Abstract

Symbolic substitution is essentially a combination of recognition and substitution process. In addition, although symbolic substitution is not restricted to space invariant operations, it is indeed based on the space invariant connectivity of optics. Therefore, holographic associative memory techniques may be alternatively applied to implement a symbolic substitution logic system. In this paper, we propose to use a high efficiency joint transform correlator to implement a symbolic subsitiution operation. Consider that the search pattern f_s(x,y) and an input image which consists of M × N input patterns f_m,n(x−x_m,y−y_n), are to be displayed on an input plane in a joint transform correlator architecture. The power spectrum recorded by a CCD camera is then replicated, using dedicated video hardware, to produce a L × L spectra array on a second spatial light modulator. Upon illuminated by a quasi-monochromatic, partially coherent parallel light source, the object irradiance at the correlation plane will be increased by L² times that of a conventional joint transform correlator.¹ Therefore, if f_mn matches with the search pattern f_s, a bright correlation peak would be located at a specific location determined by (x_m,y_n). To eliminate all of the unwanted light, a set of sampling pinholes is placed at the correlation plane. As a result, a spatial distribution of point light sources is generated. The substitution process can be accomplished by inserting a multiplexed Fourier transform hologram of the substituting pattern behind the collimating system after the sampling plane. Each of the point light source produces a plane wave front to read out the hologram. Consequently, each correlated input pattern produces a substituted output pattern at the corresponding position on the output plane, and symbolic substitution operation is completed.

© 1990 Optical Society of America