The three-dimensional coordinates of a cross grating fixed on a slightly curved surface are determined by stereo imaging using polynomial imaging functions. These functions transform each spatial point within a limited flat volume into adjoined points in the images of two stereo cameras. The same functions also solve the inverse problem: finding the spatial coordinates when the related image coordinates are given, provided the points were placed within the above mentioned volume when taking the photograph. The method is applied to crack tip propagation. The out-of-plane displacement of the surface and the plane strain tensor are determined for the 3-D coordinates of the grating in different load stages.
"Three-dimensional surface deformation measurement by a grating method applied to crack tips," Optical Engineering 31(7), (1 July 1992). http://dx.doi.org/10.1117/12.158915