Behaviors of moire fringes induced by plate thickness

Abstract

The chirped moire fringes in two superposed regularly patterned plates are investigated. When the top plate of the two superposed plates has a thickness, the periods of the moire fringes become different from that of the plate with no thickness, and the fringes shift as the viewing position changes. These variations are induced because the pattern period of the bottom plate is virtually shortened by light refraction when it is viewed through the top plate due to the top plate's refractive index. The amount of shortening is small but different for different thicknesses, viewing positions and distances and lengths of the plates. Since the shortening amount is a function of the viewing angle, its variation has a chirped signal pattern. It turns the pattern with a uniform line array into a chirp-signal-type line array pattern. As a consequence, the moire fringes will be chirped, and they become more noticeable as the plate lengths increase. The simulation and experimental results are matched very closely.