Optical implementation of integral transforms with Bessel function kernels

Abstract

Integral transforms involving Bessel function kernels are useful in analyzing effects of circularly symmetric optical systems on arbitrary inputs. Methods for performing the integral transforms optically are divided into two categories. The first category involves input data available in Cartesian (x, y) format and uses the close connection between the desired integral transform and the two-dimensional Fourier transform in Cartesian coordinates. The second category involves input data in polar (r, theta) format and uses methods such as change of variables to perform the integral transform as a correlation integral. Experimental results obtained with optical implementation for these two categories are presented.