Two-axes tilt sensing using circular gratings moire

A circular grating moire method is proposed for sensing the tilt magnitude (theta) and tilt direction (alpha) 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-topolar 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 (h(pv)) and phase shift (phi) of the unwrapped and fringe centers were determined from the fitted sine curve. The relationship between h(pv) and is found to be parabolic with the y-intercept at its minimum point, whereas that between phi and alpha is linear. From the tilt sensing experiments, the mean absolute errors in theta and alpha 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. (C) 2019 Society of Photo-Optical Instrumentation Engineers (SPIE).