Optimal imaging concentrators based on the ratio of encircled energy criterion

Abstract

We investigate the effects of spatial coherence on the design of optimal imaging concentrators where the ratio of encircled energy (REE) in the image plane is used to gauge concentrator performance. Using the REE criterion, we develop an apodization procedure which provides optimal light concentration for source fields possessing arbitrary states of spatial coherence and for arbitrary detector configurations. Our solution for the optimal pupil screen invokes the use of a generalized Fredholm-type integral equation whose integral kernel (and weighting function) are determined by the pupil field cross-spectral density function and the detector configuration in the image plane. We illustrate the effects of source coherence on the optimal apodizer design through the use of several numerically computed examples. These examples indicate the range of field coherence conditions over which concentrator performance will be improved through apodization. For the case that multiple-detector concentrators are considered, we investigate the onset of eigenvalue degeneracy in the integral eigenvalue problem and discuss its effects on the optimal pupil function solution.