Least-squares ray mapping method for freeform illumination optics design

Abstract

Computing a source-target map that yields integrable surface normal field is quite challenging for freeform illumination design. Here, we propose a least-squares ray mapping method to calculate a superior ray mapping by iteratively correcting an integrable map to approach the energy conservation and boundary condition. The process is implemented via solving three minimization problems. The first two problems can be figured out pointwise and the third can be converted to two decoupled Poisson equations with Robin boundary conditions. We demonstrate the robustness and high efficiency of the proposed method with several design examples.

Designing Freeform Micro Lens Array With Prescribed Luminous Intensity for LCD Backlight Units

“…It should be noted that all the well-developed zero-étendue methods can be used. For our purpose, we will utilize the so-called ray mapping method [24], [25] to complete the design. The ray mapping method is to solve a mapping relation between the source domain and the target domain satisfying the flux conservation and the boundary condition:…”

“…Directly solving (4) with constraints ( 5) is a complex task. Here, we employ a heuristic procedure demonstrated in our previous work [24], [25]. Instead of solving a ray map satisfying (5), this method traces the rays through the current surface which will lead to a mapping automatically satisfy (5) and corrects the mapping to satisfy (4) with limit variation of its first partial derivative.…”

Compact freeform illumination optics design by deblurring the response of extended sources

“…Notice that any well-developed zero-étendue algorithm can be employed or modified to adapt our design framework. In this paper, we will employ the least-squares ray mapping (LSRM) method proposed in our previous work [17] to accomplish the illumination design.…”

“…The basic problem of illumination design is to solve a single surface or multiple surfaces that can regulate the energy output of light sources into a prescribed irradiance distribution on a target surface, which is also one of the main concerns of nonimaging optics [3]. Extensive research has been done into designing freeform lenses for ideal sources (zero-étendue sources) [4][5][6][7][8][9][10][11][12][13][14][15][16][17] enabling to convert the light output into almost any desired irradiance distribution when the source size is negligible compared to the optic. However, for the real sources that have finite extents, the design methods for ideal sources require to design lenses with their sizes several times larger than the sources (usually more than five times) [18], which deviates from the goals of compactness and light-weight for illumination design.…”

Iterative freeform lens design for prescribed irradiance on curved target

“…Doskolovich and Bykov et al reduced the calculation of an integrable ray map to finding a solution to a linear assignment problem 26,27 . Besides, least-squares ray mapping methods created by Prins et al and modified by Wei et al could also be employed to acquire an integrable ray map [28][29][30] . In our previous work, we introduced the iterative wavefront tailoring (IWT) method to obtain an integrable ray map through immediate construction of a series of outgoing wavefronts 31 .…”