Design of optimal imaging concentrators for partially coherent sources: absolute encircled energy criterion

Abstract

Using an absolute encircled energy (AEE) measure as the criterion for imaging concentrator performance, we develop a design procedure that specifies the passive pupil screen providing optimal light concentration for sources of arbitrary coherence. The prescription for the optimal AEE pupil screen is shown to be the consequence of a maximum principle for imaging concentrators that is applicable for steady-state optical sources of arbitrary spatial coherence and for arbitrary detector configurations in the image plane. The maximum principle allows one to specify the optimal AEE pupil screen through a two-step process. The first step solves an eigenvalue problem expressed as a homogeneous Fredholm equation of the second kind, where the integral kernel is the product of the cross-spectral density function of the pupil field and a detector kernel function equal to a two-dimensional Fourier transform of the detector responsivity distribution. Step two specifies the optimal pupil screen by setting to unity the modulus of the eigenfunction corresponding to the largest eigenvalue of the eigenproblem specified in step one. We present a numerical example that illustrates the effect that source size and spatial coherence have on the specification of the optimal pupil screen.