Abstract

The linear canonical transform describes the effect of first-order quadratic phase optical systems on a wave field. Several recent papers have developed sampling rules for the numerical approximation of the transform. However, sampling an analog function according to existing rules will not generally permit the reconstruction of the analog linear canonical transform of that function from its samples. To achieve this, an additional sampling criterion has been developed for sampling both the input and the output wave fields.

© 2008 Optical Society of America

Fast linear canonical transforms

John J. Healy and John T. Sheridan
J. Opt. Soc. Am. A 27(1) 21-30 (2010)

Two-dimensional nonseparable linear canonical transform: sampling theorem and unitary discretization

Liang Zhao, John J. Healy, and John T. Sheridan
J. Opt. Soc. Am. A 31(12) 2631-2641 (2014)

Reevaluation of the direct method of calculating Fresnel and other linear canonical transforms

John J. Healy and John T. Sheridan
Opt. Lett. 35(7) 947-949 (2010)

Constraints on additivity of the 1D discrete linear canonical transform

Liang Zhao, John J. Healy, and John T. Sheridan
Appl. Opt. 54(33) 9960-9965 (2015)

Fast numerical algorithm for the linear canonical transform

Bryan M. Hennelly and John T. Sheridan
J. Opt. Soc. Am. A 22(5) 928-937 (2005)