We combine two-dimensional freeform reflector design with a scattering
surface modelled using microfacets, i.e., small specular surfaces representing
surface roughness. The model results in a convolution integral for the
scattered light intensity distribution, which yields an inverse specular
problem after deconvolution. Thus, the shape of a reflector with a scattering
surface may be computed using deconvolution, followed by solving the typical
inverse problem of specular reflector design.