Abstract

The exit pupil distribution that maximizes the mean encircled energy fraction over some interval along a system's line of symmetry is found here for both two- and three-dimensional geometries. Such a merit function has been optimized previously by using the Debye model for the diffracted field, but this is not valid for the systems studied here; the more general Kirchhoff integral must be used. Optimal pupil functions for these systems are shown to depend on an additional parameter and represent a new family of solutions with nontrivial phase. Taylor series are derived for these functions, and they provide a powerful verification of the numerical results.

© 1997 Optical Society of America

Optimal trade-off pupil for the synthesis of nondiffracting beams in free space

J. N. Provost and J. L. de Bougrenet de la Tocnaye
J. Opt. Soc. Am. A 14(10) 2748-2757 (1997)

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

Paul S. Idell
J. Opt. Soc. Am. A 4(10) 1911-1918 (1987)

Focusing of partially coherent light in systems of large Fresnel numbers

Weijian Wang, Ari T. Friberg, and Emil Wolf
J. Opt. Soc. Am. A 14(2) 491-496 (1997)

Effect of the aperture–lens separation on the focal shift in large-F-number systems

R. G. Wenzel
J. Opt. Soc. Am. A 4(2) 340-345 (1987)

Encircled energy for systems with truncated-Gaussian apertures of different Fresnel numbers. II. Maximizing beam energy concentration on a target

Yajun Li
J. Opt. Soc. Am. A 24(7) 2033-2042 (2007)