Rl. Gordon et Gw. Forbes, APODIZATION FOR SYSTEMS OF HIGH F-NUMBER, Journal of the Optical Society of America. A, Optics, image science,and vision., 14(6), 1997, pp. 1243-1254
The exit pupil distribution that maximizes the mean encircled energy f
raction over some interval along a system's line of symmetry is found
here for both two- and three-dimensional geometries. Such a merit func
tion has been optimized previously by using the Debye model for the di
ffracted field, but this is not valid for the systems studied here; th
e more general Kirchhoff integral must be used. Optimal pupil function
s for these systems are shown to depend on an additional parameter and
represent a new family of solutions with nontrivial phase. Taylor ser
ies are derived for these functions, and they provide a powerful verif
ication of the numerical results. (C) 1997 Optical Society of America.