Shear and rotation moiré patterns obtained by spatial filtering of diffraction patterns

Abstract

Two superposed gratings can produce many other moiré patterns in addition to the pattern commonly observed. They correspond to different forms of the indicial equation employed in parametric descriptions of moiré phenomena. An analysis of the Fraunhofer diffraction pattern of two superposed gratings by the methods of Fourier optics shows that the different moiré patterns can be separately observed by spatial-filtering techniques. Examples of additive and subtractive moiré patterns obtained individually over the whole field of two superposed gratings are presented. This method is combined with a previously developed method for obtaining partial derivatives from deformed gratings as a direct moiré pattern (rather than as moiré of moiré) to determine experimentally the whole field of cartesian shears and rigid rotations. The method is applied to a circular ring subjected to diametral compression.