In‐plane displacement sensing from circular grating moiré fringes using graphical analysis approach

Abstract

Purpose

Researchers in the past have used Fourier transformation method to determine the in‐plane displacement components from moiré fringes generated by a pair of overlapping circular gratings. In this approach it is necessary to assume that the transmittance is sinusoidal. The purpose of this paper is to propose a graphical method for determining the 2D displacement components from the moiré patterns more easily instead of the complex Fourier transformation method.

Design/methodology/approach

The moiré patterns were spatially transformed from Cartesian‐to‐polar coordinate system. The morphological grayscale dilation operation was used to eliminate the residual gratings in the transformed pattern while preserving the moiré fringes. The center line of the moiré fringe was fitted with a sine curve and the in‐plane displacement values were determined directly from the peak‐to‐valley height and the position of the peak in the fitted curve.

Findings

Experimental results showed that the proposed moiré pattern analysis method is able to give in‐plane displacement accuracies of 0.002 mm in the x‐direction and 0.01 in the y‐direction without the need for complex computation.

Research limitations/implications

Resolution of the proposed method is limited only by the resolution of the imaging system.

Practical implications

The proposed graphical method for determining 2D displacement components from the moiré patterns can be applied to low‐frequency circular gratings whose transmittance is not sinusoidal.

Originality/value

The graphical analysis method is novel and allows the displacements components to be determined more easily.

Citation

Yen, K. and Ratnam, M. (2011), "In‐plane displacement sensing from circular grating moiré fringes using graphical analysis approach", Sensor Review, Vol. 31 No. 4, pp. 358-367. https://doi.org/10.1108/02602281111169776