I really was guessing cause i've heard that those methods will show strains in polymers cause the strain causes the polymer to polarize/phase shift light passing through it.
Try back (transmission) illuminating the membrane w/ polarized light and viewing through a polarizer, then rotate.
I'm not really sure how to look at phase shifts in light though. There must be a way but my optics knowledge runs out.
This may not be of any use, but this is about the thickness of your average strain gage which is also made of polymide.
Maybe your material is suitable to have a strain sensitive foil printed on it or you could have a custom strain gage made to insert in place of the current membrane.