Optimization method for designing double-surface refractive optical elements for an extended light source

We propose a method for designing optical elements with two freeform refracting surfaces generating prescribed non-axisymmetric irradiance distributions in the case of an extended light source. The method is based on the representation of the optical surfaces as bicubic splines and on the subsequent optimization of their parameters using a quasi-Newton method. For the fast calculation of the merit function, we propose an efficient version of the ray tracing method. Using the proposed approach, we design optical elements generating uniform square-shaped irradiance distributions in the far- and near-field. The designed elements are very compact (the height-to-source ratio is only 1.6) and, while providing a high lighting efficiency of 89%, generate highly uniform distributions (the ratio between minimum and average irradiance values in the prescribed square-shaped region exceeds 0.9).