Index

The Alabama A & M University Department of Physics Optics and Information Processing

Fourier Optics

H. J. Caulfield, J. Shamir, and M. P. Schamschula

Abstract

Fourier analysis and physical optics are strongly entangled with each other. On the one hand, Fourier analysis is an excellent mathematical tool for the analysis and synthesis of optical systems. On the other hand, optical systems are extremely efficient in performing Fourier analysis on signals and images. Both of these aspects of the relation between optics and Fourier analysis are reviewed in this paper. For the analysis of optical systems we invoke a short-hand notation based on an operator algebra that has its roots in canonical operator theory. After a general discussion, several examples of specific optical systems are described. The second aspect of the relations between Fourier analysis and optics is demonstrated by several signal processing architectures where the special capabilities of optical systems are exploited. The signal processing applications presented include the optical implementation of a Fourier transformation, one- and two-dimensional spectrum analysis and pattern recognition. While a conventional Fourier transform processor is space (or time) invariant, space variant signal processing is also addressed briefly.