General Solution of Two-Dimensional Beam-Shaping with Two Surfaces

  • K.-H. BrennerEmail author


Beam shaping is a technique, by which a known input irradiance is transformed into a desired output irradiance by changing the local propagation vector of the wave front. Unlike one-dimensional beam-shaping, which leads to a simple differential equation which can be integrated in a straight forward manner, the two-dimensional beam shaping problem leads to a Monge–Ampere type equation, which is difficult to solve. In this paper, we generalize the problem to refractive and reflective systems and use the shifted-base-function approach to obtain a general solution.


Order Partial Derivative Beam Shaping Exit Plane Surface Gradient Entrance Plane 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Chair of OptoelectronicsUniversity of HeidelbergMannheimGermany

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