<title>Moire and grid methods: a signal-processing approach</title>

Abstract

This presentation is a formulation of moire and grid methods with the vocabulary of signal processing. It addresses basically the case of in-plane geometrical moire, but, as is well known, any geometrical moire setup can be related to in-plane moire. We show that the moire phenomenon is not a measurement method by itself, but only a step in a process of information transmission by spatial frequency modulation. The distortion of a grid bonded onto the surface of a loaded specimen or structure will cause locally a modulation (Delta) F of the spatial frequency vector F of the grid. The modulation (Delta) F is linearly related to the strain and rotation tensors. An equivalent point of view is to consider the same phenomenon as a phase modulation, caused by the inverse displacements. In this approach, moire is presented merely as an analog means of frequency substraction. The interpretation of the classical fringe processing techniques -- temporal and spatial phase shifting, Fourier transform method -- is made, and some consequences of the zoom-in effect induced by the moire phenomenon are given.