Abstract

The equations for the refraction operation in generalized ray tracing are rederived using the Frenet equations from metric differential geometry and the idea of the directional derivative. Expressions are obtained for the principal directions and curvatures of a refracted wave front in terms of those quantities on the incident wave front and on the refracting surface. This provides the geometrical properties of the refracted wave front in the neighborhood of the traced ray.

© 1976 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Simplified formula for the illuminance in an optical system

Donald G. Burkhard and David L. Shealy
Appl. Opt. 20(5) 897-909 (1981)

Local wave fronts at diffractive elements

Norbert Lindlein and Johannes Schwider
J. Opt. Soc. Am. A 10(12) 2563-2572 (1993)

Generalized Coddington equations in ophthalmic lens design

J. E. A. Landgrave and Jesús R. Moya-Cessa
J. Opt. Soc. Am. A 13(8) 1637-1644 (1996)

References

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription

Equations (37)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access OSA Member Subscription