Information-theoretic analyses of a birefringent blur filter

We present the results of an information-theoretic analysis of an undersampled imaging system that contains a birefringent blur filter. We vary the spacing between replicas of the nonblurred point-spread function produced by the birefringent blur filter to find the value that yields the maximum information density. Comparison is made between this value and that yielded by a conventional qualitative design. We then analyze the effects of defocus aberration on the design of the birefringent blur filter. A wide search of blur-defocus space yields local peaks in the information density surface. The information density at these peaks is shown to exceed the maximum information density associated with the optimized birefringent blur filter or defocus alone, particularly when the fill factor of the photodetector array is low.