LAUSR

We propose a method to design double smooth freeform surfaces applied in beam shaping with a ray mapping method in the paper. We couple the calculation of ray mapping and the construction of freeform surfaces to approach the surface normal field integrability condition based on the symplectic flow mapping scheme. In this paper, the incident beam wavefront is not limited to be planar or spherical. Several challenging design examples are presented that include transforming a circular Gaussian beam to an unconventional beam with variously shaped contour, and transforming an elliptic beam to a convergent beam with complex irradiance distribution in non-paraxial regime. The results show the high efficiency and feasibility of the proposed method in designing freeform optics for beam shaping applications.