Fast approximation of the inverse reflector problem

Abstract

Suppose we have a target radiance distribution, a light source, and a plane for receiving light. How do we design a reflector that can give a similar result as the target radiance distribution? The inverse reflector problem is of high interest for light designers and related industries, such as lamp manufacture, headlight and street light design, and interior designs. There have been some researches on this specific topic. Nevertheless, the existing algorithms are either not fully compatible with parallel acceleration or have a narrow application scope (can only handle the far-field problem). This thesis's goal is to design a method that can have a fast approximation of the inverse reflector problem and handle different application scenarios. The core of the proposed method in this thesis is a modified simulated annealing algorithm. I first give the definition of the inverse reflector problem and explain why I choose simulated annealing in the proposed method by analysing the related works and various optimisation algorithms. Then, I detail what issues the plain simulated annealing algorithm will have and why it cannot achieve satisfactory results. Moreover, to solve the issues and improve performance, I propose additional strategies, such as Phong tessellation, randomisation strategy, multi-level strategy, history-decision strategy and penalising strategy. I also discuss the system design based on the proposed method and how to accelerate the optimisation process in this system. I evaluate and validate the proposed method by running test cases in different scenarios and compare the results with other algorithms. The results show that the method, as a general optimisation algorithm, can achieve good results in different application scenarios. The compatibility, speed and accuracy are the main advantages. The result of the proposed method can also serve as the initial guess for a finer optimisation.