The aim of this work is the evaluation of the capability of different optical systems to experimentally produce the Fourier Transform of an image. The experimental setup we analyze consists of a converging diffractometer, which in turn is intended to be used as the first diffraction stage of an optical correlator designed for pattern recognition applications. The diffractometer consists of (i) a coherent light source (laser) of wavelength ~. and gaussian profile, (ii) the optical system that produces the diffraction, (iii) a spatial light modulator (SLM) acting as the exit pupil, on which we display the image to be transformed, and (iv) the observation plane (that is, the Fourier plane) placed at a distance d from the SLM, at the image point of the light source. In this plane we obtain the Fourier Transform of the image, scaled by a factor ~.d [1].
The method we have developed evaluates the quality of the diffracting optical system by computing the complex amplitude distribution at the Fourier plane, based on the wave aberration at the exit pupil. This is obtained by means of an exact ray tracing ,algorithm and the relation between the rays coordinates at the image plane and the wave aberration at the exit pupil [2]. To assess the influence of the quality of this Fourier Transform in the correlation process, we simulate this latter in the following way: we compute digital correlations by means of two cascaded Fourier Transforms according to the convolution theorem [1], where the first Fourier Transform is that produced by the optical system and the second one is computed by means of a discrete Fourier transform algorithm (DFT), that is, it is an ideal one. In this way, analyzing the resulting correlation peak we can determine the inaccuracy introduced by the defects of the optical system. We will present the results obtained when different optical systems are evaluated by means of this method.