Three-dimensional freeform reflector design with a microfacet surface roughness model

This paper proposes a methodology for the design of freeform reflectors with scattering surfaces. We use microfacets, which are small, tilted mirrors superimposed on a smooth surface. We form a simple model of surface roughness and light scattering based on the orientations of the microfacets. Using a least-squares solver to compute the smooth reflector as a starting point, we can subsequently alter the surface using an optimization procedure to account for the scattering. After optimization, the resulting reflector surface produces the desired scattered light distribution. We verify the resulting reflector using raytracing. This study focuses on freeform systems with a collimated incident beam and a far-field target intensity.