Optimization method for designing optical elements with an extended light source

A method for designing an optical element with two free-form surfaces generating a prescribed illuminance distribution in the case of an extended light source is considered. The method is based on the representation of the optical element surfaces by bicubic splines and on the subsequent optimization of their parameters using a quasi-Newton method implemented in the Matlab software. To calculate the merit function, a version of the ray tracing method is proposed. Using the proposed method, an optical element with record characteristics was designed: the ratio of the element height to the source size is 1.6; luminous efficiency is 89.1 %; uniformity of the generated distribution (the ratio of the minimum and average illuminance) in a given square region is 0.92.