The effects of small displacements of spatial filters.

In a coherent optical system any displacement of a spatial filter from its optimum position degrades the performance of the system. In this paper the performance of a matched filtering system is related to the degree of displacement for both uniform and nonuniform noise spectral densities. Static displacements of the filter normal or parallel to the optical axis are treated, as well as random motion of the filter normal to the optical axis. Displacements normal to the optical axis cause the performance to decrease more rapidly than those parallel to the axis. For both kinds, the positioning tolerances are more critical when the noise spectral density is nonuniform. A dual frequency-plane optical precessor is described; this processor helps overcome the tolerance problem when the noise is nonuniform because the fixed part of the matched filter can be placed in one frequency plane and the changeable part in another.