Optimized design of LED freeform lens for uniform circular illumination

An optimization method is proposed for designing an LED freeform lens which produces a uniform circular pattern with high energy efficiency.This method is composed of three main aspects：design of the initial guess,parameterization of the freeform surface,and construction of the merit function.The initial guess is created by solving an ordinary differential equation numerically.An approach of selecting optimization points is introduced for parameterization of the freeform surface.The merit function is constructed by use of the irradiance uniformity and the efficiency of the lens.Design examples are given,and the results show that the irradiance distribution is well controlled with a maximum uniformity（the relative standard deviation of irradiance,RSD） of 0.0122 and a maximum efficiency of 93.88%.This optimization method can be generalized to design freeform lenses with different lighting patterns or without rotational symmetry.