Implementation of the linear programming algorithm for freeform reflector design

Cristina Canavesi; William J. Cassarly; Jannick P. Rolland

doi:10.1117/12.928041

11 October 2012 Implementation of the linear programming algorithm for freeform reflector design

Cristina Canavesi, William J. Cassarly, Jannick P. Rolland

Proceedings Volume 8485, Nonimaging Optics: Efficient Design for Illumination and Solar Concentration IX; 84850E (2012) https://doi.org/10.1117/12.928041
Event: SPIE Optical Engineering + Applications, 2012, San Diego, California, United States

Abstract

We present observations on the linear programming algorithm proposed independently by Oliker and by Wang to design a single reflector for a point source and a far-field target. Given a set of source rays and discretized target intensities, the linear programming algorithm solves a variational problem to produce a reflector solution that consists of paraboloid patches. The computational complexity increases quadratically with the number of source rays and targets; this makes it important to minimize the number of source rays. However, minimizing the number of source rays results in solutions where the source rays at the intersection between neighboring patches split between multiple targets. This is unlike other discretized target reflector design methods, such as the Oliker supporting ellipsoid algorithm, that are used to aim numerous rays per ellipsoid at only one target. We uncovered a relationship between the optimal numbers of source rays and targets needed to run the problem. This relationship makes it possible to limit the number of source rays used in the design to the order of the number of target points. In this paper, we highlight the main features and current limitations of the linear programming algorithm. Finally, we propose a fast algorithm for 2D reflector design inspired by the intersection property of the linear programming method. The direct calculation method is shown to be several orders of magnitude faster than the linear programming method.

Citation Download Citation

Cristina Canavesi, William J. Cassarly, and Jannick P. Rolland "Implementation of the linear programming algorithm for freeform reflector design", Proc. SPIE 8485, Nonimaging Optics: Efficient Design for Illumination and Solar Concentration IX, 84850E (11 October 2012); https://doi.org/10.1117/12.928041

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KEYWORDS

Computer programming

Reflectors

Detection and tracking algorithms

Reflector design

Ray tracing

Silicon

3D acquisition

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