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
Original Manuscript: August 20, 1993
Revised Manuscript: December 14, 1993
Published: August 1, 1994
Yoon-Chang Park and Seung-Woo Kim, "Determination of two-dimensional planar displacement by moiré fringes of concentric-circle gratings," Appl. Opt. 33, 5171-5176 (1994)