Gradient-Index Optical Imaging Systems: A New Efficient Technique for Design and Analysis

Abstract

The analysis and design of the gradient index (GRIN) lens systems, like those of conventional homogenous lens systems, involve extensive raytracing. However, in GRIN lenses the rays are curved and the ray paths are generally obtained by a numerical solution of the ray equation. We have developed new techniques for each of the steps involved in the analysis and design of GRIN systems, ie, the transfer of ray, ray-surface intersection and the optical path length (OPL) computation for the calculation of optical transfer function which gives the overall performance of a system. In particular, we have been able to obtain a new form of the ray equation which makes the transfer of ray very efficient and fast. The ray-surface intersection point has hitherto been obtained by iterative raytracing which often requires more computations than the transfer of ray itself. The method that we have developed reduces these computations to simple analytical ones. For OPL computations, our method is at least two orders of mag...