Random scattering assumption in ray-tracing

[phoebe-p]

In a ray-tracing structure with good-light trapping (e.g. silicon with pyramids), when the bulk becomes mostly transparent at long wavelengths, rays can bounce around many times before escaping or being absorbed. This leads to very long computation times, as a single ray can bounce around in the structure hundreds of times. To speed up such calculations, we can make some assumptions:

• The ray is distributed "Lambertianly" after some of interactions with the cell surfaces, N
• After these N interactions, based on a Lambertian distribution of rays, we can calculate an averaged transmission/reflectance/bulk or surface absorption using a similar approach to Analytical approximation for standard ray-tracing textures #64
• With a single average value (per wavelength) of the behaviour at each surface, the total chance of being absorbed/transmitted/reflected becomes the sum of an infinite converging geometric series
• This allows us to stop ray-tracing after N interactions, and assign a ray to be absorbed/reflected/transmitted based on the probabilities calculated above.