Design of axisymmetric double-surface refractive optical elements generating required illuminance distributions

Abstract We propose a novel technique for designing double-surface axisymmetric refractive optical elements with minimized Fresnel losses and maximized lighting efficiency. The design of the optical element is reduced to the integration of three explicit ordinary differential equations. Minimization of the Fresnel losses is provided by ensuring equal refraction angles on both “working” surfaces of the optical element. To demonstrate high performance of the method, we designed axisymmetric double-surface optical elements generating uniform illuminance distributions both in the far (angular size of 50°) and in the near (angular size of 90°) field. The lighting efficiency exceeds 87.8% for both point and extended light sources. Besides, we demonstrated that optical surfaces designed using the proposed method can serve as an excellent initial approximation in the case of a large extended light source. In the considered example with the ratio of the element height to the source diameter of only 2.2, the lighting efficiency of the optimized element exceeds 89.5%, whereas the uniformity of the resulting illuminance distribution exceeds 96%.