Design of freeform LED optical elements for direct backlight systems

A method is suggested for design of refractive optical surface intended for generation of the prescribed irradiance distribution. The method is based on the gradient optimization of the refractive surface represented as a bicubic spline in spherical coordinates. An optical element for direct-type backlight system was designed. The element produces uniformly illuminated hexagonal region with angular size of 143 degrees at the distance of 15 mm from the Luxeon (R) Rebel Cool-White LED. The RMS error of generated irradiance distribution from the constant value is 3-4% with an energy efficiency greater than 81%. The simulation data shows that a large, uniformly illuminated region can be formed by means of a system of the indicated elements, located at the nodes of a rhombic grid.