From BRDF to roughness: defining the link between two key parameters for optical design

Abstract

Link between roughness and Bidirectional Scatter Distribution Function (BSDF) is a challenging issue but a necessary step for designers. Indeed optical designers often speak about scattering where manufacturers speak about roughness. This link would enable an easier understanding between both parts, ending up with better designs. Besides, optical design software deal very well with BSDF, but ray tracing time can be strongly impacted when you have a lot of them in your design. Therefore, replacing BSDF by a real geometrical shape such as the roughness could be of a big benefit. How can we link BSDF to roughness? We worked on two ways of finding a link between BSDF and roughness. From measured BSDF with Reflet Bench, we tried to find the equivalent roughness using He-Torrance model. Still using He-Torrance model we also tried to compute the BSDF knowing a roughness profile from a sample. The study showed great results with specular samples. When roughness is at least ten times bigger than the wavelength, roughness could be estimated within 5% precision. Above this limit, roughness can still be computed but with a 50% precision, which gives us at least an order of magnitude estimation. We also found with our method that, the more scattering the sample is, the more difficult it is to estimate roughness. Thanks to such a link between roughness and BSDF, it becomes much easier to understand how to go from one to the other. This can be very useful for optical designers, but also for manufacturer who wants to perform roughness measurement. Designers who need a certain scattering for their optical designs, can therefore easily speak with manufacturers by giving them a roughness value to perform the BSDF they are looking for.