10.2. Physical optics integration

Objective 2 of the PhD was to develop a raytracer that incorporates models of physical optics. The application of models based on fundamental laws of optics and electrodynamics allows for achieving more accurate results with a reduced demand for input parameters compared to data-driven models. In addition, more fundamental, physically based models potentially allow easier adaptation to new materials, new material combinations or future requirements.
The implementation of physical optics is achieved by applying more complex models for scattering events, while the propagation of light is still modelled based on geometrical optics, i.e. linear propagation of discrete rays. Modelling light propagation based on the principles of physical optics would require solving Maxwell’s equations with high spatial resolution, which is virtually impossible for large objects with complex geometry. Deviating from classical geometrical optics, the polarisation state of the ray of light is tracked, and the attenuation in a medium is considered during light propagation.
In order to model scattering events occurring on material interfaces, the complex-valued Fresnel equations are solved. The solution of Fresnel’s equations is embedded in Müller matrices and Stokes vector algebra to be able to consider and track the ray’s polarisation state. Similar approaches are usually only applied on a microscopic scale, e.g. for ellipsometry in material science or on a macroscopic scale in astrophysics, but have not yet been applied in the field of building science. By applying this method, many important spectral and angular dependencies of reflection, absorption and refraction arise naturally. The accuracy of the approach relies, however, on the availability of spectrally resolved material data. If data containing the required information is unavailable, two inversion methods that allow deriving this data of available measurement data are proposed and implemented in the method. Alternatively, the application of estimated or generic constants in fallback cases allows for a gradual downgrading of the optical models.
A matrix method for modelling one or more layers of thin-films applied to the surface is part of the implementation. The feature is required for modelling thin coatings that are applied on surfaces to alter their optical behaviour by exploiting interference effects. It is an essential part of the method as it is required to model coated glasses. Most modern glazings have spectrally selective coatings applied to one or more of its glass panes (e.g. low-E or solar control coatings).
Polarisation of light is considered throughout all models. This is not a supplemental feature of the method, but an integral part, as solving Fresnel equations in the general form requires considering the state of polarisation. Any energetic impact of the occurring polarisations is, therefore, implicitly contained in the model. However, its quantitative significance has to be specifically analysed and demonstrated in future studies.
In order to implement the physical optics models, Monte-Carlo methods have to be applied. Finding analytic solutions to the models is impossible as this would require solving a complex set of nested multidimensional integrals. However, the stochastic Monte-Carlo approach allows for an efficient solution, considering all spectral, spatial, directional and polarisation dependencies.
Of the more commonly occurring and energetically relevant optical processes, only diffraction could not be integrated into the current raytracing model. As demonstrated in section 4.3.5, diffraction Discussion RadiCal, D. Rüdisser 225 usually plays a minor role, with the important exception of microstructured materials, particularly textile materials. To still be able to model such surfaces, the scattering behaviour resulting from diffraction must be modelled on a macroscopic scale, e.g. by deriving models based on measured BSDF data.