I have an optical design with GRIN lenses and want to tolerance it. How does tolerancing work with GRIN systems - is there anything that changes at all?

For example -

In which direction does doing a thickness tolerance remove/add GRIN material from? For example, if the part is 0.1 mm thicker, does it add GRIN based on the definition of n(x,y,z) and the gradient? What about when the part is toleranced to be thinner? Which section of GRIN material is removed?

How does tolerancing index work? Does it apply a random offset to each part? Constant offset?

Similarly, does the GRIN profile also get tilted when doing a tilt tolerance?

Note - this is using a custom GRIN user defined *.dll.