Determination of two-dimensional planar displacement by moiré fringes of concentric-circle gratings

We investigate the moiré fringe pattern of two concentric-circle gratings with the aim of measuring the relative two-dimensional planar displacement induced between the gratings. In the first stage we give a comprehensive mathematical approach for the analysis of fringe patterns. Then we suggest a fast computational measurement algorithm that uses a Fourier transformation technique. Finally, our experimental results prove that a measuring accuracy of 0.01 µm can be achieved with this method.