Abstract

Using the ratio of encircled energy (REE) measure as the criterion for imaging-concentrator performance, we present a procedure that specifies the pupil screen that provides optimal light concentration for sources of arbitrary spatial coherence. Applying the REE performance measure to the imaging-concentrator problem leads us to consider a Fredholm integral equation similar to that encountered in an earlier study of absolute encircled energy (AEE) concentrators [ J. Opt. Soc. Am. A 3, 943 ( 1986)]. For the REE case studied here, we find that the Fredholm integral equation is of a generalized type and that the optimal pupil screen solution generally introduces a spatially varying weighting of the pupil field amplitude, a weighting that depends on the source field coherence and the particular concentrator configuration considered. We show how our formulation provides a straightforward extension of the classical apodization results of Barakat and Slepian for the case of extended, partially coherent sources and present some numerically computed examples that demonstrate the effect that source coherence has on the optimal REE pupil screen specification.

© 1987 Optical Society of America

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

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J. Opt. Soc. Am. A 3(7) 943-953 (1986)

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Axially symmetric nonimaging flux concentrators with the maximum theoretical concentration ratio

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