I. Amidror
Journal of Modern Optics, Vol. 41, No. 9, 1994, 1837-1862
When repetitive structures such as line-gratings or dot-screens are superposed, a new
pattern may become clearly visible in the superposition, although it does not exist in
any of the original structures. This phenomenon, which in some cases appears to be very
spectacular, is known as the superposition moiré effect. In this article we analyze
the 2D envelope-forms of these moiré patterns, based on the Fourier theory, and we
show how they can be derived analytically from the original superposed structures,
either in the spectral domain or directly in the image domain. This approach not only
offers a qualitative geometric analysis of each superposition moiré, but also enables
the intensity levels of each moiré to be determined quantitatively. We first develop
this analysis method for the simple case of line-grating superpositions, and then we
generalize it to the superposition of doubly periodic structures such as dot screens,
for any order moiré. We finally show how, by means of this analysis method, we can
fully explain the surprising envelope-forms generated in the superpositions of screens
with any desired dot-shapes, for any order of moiré.