Abstract

This paper considers the maximum performance of annular apertures. Pupil functions are found that place the largest possible fraction of energy on circular, far-field targets, thus establishing the truly diffraction-limited performance of annuli. Properly contoured pupil functions can put significantly more energy on targets than do the uniform pupil functions that presently are used as the measure of diffraction-limited performance in laser technology. For example, an annulus with a ratio of inside to outside diameter of 0.1, with the optimum function, places 12% more energy on a target that is one Airy disk in size than does a uniform pupil function. The optimal propagation of energy from annulus to target is found to be described by the same integral equation that describes the hole-coupled resonator. Design and evaluation of annular devices should be based on these optimal pupil functions rather than on uniform illumination.

© 1975 Optical Society of America

Optical-wave near field specified from far-field data

H. G. Schmidt-Weinmar
J. Opt. Soc. Am. 65(9) 1059-1066 (1975)

Diffraction of light from an aperture on a spherical surface

A. S. Marathay
J. Opt. Soc. Am. 65(8) 909-913 (1975)

Restoration of astigmatism and curvature of field*

A. A. Sawchuk and M. J. Peyrovian
J. Opt. Soc. Am. 65(6) 712-715 (1975)

Transparency of pair-correlated, random distributions of small scatterers, with applications to the cornea*

Victor Twersky
J. Opt. Soc. Am. 65(5) 524-530 (1975)

Apodization for maximum Strehl criterion and specified Sparrow limit of resolution for incoherent illumination

Patra W. Peng and J. Ernest Wilkins
J. Opt. Soc. Am. 65(11) 1292-1299 (1975)