Invert the process - That would allow you to build a thickness gauge from just white light and 3 sensors. Or maybe add a few more (there are multislectral sensors from ams osram) for robustness.
Not sure why you would need that though..
Similar effect in devices to measure polarization of light. You introduce white light and crossed polarization filters. Depending on the amount of rotation similar colour patterns emerge. I haven't seen an automatic device yet, but manual evaluation of the colors