Space-variant joint transform image correlation using a binary spatial light modulator at the Fourier plane

Abstract

A joint Fourier transform image correlator that uses a binary spatial light modulator (SLM) at the Fourier plane is described. It is shown that binarizing the Fourier transform’s interference intensity does not seriously degrade the performance of the system. The implementation of joint transform correlation using an electrically addressed SLM at the Fourier plane requires magnification of the Fourier transform's interference intensity to pre serve spatial invariance. Due to the low resolution of available SLMs, magnification is necessary to resolve the high spatial frequencies of the interference intensity which are associated with the input signals’ positions. However, such magnifications can result in the loss of the space-band width product (SBWP), which can degrade the performance of the system. Here we also show that by compromising the spatial invariance, the correlation signals can be formed without such magnifications and without significant losses in the SBWP. Undersampling of the interference intensity results in aliasing effects and loss of the high spatial frequencies associated with the input signals’ locations which also correspond to the correlation positions at the output plane. We show that the correlation functions can be recovered if their positions are known; therefore, the proposed technique is called space-variant image correlation. It is shown that the correlation performance of the proposed system is superior to those systems that employ magnification at the Fourier plane to preserve spatial invariance.