| Nonimaging optics has always been intertwined with geometry - in the beginning years of the modern nonimaging optics field, the main task that was investigated was to collect the radiation from the sun using solar concentrators, in which conic shapes often played an important role. More recently, nonimaging optics has expanded to address illumination tasks. The field of illumination is focused on improving the design of illumination systems to leverage the energy efficient solid-state lighting sources, to reduce light pollution and energy waste. In this research, we use geometry concepts, including the properties of conics and their intersections, to propose new design tools. Used in conjunction with the currently available design procedures, these tools offer significant advantages both in terms of efficiency and of computation time. Specifically, this work has led to three major findings. First of all, a thorough implementation of the linear programming method was performed. A relationship between the number of rays and targets was uncovered, and led to identifying the best parameters with which the linear programming can produce the solution in the fastest time. Additionally, the property uncovered inspired a new design method---direct calculation. The direct calculation method stitches different conics together to provide the desired illumination distribution, and is shown to have better accuracy than standard 2D numerical integration. Finally, a new flux estimation method based on the calculation of the intersections between neighboring conic patches was proposed. The intersection method is several orders of magnitude faster and more accurate than standard Monte Carlo ray tracing. All contributions of this research are aimed at providing advanced design tools for illumination tasks, with particular interest in optimizing computational speed and efficiency. |
