Fast design method of smooth freeform lens with an arbitrary aperture for collimated beam shaping

A method is presented for the fast design of a smooth freeform lens to tailor a collimated light beam with an arbitrary contour. This method begins by calculating an initial surface based on a simplified ray mapping. Then the surface is fitted by a system of Zernike polynomials, whose weights are treated as the optimization variables for further optimization. In the optimization, the objective function is analytically calculated using a partial differential-equation-based approach. To validate the effectiveness of the proposed method, a freeform lens is designed for a collimated Gaussian beam with a spline contour to form a uniform illumination distribution with another spline contour, which takes only 26 s. A freeform lens is also fabricated and experimented, and its practical performance approaches the design.