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

This paper explores the possibility of using dual geometry representation to improve the speed of ray tracing and ensure the robustness of light propagation simulations in complex optical systems containing free-form surfaces defined by high-order polynomials (up to order 34) or Jacobi polynomials. An analysis was carried out of traditional methods of representing this geometry both in the form of a triangular mesh and in the form of an analytical expression. The analysis demonstrated the disadvantages of traditional approaches, which consist in the insufficient accuracy of calculating the coordinates of the meeting point of the ray with a triangular mesh, as well as the instability of the results of searching for the hit point of tangent rays with the analytically defined surface when using existing calculation methods. As a result, it was proposed to use a dual representation of the geometry in the form of a rough approximation of the surface by a triangular mesh, which is subsequently used as an initial approximation to find the point where the ray hits the surface specified by the analytical expression. This solution made it possible to significantly speed up the convergence of analytical methods and increase their stability. Moreover, using the Intel® Embree library to quickly find the point of intersection of a ray with a coarse triangular mesh and a vector calculation model to refine the coordinates of the point of intersection of the ray with the geometry represented analytically allowed authors to develop and implement a ray tracing algorithm in an optical system containing surfaces with dual geometry representation. Experiments conducted using the developed and implemented algorithm show the significant acceleration of ray tracing while maintaining computational accuracy and high stability of results. The results were demonstrated by calculating the point and flare spread function for two lenses with free-form surfaces defined by Jacobi polynomials. In addition, for these two lenses, the image formed by an RGB-D object simulating a real scene was calculated.