Determination of small in-plane angular displacement in machine tool alignment using two matched moiré fringes

Small in-plane angular displacement is determined by adopting two matched moiré fringes and frequency analysis method in this paper. The gratings in the specimen and reference have a complementary configuration; when the specimen has an angular displacement with respect to the reference, two matched moiré fringes rotate in opposite directions, and thus this angle determination method does not depend on the direction of the moiré fringe in a charge-coupled device (CCD) camera. The frequency components acquired by fast Fourier transfer and local frequency spectrum zooming process are used to determine the fringe inclination. Different from the two-dimensional fast Fourier transform (FFT) method, this method can realize the accurate measurement of fringe inclination in any direction by selecting different orthogonal frequency components. After the magnitude of fringe inclination is determined, automatic detection of fringe orientation is realized by comparing the peak frequencies in their possible directions. This method can be used to determine the angular displacement automatically and accurately.