A matrix equation for the refraction of a thin pencil of rays by a surface of arbitrary shape is derived. The equivalence of this equation and previous nonmatrix equations derived for the same purpose is established. Potential applications of this matrix equation are in the field of ophthalmic lens design. The design of progressive-addition lenses, or just the thorough evaluation of spherotoric lenses, is an example of a task that requires the ability to propagate a thin pencil of rays under very general conditions. The matrix version of the generalized Coddington equations proposed here is a fitting tool for this end.
© 1996 Optical Society of America
Original Manuscript: June 21, 1995
Revised Manuscript: January 31, 1996
Manuscript Accepted: February 12, 1996
Published: August 1, 1996
J. E. A. Landgrave and Jesús R. Moya-Cessa, "Generalized Coddington equations in ophthalmic lens design," J. Opt. Soc. Am. A 13, 1637-1644 (1996)