Abstract
Two linear ray-propagation models are discussed. In one model, the ray-direction variables are direction tangents. In the other model, direction cosines are used instead. In particular, the construction of rays to first-order accuracy according to the direction-cosine scheme is explained. The refraction invariance of the pupil coordinate, as defined by Schwarzschild [ K. Schwarzschild, Abh. Koenigl. Ges. Wiss. Goettingen Math. Phys. Kl. Neue Folge 4, 8– 9 ( 1905)], is highlighted. In the case of imaging, only the rays constructed according to the direction-cosine propagation model satisfy the sine condition. Hence it is this ray-propagation model that retains physical significance beyond the paraxial region. Moreover, it is only the direction-cosine model that is not in contradiction with the impossibility of perfect three-dimensional imaging. Therefore, as a starting point for the theory of aberrations, the direction-cosine model is to be preferred over the direction-tangent model.
© 1987 Optical Society of America
Full Article | PDF ArticleMore Like This
C. H. F. Velzel
J. Opt. Soc. Am. A 4(8) 1342-1348 (1987)
Anders H. Andersen
J. Opt. Soc. Am. A 4(8) 1385-1395 (1987)
Donald G. Burkhard and David L. Shealy
J. Opt. Soc. Am. 63(3) 299-304 (1973)