Optimization of LED-based non-imaging optics with orthogonal polynomial shapes

Starting with a seminal paper by Forbes [1], orthogonal polynomials have received considerable interest as descriptors of lens shapes for imaging optics. However, there is little information on the application of orthogonal polynomials in the field of non-imaging optics. Here, we consider fundamental cases related to LED primary and secondary optics. To make it most realistic, we avoid many of the simplifications of non-imaging theory and consider the full complexity of LED optics. In this framework, the benefits of orthogonal polynomial surface description for LED optics are evaluated in comparison to a surface description by widely used monomials.