Moiré pattern

In television and digital photography, a pattern on an object being photographed can interfere with the shape of the light sensors to generate unwanted artifacts.

In physics, its manifestation is wave interference like that seen in the double-slit experiment and the beat phenomenon in acoustics.

The similar but imperfect spacing of the threads creates a characteristic pattern which remains after the fabric dries.

In French usage, the noun gave rise to the verb moirer, "to produce a watered textile by weaving or pressing", by the 18th century.

Moiré patterns are often an artifact of images produced by various digital imaging and computer graphics techniques, for example when scanning a halftone picture or ray tracing a checkered plane (the latter being a special case of aliasing, due to undersampling a fine regular pattern).

[5] For example, an invisible phase mask is made of a transparent polymer with a wavy thickness profile.

The phase moiré effect is the basis for a type of broadband interferometer in x-ray and particle wave applications.

For purposes of discussion we shall assume the two primary patterns are each printed in greyscale ink on a white sheet, where the opacity (e.g., shade of grey) of the "printed" part is given by a value between 0 (white) and 1 (black) inclusive, with ⁠1/2⁠ representing neutral grey.

We represent the grey intensity in each pattern by a positive opacity function of distance along a fixed direction (say, the x-coordinate) in the paper plane, in the form

The average of these two functions, representing the superimposed printed image, evaluates as follows (see reverse identities here :Prosthaphaeresis ):

Other one-dimensional moiré effects include the classic beat frequency tone which is heard when two pure notes of almost identical pitch are sounded simultaneously.

The long diagonal 2D is the hypotenuse of a right triangle and the sides of the right angle are d(1 + cos α) and p. The Pythagorean theorem gives:

In graphic arts and prepress, the usual technology for printing full-color images involves the superimposition of halftone screens.

Part of the prepress art consists of selecting screen angles and halftone frequencies which minimize moiré.

This is due to interlaced scanning in televisions and non-film cameras, referred to as interline twitter.

Because of this, newscasters and other professionals who regularly appear on TV are instructed to avoid clothing which could cause the effect.

Photographs of a TV screen taken with a digital camera often exhibit moiré patterns.

To avoid the effect, the digital camera can be aimed at an angle of 30 degrees to the TV screen.

[8][9][10] An example can be found in the UK on the eastern shore of Southampton Water, opposite Fawley oil refinery (50°51′21.63″N 1°19′44.77″W / 50.8560083°N 1.3291028°W / 50.8560083; -1.3291028).

[11] Similar moiré effect beacons can be used to guide mariners to the centre point of an oncoming bridge; when the vessel is aligned with the centreline, vertical lines are visible.

Inogon lights are deployed at airports to help pilots on the ground keep to the centreline while docking on stand.

This technique is attractive because the scale of the moiré pattern is much larger than the deflection that causes it, making measurement easier.

This can for example be due to surface reconstruction of the crystal, or when a thin layer of a second crystal is on the surface, e.g. single-layer,[15][16] double-layer graphene,[17] or Van der Waals heterostructure of graphene and hBN,[18][19] or bismuth and antimony nanostructures.

[20] In transmission electron microscopy (TEM), translational moiré fringes can be seen as parallel contrast lines formed in phase-contrast TEM imaging by the interference of diffracting crystal lattice planes that are overlapping, and which might have different spacing and/or orientation.

However, if probe aberration-corrected high-angle annular dark field scanning transmission electron microscopy (HAADF-STEM) imaging is used, more direct interpretation of the crystal structure in terms of atom types and positions is obtained.

[21][22] In condensed matter physics, the moiré phenomenon is commonly discussed for two-dimensional materials.

A prominent example is in twisted bi-layer graphene, which forms a moiré pattern and at a particular magic angle exhibits superconductivity and other important electronic properties.

In materials science, known examples exhibiting moiré contrast are thin films[25] or nanoparticles of MX-type (M = Ti, Nb; X = C, N) overlapping with austenitic matrix.

Both phases, MX and the matrix, have face-centered cubic crystal structure and cube-on-cube orientation relationship.

However, they have significant lattice misfit of about 20 to 24% (based on the chemical composition of alloy), which produces a moiré effect.