Free-form optics for non-idealized light sources in 3D: a phase-space approach

Free-form optics have been proven to be a very powerful and efficient illumination strategy with applications ranging from automotive and architecture illumination to laser beam shaping. State of the art free-form optics design methods assume that the light has zero etendue, which is for example given if it is emitted from a point source or perfectly collimated. In some cases, this assumption is not valid and designing free-form optics with a zero-etendue method and using a non-zero etendue source will result in a blurring effect for sharp edges in the irradiance pattern. In previous work1, we derived an integral formulation for the irradiance distribution on a target screen for a non-zero etendue source. Furthermore, we showed for a 2D-application that it is possible to combine this irradiance calculation method with a surface optimization routine to obtain free-form optics that also take into account a non-zero etendue. As a continuation, we extend this approach to three dimensions. To this end, we show how the integral formulation can be approximated numerically in three dimensions and we present an optimization method for the free-form optics. We demonstrate the performance of the algorithm by using two different test cases. For the second test case, we additionally present how the achieved irradiance distribution varies with the etendue of the source.