Generating optical freeform surfaces considering both coordinates and normals of discrete data points

Through direct design methods, both coordinates and normals of discrete data points on a freeform surface are usually obtained, but traditionally the freeform surface is generated by only fitting the coordinates. In this paper, a novel generating method that fits both the coordinates and the normals is proposed based on the mathematical multiobjective optimization theory. This new method is suited for generating some freeform polynomial surfaces. Two design examples are introduced, and their optical performance is significantly improved when applying the new method compared with the traditional method. This new method is validated to be effective, and it is widely useful as long as the coordinates and the normals are provided in advance.