Abstract

We solve the apodization problem of determining the diffraction pattern, for a circular aperture, that has a specified Sparrow limit of resolution for coherent illumination and the maximum possible ratio of the central maximum irradiance to the overall transmittance (i.e., maximum possible Strehl criterion). Our analysis uses a mathematical description of the Sparrow limit that is correct, even for complex-valued pupil functions. Earlier work of Barakat, and of the author, on this problem used a mathematical description of the Sparrow limit that we show here to be conceptually inadequate, even for real-valued pupil functions. In spite of this inadequacy, we find the conclusions of the earlier work are valid for the correctly stated problem, provided that the specified Sparrow limit does not exceed the value it would have for the classical Airy-type objective.

© 1977 Optical Society of America

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)

Apodization for maximum Strehl ratio and specified Rayleigh limit of resolution*

J. Ernest Wilkins
J. Opt. Soc. Am. 67(8) 1027-1030 (1977)

Apodization for maximum Strehl ratio and specified Rayleigh limit of resolution. II.

J. Ernest Wilkins
J. Opt. Soc. Am. 69(11) 1526-1530 (1979)

Apodization for maximum central irradiance and specified large Rayleigh limit of resolution

John N. Kibe and J. Ernest Wilkins
J. Opt. Soc. Am. 73(3) 387-391 (1983)

Application of Apodization to Increase Two-Point Resolution by the Sparrow Criterion. I. Coherent Illumination

Richard Barakat
J. Opt. Soc. Am. 52(3) 276-283 (1962)