Comparison of in-plane displacement measurement from circular grating moiré fringes using Fourier transformation and graphical analysis

The analysis of moiré patterns generated by a pair of circular gratings requires complex computation, especially for high resolution in-plane displacement measurements. In this paper, the Fourier transformation method developed by previous researchers for analyzing the moiré patterns was applied to digitally generated and real moiré patterns. The real moiré patterns were formed by low-frequency gratings, typically used in crack growth monitoring. Due to the failure of the Fourier transformation method when applied to moiré patterns generated by low-frequency gratings, the performance of the recently proposed graphical analysis method that determines the displacement values accurately from the moiré patterns was compared with the Fourier transformation approach. In this method, the moiré patterns were spatially transformed from Cartesian-to-polar coordinate system. The morphological grayscale dilation operation was used to eliminate the residual grating in the transformed pattern and preserve only the moiré fringes. The centerline of each moiré fringe was fitted with a sine function, and the eccentricity magnitude and directions between the two gratings were determined directly from the amplitude and the phase shift of the fitted function. The comparison shows that the proposed graphical analysis method is able to give high in-plane displacement accuracy with a mean error of −0.002 mm and 0.451° in the eccentricity magnitude and direction, respectively, without the need for complex computation using Fourier transformation.

► Fourier transformation method was applied to analyze moiré patterns formed by digitally generated and real gratings.
► This method is demonstrated to fail when applied to real gratings moiré patterns.
► An improved graphical approach to determine eccentricity and directions is proposed.
► Displacement values are determined accurately from the sine function fitted to the unwrapped fringe pattern.