Moiré pattern

In mathematics, physics, and art, moiré patterns (UK: /ˈmwɑːreɪ/ MWAH-ray, US: /mwɑːˈreɪ/ mwah-RAY, French: [mwaʁe] ^ⓘ) or moiré fringes are large-scale interference patterns that can be produced when a partially opaque ruled pattern with transparent gaps is overlaid on another similar pattern. For the moiré interference pattern to appear, the two patterns must not be completely identical, but rather displaced, rotated, or have slightly different pitch.

Moiré patterns appear in many situations. In printing, the printed pattern of dots can interfere with the image. 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. They are also sometimes created deliberately; in micrometers, they are used to amplify the effects of very small movements.

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

The term originates from moire (moiré in its French adjectival form), a type of textile, traditionally made of silk but now also made of cotton or synthetic fiber, with a rippled or "watered" appearance. Moire, or "watered textile", is made by pressing two layers of the textile when wet. The similar but imperfect spacing of the threads creates a characteristic pattern which remains after the fabric dries.

In French, the noun moire is in use from the 17th century, for "watered silk". It was a loan of the English mohair (attested 1610). In French usage, the noun gave rise to the verb moirer, "to produce a watered textile by weaving or pressing", by the 18th century. The adjective moiré formed from this verb is in use from at least 1823.

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). This can be overcome in texture mapping through the use of mipmapping and anisotropic filtering.

The drawing on the upper right shows a moiré pattern. The lines could represent fibers in moiré silk, or lines drawn on paper or on a computer screen. The nonlinear interaction of the optical patterns of lines creates a real and visible pattern of roughly parallel dark and light bands, the moiré pattern, superimposed on the lines.

The moiré effect also occurs between overlapping transparent objects. For example, an invisible phase mask is made of a transparent polymer with a wavy thickness profile. As light shines through two overlaid masks of similar phase patterns, a broad moiré pattern occurs on a screen some distance away. This phase moiré effect and the classical moiré effect from opaque lines are two ends of a continuous spectrum in optics, which is called the universal moiré effect. The phase moiré effect is the basis for a type of broadband interferometer in x-ray and particle wave applications. It also provides a way to reveal hidden patterns in invisible layers.