<title>Accuracy of the output peak localization in two-dimensional matched filtering</title>

Abstract

The niatched filter has been developed historically as an one—dimensional detection filter for various communication systems1'2'3. It is the optimal filter for maximizing the signal-to-'noise ratio (SNR) . The concept of filtering in two dimensions has been introduced into two—dimensional linear systems as a simple extension of one-dimensional linear filter theory. Optical implementation of a matched filtering was a resuit of the development of the coherent light techniques and holography . In the past few years several correlation filters have been proposed. However, in many applications not only SNR, but also output peak sharpness, peak location, light efficiency, discriminability, and distortion invariance are very important filter parameters. A lot of problems related with optical pattern recognition may be reduced to detection and localization of search target. Various modifications of classical matched filtering are suggested in order to improve detection quality. All of them provide output peak sharpness minimalization. The sharper the correlation peak, the better location accuracy. Recently there are three basic realizations of the two dimensional correlation function in optics: - matched filtering including classical matched filtering (CMF), gradient filters (GF) , phase—only matched filtering (POF) , nonlinear matched filtering (NMF) , inverse filtering (IF) etc., - matched filtering with preprocessing, — joint transform correlator and its nonlinear version. In the present paper various modifications related to improvement of detection quality of the optical correlation methods mentioned above are presented and the output peak sharpness measured according to the peak-to--correlation energy (PCE) criterion is discussed.