Editing Moiré pattern (section)

== Pattern formation ==
[[File:070309-moire-a5-a5-upward-movement.gif|thumb|Line moiré with slow movement of the revealing layer upward]]
[[File:070320-a6-shape-moire-pr-gt-pb.gif|thumb|Shape moiré]]
[[File:Moire.gif|thumb|Moiré pattern created by overlapping two sets of concentric circles]]

Moiré patterns are often an [[Artifact (observational)|artifact]] of [[Digital image|images]] produced by various [[digital imaging]] and [[computer graphics]] techniques, for example when [[Image scanner|scanning]] a [[halftone]] picture or [[Ray tracing (graphics)|ray tracing]] a checkered plane (the latter being a special case of [[aliasing]], due to [[undersampling]] a fine regular pattern).<ref>{{cite web|title=Scanning Images in Books/Magazines/Newspapers (Moire patterns)|url=http://www.scantips.com/basics06.html|website=www.scantips.com|access-date=2020-02-27}}</ref>  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 optics|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.<ref>{{cite book
| title = Energy Minimization Methods in Computer Vision and Pattern Recognition
| editor1-first = Anil K.
| editor1-last = Jain
| first1 = Mário 
| last1 = Figueiredo
| first2 = Josiane
| last2 = Zerubia
| publisher = Springer
| year = 2001
| url = https://books.google.com/books?id=yb8otde21fcC&q=%22moire+pattern%22+nonlinear&pg=RA1-PA198| isbn = 9783540425236
}}</ref>

The moiré effect also occurs between overlapping transparent objects.<ref>{{Cite journal|last1=Miao|first1=Houxun|last2=Panna|first2=Alireza|last3=Gomella|first3=Andrew A.|last4=Bennett|first4=Eric E.|last5=Znati|first5=Sami|last6=Chen|first6=Lei|last7=Wen|first7=Han|title=A universal moiré effect and application in X-ray phase-contrast imaging|journal=Nature Physics|volume=12|issue=9|pages=830–834|doi=10.1038/nphys3734|year=2016|bibcode=2016NatPh..12..830M|pmc=5063246|pmid=27746823}}</ref> 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.

===Line moiré===
{{main|Line moiré}}

Line moiré is one type of moiré pattern; a pattern that appears when superposing two transparent layers containing correlated opaque patterns. Line moiré is the case when the superposed patterns comprise straight or curved lines. When moving the layer patterns, the moiré patterns transform or move at a faster speed. This effect is called optical moiré speedup.

More complex [[line moiré]] patterns are created if the lines are curved or not exactly parallel.

===Shape moiré===
{{main|Shape moiré}}

Shape moiré is one type of moiré pattern demonstrating the phenomenon of moiré magnification.<ref>{{cite conference
| title = Optical Inspection of Arrays and Periodic Structures Using Moire Magnification
| first1 = M.C. | last1 = Hutley
| first2 = R.F. | last2 = Stevens
| conference = IEE Colloquium, Microengineering in Optics and Optoelectronics
| date = 1999-11-16
| url = http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=IEESEM001999000187000008000001&idtype=cvips&gifs=yes
}}</ref><ref>{{cite journal
 |title      = Properties of Moiré Magnifiers
 |first1     = Hala
 |last1      = Kamal
 |first2     = Reinhard
 |last2      = Völkel
 |first3     = Javier
 |last3      = Alda
 |journal    = Optical Engineering
 |volume     = 37
 |issue      = 11
 |pages      = 3007–3014
 |date       = November 1998
 |url        = https://www.suss-microoptics.com/suss-microoptics/technical-publications/Moire_Magnifiers.pdf
 |archive-url = https://web.archive.org/web/20201108012304/https://www.suss-microoptics.com/suss-microoptics/technical-publications/Moire_Magnifiers.pdf
 |url-status = usurped
 |archive-date = November 8, 2020
 |access-date = 2021-03-30
 |doi        = 10.1117/1.601889
 |bibcode    = 1998OptEn..37.3007K
}}</ref> 1D shape moiré is the particular simplified case of 2D shape moiré. [[Dimension|One-dimensional]] patterns may appear when superimposing an [[Opacity (optics)|opaque]] layer containing tiny horizontal [[Transparency and translucency|transparent]] lines on top of a layer containing a complex shape which is periodically repeating along the [[Cartesian coordinate system|vertical axis]].

Moiré patterns revealing complex shapes, or sequences of symbols embedded in one of the layers (in form of periodically repeated compressed shapes) are created with shape moiré, otherwise called ''band moiré'' patterns. One of the most important properties of shape moiré is its ability to magnify tiny shapes along either one or both axes, that is, stretching. A common 2D example of moiré magnification occurs when viewing a [[chain-link fence]] through a second chain-link fence of identical design.  The fine structure of the design is visible even at great distances.