Abstract
The design theory and method for illumination systems with free-form reflectors are studied. Uniform bicubic B-spline surfaces are used to describe the shape of the reflector, and the control point coordinates are calculated by equation solving after the shape points of the reflector are obtained. An iterative method is developed to calculate the coordinates of the intersection point of an incident ray with a B-spline surface in 3D space. Formulae are given to calculate the direction cosines of the surface normal at the intersection point. For segmented reflectors, a method is presented to rapidly determine the segment with which the incident ray strikes, which can greatly improve the efficiency of ray-tracing for segmented reflectors. The damped-least- squares method is used to optimize the B-spline surface reflector. The Z-coordinates of the control points are adjusted through the optimization, so that the light distribution generated by the reflector with a real (extended) source meets the design requirements.
| Original language | English |
|---|---|
| Article number | 14 |
| Pages (from-to) | 88-96 |
| Number of pages | 9 |
| Journal | Proceedings of SPIE - The International Society for Optical Engineering |
| Volume | 5638 |
| Issue number | PART 1 |
| DOIs | |
| Publication status | Published - 2005 |
| Event | Optical Design and Testing II - Beijing, United States Duration: 8 Nov 2004 → 11 Nov 2004 |
Keywords
- Bicubic B-spline surface
- Control points
- Damped-least- Squares method
- Ray-tracing
- Shape points