Abstract
The tutorial describes essential features of moire patterns, as well as the circumstances, when the moire patterns appear and how to estimate their characteristics (parameters) such as the orientation and period. The moire effect is described in two domains, the image space (spatial domain) and in the spectral domain using the complex numbers. The tutorial covers the indicial equation method, the coplanar and noncoplanar sinusoidal gratings, the moire effect in a spatial object (a cylinder), as well as explains the moire wave vector, the moire spectra, the spectral trajectories, and summarizes behavior of the visible patterns in moved/rotated gratings.
Highlights
The moiré effect is a physical phenomenon of linear optics
The moiré patterns appear as a result of an interaction between transparent layers of a repeated structure[1] when superposed layers are viewed through
The sketch lines of the gratings are shown by solid lines in Fig. 5; the moiré patterns comprise the third family of lines with the period Tm at the angle θ
Summary
The moiré effect is a physical phenomenon of linear optics. The moiré patterns appear as a result of an interaction between transparent layers of a repeated structure[1] when superposed layers are viewed through. Dealing with spectra represents a generalized approach.[54,55,56] Using spectral trajectories,[57] the behavior of the patterns can be estimated geometrically. As the equations of the trajectories are derived from the geometric characteristics of the gratings, the estimation can be made without calculations of spectra. This makes the spectral trajectories suitable for an interactive computer simulation. After discussion about the visual effects in displaced or rotated plane gratings in Sec. 9, a conclusion finalizes the tutorial
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