Freeform construction method for illumination design by using two orthogonal tangent vectors based on ray mapping

Abstract

To construct freeform surface that best fits the normal field, an efficient numerical method is put forward in this paper. In this method, the normal vectors are constructed by two adjacent orthogonal tangent vectors at each point, and then the normal vectors are substituted into Snell's law to obtain the nonlinear equations describing the surface coordinates. Finally, the continuous and accurate freeform surface can be obtained by solving these nonlinear equations. The simulation results show that the proposed method provides lower RSD and normal deviation than the traditional freeform construction method.