Although thick volume photorefractive (PR) crystal offers promise in application to large-storage-capacity holographic memories, the thickness of the material also impairs the shift-invariant properties of the correlator. We discuss the influence of the angular and the wavelength selectivity in a thick PR crystal filter. The shift tolerances of Bragg diffraction-limited PR-based correlators are analyzed, which include the Vander Lugt, joint transform, and reflection-type (RC) correlators. We have shown that the RC correlator performs the best. A simple experiment to Illustrate the shift-invariant capability of PR-based reflection-type correlators is also described.