Two simple calculating schemes for use in ophthalmic optics--II. Tracing axial pencils through systems including astigmatic surfaces at random axes.

A paraxial computing scheme is described for tracing an axial pencil of rays through any system containing astigmatic surfaces with their axes at random. In conjunction with a scheme for tracing oblique rays (Bennett, 1986) it is applied to a problem in visual optics posed by Keating (1982). This involves determining the spectacle magnification for a schematic eye with three strongly astigmatic surfaces, corrected by a spectacle lens of bi-toroidal form, the axes of all five surfaces being mutually oblique. It is shown that the suggested computing schemes yield very similar results to those found by the matrix methods of Keating. Although only two rays are needed to determine the principal dimensions of the basic retinal image of a circle, further insight into its true shape is obtained from a multiple trace, using a computerized version of the ray tracing scheme.