Aberration functions that are a complete, orthogonal, and normalized set over a weighted spherical pupil are developed. A general weighting is considered, for which special cases are applicable to systems satisfying the Abbe sine condition and the Herschel condition. Paraboloidal mirrors are also considered. This weighting can also be used to account empirically for Fresnel reflection losses in the optical system. The functions can be expressed in an analytic form. Expressions are given for 24 low-order aberrations.
© 2004 Optical Society of America
Original Manuscript: April 29, 2003
Revised Manuscript: October 6, 2003
Manuscript Accepted: October 6, 2003
Published: May 1, 2004
Colin J. R. Sheppard, "Orthogonal aberration functions for high-aperture optical systems," J. Opt. Soc. Am. A 21, 832-838 (2004)