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Holographic correlators can implement many correlations in parallel. For most systems shift invariance limits the number of correlation templates that can be stored in one correlator. This is because the output plane must be divided among the individual templates in the system. When the system is completely shift invariant, the correlation peak from one correlator can shift into an area that has been reserved for a different template; in this case a shifted version of one object might be mistaken for a well-centered version of a different object. We describe a technique for controlling the shift invariance of a correlator system by moving the holographic material away from the Fourier plane. (C) 1999 Optical Society of America.