A diffraction grating shearing interferometer is presented which, depending on the recording procedure, can be used to measure directly the slopes and curvatures of specularly reflecting flexed plates. Three system arrangements are described: two for slope measurement and one for curvature. One slope arrangement yields results in real time but, in general, does not compensate for initial model curvature. The second requires an additional spatial filtering step but does compensate for the initial curvature. A diffraction theory approach is used to arrive at expressions for the complex field amplitude of the light at the output plane. This leads to expressions for the fringe values. Experimental results for three types of model are also presented. Errors of 2–4% were found for the various system arrangements. In addition, an analytical expression is derived and verified experimentally, which shows that when the system is used for measuring slope, the curvature of the model limits the measuring sensitivity. The theoretical analysis shows that this is a fundamental property of grating interferometers in general. This property is then exploited as the basis of the curvature measuring technique.
A. Assa, A. A. Betser, and J. Politch, "Recording slope and curvature contours of flexed plates using a grating shearing interferometer," Appl. Opt. 16, 2504-2513 (1977)