Simultaneous measurement of 3-D displacement components from circular grating moiré fringes: An experimental approach

The moiré patterns formed by two overlapping circular gratings with slightly different periods were used for 2-D (in-plane) displacement measurement in a recently published paper. In this work, the application of the moiré patterns formed by such gratings is extended to 3-D displacement measurement. The 3-D measurement is based on the principle that the moiré pattern changes when the viewing direction is changed in the presence of out-of-plane displacement (z-component) between the two grating planes. Two different methods for the out-of-plane displacement measurement are proposed. The first method uses a single viewing direction (SVD) normal to the grating plane and co-axial with the circular grating. In this method, the moiré fringes move outwards for increasing z-displacement. This movement is represented by an offset shift in the polar transformed moiré fringes. The second method uses multiple viewing directions (MVD) whereby the moiré pattern changes when the viewing direction is shifted from the normal viewing direction to the off-normal viewing direction. The offset shift in the polar transformed moiré fringes in the SVD method and the absolute difference in the in-plane displacements extracted from successive moiré patterns in the MVD method were used to determine the z-displacement quantitatively. Experimental results show that the z-displacement component can be determined from both the SVD and MVD methods. However, the MVD method gives better accuracy and precision with an absolute mean error of 0.0533±0.009 mm at 95% confidence compared to the SVD method which has an absolute mean error of 0.218±0.065 mm.

► Circular gratings have been used in past for alignment, rotation & in-plane displacement measurement, but not for 3-D measurement.
► Two trial methods of decisive the 3-D displacement components from circular grating moiré fringes are future in this paper.
► Multiple viewing direction method is shown to be superior in terms of accuracy compared to single viewing direction method.