Fourier-plane windowing in the binary joint transform correlator for multiple target detection

With recent advances in state-of-the-art spatial light modulators, the optical joint transform correlator (JTC) and the binary joint transform correlator (BJTC) are becoming practical signal-processing tools. The performance of these devices is limited by the difficulty of separating the cross correlation between the reference and the targets in the scene from signals resulting from cross correlations between objects in the target scene. One technique that reduces this problem is to use a sliding window in the Fourier plane as a convolution mask filter to set an adaptive binarization threshold. This suppresses the autocorrelation response and reduces the dynamic range of the Fourier-plane signal. This results in correlation performance improvement by a factor of 2 to 4. A mathematical model is developed to describe the windowing process for both the JTC and BJTC for the case in which the scene contains multiple targets and background clutter. The derivation of the windowing process is general and includes any spatial high-pass or bandpass filtering in the Fourier plane. The results are supported with experimental data.