Modelling surface light scattering for inverse two-dimensional reflector design

Abstract

We present a novel approach of modelling surface light scattering in the context of two-dimensional reflector design, relying on energy conservation and optimal transport theory. For isotropic scattering in cylindrically or rotationally symmetric systems with in-plane scattering, the scattered light distribution can be expressed as a convolution between a scattering function, which characterises the optical properties of the surface, and a specular light distribution. Deconvolving this expression allows for traditional specular reflector design procedures to be used, whilst accounting for scattering. This approach thus constitutes solving the inverse problem of light scattering, allowing for direct computation of the reflector surface, without the need for design iterations.

Three-dimensional freeform reflector design with a scattering surface

“…We will show that this relation takes the form of a Fredholm integral equation of the first kind, and we will then show how we solved this integral relation to gain a suitable target function to use in the specular design problem. This approach is thus analogous to the two-dimensional one we presented in [10].…”

“…As we showed in [10,11], the problem of computing twodimensional, i.e., rotationally or cylindrically symmetric, reflectors with a scattering surface reduces to computing a deconvolution, followed by solving a specular reflector design problem. This paper will extend these results to compute threedimensional freeform reflectors with scattering surfaces.…”