A general equation of high-order surfaces is given. If its second term is equal to zero, this equation will automatically reduce to the conic surfaces. By adding two parameters g and k into the conic equation, we are able to use only one euqation to describe the planar, cylindrical, and conic surfaces. A set of skew ray tracing formulas for these surfaces, including tilted and decentered elements, is derived. The formulas analytical and easy to use. Based on the tracing of skew rays, a merit function of the optical system is defined and an analytical formula for determining the narrowest cross-sectional position of skew rays is given. A program of skew ray tracing is edited for the Sharp-1500 pocket computer. An example for a 2-D infrared scanner is given. Based on the skew ray tracing formulas and by using the damped least-squares method, some examples for automatic design of optical systems are also shown on the IBM PC/XT personal computer.
© 1988 Optical Society of America
You-Wen Zhang, Mo-Jun Chang, Cu-Wu Yang, and Hai-Cheng Tu, "Automatic design of optical systems using a set of general skew ray tracing formulas," Appl. Opt. 27, 1574-1580 (1988)