Abstract

For an optical system with a large amount of aberration, a merit function ∫ ∫_A M (s,ψ) g(s) sd sdψ is proposed, where M(s,ψ) is a relative modulation function introduced by Hopkins, g(s) is a weighting function, and A denotes a circular region in the spatial frequency domain (s,ψ). It is shown that the above quantity can be expressed as a quadratic form of the aberration coefficients by using an appropriate approximation. As a numerical example, we set g(s) = 1 and calculate the coefficients of the quadratic terms of the wave-front aberrations.

© 1971 Optical Society of America

Use of the Modulation-Transfer Function (MTF) as an Aberration-Balancing Merit Function in Automatic Lens Design

William B. King
J. Opt. Soc. Am. 59(9) 1155-1158 (1969)

Analytic merit function based on Buchdahl’s aberration coefficients

Paul N. Robb
J. Opt. Soc. Am. 66(10) 1037-1041 (1976)

Modulation-Transfer-Function-Based Merit Function for Automatic Lens Design, II*

William B. King
J. Opt. Soc. Am. 62(2) 230-233 (1972)

Phase-Only Complex-Valued Spatial Filter*

Joseph P. Kirk and Alan L. Jones
J. Opt. Soc. Am. 61(8) 1023-1028 (1971)

Asymptotic Expansions for Correcting Truncation Error in Transfer-Function Calculations

Berge Tatian
J. Opt. Soc. Am. 61(9) 1214-1224 (1971)