That is, given a specific image, to determine a surface whose refracted or reflected light forms this image. In the discrete version of this problem, the surface is divided into several micro-surfaces which are assumed smooth, i.e. the light reflected/refracted by each micro-surface forms a Gaussian caustic. Gaussian caustic means that each micro-surface obey gaussian distribution. The position and orientation of each of the micro-surfaces is then obtained using a combination of Poisson integration and simulated annealing. There have been many different approaches to address the continuous problem. One approach uses an idea from transportation theory called optimal transport to find a mapping between incoming light rays and the target surface. After obtaining such a mapping, the surface is optimized by adapting it iteratively using Snell's law of refraction. Optimal-transport-based caustic pattern design Basic principle Controlling caustic pattern is rather a challenging problem as very minor changes of the surface will significantly affect the quality of the pattern since light ray directions might be interfered by other light rays as they intersect with and refract through the material. This will lead to a scattered, discontinuous pattern. To tackle this problem, optimal-transport-based is one of the existing proposed methods to control caustic pattern by redirecting light's directions as it propagates through the surface of a certain transparent material. This is done by solving an inverse optimization problem based on optimal transport. Given a reference image of an object/pattern, the target is to formulate the mathematical description of the material surface through which light refracts and converges to the similar pattern of the reference image. This is done by rearranging/recomputing the initial light intensity until the minimum of the optimization problem is reached. Design pipeline Here considering only refractive caustic, the objective can be determined as follows (similar principle for reflective caustic with different output): Input: image of pattern to be obtained after propagating lights through the material, given the light source position. Output: caustic geometry on the receiver (flat solid surface, e.g.: floor, wall, etc...) In order to achieve the target pattern, the surface where light refracts through and exits to the outer environment must be manufactured into certain shape to achieve desired pattern on the other side of the material. As mentioned, given an input image, this process will produce the similar caustic pattern as the output. In principle, there are two core stages with each includes two sub-stages: Solving