<title>Comparison of the performance of 2-f vs 4-f correlators with limited coding domain SLM</title>

Abstract

A new interesting hybrid digital/optical correlator, which performs the first Fourier transform electronically, hereafter referred to as a 2-f correlator, has been presented by Young. One of the advantages of this architecture compared to the classical 4-f correlator, an example of this architecture is presented by Chao, is that the optical system becomes less complex and does not require the same strict optical tolerances. The signal processing performance of these two architectures is expected to be the same if ideal Spatial Light Modulators (SLMs) with fully complex-valued coding domains are available. This study investigates the influence of a limited coding domain on the signal processing performance provided by current available SLMs. Optimal trade-off filters3 have been used for this investigation since they can be tuned, as the name suggests, to an optimal trade-off between being discriminant against distortions and being robust against noise. This has been used to evaluate the influence of different coding domains on the two optical correlator architectures. The coding domains of some commercially available SLMs have been implemented and their effect on the different correlator architectures have been analysed. These SLMs are: binary phase/amplitude SLM from Displaytech, Colorado, USA; micromirror SLM from Fraunhofer Institute, Dresden, Germany and the bipolar grey-scale FLC SLM from Boulder Nonlinear Systems, Colorado, USA. The coding domain has a strong influence on the signal processing capabilities. Generally, the 2-f architecture shows to be more discriminant and the 4-f architecture more robust to noise. The final choice between the two correlator systems depends however on available SLMs and the required trade-off between robustness and discriminance that is needed for the application.