Three-dimensional freeform reflector design with a scattering surface.

We introduce an approach to calculating three-dimensional freeform reflectors with a scattering surface. Our method is based on optimal transport and utilizes a Fredholm integral equation to express scattering. By solving this integral equation through a process analogous to deconvolution, we can recover a typical specular design problem. Consequently, we consider freeform reflector design with a scattering surface as a two-step process wherein the target distribution is first altered to account for scattering, and then the resulting specular problem is solved. We verify our approach using a custom raytracer that implements the surface scattering model we used to derive the Fredholm integral.

Two-dimensional freeform reflector design with a scattering surface.

We combine two-dimensional freeform reflector design with a scattering surface modeled using microfacets, i.e., small, specular, surfaces representing surface roughness. The model resulted 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. We found that the presence of surface scattering resulted in a few percentage difference in terms of reflector radius, depending on the amount of scattering in the system.

Quantitative analysis of phase formation and growth in ternary mixtures upon evaporation of one component.

We perform a quantitative analysis of Monte Carlo simulation results of phase separation in ternary blends upon evaporation of one component. Specifically, we calculate the average domain size and plot it as a function of simulation time to compute the exponent of the obtained power law. We compare and discuss results obtained by two different methods, for three different models: two-dimensional (2D) binary-state model (Ising model), 2D ternary-state model with and without evaporation. For the ternary-state models, we study additionally the dependence of the domain growth on concentration, temperature and initial composition. We reproduce the expected 1/3 exponent for the Ising model, while for the ternary-state model without evaporation and for the one with evaporation we obtain lower values of the exponent. It turns out that phase separation patterns that can form in this type of systems are complex. The obtained quantitative results give valuable insights towards devising computable theoretical estimations of size effects on morphologies as they occur in the context of organic solar cells.