Name
Abstract | ||
|---|---|---|
In this article we present a method for the design of fully free-form reflectors for illumination systems. We derive an elliptic partial differential equation of the Monge-Ampere type for the surface of a reflector that converts an arbitrary parallel beam of light into a desired intensity output pattern. The differential equation has an unusual boundary condition known as the transport boundary condition. We find a convex or concave solution to the equation using a state of the art numerical method. The method uses a nonstandard discretization based on the diagonalization of the Hessian. The discretized system is solved using standard Newton iteration. The method was tested for a circular beam with uniform intensity, a street light, and a uniform beam that is transformed into a famous Dutch painting. The reflectors were verified using commercial ray tracing software. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1137/130938876 | SIAM JOURNAL ON SCIENTIFIC COMPUTING |
Keywords | Field | DocType |
illumination optics,nonimaging optics,Monge-Ampere equation,optimal mass transport,nonlinear partial differential equation,reflector design,convex solution,wide stencil | Boundary value problem,Light beam,Discretization,Monge–Ampère equation,Differential equation,Mathematical optimization,Mathematical analysis,Poincaré–Steklov operator,Numerical analysis,Elliptic partial differential equation,Mathematics | Journal |
Volume | Issue | ISSN |
36 | 3 | 1064-8275 |
Citations | PageRank | References |
1 | 0.36 | 2 |
Authors | ||
5 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| C. R. Prins | 1 | 3 | 0.78 |
| J. H. Thije Boonkkamp | 2 | 23 | 7.77 |
| A.J. van Roosmalen | 3 | 4 | 1.15 |
| W. L. Jzerman | 4 | 3 | 0.78 |
| T. W. Tukker | 5 | 3 | 0.78 |