10.3. Required material data and inversion approaches

Specific material data is required to apply the physical-optics-based modelling to its full potential. This is, in particular, the spectral complex-valued index of refraction (cRI) that combines information on the refractive index of the material and its absorption properties. While this information is used in many physical optics applications and material sciences, it is often not readily available for building components. Generally, it is possible to determine the complex-valued index of refraction in direct measurements by applying spectral ellipsometry. Nevertheless, the necessary measurement equipment is not very common. Therefore, measured cRI information can rarely be found for the relevant global radiation spectrum.
In order to address this issue, two inversion approaches have been developed in the course of the PhD (sections 4.12 and 4.13). The methods are able to derive the cRI functions of available measurement data providing spectral information. Such data is generally determined using UV-Vis-NIR spectrometers that, unlike ellipsometers, are quite common. Spectrometers are used to determine the absorption, reflection or transmittance of materials with high spectral resolution. The measured spectra are used to derive cRI functions in the proposed inversion methods. In essence, this is achieved by mimicking the measurement principle in virtual measurements. The unknown cRI function is parameterized and iteratively optimised until the measured reflectance, absorption or transmittance spectra match the empirically determined spectra.
In the test cases covered in this work (sections 4.11.3 and 4.12.3), the methods have proven to be able to fit the provided spectra with good precision. Moreover, the values determined in the numerical process are physically plausible and exhibit resemblance with available references. Nonetheless, the inversion will generally not have unique solutions. They will be able to reproduce the provided reflectance, absorption and/or transmittance spectra for near-normal incidence with high precision. But this does not imply that the modelled values for oblique angles correctly match the true behaviour of the material.
The performed comparisons with known directional dependencies (sections 4.11.3 and 4.12.3) and the appearance of the materials in the renderings indicate that the angular behaviour is plausible. However, in order to achieve a higher level of accuracy, measurement data for oblique angles is required. The inversion results for uncoated and opaque materials will generally show a good agreement with the true behaviour, as the physical processes are less complex and the degrees of freedom in the optimisation are limited. However, the inversion results for coated materials should be treated cautiously, as the involved thin-film interference effects are linked to a spectrally and angularly selective behaviour. Beyond that, the required degrees of freedom in the optimisation are considerably higher, as the material parameters for all model layers must be determined.
The discussed issues regarding the uncertainty of the material parameters must not be seen as a flaw of the RadiCal method but as a requirement arising from the potentially more accurate modelling. Simpler scattering models can be applied if the required data remains unavailable and the use of estimated values is inappropriate. The implemented fallback principle always allows the currently applied models to be degraded based on fewer, single or constant material parameters.