Pupil function design algorithm for bipolar incoherent spatial filtering.

A two-step iterative algorithm is described for designing pupil functions for synthesis of bipolar point spread functions in a two-channel incoherent spatial filtering system. The first step uses the method of projections onto convex sets to determine an appropriate bias for the system pupil functions. This bias determines the complementary point spread functions and therefore the magnitude of the corresponding coherent spread functions. The phase of the coherent spread functions is obtained in the second step via iterative application of a magnitude constraint and a finite support constraint. With both magnitude and phase of the coherent spread functions established, the corresponding pupil functions are realized via Fourier transformation. Results are presented for a 2-D bandpass filter and compared with analytically obtained results. The comparison suggests that the iterative algorithm yields bias functions having less energy than bias functions determined by previously proposed analytic methods.