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.
© 1994 Optical Society of America
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