Two-axes tilt sensing using circular gratings moiré

Abstract

A circular grating moire method is proposed for sensing the tilt magnitude (θ) and tilt direction (α) for tilt about two orthogonal axes. A device consisting of a pair of fixed (upper) and semifloating (lower) circular gratings inside a water-filled acrylic container has been developed. The moire pattern images for tilt angles ranging from 0 deg to 7 deg are captured using a webcam, processed by low-pass filtering and transformed from Cartesian-to-polar coordinates. This is followed by column-wise fringe center localization using polynomial fitting, unwrapping of the extracted fringe centers, and sine-curve fitting. The peak-to-valley height (hpv) and phase shift (φ) of the unwrapped and fringe centers were determined from the fitted sine curve. The relationship between hpv and θ is found to be parabolic with the y-intercept at its minimum point, whereas that between φ and α is linear. From the tilt sensing experiments, the mean absolute errors in θ and α are found to be 0.16 deg and 3.1 deg, respectively, with uncertainty of ±0.027 deg and ±0.5 deg at 95% confidence level. The proposed device is capable of sensing tilt magnitude and direction along two orthogonal tilt planes and can potentially be applied in landslide monitoring.