Abstract

In order to use high-speed calculating machines in ray tracing, it is advisable to replace trigonometrical formulas by formulas involving the solution of quadratic equations. It is shown that the tracing of skew as well as of meridian rays is accomplished by solving two quadratic equations and an iterative process (based on Newton’s method) is suggested for solving the equations speedily by machine calculation. A numerical example is given.

© 1951 Optical Society of America

Ray Tracing Using the IBM Card Programmed Electronic Calculator*

William A. Allen and Richard H. Stark
J. Opt. Soc. Am. 41(9) 636-640 (1951)

Optical Calculations with Automatic Computing Machinery*

Donald P. Feder
J. Opt. Soc. Am. 41(9) 630-635 (1951)

Automatic Ray Tracing*

M. Herzberger
J. Opt. Soc. Am. 47(8) 736-739 (1957)

New Ray Tracing Scheme

P. W. Ford
J. Opt. Soc. Am. 50(6) 528-533 (1960)

Graphical Ray-Trace and Surface Generation Methods for Aspheric Surfaces

Robert E. Lewis
J. Opt. Soc. Am. 41(7) 456-459 (1951)