3D Phase-Space Ray Tracing for Illumination Optics

The efficiency of a lighting system is determined by both the performance of the light source and the design of the optical components that redirect and shape the emitted light. Lighting systems based on light-emitting diodes (LEDs) have become the standard in many applications due to their high efficiency. Nevertheless, careful optimization of the optical components remains crucial to achieve the desired light distribution at a target surface. This optimization process is iterative, with the target distribution computed at each iteration. The process continues until the resulting target distribution closely matches the desired one. Consequently, fast and accurate simulation tools are essential for computing the target distribution of optical systems. The goal of the research presented in this thesis is to develop novel phase-space-based ray-tracing methods for the efficient and accurate computation of the target intensity distribution of an optical system. We developed ray-tracing methods for both 2D and 3D optical systems. An optical system consists of a light source, a target, and several optical surfaces, such as lenses or reflectors. The phase space (PS) of a surface is the set of all position and direction coordinates of light rays intersecting that surface; each point in PS corresponds to a specific ray. For 2D optical systems, the PS is two-dimensional, while for 3D systems it is four-dimensional. Each optical surface (except the source and target) has two phase spaces: one representing rays emitted from it and another representing rays incident upon it. The source only has a PS representing emitted rays and the target only has one representing incident rays. First, we introduce a modified PS ray-tracing algorithm for 2D optical systems that can be extended more easily to three dimensions compared to the original algorithm. PS ray tracing utilizes information from the phase spaces of both the source and the target; they can be partitioned into regions corresponding to rays that encounter the same sequence of optical components along their path from source to target. The algorithm recursively computes an approximation of the boundaries of these regions. Once the approximate boundaries are determined, the target intensity distribution can be computed. The recursive procedure traces many rays near the boundaries of the PS regions and fewer rays within their interior. PS ray-tracing requires significantly fewer rays compared to classical Monte Carlo (MC) and Quasi-Monte Carlo (QMC) ray-tracing. The performance of PS ray tracing was compared to that of (Q)MC ray tracing using two optical systems. The results demonstrate that PS ray tracing offers improved performance over MC ray tracing and that it performs similar to QMC ray tracing. Subsequently, we generalized the concatenated backward ray mapping (CBRM) algorithm to extend its applicability to optical systems containing both flat and curved surfaces. The original algorithm performs well but is limited to systems consisting entirely of flat surfaces. Generalized CBRM is an alternative to PS ray tracing that utilizes the phase spaces of all optical surfaces, rather than only those of the source and target. The phase spaces of an optical system are connected through two mapping functions, which are used by the algorithm to identify rays located on the boundaries of the PS regions of the target. Only these rays are then traced from the source to the target and used to compute the target intensity distribution. The performance of classical and generalized CBRM was compared to each other. The results indicate that generalized CBRM provides superior performance in high-accuracy computations. In addition, numerical experiments demonstrate that generalized CBRM achieves a lower error than PS ray tracing while requiring less computation time. The next step was to extend PS ray tracing from two to three dimensions. We developed a 3D PS ray-tracing algorithm for rotationally symmetric optical systems. The 4D PS of a 3D optical system reduces to a 2D space of position coordinates when light along a fixed direction is considered. The intensity distribution can be computed using many such 2D spaces corresponding to different directions. Exploiting the rotational symmetry that exists in certain optical systems, significantly reduces the number of 2D spaces needed. The 3D algorithm follows a similar approach to the 2D PS ray-tracing method but operates on the 2D position spaces corresponding to fixed directions. The performance of 3D PS ray tracing was compared against QMC ray tracing on a rotationally symmetric optical system. The results demonstrate that PS ray tracing outperforms QMC ray tracing. Finally, we show that the 3D PS ray-tracing algorithm can also be applied to optical systems that lack rotational symmetry, but at the cost of increased computation time. This was confirmed through numerical experiments.