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

Full Article  |  PDF Article
OSA Recommended Articles
Design of optimal imaging concentrators for partially coherent sources: absolute encircled energy criterion

Paul S. Idell and Joseph W. Goodman
J. Opt. Soc. Am. A 3(7) 943-953 (1986)

Apodization for maximum encircled-energy ratio and specified Rayleigh limit*

Audrey M. Clements and J. Ernest Wilkins
J. Opt. Soc. Am. 64(1) 23-27 (1974)

Optimal pupil screen design for the estimation of partially coherent images

Roy M. Matic and Joseph W. Goodman
J. Opt. Soc. Am. A 4(12) 2213-2227 (1987)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Figures (7)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (40)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Metrics

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription