Abstract

Ray tracing in graded-index media forms an essential part of the design of inhomogeneous lenses. However, since the path of rays in such media are curved, in general, one has to solve the ray equation numerically, except in a few cases in which analytical solutions are possible (see, e.g., Refs.1-3). As such, some algorithms have been developed for tracing rays through a general medium^(4-7). We present here a new numerical method for tracing rays through graded index media and have shown that this method requires much less computational effort (in comparison to other methods) for obtaining a desired accuracy. The method essentially consists of putting the ray equation in a convenient form by appropriately defining a new variable and solving the resulting equation using a standard numerical technique⁽⁸⁾. In Sec.2, we have described the method and in Sec. 3, we have presented numerical results corresponding to graded index media which are of considerable practical importance and have also compared the computational effort with other methods^(6,7).

© 1981 Optical Society of America