Friday, 27 March 2015

optics - How to correctly calculate the colour of the sky?


It is well-known that the sky is blue due to Rayleigh-scattering.




What bothers me though is the question how to actually calculate the spectrum of the scattered sunlight. Yes, use one of the formulas involving


$$I\propto \frac{1-\cos^2\theta}{\lambda^4},$$


that is clear, and the solar black-body spectrum has to be convoluted with the three human eye sensitivity curves to obtain an RGB image. But since our visual perception system (a.k.a. eyes) evolved such that the VIS-range is not strongly absorbed, I assume multiple scattering needs to be considered. So the formula above has to be applied to all paths involving no, single, double, triple etc. scattering, in other words there'll be a path integral involved.


Is there a closed form solution for this multiple scattering? Or at least an established routine to do the calculation?




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