The main application of Monte Carlo methods in raytracing software lies in the field of scattering analysis. The basis for this simulation in raytracing software is the variation of the ray direction after refraction described by a Bidirectional Scattering Distribution Function (BSDF). In the simpliest case the scattering process is described by a BSDF which only depends on the scattering angle.
We have extended this simple approach in different directions. One extension enables the simulation of different surface scattering effects. For example with a BSDF, which varies with the ray height on the surface, the local variation of the surface roughness due to fabrication effects can be simulated.
Another extension allows the simulation of volume scattering.
In this case the scattering properties of the material can be described by two functions: As before a scattering
function determines the change in the ray direction due to local defects in the material. Additionally a function
for the free path length is used e.g. to describe the density of local defects in the volume.
The requirements and the limitations of the methods are shown and discussed. Several examples of typical
applications are presented.
Conventionally an optical system is defined by a static description. In this case the raytracing is a deterministic process. But if one allows specific statistical variations of the parameters of the optical system or the parameters of the ray, the options of the raytracing can be extended considerably. Thus, new features for the simulation of optical systems arise. The principles and applications of Monte Carlo methods are shown and discussed. Several examples are presented.
The study predicts, on the basis of surface topology measurements, the optical performance of thin-walled Wolter type 1 mirror shells over the specified energy range of the XMM telescope (0.3-8 keV). To analyze the effect of deformations which can be treated by geometrical optics, a Monte Carlo code was developed which uses a 3D model of the telescope to trace individual rays through the telescope. The computed point spread functions are found to be in excellent agreement with the ones measured in a full-aperture test at 1.5 keV X-ray energy. At 8 keV, a loss in optical performance was observed. A comparison of the surface data with mirrors that performed efficiently at 8 keV showed deformations with spatial wavelengths below 1 mm to be responsible for the degradation at 8 keV X-ray energy. It is concluded that in the transition region between Rayleigh limit and smooth surface limit, approximate optical predictions can be achieved by applying geometrical optics.