191:
44:
2819:
2831:
309:
2563:
2847:. The effect occurs when there is mismatch between the lattice parameter or angle of the 2D layer and that of the underlying substrate, or another 2D layer, such as in 2D material heterostructures. The phenomenon is exploited as a means of engineering the electronic structure or optical properties of materials, which some call moiré materials. The often significant changes in electronic properties when twisting two atomic layers and the prospect of electronic applications has led to the name
2278:
2551:
58:
545:
32:
533:
886:
457:
2260:
2269:
1703:
317:
379:
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.
74:
301:
2097:
2507:
the frequencies are not exactly the same and aligned perfectly together, beats (or samples) will align closely at some moments in time and far apart at other times. The closer together beats are, the darker it is at that spot; the farther apart, the lighter. The result is periodic in the same way as a graphic moiré pattern. See:
1430:
2604:
effect creates arrows that point towards an imaginary line marking the hazard or line of safe passage; as navigators pass over the line, the arrows on the beacon appear to become vertical bands before changing back to arrows pointing in the reverse direction. An example can be found in the UK on the eastern shore of
2250:
2603:
The moiré effect is used in shoreside beacons called "Inogon leading marks" or "Inogon lights", manufactured by Inogon Licens AB, Sweden, to designate the safest path of travel for ships heading to locks, marinas, ports, etc., or to indicate underwater hazards (such as pipelines or cables). The moiré
893:
The essence of the moiré effect is the (mainly visual) perception of a distinctly different third pattern which is caused by inexact superimposition of two similar patterns. The mathematical representation of these patterns is not trivially obtained and can seem somewhat arbitrary. In this section we
393:
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
378:
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.
897:
The visibility of these patterns is dependent on the medium or substrate in which they appear, and these may be opaque (as for example on paper) or transparent (as for example in plastic film). For purposes of discussion we shall assume the two primary patterns are each printed in greyscale ink on a
588:
If the lines of the patterns are superimposed at the left of the figure, the shift between the lines increases when going to the right. After a given number of lines, the patterns are opposed: the lines of the second pattern are between the lines of the first pattern. If we look from a far distance,
2594:
often exhibit moiré patterns. Since both the TV screen and the digital camera use a scanning technique to produce or to capture pictures with horizontal scan lines, the conflicting sets of lines cause the moiré patterns. To avoid the effect, the digital camera can be aimed at an angle of 30 degrees
213:
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
2874:
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),
2527:
screens. These are regular rectangular dot patterns—often four of them, printed in cyan, yellow, magenta, and black. Some kind of moiré pattern is inevitable, but in favorable circumstances the pattern is "tight"; that is, the spatial frequency of the moiré is so high that it is not noticeable. In
2506:
The product of two "beat tracks" of slightly different speeds overlaid, producing an audible moiré pattern; if the beats of one track correspond to where in space a black dot or line exists and the beats of the other track correspond to the points in space where a camera is sampling light, because
2797:
imaging by the interference of diffracting crystal lattice planes that are overlapping, and which might have different spacing and/or orientation. Most of the moiré contrast observations reported in the literature are obtained using high-resolution phase contrast imaging in TEM. However, if probe
917:
We shall also choose to represent the opacity of the pattern resulting from printing one pattern atop the other at a given point on the paper as the average (i.e. the arithmetic mean) of each pattern's opacity at that position, which is half their sum, and, as calculated, does not exceed 1. (This
2643:). 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.
921:
We now consider the "printing" superimposition of two almost similar, sinusoidally varying, grey-scale patterns to show how they produce a moiré effect in first printing one pattern on the paper, and then printing the other pattern over the first, keeping their coordinate axes in register. We
2681:
in materials: by deforming a grid with respect to a reference grid and measuring the moiré pattern, the stress levels and patterns can be deduced. This technique is attractive because the scale of the moiré pattern is much larger than the deflection that causes it, making measurement easier.
1887:
918:
choice is not unique. Any other method to combine the functions that satisfies keeping the resultant function value within the bounds will also serve; arithmetic averaging has the virtue of simplicity—with hopefully minimal damage to one's concepts of the printmaking process.)
1721:
2536:
moiré pattern. Part of the prepress art consists of selecting screen angles and halftone frequencies which minimize moiré. The visibility of moiré is not entirely predictable. The same set of screens may produce good results with some images, but visible moiré with others.
1215:
1183:
77:
2102:
76:
81:
80:
75:
2478:
If we choose to measure the angle, the final error is proportional to the measurement error. If we choose to measure the spacing, the final error is proportional to the inverse of the spacing. Thus, for the small angles, it is best to measure the spacing.
192:
82:
2387:
271:, 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.
1619:
frequency tone which is heard when two pure notes of almost identical pitch are sounded simultaneously. This is an acoustic version of the moiré effect in the one dimension of time: the original two notes are still present—but the listener's
2493:
209:
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.
79:
802:
438:
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
989:
represents the periodic variation (i.e., spatial frequency) of the pattern's grey intensity, measured as the number of intensity cycles per unit distance. Since the sine function is cyclic over argument changes of
894:
shall give a mathematical example of two parallel patterns whose superimposition forms a moiré pattern, and show one way (of many possible ways) these patterns and the moiré effect can be rendered mathematically.
2583:. As the person moves about, the moiré pattern is quite noticeable. Because of this, newscasters and other professionals who regularly appear on TV are instructed to avoid clothing which could cause the effect.
2495:
1045:
1220:
49:
The fine lines that make up the sky in this image create moiré patterns when shown at some resolutions for the same reason that photographs of televisions exhibit moiré patterns: the lines are not absolutely
2824:
When graphene is grown on the (111) surface of iridium, its long-wavelength height modulation can be thought of as a moiré pattern arising from the superposition of the two mismatched hexagonal lattices.
2107:
1892:
1050:
2092:{\displaystyle {\begin{aligned}(2D)^{2}&={\frac {p^{2}}{\sin ^{2}\alpha }}(1+\cos \alpha )^{2}+p^{2}\\&=p^{2}\cdot \left({\frac {(1+\cos \alpha )^{2}}{\sin ^{2}\alpha }}+1\right)\end{aligned}}}
1882:
434:
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
2330:
2325:
2423:
856:
666:
2476:
1551:
2666:
1624:
is of two pitches that are the average of and half the difference of the frequencies of the two notes. Aliasing in sampling of time-varying signals also belongs to this moiré paradigm.
1489:
978:
710:
66:
1425:{\displaystyle {\begin{aligned}f_{3}&={\frac {f_{1}+f_{2}}{2}}\\&={\frac {1}{2}}+{\frac {\sin(k_{1}x)+\sin(k_{2}x)}{4}}\\&={\frac {1+\sin(Ax)\cos(Bx)}{2}}\end{aligned}}}
2735:
exploit the tendency of digital scanners to produce moiré patterns by including fine circular or wavy designs that are likely to exhibit a moiré pattern when scanned and printed.
78:
2245:{\displaystyle {\begin{aligned}(2D)^{2}&=2p^{2}\cdot {\frac {1+\cos \alpha }{\sin ^{2}\alpha }}\\D&={\frac {\frac {p}{2}}{\sin {\frac {\alpha }{2}}}}.\end{aligned}}}
2700:
image of the object to the object itself: the hologram is the reference step, and the difference with the object are the deformations, which appear as pale and dark lines.
2494:
2669:
Use of the moiré effect in strain measurement: case of uniaxial traction (top) and of pure shear (bottom); the lines of the patterns are initially horizontal in both cases
3523:
Tang, Shujie; Wang, Haomin; Zhang, Yu; Li, Ang; Xie, Hong; Liu, Xiaoyu; Liu, Lianqing; Li, Tianxin; Huang, Fuqiang; Xie, Xiaoming; Jiang, Mianheng (16 September 2013).
3148:
922:
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
375:
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.
719:
415:
Shape moiré is one type of moiré pattern demonstrating the phenomenon of moiré magnification. 1D shape moiré is the particular simplified case of 2D shape moiré.
371:
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
3858:
Yin, Xi; Liu, Xinhong; Pan, Yung-Tin; Walsh, Kathleen A.; Yang, Hong (10 December 2014). "Hanoi Tower-like
Multilayered Ultrathin Palladium Nanosheets".
2615:
589:
we have the feeling of pale zones when the lines are superimposed (there is white between the lines), and of dark zones when the lines are "opposed".
2752:
3765:"Atomic resolution characterization of strengthening nanoparticles in a new high-temperature-capable 43Fe-25Ni-22.5Cr austenitic stainless steel"
3804:
Liu, Yuan; Weiss, Nathan O.; Duan, Xidong; Cheng, Hung-Chieh; Huang, Yu; Duan, Xiangfeng (2016). "Van der Waals heterostructures and devices".
898:
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
2575:
Moiré patterns are commonly seen on television screens when a person is wearing a shirt or jacket of a particular weave or pattern, such as a
1797:
3389:
Kobayashi, Katsuyoshi (1996-01-01). "Moiré pattern in scanning tunneling microscopy: Mechanism in observation of subsurface nanostructures".
3496:
K. Schouteden, N. Galvanetto (2015). "Scanning probe microscopy study of chemical vapor deposition grown graphene transferred to Au(111)".
1206:
The average of these two functions, representing the superimposed printed image, evaluates as follows (see reverse identities here :
3064:
2802:
2805:(HAADF-STEM) imaging is used, more direct interpretation of the crystal structure in terms of atom types and positions is obtained.
2392:
807:
629:
2448:
3663:
Le Ster, Maxime; Maerkl, Tobias; Kowalczyk, Pawel J.; Brown, Simon A. (2019). "Moiré patterns in van der Waals heterostructures".
3271:
2894:
1498:
3763:
Heczko, M.; Esser, B.D.; Smith, T.M.; Beran, P.; Mazánová, V.; McComb, D.W.; Kruml, T.; Polák, J.; Mills, M.J. (14 March 2018).
3165:
1439:
927:
869:, the closer the dark and pale zones; a great spacing between dark and pale zones mean that the patterns have very close steps.
671:
2969:
982:
where the presence of 1 keeps the function positive definite, and the division by 2 prevents function values greater than 1.
443:
through a second chain-link fence of identical design. The fine structure of the design is visible even at great distances.
1178:{\displaystyle {\begin{aligned}f_{1}&={\frac {1+\sin(k_{1}x)}{2}}\\f_{2}&={\frac {1+\sin(k_{2}x)}{2}}\end{aligned}}}
2719:, called a "descreen" filter, to remove moiré pattern artifacts which would otherwise be produced when scanning printed
914:
representing neutral grey. Any value less than 0 or greater than 1 using this grey scale is essentially "unprintable".
3949:, interactive vector graphics with links to the physics and mathematics of the Moiré effect and artistic contributions
3736:
3370:
3320:
3074:
560:
Consider two patterns made of parallel and equidistant lines, e.g., vertical lines. The step of the first pattern is
504:
172:
129:
486:
478:
3904:
2790:
2689:
measurement: the operator just has to draw a pattern on the object, and superimpose the reference pattern to the
482:
3917:
3090:
Miao, Houxun; Panna, Alireza; Gomella, Andrew A.; Bennett, Eric E.; Znati, Sami; Chen, Lei; Wen, Han (2016).
2759:
424:
2770:
of the crystal, or when a thin layer of a second crystal is on the surface, e.g. single-layer, double-layer
2382:{\displaystyle {\begin{aligned}\sin \alpha &\approx \alpha \\\cos \alpha &\approx 1\end{aligned}}}
37:
A moiré pattern formed by two units of parallel lines, one unit rotated 5° clockwise relative to the other
2744:
804:
the distance between the middle of two dark zones, which is also the distance between two pale zones, is
428:
3525:"Precisely aligned graphene grown on hexagonal boron nitride by catalyst free chemical vapor deposition"
2799:
2686:
2678:
2660:
1040:
Consider now two such patterns, where one has a slightly different periodic variation from the other:
3435:
N’Diaye, Alpha T. (2006-01-01). "Two-Dimensional Ir
Cluster Lattice on a Graphene Moiré on Ir(111)".
2990:"Surpassing the lateral resolution limit by a factor of two using structured illumination microscopy"
2933:
2844:
2690:
2319:
1640:. Seen from afar, we can also see darker and paler lines: the pale lines correspond to the lines of
467:
325:
2556:
Strong moiré visible in this photo of a parrot's feathers (more pronounced in the full-size image)
3940:
471:
2928:
43:
3728:
2794:
2767:
2579:
jacket. This is due to interlaced scanning in televisions and non-film cameras, referred to as
349:
226:
20:
3595:"Silane-catalysed fast growth of large single-crystalline graphene on hexagonal boron nitride"
3967:
3285:
2994:
2889:
427:
lines on top of a layer containing a complex shape which is periodically repeating along the
365:
3720:
1586:, the moiré effect is distinctively demonstrated by the sinusoidal envelope "beat" function
288:, "to produce a watered textile by weaving or pressing", by the 18th century. The adjective
61:
Difference in distance of the front and rear picket fence on a bridge create moiré patterns.
3867:
3813:
3672:
3616:
3546:
3454:
3398:
3180:
3103:
2910:
2652:
8:
2923:
2905:
2775:
1791:
215:
3871:
3817:
3676:
3620:
3550:
3458:
3402:
3238:
3184:
3107:
2818:
3698:
3637:
3606:
3594:
3567:
3536:
3524:
3478:
3444:
3124:
3091:
3021:
3910:
A live demonstration of the moiré effect that stems from interferences between circles
2523:, the usual technology for printing full-color images involves the superimposition of
3977:
3972:
3962:
3883:
3829:
3786:
3742:
3732:
3721:
3702:
3642:
3572:
3470:
3414:
3366:
3316:
3129:
3070:
3013:
3008:
2989:
2965:
2863:
2763:
2748:
2716:
2605:
2580:
2501:
360:
a fine regular pattern). This can be overcome in texture mapping through the use of
337:
300:
222:
202:
3482:
2830:
2793:(TEM), translational moiré fringes can be seen as parallel contrast lines formed in
626:
th line of the first network. The middle of the first dark zone thus corresponds to
3875:
3821:
3776:
3688:
3680:
3632:
3624:
3562:
3554:
3505:
3462:
3406:
3188:
3119:
3111:
3025:
3003:
2900:
2836:
Moiré pattern arising from the superposition of two graphene lattices twisted by 4°
2747:, the moiré pattern can be used to obtain images with a resolution higher than the
2712:
1616:
1207:
440:
420:
372:
230:
146:
140:
103:
3905:
A series of oil paintings based on moiré principles by
British artist, Pip Dickens
3466:
550:
Moiré obtained by the superimposition of two similar patterns rotated by an angle
278:
is in use from the 17th century, for "watered silk". It was a loan of the
English
3921:
3509:
2609:
2508:
1741:
of the neighbouring sides, we can see that the pale line makes an angle equal to
333:
308:
268:
185:
97:
3825:
3781:
3764:
3684:
2591:
1641:
797:{\displaystyle d=n\cdot (p+\delta p)={\frac {p^{2}}{2\delta p}}+{\frac {p}{2}}}
247:
3932:
3410:
3289:
3212:
3150:
Optical
Inspection of Arrays and Periodic Structures Using Moire Magnification
2562:
410:
3956:
3833:
3790:
3746:
2953:
2709:
2674:
2656:
2630:
2617:
1594:, whose periodic variation is half the difference of the periodic variations
874:
862:
the bigger the step, the bigger the distance between the pale and dark zones;
357:
341:
329:
2843:
In condensed matter physics, the moiré phenomenon is commonly discussed for
398:
388:
57:
3887:
3646:
3576:
3474:
3133:
3017:
2871:
2550:
2516:
2438:), the spacing between the pale lines is infinite (there is no pale line).
1775:
is the hypotenuse of a right triangle and the sides of the right angle are
3846:
3418:
3092:"A universal moiré effect and application in X-ray phase-contrast imaging"
2277:
889:
Moiré pattern (bottom) created by superimposing two grids (top and middle)
3449:
2918:
2848:
2576:
3928:
A universal moiré effect and application in X-ray phase-contrast imaging
3723:
Transmission electron microscopy : a textbook for materials science
3336:
3039:
1644:, that is, lines passing through the intersections of the two patterns.
544:
3693:
3628:
2587:
2431:
is, the farther apart the pale lines; when both patterns are parallel (
361:
3879:
3558:
3363:
Counterfeit deterrent features for the next-generation currency design
3115:
3066:
Energy
Minimization Methods in Computer Vision and Pattern Recognition
2859:
exhibits superconductivity and other important electronic properties.
2665:
401:
patterns are created if the lines are curved or not exactly parallel.
3192:
2867:
1738:
1702:
1647:
If we consider a cell of the lattice formed, we can see that it is a
416:
234:
65:
31:
3927:
456:
3909:
3611:
2884:
2852:
2783:
2771:
2732:
2720:
2697:
2524:
2520:
1734:
1679:
353:
345:
320:
Moiré pattern created by overlapping two sets of concentric circles
3914:
3541:
885:
284:(attested 1610). In French usage, the noun gave rise to the verb
3936:
3153:. IEE Colloquium, Microengineering in Optics and Optoelectronics.
3063:
Figueiredo, Mário; Zerubia, Josiane (2001). Jain, Anil K. (ed.).
2961:
2808:
2779:
2762:, moiré fringes appear if surface atomic layers have a different
1648:
532:
256:
206:
3365:. Washington DC: National Materials Advisory Board. p. 61.
3040:"Scanning Images in Books/Magazines/Newspapers (Moire patterns)"
2259:
592:
The middle of the first dark zone is when the shift is equal to
218:, they are used to amplify the effects of very small movements.
280:
264:
69:
Moiré pattern appearing on scaled camera captures of LCD screen
2268:
3946:
3164:
Kamal, Hala; Völkel, Reinhard; Alda, Javier (November 1998).
2677:
industries, these patterns are used for studying microscopic
538:
The patterns are superimposed in the mid-width of the figure.
394:
a faster speed. This effect is called optical moiré speedup.
155:
115:
3847:
APS Physics - Trend: Bilayer
Graphene's Wicked, Twisted Road
2445:: by the orientation of the pale lines and by their spacing
3662:
3315:(3 ed.). Bingley, England: Emerald. pp. 204–205.
2696:
A similar effect can be obtained by the superposition of a
1564:, clearly lies in the range . Since the periodic variation
304:
Line moiré with slow movement of the revealing layer upward
260:
164:
121:
2851:
of this field. A prominent example is in twisted bi-layer
1720:
3262:
1877:{\displaystyle (2D)^{2}=d^{2}(1+\cos \alpha )^{2}+p^{2}}
1615:
Other one-dimensional moiré effects include the classic
316:
3089:
2568:
Moiré pattern seen over a cage in the San
Francisco Zoo
19:"Moiré" and "Moire" redirect here. For other uses, see
2766:
than the bulk crystal. This can for example be due to
352:
a checkered plane (the latter being a special case of
3762:
2540:
2451:
2395:
2328:
2105:
1890:
1800:
1501:
1442:
1218:
1048:
930:
810:
722:
716:
between the middle of a pale zone and a dark zone is
674:
632:
173:
152:
130:
112:
1764:
Additionally, the spacing between two pale lines is
292:
formed from this verb is in use from at least 1823.
161:
118:
3719:Williams, David B.; Carter, C. Barry (2009-01-01).
158:
149:
109:
106:
3593:Tang, Shujie; Wang, Haomin; Wang, Huishan (2015).
2855:, which forms a moiré pattern and at a particular
2470:
2417:
2381:
2244:
2091:
1876:
1545:
1483:
1424:
1177:
1001:per intensity cycle (the wavelength) obtains when
972:
850:
796:
704:
660:
3803:
3062:
880:
3954:
3915:An interactive example of various moiré patterns
2482:
1636:, but the second pattern is rotated by an angle
3933:"The Moiré Effect Lights That Guide Ships Home"
3522:
3337:"Scanning Images in Magazines/Books/Newspapers"
3163:
2866:, known examples exhibiting moiré contrast are
1768:, half of the long diagonal. The long diagonal
1761:with the perpendicular of each pattern's line.
3924:Use arrow keys and mouse to manipulate layers.
3857:
3718:
2983:
2981:
2809:Materials science and condensed matter physics
2418:{\displaystyle D\approx {\frac {p}{\alpha }}.}
851:{\displaystyle 2d={\frac {p^{2}}{\delta p}}+p}
661:{\displaystyle n\cdot \delta p={\frac {p}{2}}}
3495:
3291:The Moiré Effect Lights That Guide Ships Home
3146:
2487:
2471:{\displaystyle \alpha \approx {\frac {p}{D}}}
873:The principle of the moiré is similar to the
517:
205:that can be produced when a partially opaque
3797:
3592:
3236:
616:th line of the second pattern is shifted by
3943:about the Moiré Inogon light in Southampton
2978:
1546:{\displaystyle B={\frac {k_{1}-k_{2}}{2}}.}
485:. Unsourced material may be challenged and
86:Moiré pattern of double layered shading net
3310:
3147:Hutley, M.C.; Stevens, R.F. (1999-11-16).
2987:
1484:{\displaystyle A={\frac {k_{1}+k_{2}}{2}}}
419:patterns may appear when superimposing an
255:in its French adjectival form), a type of
3780:
3692:
3636:
3610:
3566:
3540:
3448:
3388:
3360:
3123:
3007:
2803:scanning transmission electron microscopy
1737:of the rhombus. As the diagonals are the
1632:Consider two patterns with the same step
1612:(and evidently much lower in frequency).
1568:is the average of and therefore close to
973:{\displaystyle f={\frac {1+\sin(kx)}{2}}}
705:{\displaystyle n={\frac {p}{2\delta p}}.}
505:Learn how and when to remove this message
2778:heterostructure of graphene and hBN, or
2664:
2491:
884:
315:
307:
299:
72:
64:
56:
3434:
3272:International Hydrographic Organization
2895:Barrier grid animation and stereography
1733:The pale lines correspond to the small
522:
3955:
3311:Kazda, Antonín; Caves, Robert (2015).
3758:
3756:
3714:
3712:
3658:
3656:
3588:
3586:
3430:
3428:
3384:
3382:
3284:
2952:
2646:
2441:There are thus two ways to determine
184:
3769:Materials Science and Engineering: A
2598:
858:From this formula, we can see that:
483:adding citations to reliable sources
450:
295:
2703:
1686:and the side opposite to the angle
1627:
13:
3753:
3709:
3653:
3583:
3425:
3379:
2753:structured illumination microscopy
2723:images to produce digital images.
2541:Television screens and photographs
90:In mathematics, physics, and art,
14:
3989:
3898:
3361:Sincerbox, Glenn T., ed. (1991).
423:layer containing tiny horizontal
221:In physics, its manifestation is
3166:"Properties of Moiré Magnifiers"
3009:10.1046/j.1365-2818.2000.00710.x
2958:Longman Pronunciation Dictionary
2829:
2817:
2791:transmission electron microscopy
2693:pattern on the deformed object.
2685:The moiré effect can be used in
2561:
2549:
2276:
2267:
2258:
1719:
1701:
543:
531:
455:
145:
102:
42:
30:
3851:
3840:
3516:
3489:
3354:
3329:
3304:
3278:
3253:
446:
3230:
3205:
3157:
3140:
3083:
3056:
3032:
2946:
2875:which produces a moiré effect.
2120:
2110:
2044:
2025:
1972:
1953:
1905:
1895:
1852:
1833:
1811:
1801:
1434:where it is easily shown that
1409:
1400:
1391:
1382:
1348:
1332:
1320:
1304:
1162:
1146:
1101:
1085:
961:
952:
881:Mathematical function approach
750:
735:
404:
1:
3467:10.1103/PhysRevLett.97.215501
2988:Gustafsson, M. G. L. (2000).
2939:
2800:high-angle annular dark field
2760:scanning tunneling microscopy
2751:, using a technique known as
2738:
2483:Implications and applications
1651:with the four sides equal to
382:
340:techniques, for example when
3510:10.1016/j.carbon.2015.08.033
3313:Airport design and operation
2726:
2427:We can see that the smaller
564:, the step of the second is
324:Moiré patterns are often an
240:
7:
2878:
2745:super-resolution microscopy
2528:the graphic arts, the term
865:the bigger the discrepancy
10:
3994:
3826:10.1038/natrevmats.2016.42
3782:10.1016/j.msea.2018.02.004
3685:10.1103/PhysRevB.99.075422
2661:Holographic interferometry
2650:
2488:Printing full-color images
2320:small-angle approximations
518:Moiré of parallel patterns
408:
386:
18:
3411:10.1103/PhysRevB.53.11091
2934:Multidimensional sampling
2845:two-dimensional materials
1708:Unit cell of the "net"; "
994:, the distance increment
245:The term originates from
214:created deliberately; in
3806:Nature Reviews Materials
3260:"inogen light [
2960:(3rd ed.). Pearson
2631:50.8560083°N 1.3291028°W
1726:Effect of changing angle
259:, traditionally made of
3437:Physical Review Letters
3268:Hydrographic Dictionary
1555:This function average,
3270:(5 ed.). Monaco:
3239:"Prohibited anchorage"
2768:surface reconstruction
2670:
2636:50.8560083; -1.3291028
2512:
2472:
2419:
2383:
2286:Effect on curved lines
2246:
2093:
1878:
1547:
1485:
1426:
1179:
974:
890:
852:
798:
706:
662:
321:
313:
305:
227:double-slit experiment
225:like that seen in the
87:
70:
62:
21:Moire (disambiguation)
3727:. Springer. pp.
3599:Nature Communications
3213:"US Patent 4,629,325"
2995:Journal of Microscopy
2890:Angle-sensitive pixel
2798:aberration-corrected
2668:
2498:
2473:
2420:
2384:
2247:
2094:
1879:
1548:
1486:
1427:
1180:
975:
888:
853:
799:
707:
663:
366:anisotropic filtering
319:
311:
303:
263:but now also made of
203:interference patterns
85:
68:
60:
3274:. 2003. p. 113.
2929:Moiré Phase Tracking
2715:provide an optional
2653:Theory of elasticity
2590:screen taken with a
2500:Warning: audiogenic
2449:
2393:
2326:
2103:
1888:
1798:
1712:" means "pale line".
1682:whose hypotenuse is
1499:
1440:
1216:
1046:
928:
808:
720:
672:
630:
523:Geometrical approach
479:improve this section
332:produced by various
274:In French, the noun
16:Interference pattern
3872:2014NanoL..14.7188Y
3818:2016NatRM...116042L
3677:2019PhRvB..99g5422L
3621:2015NatCo...6.6499T
3551:2013NatSR...3E2666T
3459:2006PhRvL..97u5501N
3403:1996PhRvB..5311091K
3397:(16): 11091–11099.
3185:1998OptEn..37.3007K
3173:Optical Engineering
3108:2016NatPh..12..830M
2924:Lenticular printing
2627: /
2610:Fawley oil refinery
2534:excessively visible
1792:Pythagorean theorem
1678:; (we have a right
3947:"The Moiré Museum"
3920:2011-07-24 at the
3629:10.1038/ncomms7499
3529:Scientific Reports
3237:Alexander Trabas.
2795:phase-contrast TEM
2671:
2647:Strain measurement
2595:to the TV screen.
2513:
2468:
2415:
2379:
2377:
2242:
2240:
2089:
2087:
1874:
1543:
1481:
1422:
1420:
1175:
1173:
970:
891:
848:
794:
702:
658:
322:
314:
306:
88:
71:
63:
3880:10.1021/nl503879a
3866:(12): 7188–7194.
3665:Physical Review B
3559:10.1038/srep02666
3391:Physical Review B
3241:. Light of Lights
3179:(11): 3007–3014.
3116:10.1038/nphys3734
2971:978-1-4058-8118-0
2864:materials science
2764:crystal structure
2749:diffraction limit
2713:computer programs
2606:Southampton Water
2599:Marine navigation
2586:Photographs of a
2581:interline twitter
2502:epileptic seizure
2496:
2466:
2410:
2233:
2230:
2214:
2189:
2072:
1951:
1538:
1479:
1416:
1355:
1290:
1270:
1169:
1108:
968:
840:
792:
779:
697:
656:
515:
514:
507:
338:computer graphics
296:Pattern formation
223:wave interference
83:
3985:
3935:, an article on
3892:
3891:
3855:
3849:
3844:
3838:
3837:
3801:
3795:
3794:
3784:
3760:
3751:
3750:
3726:
3716:
3707:
3706:
3696:
3660:
3651:
3650:
3640:
3614:
3590:
3581:
3580:
3570:
3544:
3520:
3514:
3513:
3493:
3487:
3486:
3452:
3450:cond-mat/0609286
3432:
3423:
3422:
3386:
3377:
3376:
3358:
3352:
3351:
3349:
3347:
3333:
3327:
3326:
3308:
3302:
3301:
3300:
3298:
3288:(5 March 2018),
3282:
3276:
3275:
3257:
3251:
3250:
3248:
3246:
3234:
3228:
3227:
3225:
3223:
3209:
3203:
3202:
3200:
3199:
3193:10.1117/1.601889
3170:
3161:
3155:
3154:
3144:
3138:
3137:
3127:
3087:
3081:
3080:
3060:
3054:
3053:
3051:
3050:
3044:www.scantips.com
3036:
3030:
3029:
3011:
2985:
2976:
2975:
2956:(3 April 2008).
2950:
2906:Euclid's orchard
2901:Beat (acoustics)
2833:
2821:
2786:nanostructures.
2704:Image processing
2642:
2641:
2639:
2638:
2637:
2632:
2628:
2625:
2624:
2623:
2620:
2565:
2553:
2497:
2477:
2475:
2474:
2469:
2467:
2459:
2444:
2437:
2430:
2424:
2422:
2421:
2416:
2411:
2403:
2388:
2386:
2385:
2380:
2378:
2318:) the following
2317:
2316:
2314:
2313:
2310:
2307:
2295:
2280:
2271:
2262:
2251:
2249:
2248:
2243:
2241:
2234:
2232:
2231:
2223:
2207:
2206:
2190:
2188:
2181:
2180:
2170:
2153:
2148:
2147:
2128:
2127:
2098:
2096:
2095:
2090:
2088:
2084:
2080:
2073:
2071:
2064:
2063:
2053:
2052:
2051:
2023:
2013:
2012:
1997:
1993:
1992:
1980:
1979:
1952:
1950:
1943:
1942:
1932:
1931:
1922:
1913:
1912:
1883:
1881:
1880:
1875:
1873:
1872:
1860:
1859:
1832:
1831:
1819:
1818:
1789:
1785:
1774:
1767:
1760:
1759:
1757:
1756:
1753:
1750:
1723:
1705:
1693:
1689:
1685:
1677:
1676:
1674:
1673:
1667:
1664:
1639:
1635:
1628:Rotated patterns
1611:
1602:
1593:
1585:
1576:
1567:
1563:
1552:
1550:
1549:
1544:
1539:
1534:
1533:
1532:
1520:
1519:
1509:
1490:
1488:
1487:
1482:
1480:
1475:
1474:
1473:
1461:
1460:
1450:
1431:
1429:
1428:
1423:
1421:
1417:
1412:
1368:
1360:
1356:
1351:
1344:
1343:
1316:
1315:
1296:
1291:
1283:
1275:
1271:
1266:
1265:
1264:
1252:
1251:
1241:
1232:
1231:
1208:Prosthaphaeresis
1202:
1184:
1182:
1181:
1176:
1174:
1170:
1165:
1158:
1157:
1132:
1123:
1122:
1109:
1104:
1097:
1096:
1071:
1062:
1061:
1036:
1035:
1033:
1032:
1027:
1024:
1011:
1000:
993:
988:
979:
977:
976:
971:
969:
964:
938:
913:
911:
910:
907:
904:
868:
857:
855:
854:
849:
841:
839:
831:
830:
821:
803:
801:
800:
795:
793:
785:
780:
778:
767:
766:
757:
715:
711:
709:
708:
703:
698:
696:
682:
667:
665:
664:
659:
657:
649:
625:
622:compared to the
621:
615:
611:
610:
608:
607:
604:
601:
584:
573:
563:
553:
547:
535:
510:
503:
499:
496:
490:
459:
451:
441:chain-link fence
201:are large-scale
196:
195:
194:
188:
183:
177:
171:
170:
167:
166:
163:
160:
157:
154:
151:
144:
133:
128:
127:
124:
123:
120:
117:
114:
111:
108:
101:
84:
46:
34:
3993:
3992:
3988:
3987:
3986:
3984:
3983:
3982:
3953:
3952:
3922:Wayback Machine
3901:
3896:
3895:
3856:
3852:
3845:
3841:
3802:
3798:
3761:
3754:
3739:
3717:
3710:
3661:
3654:
3591:
3584:
3521:
3517:
3494:
3490:
3433:
3426:
3387:
3380:
3373:
3359:
3355:
3345:
3343:
3335:
3334:
3330:
3323:
3309:
3305:
3296:
3294:
3283:
3279:
3259:
3258:
3254:
3244:
3242:
3235:
3231:
3221:
3219:
3211:
3210:
3206:
3197:
3195:
3168:
3162:
3158:
3145:
3141:
3088:
3084:
3077:
3061:
3057:
3048:
3046:
3038:
3037:
3033:
2986:
2979:
2972:
2951:
2947:
2942:
2881:
2841:
2840:
2839:
2838:
2837:
2834:
2826:
2825:
2822:
2811:
2741:
2729:
2706:
2663:
2649:
2635:
2633:
2629:
2626:
2621:
2618:
2616:
2614:
2613:
2601:
2573:
2572:
2571:
2570:
2569:
2566:
2558:
2557:
2554:
2543:
2492:
2490:
2485:
2458:
2450:
2447:
2446:
2442:
2432:
2428:
2402:
2394:
2391:
2390:
2376:
2375:
2365:
2353:
2352:
2342:
2329:
2327:
2324:
2323:
2311:
2308:
2305:
2304:
2302:
2297:
2296:is very small (
2293:
2290:
2289:
2288:
2287:
2283:
2282:
2281:
2273:
2272:
2264:
2263:
2239:
2238:
2222:
2215:
2205:
2198:
2192:
2191:
2176:
2172:
2171:
2154:
2152:
2143:
2139:
2129:
2123:
2119:
2106:
2104:
2101:
2100:
2086:
2085:
2059:
2055:
2054:
2047:
2043:
2024:
2022:
2021:
2017:
2008:
2004:
1995:
1994:
1988:
1984:
1975:
1971:
1938:
1934:
1933:
1927:
1923:
1921:
1914:
1908:
1904:
1891:
1889:
1886:
1885:
1868:
1864:
1855:
1851:
1827:
1823:
1814:
1810:
1799:
1796:
1795:
1787:
1776:
1769:
1765:
1754:
1751:
1746:
1745:
1743:
1742:
1731:
1730:
1729:
1728:
1727:
1724:
1715:
1714:
1713:
1706:
1691:
1687:
1683:
1668:
1665:
1660:
1659:
1657:
1652:
1637:
1633:
1630:
1610:
1604:
1601:
1595:
1587:
1584:
1578:
1575:
1569:
1565:
1562:
1556:
1528:
1524:
1515:
1511:
1510:
1508:
1500:
1497:
1496:
1469:
1465:
1456:
1452:
1451:
1449:
1441:
1438:
1437:
1419:
1418:
1369:
1367:
1358:
1357:
1339:
1335:
1311:
1307:
1297:
1295:
1282:
1273:
1272:
1260:
1256:
1247:
1243:
1242:
1240:
1233:
1227:
1223:
1219:
1217:
1214:
1213:
1201:
1194:
1188:
1172:
1171:
1153:
1149:
1133:
1131:
1124:
1118:
1114:
1111:
1110:
1092:
1088:
1072:
1070:
1063:
1057:
1053:
1049:
1047:
1044:
1043:
1028:
1025:
1022:
1021:
1019:
1013:
1002:
995:
991:
986:
939:
937:
929:
926:
925:
908:
905:
902:
901:
899:
883:
866:
832:
826:
822:
820:
809:
806:
805:
784:
768:
762:
758:
756:
721:
718:
717:
713:
686:
681:
673:
670:
669:
648:
631:
628:
627:
623:
617:
613:
605:
602:
597:
596:
594:
593:
575:
565:
561:
558:
557:
556:
555:
554:
551:
548:
540:
539:
536:
525:
520:
511:
500:
494:
491:
476:
460:
449:
417:One-dimensional
413:
407:
391:
385:
334:digital imaging
298:
269:synthetic fiber
243:
231:beat phenomenon
190:
189:
186:[mwaʁe]
181:
175:
148:
139:
138:
131:
105:
96:
95:
73:
55:
54:
53:
52:
51:
47:
39:
38:
35:
24:
17:
12:
11:
5:
3991:
3981:
3980:
3975:
3970:
3965:
3951:
3950:
3944:
3930:
3925:
3912:
3907:
3900:
3899:External links
3897:
3894:
3893:
3850:
3839:
3796:
3752:
3737:
3708:
3652:
3582:
3515:
3488:
3443:(21): 215501.
3424:
3378:
3371:
3353:
3328:
3321:
3303:
3277:
3252:
3229:
3217:Google Patents
3204:
3156:
3139:
3102:(9): 830–834.
3096:Nature Physics
3082:
3075:
3055:
3031:
2977:
2970:
2944:
2943:
2941:
2938:
2937:
2936:
2931:
2926:
2921:
2916:
2908:
2903:
2898:
2892:
2887:
2880:
2877:
2835:
2828:
2827:
2823:
2816:
2815:
2814:
2813:
2812:
2810:
2807:
2740:
2737:
2728:
2725:
2705:
2702:
2648:
2645:
2600:
2597:
2592:digital camera
2567:
2560:
2559:
2555:
2548:
2547:
2546:
2545:
2544:
2542:
2539:
2489:
2486:
2484:
2481:
2465:
2462:
2457:
2454:
2414:
2409:
2406:
2401:
2398:
2374:
2371:
2368:
2366:
2364:
2361:
2358:
2355:
2354:
2351:
2348:
2345:
2343:
2341:
2338:
2335:
2332:
2331:
2285:
2284:
2275:
2274:
2266:
2265:
2257:
2256:
2255:
2254:
2253:
2237:
2229:
2226:
2221:
2218:
2213:
2210:
2204:
2201:
2199:
2197:
2194:
2193:
2187:
2184:
2179:
2175:
2169:
2166:
2163:
2160:
2157:
2151:
2146:
2142:
2138:
2135:
2132:
2130:
2126:
2122:
2118:
2115:
2112:
2109:
2108:
2083:
2079:
2076:
2070:
2067:
2062:
2058:
2050:
2046:
2042:
2039:
2036:
2033:
2030:
2027:
2020:
2016:
2011:
2007:
2003:
2000:
1998:
1996:
1991:
1987:
1983:
1978:
1974:
1970:
1967:
1964:
1961:
1958:
1955:
1949:
1946:
1941:
1937:
1930:
1926:
1920:
1917:
1915:
1911:
1907:
1903:
1900:
1897:
1894:
1893:
1871:
1867:
1863:
1858:
1854:
1850:
1847:
1844:
1841:
1838:
1835:
1830:
1826:
1822:
1817:
1813:
1809:
1806:
1803:
1725:
1718:
1717:
1716:
1707:
1700:
1699:
1698:
1697:
1696:
1629:
1626:
1608:
1599:
1582:
1573:
1560:
1542:
1537:
1531:
1527:
1523:
1518:
1514:
1507:
1504:
1478:
1472:
1468:
1464:
1459:
1455:
1448:
1445:
1415:
1411:
1408:
1405:
1402:
1399:
1396:
1393:
1390:
1387:
1384:
1381:
1378:
1375:
1372:
1366:
1363:
1361:
1359:
1354:
1350:
1347:
1342:
1338:
1334:
1331:
1328:
1325:
1322:
1319:
1314:
1310:
1306:
1303:
1300:
1294:
1289:
1286:
1281:
1278:
1276:
1274:
1269:
1263:
1259:
1255:
1250:
1246:
1239:
1236:
1234:
1230:
1226:
1222:
1221:
1199:
1192:
1168:
1164:
1161:
1156:
1152:
1148:
1145:
1142:
1139:
1136:
1130:
1127:
1125:
1121:
1117:
1113:
1112:
1107:
1103:
1100:
1095:
1091:
1087:
1084:
1081:
1078:
1075:
1069:
1066:
1064:
1060:
1056:
1052:
1051:
967:
963:
960:
957:
954:
951:
948:
945:
942:
936:
933:
882:
879:
871:
870:
863:
847:
844:
838:
835:
829:
825:
819:
816:
813:
791:
788:
783:
777:
774:
771:
765:
761:
755:
752:
749:
746:
743:
740:
737:
734:
731:
728:
725:
701:
695:
692:
689:
685:
680:
677:
655:
652:
647:
644:
641:
638:
635:
549:
542:
541:
537:
530:
529:
528:
527:
526:
524:
521:
519:
516:
513:
512:
463:
461:
454:
448:
445:
409:Main article:
406:
403:
387:Main article:
384:
381:
297:
294:
242:
239:
92:moiré patterns
48:
41:
40:
36:
29:
28:
27:
26:
25:
15:
9:
6:
4:
3:
2:
3990:
3979:
3976:
3974:
3971:
3969:
3966:
3964:
3961:
3960:
3958:
3948:
3945:
3942:
3938:
3934:
3931:
3929:
3926:
3923:
3919:
3916:
3913:
3911:
3908:
3906:
3903:
3902:
3889:
3885:
3881:
3877:
3873:
3869:
3865:
3861:
3854:
3848:
3843:
3835:
3831:
3827:
3823:
3819:
3815:
3811:
3807:
3800:
3792:
3788:
3783:
3778:
3774:
3770:
3766:
3759:
3757:
3748:
3744:
3740:
3738:9780387765013
3734:
3730:
3725:
3724:
3715:
3713:
3704:
3700:
3695:
3690:
3686:
3682:
3678:
3674:
3671:(7): 075422.
3670:
3666:
3659:
3657:
3648:
3644:
3639:
3634:
3630:
3626:
3622:
3618:
3613:
3608:
3604:
3600:
3596:
3589:
3587:
3578:
3574:
3569:
3564:
3560:
3556:
3552:
3548:
3543:
3538:
3534:
3530:
3526:
3519:
3511:
3507:
3503:
3499:
3492:
3484:
3480:
3476:
3472:
3468:
3464:
3460:
3456:
3451:
3446:
3442:
3438:
3431:
3429:
3420:
3416:
3412:
3408:
3404:
3400:
3396:
3392:
3385:
3383:
3374:
3372:9780309050289
3368:
3364:
3357:
3342:
3338:
3332:
3324:
3322:9781784418700
3318:
3314:
3307:
3293:
3292:
3287:
3281:
3273:
3269:
3265:
3264:
3256:
3240:
3233:
3218:
3214:
3208:
3194:
3190:
3186:
3182:
3178:
3174:
3167:
3160:
3152:
3151:
3143:
3135:
3131:
3126:
3121:
3117:
3113:
3109:
3105:
3101:
3097:
3093:
3086:
3078:
3076:9783540425236
3072:
3068:
3067:
3059:
3045:
3041:
3035:
3027:
3023:
3019:
3015:
3010:
3005:
3001:
2997:
2996:
2991:
2984:
2982:
2973:
2967:
2963:
2959:
2955:
2949:
2945:
2935:
2932:
2930:
2927:
2925:
2922:
2920:
2917:
2915:
2913:
2909:
2907:
2904:
2902:
2899:
2896:
2893:
2891:
2888:
2886:
2883:
2882:
2876:
2873:
2872:nanoparticles
2869:
2865:
2860:
2858:
2854:
2850:
2846:
2832:
2820:
2806:
2804:
2801:
2796:
2792:
2787:
2785:
2781:
2777:
2776:Van der Waals
2773:
2769:
2765:
2761:
2756:
2754:
2750:
2746:
2736:
2734:
2724:
2722:
2718:
2714:
2711:
2710:image scanner
2701:
2699:
2694:
2692:
2688:
2683:
2680:
2676:
2675:manufacturing
2667:
2662:
2658:
2657:Strain tensor
2654:
2644:
2640:
2619:50°51′21.63″N
2611:
2607:
2596:
2593:
2589:
2584:
2582:
2578:
2564:
2552:
2538:
2535:
2531:
2526:
2522:
2518:
2510:
2505:
2503:
2480:
2463:
2460:
2455:
2452:
2439:
2435:
2425:
2412:
2407:
2404:
2399:
2396:
2372:
2369:
2367:
2362:
2359:
2356:
2349:
2346:
2344:
2339:
2336:
2333:
2322:can be made:
2321:
2300:
2279:
2270:
2261:
2252:
2235:
2227:
2224:
2219:
2216:
2211:
2208:
2202:
2200:
2195:
2185:
2182:
2177:
2173:
2167:
2164:
2161:
2158:
2155:
2149:
2144:
2140:
2136:
2133:
2131:
2124:
2116:
2113:
2081:
2077:
2074:
2068:
2065:
2060:
2056:
2048:
2040:
2037:
2034:
2031:
2028:
2018:
2014:
2009:
2005:
2001:
1999:
1989:
1985:
1981:
1976:
1968:
1965:
1962:
1959:
1956:
1947:
1944:
1939:
1935:
1928:
1924:
1918:
1916:
1909:
1901:
1898:
1869:
1865:
1861:
1856:
1848:
1845:
1842:
1839:
1836:
1828:
1824:
1820:
1815:
1807:
1804:
1793:
1783:
1779:
1773:
1762:
1749:
1740:
1736:
1722:
1711:
1704:
1695:
1681:
1672:
1663:
1655:
1650:
1645:
1643:
1625:
1623:
1618:
1613:
1607:
1598:
1591:
1581:
1572:
1559:
1553:
1540:
1535:
1529:
1525:
1521:
1516:
1512:
1505:
1502:
1494:
1491:
1476:
1470:
1466:
1462:
1457:
1453:
1446:
1443:
1435:
1432:
1413:
1406:
1403:
1397:
1394:
1388:
1385:
1379:
1376:
1373:
1370:
1364:
1362:
1352:
1345:
1340:
1336:
1329:
1326:
1323:
1317:
1312:
1308:
1301:
1298:
1292:
1287:
1284:
1279:
1277:
1267:
1261:
1257:
1253:
1248:
1244:
1237:
1235:
1228:
1224:
1211:
1209:
1204:
1198:
1191:
1185:
1166:
1159:
1154:
1150:
1143:
1140:
1137:
1134:
1128:
1126:
1119:
1115:
1105:
1098:
1093:
1089:
1082:
1079:
1076:
1073:
1067:
1065:
1058:
1054:
1041:
1038:
1031:
1017:
1009:
1005:
999:
985:The quantity
983:
980:
965:
958:
955:
949:
946:
943:
940:
934:
931:
923:
919:
915:
895:
887:
878:
876:
875:Vernier scale
864:
861:
860:
859:
845:
842:
836:
833:
827:
823:
817:
814:
811:
789:
786:
781:
775:
772:
769:
763:
759:
753:
747:
744:
741:
738:
732:
729:
726:
723:
712:The distance
699:
693:
690:
687:
683:
678:
675:
653:
650:
645:
642:
639:
636:
633:
620:
600:
590:
586:
583:
579:
572:
568:
546:
534:
509:
506:
498:
488:
484:
480:
474:
473:
469:
464:This section
462:
458:
453:
452:
444:
442:
437:
432:
430:
429:vertical axis
426:
422:
418:
412:
402:
400:
397:More complex
395:
390:
380:
376:
374:
369:
367:
363:
359:
358:undersampling
355:
351:
347:
343:
339:
335:
331:
327:
318:
310:
302:
293:
291:
287:
283:
282:
277:
272:
270:
266:
262:
258:
254:
250:
249:
238:
236:
232:
228:
224:
219:
217:
211:
208:
207:ruled pattern
204:
200:
199:moiré fringes
193:
187:
179:
178:
169:
142:
136:
135:
126:
99:
93:
67:
59:
45:
33:
22:
3968:Interference
3863:
3860:Nano Letters
3859:
3853:
3842:
3812:(9): 16042.
3809:
3805:
3799:
3772:
3768:
3722:
3668:
3664:
3602:
3598:
3532:
3528:
3518:
3501:
3497:
3491:
3440:
3436:
3394:
3390:
3362:
3356:
3344:. Retrieved
3341:ScanTips.com
3340:
3331:
3312:
3306:
3295:, retrieved
3290:
3280:
3267:
3261:
3255:
3243:. Retrieved
3232:
3220:. Retrieved
3216:
3207:
3196:. Retrieved
3176:
3172:
3159:
3149:
3142:
3099:
3095:
3085:
3069:. Springer.
3065:
3058:
3047:. Retrieved
3043:
3034:
3002:(2): 82–87.
2999:
2993:
2957:
2948:
2911:
2861:
2856:
2842:
2788:
2757:
2742:
2730:
2707:
2695:
2684:
2672:
2622:1°19′44.77″W
2602:
2585:
2574:
2533:
2529:
2517:graphic arts
2514:
2499:
2440:
2433:
2426:
2298:
2291:
1781:
1777:
1771:
1763:
1747:
1732:
1710:ligne claire
1709:
1670:
1661:
1653:
1646:
1631:
1621:
1614:
1605:
1596:
1589:
1579:
1570:
1557:
1554:
1495:
1492:
1436:
1433:
1212:
1205:
1196:
1189:
1186:
1042:
1039:
1029:
1015:
1007:
1003:
997:
984:
981:
924:
920:
916:
896:
892:
872:
618:
598:
591:
587:
581:
577:
570:
566:
559:
501:
492:
477:Please help
465:
447:Calculations
435:
433:
414:
396:
392:
377:
370:
323:
289:
285:
279:
275:
273:
252:
246:
244:
220:
212:
198:
91:
89:
3694:10092/16978
3535:(1): 2666.
3504:: 318–322.
2954:Wells, John
2919:Kell factor
2914:(sculpture)
2857:magic angle
2849:twistronics
2698:holographic
2634: /
2608:, opposite
2577:houndstooth
425:transparent
411:Shape moiré
405:Shape moiré
350:ray tracing
348:picture or
312:Shape moiré
216:micrometers
3957:Categories
3612:1503.02806
3286:Scott, Tom
3245:9 December
3198:2021-03-30
3049:2020-02-27
2940:References
2897:(kinegram)
2868:thin films
2739:Microscopy
2651:See also:
1622:perception
1187:such that
495:April 2018
436:band moiré
399:line moiré
389:Line moiré
383:Line moiré
362:mipmapping
3941:Tom Scott
3834:2058-8437
3791:0921-5093
3775:: 49–60.
3747:876600051
3703:128326155
3542:1309.0172
2733:banknotes
2727:Banknotes
2532:means an
2456:≈
2453:α
2408:α
2400:≈
2370:≈
2363:α
2360:
2350:α
2347:≈
2340:α
2337:
2225:α
2220:
2186:α
2183:
2168:α
2165:
2150:⋅
2069:α
2066:
2041:α
2038:
2015:⋅
1969:α
1966:
1948:α
1945:
1884:that is:
1849:α
1846:
1780:(1 + cos
1739:bisectors
1522:−
1398:
1380:
1330:
1302:
1144:
1083:
950:
834:δ
773:δ
745:δ
733:⋅
691:δ
640:δ
637:⋅
466:does not
373:nonlinear
356:, due to
241:Etymology
235:acoustics
3978:Printing
3973:Patterns
3963:Geometry
3918:Archived
3888:25369350
3647:25757864
3605:: 6499.
3577:24036628
3483:19791195
3475:17155746
3346:22 April
3266:]".
3134:27746823
3018:10810003
2912:Guardian
2885:Aliasing
2879:See also
2853:graphene
2784:antimony
2772:graphene
2721:halftone
2691:deformed
2525:halftone
2521:prepress
1735:diagonal
1680:triangle
668:that is
354:aliasing
346:halftone
342:scanning
326:artifact
229:and the
3937:YouTube
3868:Bibcode
3814:Bibcode
3673:Bibcode
3638:4382696
3617:Bibcode
3568:3773621
3547:Bibcode
3455:Bibcode
3419:9982681
3399:Bibcode
3297:5 March
3222:5 March
3181:Bibcode
3125:5063246
3104:Bibcode
3026:9257781
2962:Longman
2780:bismuth
2509:phasing
2504:hazard.
2315:
2303:
1794:gives:
1758:
1744:
1675:
1658:
1649:rhombus
1034:
1020:
912:
900:
609:
595:
576:0 <
574:, with
487:removed
472:sources
257:textile
182:French:
3886:
3832:
3789:
3745:
3735:
3731:–397.
3701:
3645:
3635:
3575:
3565:
3498:Carbon
3481:
3473:
3417:
3369:
3319:
3132:
3122:
3073:
3024:
3016:
2968:
2717:filter
2687:strain
2679:strain
2659:, and
1790:. The
612:. The
421:opaque
330:images
286:moirer
281:mohair
265:cotton
50:level.
3699:S2CID
3607:arXiv
3537:arXiv
3479:S2CID
3445:arXiv
3169:(PDF)
3022:S2CID
2774:, or
2731:Many
2708:Some
2530:moiré
2389:thus
2301:<
2292:When
2099:thus
1642:nodes
1012:, or
580:<
290:moiré
276:moire
253:moiré
248:moire
197:) or
174:mwah-
3884:PMID
3830:ISSN
3787:ISSN
3743:OCLC
3733:ISBN
3643:PMID
3573:PMID
3471:PMID
3415:PMID
3367:ISBN
3348:2010
3317:ISBN
3299:2018
3247:2016
3224:2018
3130:PMID
3071:ISBN
3014:PMID
2966:ISBN
2782:and
2519:and
1786:and
1669:sin
1617:beat
1603:and
1588:cos(
1577:and
1493:and
1010:= 2π
619:n δp
470:any
468:cite
364:and
336:and
261:silk
134:-ray
132:MWAH
3939:by
3876:doi
3822:doi
3777:doi
3773:719
3729:393
3689:hdl
3681:doi
3633:PMC
3625:doi
3563:PMC
3555:doi
3506:doi
3463:doi
3407:doi
3263:sic
3189:doi
3120:PMC
3112:doi
3004:doi
3000:198
2870:or
2862:In
2789:In
2758:In
2743:In
2673:In
2515:In
2436:= 0
2357:cos
2334:sin
2217:sin
2174:sin
2162:cos
2057:sin
2035:cos
1963:cos
1936:sin
1843:cos
1694:).
1690:is
1395:cos
1377:sin
1327:sin
1299:sin
1210:):
1141:sin
1080:sin
947:sin
481:by
328:of
267:or
233:in
176:RAY
3959::
3882:.
3874:.
3864:14
3862:.
3828:.
3820:.
3808:.
3785:.
3771:.
3767:.
3755:^
3741:.
3711:^
3697:.
3687:.
3679:.
3669:99
3667:.
3655:^
3641:.
3631:.
3623:.
3615:.
3601:.
3597:.
3585:^
3571:.
3561:.
3553:.
3545:.
3531:.
3527:.
3502:95
3500:.
3477:.
3469:.
3461:.
3453:.
3441:97
3439:.
3427:^
3413:.
3405:.
3395:53
3393:.
3381:^
3339:.
3215:.
3187:.
3177:37
3175:.
3171:.
3128:.
3118:.
3110:.
3100:12
3098:.
3094:.
3042:.
3020:.
3012:.
2998:.
2992:.
2980:^
2964:.
2755:.
2655:,
2588:TV
1656:=
1590:Bx
1203:.
1195:≈
1037:.
1023:2π
1018:=
992:2π
877:.
867:δp
585:.
578:δp
571:δp
569:+
431:.
368:.
344:a
237:.
180:,
165:eɪ
156:ɑː
143::
141:US
137:,
122:eɪ
116:ɑː
100::
98:UK
3890:.
3878::
3870::
3836:.
3824::
3816::
3810:1
3793:.
3779::
3749:.
3705:.
3691::
3683::
3675::
3649:.
3627::
3619::
3609::
3603:6
3579:.
3557::
3549::
3539::
3533:3
3512:.
3508::
3485:.
3465::
3457::
3447::
3421:.
3409::
3401::
3375:.
3350:.
3325:.
3249:.
3226:.
3201:.
3191::
3183::
3136:.
3114::
3106::
3079:.
3052:.
3028:.
3006::
2974:.
2612:(
2511:.
2464:D
2461:p
2443:α
2434:α
2429:α
2413:.
2405:p
2397:D
2373:1
2312:6
2309:/
2306:π
2299:α
2294:α
2236:.
2228:2
2212:2
2209:p
2203:=
2196:D
2178:2
2159:+
2156:1
2145:2
2141:p
2137:2
2134:=
2125:2
2121:)
2117:D
2114:2
2111:(
2082:)
2078:1
2075:+
2061:2
2049:2
2045:)
2032:+
2029:1
2026:(
2019:(
2010:2
2006:p
2002:=
1990:2
1986:p
1982:+
1977:2
1973:)
1960:+
1957:1
1954:(
1940:2
1929:2
1925:p
1919:=
1910:2
1906:)
1902:D
1899:2
1896:(
1870:2
1866:p
1862:+
1857:2
1853:)
1840:+
1837:1
1834:(
1829:2
1825:d
1821:=
1816:2
1812:)
1808:D
1805:2
1802:(
1788:p
1784:)
1782:α
1778:d
1772:D
1770:2
1766:D
1755:2
1752:/
1748:α
1692:p
1688:α
1684:d
1671:α
1666:/
1662:p
1654:d
1638:α
1634:p
1609:2
1606:k
1600:1
1597:k
1592:)
1583:2
1580:k
1574:1
1571:k
1566:A
1561:3
1558:f
1541:.
1536:2
1530:2
1526:k
1517:1
1513:k
1506:=
1503:B
1477:2
1471:2
1467:k
1463:+
1458:1
1454:k
1447:=
1444:A
1414:2
1410:)
1407:x
1404:B
1401:(
1392:)
1389:x
1386:A
1383:(
1374:+
1371:1
1365:=
1353:4
1349:)
1346:x
1341:2
1337:k
1333:(
1324:+
1321:)
1318:x
1313:1
1309:k
1305:(
1293:+
1288:2
1285:1
1280:=
1268:2
1262:2
1258:f
1254:+
1249:1
1245:f
1238:=
1229:3
1225:f
1200:2
1197:k
1193:1
1190:k
1167:2
1163:)
1160:x
1155:2
1151:k
1147:(
1138:+
1135:1
1129:=
1120:2
1116:f
1106:2
1102:)
1099:x
1094:1
1090:k
1086:(
1077:+
1074:1
1068:=
1059:1
1055:f
1030:k
1026:/
1016:x
1014:Δ
1008:x
1006:Δ
1004:k
998:x
996:Δ
987:k
966:2
962:)
959:x
956:k
953:(
944:+
941:1
935:=
932:f
909:2
906:/
903:1
846:p
843:+
837:p
828:2
824:p
818:=
815:d
812:2
790:2
787:p
782:+
776:p
770:2
764:2
760:p
754:=
751:)
748:p
742:+
739:p
736:(
730:n
727:=
724:d
714:d
700:.
694:p
688:2
684:p
679:=
676:n
654:2
651:p
646:=
643:p
634:n
624:n
614:n
606:2
603:/
599:p
582:p
567:p
562:p
552:α
508:)
502:(
497:)
493:(
489:.
475:.
251:(
168:/
162:r
159:ˈ
153:w
150:m
147:/
125:/
119:r
113:w
110:m
107:ˈ
104:/
94:(
23:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
