Analysis of the influence of aberrated convergent Fourier-transform setupsin optical correlation

One of the simplest optical setup used to produce Fraunhofer diffraction at finite distances is the convergent arrangement, which enables an easy cont rol over the size of the diffraction pattern. In this setup, the diffractin g object is illuminated by a spherical wavefront produced by a convergent o ptical system. Convergent diffractometers are frequently used in optical co rrelators as a means to obtain the Fourier transform of the input scene. In this paper, we analyze the effect of the wave aberration introduced by the optical system in the resulting Fourier transform, and how this aberration affects the results in the correlation plane. The study is developed both experimentally and by a computer simulation and a simple optimization metho d, which improves the space invariance of the correlation process, is also introduced. (C) 2000 Published by Elsevier Science B.V.