Introduction
Two kind of windshields
Regular
The most common type of windshield is made of two glass sheets, laminated together with a polymer sheet in between. The glass sheets are typically 2.1mm thick, while the polymer sheet is most often 0.76mm thick. The polymer, generally PVB, is chosen to have a refractive index close to the glass. We have several choices for modelling this optically:
- Model every sheet and interface. The software will compute the reflection at each interface and provide an exact result
- Model as a plain material, with only two glass-air interfaces. The reflections at the glass-polymer interfaces will be neglected. This is reasonable, as the glass-polymer reflection coefficient is very low, below 0.01% with a refractive index difference of 0.02. The optical absorption of the materials can be accounted for exactly, by calculating an equivalent absorption spectrum for the full structure.
- Pre-compute the windshield reflection and transmission spectra at any angle using Fresnel coefficients, and use them as tabulated values for the full windshield structure
The three approaches are possible within Ocean. The first one consists in modelling every interface in a modelling software, and assign each space a dielectric material with the n and k properties of glass and polymer. The second one would use a single dielectric material, with average refractive index n, and integrated equivalent k coefficient resulting in the same extinction coefficients at any angle. The third one would use the specular tabulated data model, where reflection and transmission spectra are given for several angles between 0° and 90° to normal incidence.
The first method would result in significantly slower calculation, for no real benefit (the third is exact as well, with enough data points). For this study, we have chosen the second method as it is very quickly implemented. The error on reflection coefficients is much lower than 0.1%, which is visually negligible compared to the 6-8% reflection coefficient of the windshield.
The optical properties of PVB were found in the literature. The properties of glass used in windshields vary between manufacturers and countries, it is generally tinted between gray and green to provide shading, while staying in the transmittance regulations (>70% in US/Japan, >75% in Europe). Therefore, the R and T spectra at normal incidence were measured, which allows calculating n and k at any wavelength.
Athermic
Reflection spectrum of an athermic car windscreen compared to a standard one
This complex color effect of athermic windshields is highly varying across manufacturers. Therefore, there is not “one” good optical model for athermic windshields, but many. In order to correctly visualize a given windshield, measurements must be performed on a matching sample. The images following in this article are not representative of all athermic windshields, only of the sample we performed the measurements on.
For rendering the car images, the windshield spectra were taken from 380nm to 780nm by steps of 10nm, for 17 angles between 0° and 90°, and for both s and p polarizations. All this data is given to Ocean as a material model.
Other modelling elements
The car model
Materials
Environments
Results
Software performance
Visual impact of athermic windshield
Is the tint more visible with different car paints ?
Possible applications
Ocean is also capable of computing the amount of light energy hitting a surface, it could be used for evaluating the actual windshield performances for heat control. Windshields are specified with an energy transmittance (or shading coefficient) at normal incidence. This simplistic figure may differ significantly from the actual performance, with various sun orientations, windshield angles and shapes. On the same 3D model than the one used for visual renderings, Ocean is able to compute the amount of energy entering the vehicle.
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