Iterative technique for the synthesis of optical correlation filters

Abstract

A matched filter implemented by an optical correlator will identify an image from an infinite set. Although the matched filter is specific for that image, it is not rotationally invariant. A 3-D correlator can preserve translational and rotational invariance and still preserve specificity. Such a 3-D correlation integral can be determined by Fourier analysis of the angular signature obtained by rotating a correlation filter. To construct the full 3-D correlation, a correlation filter must consist of all significant angular harmonics of the target image. An iterative technique similar to the convex projection method of Gerchberg, Papoulis, and Youla and Webb is applied to form filters by rephasing the angular harmonics of the image to detect while maintaining approximately the same energy in the Fourier angular harmonics. The second Fourier domain is the rotational response, where the requirement of constant amplitude is imposed. The angular harmonics are keyed to the target image so that a constant-amplitude Fourier sum is produced. Rotating this lock-and-tumbler filter in the Fourier plane of an optical correlator produces a constant-amplitude Fourier sum at the locations of the target image. Input images having different angular harmonic components yield Fourier sums with time-varying amplitudes and are not recognized. Examples show that this filter is able to discriminate between similar objects while preserving translational, rotational, and intensity invariance.