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A Moiré pattern is a large-scale modulation produced by superposing similar periodic structures. Two identical two-dimensional lattices rotated by a small angle $\theta$ have geometric period $L=a/[2\sin (\theta /2)]\simeq a/|\theta |$ in the usual matching geometry. In layered crystals this modulation can act as an electronic superlattice; the actual bands additionally depend on interlayer coupling and orbital structure.

Atomic-resolution contrast is primarily electron phase contrast. elastic scattering by the specimen potential changes the phase of the transmitted electron wave. interference between transmitted and diffracted components, modified by the objective lens, converts that phase change into intensity variations. Appropriate defocus, sufficiently small optical aberrations, good spatial optical coherence and transfer of the graphene spatial frequencies are needed. At exact focus an ideal weak phase object need not give a strong visible lattice.

Mass–thickness or amplitude contrast can also distinguish thicker overlap regions, folds, contamination and support film, especially when scattered electrons are excluded by an aperture. It is comparatively weak for a clean monolayer of low-$Z$ carbon. diffraction contrast becomes important in crystalline, multilayer or differently oriented regions when Bragg-scattered beams are selected or excluded. Relative rotation of layers can additionally produce a moiré pattern.

A dark region alone is not a reliable layer count: electron phase contrast can change sign with defocus, and contamination also changes intensity. Use fold-edge fringes, diffraction information and calibrated image simulations or thickness-sensitive measurements together. Defect identification should likewise compare a structural model with the actual imaging conditions, rather than reading every dark lattice site as a missing atom.

The Moiré pattern sets a superlattice periodFor the stipulated scalar one-dimensional model, right- and left-moving states have $E(k)=\hslash v|k|$. The $n$th Bragg crossing satisfies $E(k)=E(k-nG)$ and hence $k=nG/2$. The Bragg gap ladder for a linear dispersion therefore has centresThis is the spacing of successive possible Bragg gaps. The corresponding atomic-lattice scale is $hv/(2a)\simeq 8.27\mathrm{eV}$, fifty times larger.

Shifting a linear branch by one full reciprocal period $G$ instead gives $\hslash vG\simeq 0.331\mathrm{eV}$, twice the consecutive Bragg-threshold spacing; the first zone boundary is at $G/2$. These scales should not be confused with the gap width, which depends on the weak potential's Fourier coefficients. The geometry alone does not guarantee equally wide or even observable gaps at every threshold, nor an exactly periodic full spectrum. The estimate neglects graphene's additional pseudospin selection rules and interlayer correlations, as required by the scalar-chain approximation.