A Ray-Mapping Design Method of Freeform Illumination System Based on Solving a Simplified Monge–Ampère Equation

The difficulty of the ray-mapping design method of the freeform illumination system is to obtain a suitable ray-mapping, not only to meet the requirements of the desired output, but also to maintain the continuity of the freeform surface. This paper presents a ray-mapping design method based on solving a simplified Monge-Ampere (M-A) equation. According to this design method, a suitable ray-mapping between the light source and the target is obtained, and the overall system can be built based on this ray-mapping. To verify the effectiveness of the design method, two examples with a desired illumination output that is highly complex and challenging are adopted. The experimental result of example 1 shows that the output formed the shape of letter "A" as desired, and the ratio between the letter and the background is about 1.59:1, which is not good enough as desired 2:1. The difference between experimental output and the desired output is that the energy of the vertex of the experimental output is lower than the expected, and the band width is larger. The design results in Example 2 show that the simulation results of the point light source and the 1 mmx1 mm extended light source are very similar, both have reached satisfactory results.