Impact of sampled data on an optical joint transform correlator

Coherent optical systems are well known for performing certain operations such as Fourier and Fresnel transformation and pattern recognition. The basis for pattern recognition in many coherent optical systems is the correlator. This paper discusses the effect of undersampling in an optical joint transform correlator which has a sampled-data input, detectors of size 1 x i resolution elements in the Fourier plane, and detectors of size 1 x 1 resolution elements in the correlation plane, where i is an integer. After the undersampling, it is shown that the correlation plane still contains the needed data, the shape of the correlation surfaces are unchanged, and the different correlation terms just move closer together. It is shown that the penalty for undersampling is that the amount of input data must be reduced by a factor of i. It is also shown that a digital simulation using a discrete Fourier transform gives an accurate prediction of the optical correlator performance. Results from the simulation are given to verify the theory.