Dual Representation of Geometry for Ray Tracing Acceleration in Optical Systems with Freeform Surfaces.

This paper explores the possibility of using dual representation of geometry to speed up ray tracing and ensure robustness of light propagation simulation in complex optical systems with freeform surfaces defined by high-degree polynomials (up to order 34) or Jacobi polynomials. Traditional methods for representing this geometry both as a triangular mesh and as an analytical expression are analyzed. The analysis demonstrates the disadvantages of the traditional approaches due to the insufficient accuracy of calculating coordinates of the point at which the ray intersects the triangular mesh, as well as the non-robustness of the conventional procedures for finding the point of intersection between the tangent ray and the analytical surface. Thus, it is proposed to use a dual representation of geometry as a rough approximation of the surface by a triangular mesh, which is subsequently used as an initial approximation to find the point at which the ray intersects the surface defined by an analytical expression. This approach significantly speeds up convergence of the analytical methods and improves robustness of their solutions. The use of the Intel® Embree library to quickly find the point of intersection between the ray and the rough triangular mesh, as well as a vector model to refine the coordinates of the point of intersection between the ray and the analytically represented geometry, allows us to develop and implement a ray tracing algorithm for an optical system that has surfaces with dual representation of geometry. Experiments carried out using the developed algorithm show a significant speedup of ray tracing while preserving computational accuracy and high robustness of the results. The results are demonstrated by evaluating the point spread function and glare for two lenses with freeform surfaces defined by Jacobi polynomials. In addition, for these two lenses, an image formed by an RGB-D object that simulates a real scene is calculated. [ABSTRACT FROM AUTHOR]