Abstract

The joint transform architecture is well known in optical processing. Normally object and reference are presented to the system as purely real scenes. If the reference and object are identical, the joint transform power spectrum (JTPS) is the Fourier transform modulated by a cosinusoidal fringe pattern. This pattern is then itself transformed to produce the two correlation signals. Our analysis assumes that reference and object are real but that they are displayed on a device that can only modulate phase. A calculation is done for the resulting power spectrum, and the effect of displaying this power spectrum itself on a device that can only modulate phase is also modeled. Results indicate that good correlation peaks should be experimentally obtained. The effect of using an on-axis stop in the Fourier transform plane is also modeled. The correlation width can be improved greatly with a judicious choice of stops. This can be thought of as an extreme nonlinearity that imitates the behavior of photographic film in a joint transform correlator.¹

© 1991 Optical Society of America