear canonical transforms book digital holography fourier optics optical signal processing speckle metrology transforms in optics

Editors and affiliations

  • John J. Healy
    • 1
  • M. Alper Kutay
    • 2
  • Haldun M. Ozaktas
    • 3
  • John T. Sheridan
    • 4
  1. 1.School of Electrical and Electronic EngineeringUniversity College DublinDublinIreland
  2. 2.The Scientific and Technological Research Council of TurkeyAnkaraTurkey
  3. 3.Department of Electrical EngineeringBilkent UniversityAnkaraTurkey
  4. 4.School of Electrical and Electronic EngineeringUniversity College DublinDublinIreland

Bibliographic information