Optimization design of double freeform surface uniform lenses for LED extended light sources based on NURBS curve

Based on the edge ray theory, an optimization method for the design of double freeform surface uniform lenses for LED extended light sources was proposed. The initial surface shape was calculated by Snell's law of refraction and energy conservation law. The NURBS (non-uniform rational B-splines) curve was used to fit and parameterize the free surface. The RSD (relative standard deviation) and energy efficiency of simulated illumination and desired illumination were taken as the indexes in the optimization process. The simulation results show that the ratio of lens height to light source diameter is 2.32∶1, RSD<0.113, energy efficiency up to 98%, uniformity of target surface illumination up to 95.9%, illumination uniformity and optical system compactness are effectively improved.