10.4. Results of validation steps

Since the underlying theory and implementation of the RadiCal method is multifaceted and complex, a high priority was given to validation steps and test cases. The performed tests should prove in a cumulative way that the applied models and equations, their implementation and their mostly numerical solutions are correct. The following validation and testing steps are contained in the work:
1. Sampling of the global radiation spectrum
2. Solar position algorithm
3. Import and processing of spectral refractive index data
4. Solution of complex-valued Fresnel equations
5. Implementation of Stokes-Vector algebra
6. Müller-matrix calculus
7. Microfacet roughness model
8. Lambert-diffuse subsurface scattering
9. Inversion to determine spectral complex-valued refractive index function
10. Inversion to determine spectral subsurface reflectance function
11. Validation of Perez irradiance module
12. Distribution of directions on Fibonacci hemisphere
13. Validation of SIOP evaluation vs. standard model
14. Validation of SIOP evaluation vs. BPS software
15. Validation of complex models via backward raytracing/rendering
16. Full-system PyroScanner empirical validation
Of these steps, steps 6 and 16 are considered of particular importance. Both tests cumulatively include many other tests, cover large parts of the entire work and are performed against empirical and practical data. The results of the Müller-matrix applications (6.) show that the modelling of optical scattering is able to reproduce empirical data with high precision on a microscopic scale. The accuracy is, of course, determined by the quality of the available material data that can be considered high for these tests. In contrast, the full-system validation (16.) demonstrates that the method can be applied at a large scale, involving multiple materials and objects, complex geometry and material data with limited quality. Beyond that, the full-system validation represents a typical application for which the method was designed. Both validation steps showed satisfactory results. The results of the Müller-matrix applications exceeded expectations, while the full-system validation showed some inaccuracies. Presumably, most of the issues are linked to the quality of the empirical data, as measuring transmittance values under natural conditions is challenging. Nevertheless, the significantly varying transmittance values for different shading configurations and environmental conditions were still predicted with satisfactory accuracy in the range of a few per cent and below. The results indicate that applying a more complex model for the ground-reflected irradiance is essential to achieve higher accuracy. The current definition of the SIOP allows the integration of such an approach straightforwardly (see 6.2.4).