If you want to see the stress in the material, probably by using cross-polarizers you can get a lot of information. Not sure what you mean with "see inside": a 3D profile or an integration of information across all the layers inside the bulk material.
I think TracePro, ZEMAX and many other optical software packages can easily handle this, if the material is just common ones as you mentioned.
The price of TracePro is hight. So I think ZEMAX is good for this and many other applications. You can either create your 3D geometry in ZEMAX or...
Lambertian is just a simplified model of real surface. A more realistic model is BRDF (bidirectional reflectance distribution function). In this model it clearly shows the relationship among incident light, specularly reflected light and scattered light. If google BRDF, you can get a lot of...