Abstract

An optical correlator with a volume hologram as a matched filter is usually not shift-invariant in both directions. If the input image is shifted along the degeneracy direction, correlation peak can still be obtained.^1,2 But if the input image is shifted perpendicular to the direction of degeneracy, there will be no correlation peak from the Bragg mismatch. We propose a 2-D shift-invariant optical correlator with a volume hologram as a matched filter. The shift-invariance along the degeneracy direction is obtained directly through Fourier transform. In the direction perpendicular to that of degeneracy, the image is shifted to obtain the correlation peak. Image shifting is achieved by deflecting the plane waves (Fourier components) at the Fourier plane. Either a rotating mirror or a Bragg cell can be employed as the deflector. Other methods to achieve image shifting that may be potentially applicable are also discussed. In addition, the amount of shift-invariance along the degeneracy direction is evaluated. The result shows that the amount of shift-invariance depends on the size of the image, focal length and also the angle between the reference and object beams. The combination of degeneracy and image shifting provides the 2-D shift-invariant optical correlation.

© 1991 Optical Society of America