Abstract

Ternary phase–amplitude filters (TPAFs) are essentially binary phase-only filters (BPOFs) with a carefully selected passband or support function. Results have been reported on TPAFs used to maximize the signal to noise ratio (SNR)¹ of an optical correlator. In this paper we present a simple algorithm to design a TPAF yielding maximum SNR. The algorithm, similar to the one of Ref. ¹ in that it optimizes both the decision line and the passband of a BPOF, is more general (applicable to complex input) and increases computation speed further by reducing the 2-dimensional search to a 1-dimensional one. A decision line for the value assignment (π or - π) of a filter pixel is defined by its normal. A threshold along the normal determines the passband of the filter. For each tested decision line, the spectral components of the reference signal are projected onto its normal. The threshold is iteratively determined such that only those components with the largest projection are included in the passband. It is shown that the threshold thus selected results in a maximized SNR. The algorithm also makes it easier to achieve a trade-off between the SNR and correlation peak intensity.

© 1992 Optical Society of America