We investigate the properties of the moiré fringes of matched radial–parallel (MRP) gratings that are useful for the fine visual indication of angular displacements. Moiré patterns formed by overlapping two different MRP gratings of angular pitches, <i>P</i><sub>θ</sub> and <i>P</i><sub>θ</sub>′ (<<i>P</i><sub>θ</sub>), can provide a simple fringe-counting method for determining both the angle and the direction of the relative angular displacement of the gratings within the accuracy of (<i>P</i><sub>θ</sub>′/<i>M</i><sub>θ</sub>), where <i>M</i><sub>θ</sub> is the angular magnification for radial vernier fringes.
© 1997 Optical Society of America
B. J. Kim, J. S. Song, J. T. Kim, J. H. Jo, S. Chang, and K. C. Yuk, "Determination of small angular displacement by moiré fringes of matched radial-parallel gratings," Appl. Opt. 36, 2848-2855 (1997)