Influence of the aberrations of optical Fourier-transform systems in a joint transform correlator

The operation of a joint transform correlator is based on two Fourier transforms in cascade. The first one produces the joint power spectrum; the second one yields the correlation. In this work, we study the influence of the aberrations that affect the optical systems that produce the two Fourier transforms, by computing the wave aberration of the diffraction setups from data obtained by ray tracing. First, we consider the aberration only in the power spectrum, then only in the transformation of power spectrum to give the correlation and finally, in the two steps at the same time. In the study, real conditions have been reproduced and the dimensions and resolutions of real liquid crystal-displays have been used. The results show that the quality of the correlation is determined mostly by the aberrations of the first diffraction stage.