Abstract

A novel technique for designing holographic optical elements that can perform general types of coordinate transformation is presented. The design is based on analytic ray-tracing techniques for finding the grating vector of the element, from which the holographic grating function is obtained as a solution of a Poissonlike equation. The grating function can be formed either as a computer-generated or as a computer-originated hologram. The design and realization procedure are illustrated for a specific holographic element that performs a logarithmic coordinate transformation on two-dimensional patterns.

© 1992 Optical Society of America

Coordinate transformations realizable with multiple holographic optical elements

M. A. Stuff and J. N. Cederquist
J. Opt. Soc. Am. A 7(6) 977-981 (1990)

Real-time deformation invariant optical pattern recognition using coordinate transformations

David Casasent, Shao-Feng Xia, Andrew J. Lee, and Jian-Zhong Song
Appl. Opt. 26(5) 938-942 (1987)

Optical-coordinate transformation methods and optical-interconnection architectures

David Mendlovic and Haldun M. Ozaktas
Appl. Opt. 32(26) 5119-5124 (1993)

General linear optical coordinate transformations

Dayong Wang, Avi Pe’er, Asher A. Friesem, and Adolf W. Lohmann
J. Opt. Soc. Am. A 17(10) 1864-1869 (2000)

Deformation invariant optical processors using coordinate transformations

Demetri Psaltis and David Casasent
Appl. Opt. 16(8) 2288-2292 (1977)