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
Orestes N. Stavroudis, "Simpler derivation of the formulas for generalized ray tracing," J. Opt. Soc. Am. 66, 1330-1333 (1976)