Nonlinear joint transform correlator using one-dimensional Fourier transformation

Abstract

We present a new method for processing the data in a nonlinear joint transform correlator (NJTC). The output of the NJTC is obtained after two steps. The first step consists of the acquisition of the joint power spectrum (JPS) of the images to be correlated. The JPS is in principle a bidimensional image. The second step is the calculation of the cross-correlation function. To do this, the JPS image is compressed to one dimension and a 1-D Fourier transform is performed. This significantly reduces the number of operations required to evaluate the cross-correlation. To improve the cross-correlation sensitivity, a degree of nonlinearity is introduced using an illumination level above the saturation threshold of the camera used to acquire the JPS.