Prescribed intensity in 3D rotational geometry for extended sources by using a conversion function in 2D design

To obtain a prescribed intensity in three-dimensional (3D) rotationally symmetric geometry for an extended source, a two-dimensional (2D) intensity design method is often used. The 3D entity of the lens can be gained by rotating the profile of the lens obtained by the 2D design method. However, the intensity we set in 2D design is quite different from the one we obtain through ray-tracing by the Monte Carlo method in the 3D rotational geometry. Noting the differences of intensity patterns between 2D and 3D, a 3D conversion function (3DCF) should be deduced to convert the prescribed 3D intensity into a 2D intensity in the 2D design process. The extended Lambertian source properties are taken into account during the derivation process. Using the 3DCF, we can quickly obtain the prescribed intensity in 3D rotationally symmetric geometry for an LED extended source without the fussy feedback strategy. The error is small enough for most general illumination. Three examples are presented to demonstrate the correction effectiveness of the proposed conversion function. (C) 2017 Optical Society of America