Sensitivity of a nonlinear joint-transform correlator

Abstract

Theoretical and experimental studies have shown that the nonlinear joint-transform correlator (JTC) can produce reasonably good correlation performance.1,2 The nonlinear JTC uses nonlinearity at the Fourier plane to nonlinearly transform the Fourier-transform interference intensity. It has been shown that the compression type of nonlinear, joint-transform correlator provides higher peak intensity, larger peak-to-sidelobe ratio, narrower correlation width, and better cross-correlation sensitivity than does the classical correlator. In this paper, we provide an experimental investigation of nonlinear JTC sensitivity in the presence of the rotational and scaling changes of the input signal. Experiments determine the correlation peak intensity and peak-to-sidelobe ratio for various degrees of the nonlinearity at the Fourier plane. The sensitivity of the nonlinear JTC for different scaling and rotational distortion of the input image is determined for each nonlinear transformation. The experiments are performed in the presence of the input scene noise. The spatial light modulator (SLM) used at the Fourier plane is a Hughes liquid-crystal light valve operating in different degrees of the nonlinear mode, as determined by adjusting parameters such as the bias voltage, and input frequency. The nonlinear JTC tests indicate that as the severity of the nonlinear transformation of the joint power spectrum increases, the peak intensity increases, the correlation peak-to-sidelobe ratio increases, and the correlation width decreases. On the other hand, the nonlinear JTC is more sensitive to the input plane rotational and scaling changes than is with the linear JTC. The sensitivity of the nonlinear JTC depends on the severity of the nonlinear transformation that is used at the Fourier plane.