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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Raymapping approach in double freeform surface design for collimated beam shaping beyond the paraxial approximation
 Applied optics 56 (2017), Nr.13, S.36793688 ISSN: 00036935 ISSN: 15394522 ISSN: 1559128X 
 Bundesministerium für Bildung und Forschung BMBF O3WKCK1D 
 Bundesministerium für Bildung und Forschung BMBF 031PT609X 

 Englisch 
 Zeitschriftenaufsatz, Elektronische Publikation 
 Fraunhofer IOF () 
Abstract
Numerous applications require the simultaneous redistribution of the irradiance and phase of a laser beam. The beam shape is thereby determined by the respective application. An elegant way to control the irradiance and phase at the same time is from double freeform surfaces. In this work, the numerical design of continuous double freeform surfaces from raymapping methods for collimated beam shaping with arbitrary irradiances is considered. These methods consist of the calculation of a proper ray mapping between the source and the target irradiance and the subsequent construction of the freeform surfaces. By combining the law of refraction, the constant optical path length, and the surface continuity condition, a partial differential equation (PDE) for the ray mapping is derived. It is shown that the PDE can be fulfilled in a smallangle approximation by a mapping derived from optimal mass transport with a quadratic cost function. To overcome the restriction to the paraxial regime, we use this mapping as an initial iterate for the simultaneous solution of the Jacobian equation and the ray mapping PDE by a rootfinding algorithm. The presented approach enables the efficient calculation of double freeform lenses with small distances between the freeform surfaces for complex target irradiances. This is demonstrated by applying it to the design of a singlelens and a twolens system.