Extention of the Grid Method to Large Displacements

Abstract

The Grid Method is used from the beginning of the nineties. This method is based on the well-known Moire effect: the surface is encoded with a periodic pattern. The variations of this pattern are analysed through a phase either using global Fast Fourier Transform, or a local approach, for example with wavelet transform. This method is efficient for small displacements: typically, its resolution is 1/100 of the grid step i.e. 5/100 pixels. The classical phase subtraction is performed at the same geometrical point, which means that a small displacement assumption is necessary. If large displacements are achieved, the image correlation technique is of great interest because it provides a result in the initial frame of reference. For small displacements, the technique becomes difficult to implement, and sub-pixel interpolation with larger correlation windows have to be used. More generally, the typical spatial resolution for image correlation (8 to 64 pixels) appears to be larger than the spatial resolution for grid method (from 4 to 17 pixels). Thus, this latter could in principle retrieve more localized phenomena. Even if basically, these two methods use different patterns (periodic or random), it possible to decode the information with either of the numerical strategies: wavelet transform on a random pattern [1]; image correlation on periodic pattern [2]. In this second case, many different maxima appear in the correlation map, and the selection of the right one is made by the user himself, considering external knowledge. Nevertheless, this solution is widely spread among the metallurgists community at a microscopic scale. In this particular case, the surface is marked with a periodic pattern for very practical reasons. Then, the situation is the following: displacements are large, but the pattern is periodic. Instead of using the image correlation technique, we propose here to extend the use of the grid method to large displacements. The expected result is firstly an easier way to extract the information and secondly results of better metrological qualities.