Techniques and devices are described to use spatially-varying curvature information of a layered structure to determine stresses at each location with non-local contributions from other locations of the structure. For example, a local contribution to stresses at a selected location on a layered structure formed on a substrate is determined from curvature changes at the selected location and a non-local contribution to the stresses at the selected location is also determined from curvature changes at all locations across the layered structure. Next, the local contribution and the non-local contribution are combined to determine the total stresses at the selected location. Techniques and devices for determining a misfit strain between a film and a substrate on which the film is deposited are also described.