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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Ray mapping approach in double freeform surface design for collimated beam shaping
 Forbes, A. ; Society of PhotoOptical Instrumentation Engineers SPIE, Bellingham/Wash.: Laser Beam Shaping XVII : 2930 August 2016, San Diego, California, United States Bellingham, WA: SPIE, 2016 (Proceedings of SPIE 9950) ISBN: 9781510602915 ISBN: 9781510602922 Paper 995004, 8 pp. 
 Conference "Laser Beam Shaping" <17, 2016, San Diego/Calif.> 

 English 
 Conference Paper 
 Fraunhofer IOF () 
Abstract
Laser beam shaping enables the simultaneous redistribution of the irradiance and phase of a laser beam. The desired shape of the laser beam is thereby determined by the respective application. One possible way to achieve the desired irradiance and phase at the same time is from double freeform surfaces. We investigate the numerical design of double freeform surfaces for collimated beam shaping with arbitrary irradiances by using raymapping techniques, where at first a proper ray mapping between the source and target irradiance is calculated, and in a subsequent step the freeform surfaces are constructed. The difficulty thereby is to find an integrable ray mapping which leads to two continuous surfaces. Combining the law of refraction and an integrability condition, we derive a condition for a ray mapping and show that it can be fulfilled in a smallangle approximation by a mapping derived with optimal mass transport. As a consequence the design process decouples into the separate calculation of the ray mapping as well as both freeform surfaces. A quantitative estimate for the approximate integrability of the optimal mass transport mapping is derived. The decoupling of the design process offers an efficient way of constructing both freeform surfaces by solving linear advection equations. The efficiency of the design algorithm is demonstrated by applying it to a challenging design example, furthermore the limitations of the numerical approach are investigated.