moiré: one construct, many systems

In optics, a moiré is the large-scale pattern that appears when two periodic structures (gratings, rulings, or line screens) are superposed at a small angle or slight period mismatch, producing a low-frequency beat that magnifies tiny differences between the two. Lord Rayleigh's 1874 On the manufacture and theory of diffraction-gratings used the pattern formed by superposing gratings as a sensitive test of their regularity, and Amidror's The theory of the Moiré phenomenon gives the modern spectral account. The referent is the geometry of superposed periodic layers, exploited in moiré metrology to measure strain and alignment, the same construct that plagues halftone printing and, at atomic scale, structures twisted crystals.[1][2]

Unit

The period and orientation of the beat pattern from two superposed grids

Recovery means

Not applicable

Measured by

Derived from the periods and angle of the component layers via the spectral (Fourier) theory of superposed gratings

In color printing, moiré is the unwanted repeating pattern that arises when the halftone screens of the separate inks are placed at angles or frequencies that beat against one another, or against the periodic structure of the subject, turning smooth tones into visible rosettes or blotches. Printers avoid it by setting the conventional screen angles so the superposition stays regular rather than conspicuous. Amidror's The theory of the Moiré phenomenon and Kipphan's Handbook of print media both treat screen-angle moiré in halftone reproduction. It is the identical superposed-periodic-layer construct as optical moiré, here a defect to be suppressed rather than a measuring tool.[2][3]

Unit

The visibility and period of the interference pattern between halftone screens

Recovery means

Not applicable

Measured by

Evaluated by the strength and spatial frequency of the screen-angle beat pattern seen in the printed tone

In condensed-matter physics, a moiré superlattice is the long-period pattern formed when two atomic lattices are overlaid with a small twist or lattice mismatch (for example two sheets of graphene), so the same beat geometry seen in overlaid gratings now reorganises the electronic structure into flat bands at a magic twist angle. Cao and colleagues' 2018 Unconventional superconductivity in magic-angle graphene superlattices showed such moiré superlattices host correlated and superconducting states. The referent is a periodic superposition of crystal lattices and the electronic structure it creates, the identical geometric construct as optical and printing moiré, realised at the atomic scale.[4]

Unit

The moiré period and twist angle setting the superlattice's electronic bands

Recovery means

Not applicable

Measured by

Set by the twist angle and lattice mismatch; probed by transport, the moiré period, and the resulting band structure