Moiré pattern

A large-scale pattern produced when two similar repetitive patterns overlap with a slight displacement or difference in spacing. Its broad bands arise from interference between the finer patterns.

Spatial frequency: The number of repeating cycles of a pattern per unit distance or angle. The difference between two spatial frequencies sets the spacing of the broad moiré bands.
Digital image sensor: A device that converts incoming light into a grid of measured pixel values. Its pixel grid can interact with fine repeating details in a scene to create false patterns.
Lenticular printing: A printing process that uses a ridged transparent lens sheet to display different images from different viewing angles. The lens ridges and printed image form a controlled pattern whose alignment determines the visible effect.
Aliasing: An error in which sampling makes a signal appear to have a different frequency or structure. Moiré in digital images is a visible form of aliasing, but moiré also occurs without digital sampling.
Moiré materials: Materials whose properties are shaped by long-period patterns arising from stacked or twisted layers. Moiré patterns become a design feature when their superlattices alter material behavior.
Beat frequency: The difference between two nearby frequencies, heard or measured as a slower variation in amplitude. Moiré bands are the spatial analogue of beats between nearby repeating frequencies.
Anti-aliasing: Techniques that reduce visual artifacts caused by representing continuous images on discrete grids. Filtering before sampling suppresses the frequencies most likely to produce moiré.
Twisted bilayer graphene: Two graphene sheets stacked with a small relative rotation, creating a long-period moiré superlattice. A tiny twist between atomic lattices produces a much larger repeating structure.
Diffraction: The bending and spreading of waves around obstacles or through openings. Diffraction arises from wave propagation through apertures, not from overlapping similar patterns.
Flat band: An electronic energy band with little variation in energy across momentum states. Moiré superlattices can produce narrow, nearly flat bands that strengthen electron interactions.

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