Practical considerations for GRIN raytracing with commercial software

Abstract

When designing optical sub-assemblies that include gradient-index (GRIN) elements, the designer needs to have confidence in the ray trace results. However, developing such confidence is not as straightforward for GRIN as it is for homogeneous material. In this paper, GRIN raytracing is discussed at a high-level and considerations that are important for users to understand when incorporating GRIN elements into a design are discussed. Methods for ray transfer through GRIN materials involve numerical integration of a differential equation. These methods generally require that the user specify a step parameter for the differential equation solver. While this step parameter is generally the only control the user has over the GRIN ray trace, it is important for a designer to understand how error and execution time vary with this step parameter. Another issue that designers should be aware of is that the common scheme for the GRIN ray trace does not yield continuous ray trajectories, but instead gives the position and direction at a set of discrete (approximate) points on the ray. Therefore, the integration methods need to be supplemented in order to determine optical path length. Another consequence of not having a continuous trajectory is that the algorithm for transferring the ray through the GRIN material must be supplemented with an appropriate algorithm to determine the ray-surface intersection (and the direction of the ray at this intersection point). The effect of these supplemental algorithms on the ultimate GRIN ray trace accuracy is also discussed.