APODIZATION FOR SYSTEMS OF HIGH F-NUMBER

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.