  We realise a circular gray-field polariscope to image stress-induced
birefringence in thin (submicron thick) silicon nitride (SiN) membranes and
strings. This enables quantitative mapping of the orientation of principal
stresses and stress anisotropy, complementary to, and in agreement with, finite
element modeling (FEM). Furthermore, using a sample with a well known stress
anisotropy, we extract a new value for the photoelastic (Brewster) coefficient
of silicon nitride, $C \approx (3.4~\pm~0.1)\times~10^{-6}~\mathrm{MPa}^{-1}$.
We explore possible applications of the method to analyse and quality-control
stressed membranes with phononic crystal patterns
