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

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