Formulating the design of two freeform lens surfaces for point-like light sources

Two freeform surfaces provide more degrees of freedom in designing illumination optics and can yield a better solution. The existing methods for point-like sources are mostly valid in designing one freeform surface. Designing two freeform surfaces for point-like sources still remains a challenging issue. In this Letter, we develop a general formulation of designing two freeform lens surfaces for point-like sources. The proposed method is very robust in designing freeform lenses with two elaborately designed surfaces. The examples clearly show that using two freeform surfaces yields better solutions to challenging illumination problems with ultra-high energy efficiency.