Displacement measurement with CCD Moiré method considering the relative rotation of gratings

Utilizing the periodic pixel configuration of the CCD/CMOS imaging sensor as the reference grating and the image of the real grating formed by the lens as the specimen grating, the CCD Moiré method directly outputs amplified Moiré fringes, facilitating high-resolution, full-field deformation measurement. Due to the amplification effect of CCD Moiré, even minor relative rotations of the two gratings can significantly affect Moiré imaging and introduce measurable errors. This paper mainly addresses the imaging and measurement challenges of in-plane rotation in the CCD Moiré method. Firstly, through theoretical analysis, simulations, and experimental studies, the imaging characteristics of CCD Moiré under various rotation conditions were systematically summarized and an optimal rotation angle range for accurate measurements was proposed. Secondly, the correlation between the deformation phase and displacement in rotated CCD Moiré was corrected, with the accuracy of the correction equation confirmed through simulation and experimental validation. Finally, an extensive multi-point deflection deformation measurement conducted on a large bridge further validates the proposed correction method. The measurement results showed that in the presence of rotation in the specimen grating and the camera, the correction method proposed in this paper can effectively reduce the measurement error by 3-4 times.