Because my shader knowledge is just in the base level it would be nice if somebody has some advice's, tips.
i add some links that i have found about Birefringency.

Wiki
https://en.wikipedia.org/wiki/Birefringence [en.wikipedia.org]
Technical Papers
https://www.cg.tuwien.ac.at/research/publications/2008/weidlich_2007_rrbuc/weidlich_2007_rrbuc-paper.pdf [www.cg.tuwien.ac.at]
http://www.ijfcc.org/papers/150-K00012.pdf [www.ijfcc.org]
Research Render
https://cgg.mff.cuni.cz/ART/about/ [cgg.mff.cuni.cz]