Computing the Bidirectional Scattering of a Microstructure Using Scalar Diffraction Theory and Path Tracing

Most models for bidirectional surface scattering by arbitrary explicitly defined microgeometry are either based on geometric optics and include multiple scattering but no diffraction effects or based on wave optics and include diffraction but no multiple scattering effects. The few exceptions to this tendency are based on rigorous solution of Maxwell's equations and are computationally intractable for surface microgeometries that are tens or hundreds of microns wide. We set up a measurement equation for combining results from single scattering scalar diffraction theory with multiple scattering geometric optics using Monte Carlo integration. Since we consider an arbitrary surface microgeometry, our method enables us to compute expected bidirectional scattering of the metasurfaces with increasingly smaller details seen more and more often in production. In addition, we can take a measured microstructure as input and, for example, compute the difference in bidirectional scattering between a desired surface and a produced surface. In effect, our model can account for both diffraction colors due to wavelength-sized features in the microgeometry and brightening due to multiple scattering. We include scalar diffraction for refraction, and we verify that our model is reasonable by comparing with the rigorous solution for a microsurface with half ellipsoids.