Research

Different from the traditional freeform system design method based on optimization, the direct design methods (such as the PDEs method, SMS method, and the CI method proposed by our group) can obtain a series of discrete data points (including the coordinates and surface normals) on a freeform surface. Traditionally the freeform surface is generated by fitting the coordinates based on the least-square algorithm, the normals of the data points are out of consideration. Because the propagation of light rays is sensitive to the surface normal, the optical performance achieved by such a freeform surface generated traditionally is likely to deviate from the expected result, probably to a large extent.
Our research group has proposed a novel freeform surface fitting method considering both the coordinates and the normal of the discrete data points. This method is based on least-square theory and mathematical multiobjective optimization theory. Both the coordinates and the normals of the discrete data points are controlled through the weighted error of both the two aspects. This method is a genenal fitting method of freeform surface for both the imaging applications and illumination applications, and it can be used in the design of conventional polynomial surfaces such as XY polynomial surface and Zernike polynomial surface.