Abstract

A theoretical study is presented comparing the performance of several correlation filters including the Fourier-based matched filter, the Hartley transform system, and the sine-filter-cosine configuration.¹ In principle all these can be realized in systems using incoherent illumination, but the latter two possess the distinct advantage that the filter transmittance is a real number. Both a sine filter and a binarized sine filter are studied for the sine-cosine cascade correlator, and the latter is clearly shown to be superior. The evaluation is based on calculations of the ratio of peak output signal-to-noise as is customary. Additionally it is important to consider the ambient background signal in regions near the correlation peak and the spatial variation in this local background. We show that all four systems provide matched filter performance. However, the sine transform filter and its binary version are superior, since for these the mean value of the local background is zero. Computer simulations are provided, illustrating the two important applications of sorting pictorial scenes and words.

© 1988 Optical Society of America