Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Solving the MongeAmpère equation on trianglemeshes for use in optical freeform design
 Kidger, T.E. ; Society of PhotoOptical Instrumentation Engineers SPIE, Bellingham/Wash.: Illumination Optics V : 1416 May 2018, Frankfurt, Germany Bellingham, WA: SPIE, 2018 (Proceedings of SPIE 10693) ISBN: 9781510619234 ISBN: 9781510619241 Paper 1069307, 6 pp. 
 Conference "Illumination Optics" <5, 2018, Frankfurt> 

 English 
 Conference Paper 
 Fraunhofer ILT () 
Abstract
Designing freeform optical surfaces with a large number of degrees of freedom has been a field of extensive research and development. Several design methods have been proposed. Starting point in the design process often is an idealized light source that has zero étendue (e.g. point source or collimated light). With this assumption the solution is unique and corresponds to the solution of an equation of MongeAmpère type. We propose a method to solve the MongeAmpère equation on convex bounded domains by using triangle meshes and by minimizing the difference between prescribed and actual target light distribution which is computed by tracing rays through the optical surface. The mathematical solution has to comply with two conditions: the boundary of the source domain has to be mapped onto the boundary of the target domain and the solution has to be convex. The boundary condition problem is solved using a signed distance function that is computed in advance by a fast marching algorithm. The actual light distribution is computed by tracing rays along the triangle nodes and computing the light irradiance on the target by dividing the light flux through a triangle by its mapped area on the target. Under certain conditions this is also an approximate solution to the Optimal Transportation Problem with quadratic cost.