Talk:Moiré pattern

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Contents 1 Old stuff not previously in a section 2 Moire in art reproduction 3 Bad Link 4 Moirés in digital images of TV screens 5 another example of bad resampling 6 Another example of a Moiré pattern 7 Interferometric approach 8 Animated image removal poll 9 pronunciation 10 Nonlinear interaction 11 Merge?

[edit] Old stuff not previously in a section

I deleted the following text because the explanation seemed questionable:

 "[moiré patterns sometimes occur when scanning halftones], 
 when the image interferes with itself on either side 
 of the scanner's glass surface."

I wonder whether this explanation is a fact, or only a theory. Another possible explanation is aliasing from undersampling the halftone pattern. Jorge Stolfi 20:52, 24 Mar 2004 (UTC)

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The two above concepts are both correct. Scanners scan in lines. The spacing of those lines combined with halftone patterns creates moire patterns.

Should this article include some description (and example?) of the use of moiré patterns in 1960's pop art? [[User:GK|gK ¿?]] 06:33, 18 Nov 2004 (UTC)

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common in lamps of the 60s and 70s had concentric spirals of differing pitch. One spiral is rotated and moire patterns emerge. Beer companies also made really interesting lamps that used moire patterns to simulate water flowing.

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Moire was merged into this article. JRM 15:07, 2004 Dec 3 (UTC)

[edit] Moire in art reproduction

Moire patterns can ocur when items at a regular frequency are not at proper angles to generatee a pleasing pattern. Yes, scanning screened images is a prime example of how moires occur in the reproduction industry. --Dkroll2 17:29, Dec 27, 2004 (UTC)

In everyday life.... I first observed moire patterns in fences. When you drive parallel to a chain link fence that has another parrellel chain link fence behind it, you can see large diamond shapes moving across the fence. They are moire patterns. They are diamond shapes because the chain links are diamond shaped. Circular grating creates circular moire patterns.

Helicopter blades moving at high speads create a virtual moire pattern. It is an illusion that makes the blades appear to spin in the reverse direction. The illusion is a moire pattern created by the speed of the blades in relation to the sampling speed of the human eye.

• I have to comment on this. You see the effect only in a video or film rendition of the helicopter, not in "real life". The effect is due to video and film "dividing" time into discrete fragments, or frames. The human eye doesn't do this. However, due to our persistence of vision, we see the effect when viewing the record. Just my two cents... --Janke | Talk 16:01, 7 August 2005 (UTC)

Not true. Look at a spinning tyre. It does appear to spin backwards. This is, however, not Moire interference but the stroboscopic effect

Only on film or video, or if the tyre is illuminated with a strobe lamp or other pulsed light source. With incandescent illumination and direct vision, the tyre does not appear to rotate backwards. I agree with you though that this is the stroboscopic effect, not a moiré pattern. --Srleffler 18:27, 15 March 2007 (UTC)

[edit] Bad Link

I commented out one of the links at the bottom of the page because it is broken. The site still exists, however, so I imagine that the info is still out there, but someone needs to track it down and fix the link.

[edit] Moirés in digital images of TV screens

Couple of points/questions:

• The arrow marks a scan line, but I belive the moire pattern from this is just another example of the next point.
• The remaining patterns, I believe, are not necessarily due to "interference" but that the resolution of the CCD is insufficiently small to satisfy the sampling theorem. It's not interference, but aliasing.

Cburnett 06:02, August 6, 2005 (UTC)

The camera used was 5 megapixels, so there are more than enough pixels for interference to occur. The uploaded image is reduced in size. The arrow actually marks where the first scan started - we see an image containing one partial, one full scan, interlaced. --Janke | Talk 06:11, 6 August 2005 (UTC)

Moire patterns are not a result of interference. Interference has no meaning in this context since it generally means noise, but noise doesn't cause moire patterns. 5 MP can still be insufficient to satisfy the sampling theorem.

In this case, the resolution of each pixel needs to be less than half the width of the black border around a pixel since it's the "highest frequency". Like I said, I believe it to be aliasing causing the moire patterns, not "interference" (please define this if you intend on using it further as well as in the article itself). Cburnett 04:53, August 10, 2005 (UTC)

Better now? I removed "interference", which I originally used as a general term, not a technical one. Please feel free to clarify the text further. --Janke | Talk 15:38, 11 August 2005 (UTC)

[edit] another example of bad resampling

versus

Observe how the stripes on the first and last flags appear slanted as a result. Btyner 16:14, 17 May 2006 (UTC)

[edit] Another example of a Moiré pattern

--Oden 23:34, 25 July 2006 (UTC)

[edit] Interferometric approach

I think the Interferometric Approach section is exactly wrong, but I'd welcome comment on this.

The problem is that adding the two sine waves models what would happen if you projected two sine waves onto a screen. It does not model the effect of superimposing a transparent sine-wave pattern onto another (transparent or opaque) sine-wave pattern, which is what we're talking about in the rest of this article. To model superimposition we need to multiply the sine waves and not add them.

Multiplying two sine waves close in frequency gives you the sum of two sine waves: one at the mean frequency and one at the difference frequency. It is the difference frequency that (It's exactly the same effect as heterodyne or synchronous detection in radio receivers, only in space rather than in time).

Also, you can't use the sine function directly to denote degrees of transparency, because it can take negative values. Transparency should vary from 0 to 1, which can be done by using ½(1+sin) in place of sin.

My editing skills aren't up to altering the mathematical formulae on this page but in any case I thought people should have a chance to comment first.

JoeBruno 12:05, 22 August 2006 (UTC)

Yes, you are right, and the analysis shown doesn't explain why the low-frequency envelope appears as such a prominent signal. It's easy to fix by specifying that the physical model of overlying transparent objects is multiplication of their transmittances, and that the sinues are logs of transmittances, or (negative) densities. Then, the final result, the sum is still a density, and the envelop component leads to a real intensity signal at that frequency when the log is exponentiated to get an optical intensity back. Then you avoid issues of negatives, multiplying sines, etc., and can still use an interferometric approach. Maybe I'll work on it later... Dicklyon 16:25, 22 August 2006 (UTC)

[edit] Animated image removal poll

I propose we remove from the article this visually obnoxious and distracting animation. Please response here with "*Support" or "*Oppose" followed optionally by a comment. Dicklyon 16:29, 22 August 2006 (UTC)

Hearing no objection, I'll take it out for now. If you object, say so or put it back. Dicklyon 20:30, 30 August 2006 (UTC)

[edit] pronunciation

someone should add the pronunciation of the word ... 'cause i dont know it

Sounds like as good a reason as any; in the meantime, try a dictionary. Dicklyon 23:17, 13 October 2006 (UTC)

but the dictionary wiki suggested i try here! you can see the predicament im in. and my speach is tomorrow!!

quick web search suggests "more-ay", "more-RAY", "moa-ray", "mwa-RAY", etc. Pick one. Dicklyon 20:58, 20 October 2006 (UTC)

Clearly too late now, but I'm fairly certain that this was discovered by someone who is French, so French pronunciation should be used. The last one above is correct, though the emphasis is wrong. Moiré = mwAR-eh or mwAR-ay

[edit] Nonlinear interaction

I restored the removal of nonlinear. Moire patterns do not result when optical patterns are added linearly, as by the projection of two patterns onto one screen. They require a nonlinearity, which is how the difference frequency components can be generated when they are not present in the originals. The typical nonlinearity is an "and" or an "or" function, depending on how the patterns are combined. For example, a stack of two transparent patterns is transparent when the first is transparent AND the second is transparent. For ink on paper, a spot gets ink if either one OR the other pattern would have ink at that spot. Linear combination, pretty much be definition, does not generate new frequencies. Dicklyon 05:59, 10 January 2007 (UTC)

For completeness, I'm adding a comment here (I thought I already had) that I was the person who deleted the nonlinearity reference. I'm not yet convinced, but I will consult the reference. Thanks. Victor Engel 17:42, 10 January 2007 (UTC)

I would like to see more detail about the nonlinearity. For example, if both component images are themselves nonlinear, then of course, the combination image is likely to be nonlinear. It sounds like what's being suggested here is that if both component images are linear images and the combination is nonlinear, than moire will result. Is that about the size of it? Victor Engel 20:53, 10 January 2007 (UTC)

I'm not sure what you mean by the images themselves being nonlinear. Consider any real scene, like the original brick wall image in the article. Is it linear? Nonlinear? Does it matter? I don't think so. But if you multiply it by a grid of delta functions or sampling apertures to create samples of it, you get aliasing or moire pattern due to that nonlinear multiply operator. Viewing it through a wire mesh has the same effect, since the mesh interacts nonlinearly with the original scene, like sampling it does. But projecting the original image onto a screen, and then projecting an image of a wire mesh on the same screen will not create a moire pattern, since those images just add their intensities linearly; a nonlinear warp of that image could, however induce a moire, and it's possible that in some cases there might be enough nonlinearity in your eye to induce some weak moire; but it's still due to a nonlinear interaction of the patterns. Dicklyon 22:48, 10 January 2007 (UTC)

Interesting that you don't know what I mean by the images themselves being nonlinear since my original reason for removing "nonlinear" from the article was that it was not clear what was meant by that. It certainly didn't seem to follow from the link to the nonlinearity article. I'm still unclear whay you mean by nonlinearity as it relates to Moire. Victor Engel 04:41, 11 January 2007 (UTC)

Well, we have to go back to what it means to be linear. A function or system f(x) is linear if the response to a sum of inputs is equal to the sum of the responses to the the inputs separately. The photoreceptors in your eye are not linear, but to first order they're close enough over a range of stimuli to model them as linear in optical intensity. So if you have an optical pattern x and your eye's cones respond as f(x), and another pattern y to which you respond f(y), then if you project the sum of those patterns into your eye, you get x+y and respond as f(x+y) = f(x)+f(y). That sum of x and y that you projected into your eye is a linear combination, and your eye responds linearly, and sinusoids are the eigenfunctions of continuous-domain linear systems (see LTI system theory), so no new frequencies are generated in the process; to the extent that your eye is not really quite linear it may generate weakly some difference frequencies that you perceive as weak moire patterns. Now, take those same x and y and combine them with something other than a sum; say min(x,y) or max(x,y) or x*y. The resulting optical pattern has strong "distortion" terms, with sum and difference frequencies and such, and when you project that into your eye or a linear sensor system it will respond strongly to those frequencies that were not present in either x or y but are present in their nonlinear combination; that's how moire patterns are formed. The nonlinear articles alludes to these min, max, and times operators when it says "nonlinear systems is not subject to the principle of superposition, as linear systems are". Dicklyon 05:45, 11 January 2007 (UTC)

You call the interaction between the patterns non-linear. The description of the effect is non-linear (with its quadrates and sines), but not the interaction. You mention step funtions and sampling rates: these may be discontinuous but that does not make them non-linear in the sense that the term is commonly used nowadays in dynamics. So I say remove this adjective from the intro, and just speak of "interaction of the optical patterns". Tom Peters 23:12, 10 January 2007 (UTC)

I did not mention either step functions or sampling rates. And the point of the impulse functions or sampling apertures was not their discontinuity, but rather their effective multiplication. Consider for example a mesh of fuzzy holes, with 0 transmission in the mesh lines, 1.0 in the centers of the holes, and varying smoothly and continuously from 0 to 1 around the edge of the holes. Lay that over another pattern, or illuminate a pattern through it, and you have effectively a product, a nonlinear combination of the two patterns, which will likely give rise to a moire pattern. Try it. Then, try projecting two patterns from two overhead transparency projectors onto one screen, so the optical intensities combine linearly, and you'll see that you can't make a moire pattern that way. You can do such experiments in photoshop if you're careful and knowledgeable enough, but since by default it does operations in the nonlinearly gamma compressed space, it's not so easy to simulate linear interactions of optical patterns there. Dicklyon 05:45, 11 January 2007 (UTC)

Take a look at the animation above, or this still version that's easier to analyze. What do you see? Step way back until you can't see the lines at all any more. Do you see just a gray area with some bright stripes running across it? I do. What makes those stripes bright? If you look carefully, you can see that there are fewer black pixels in those bright rows, because where the lines land on top of each other you only get 1 black pixel instead of the 2 that you get in other rows. In the animation, the light stripes follow the places where the lines overlap each other and give less blackness than when they don't. This low-frequency pattern of light stripes in gray is not in the original fine stripe patterns--it is induced by the nonlinearity, which you can take to be min(x,y) if x and y are optical intensity, or max(x,y) if x and y are an amount of ink, or x*y if x and y are 0 for black and 1 for white. But there's no way that a combination like x+y would generate such a pattern, because when you'd stand back far enough to blur it out there'd be nothing left but the sum of the average gray values of x and y. Get it? Dicklyon 05:55, 11 January 2007 (UTC)

Here are some more refs: [1] [2]. They both indicate that if you combine patterns nonlinearly you get a strong moire, and they also concede that if you combine them linearly there is still a weak effect due to perceptual effects; this is still a nonlinear interaction, only it's in your eye, as I said before, and it usually won't be enough to notice.

My little brother once did a project on moire that got written up in Scientific American's amateur scientist column, circa 1970, in which he photographed white 3D shapes through a grid of strings, and also illuminated through the strings, so the camera saw the nonlinear occlusion by strings of shadows of strings on the object, the result being moire fringes that traced out contours of the object. This is sort of like what came to be known as "structured light", a technique invented by Peter Will at IBM about the same time, iirc, to give machine vision cameras a way to see 3D structure. If we could find that old article, it might have an explanation worth quoting. Or maybe some of the old Edmund Scientific moire pattern kits have a good explanation. Dicklyon 06:11, 11 January 2007 (UTC)

Here's a PDF of a paper that analyzes the heck out of moire patterns caused by "superposition". He doesn't use the term nonlinear, but models reflectance or transmittance as numbers from 0 to 1 and "Since the superposition of black and any other shade always gives black, this suggests a multiplicative model for the superposition of monochromatic images." The multiplicative model is nonlinear, and an additive (linear) model in his Fourier approach would lead to no moire at all, so it pretty much supports the point without saying so. Another one I looked at talked about "intersection" of the patterns (I guess me means a logical AND function, again highly nonlinear). Dicklyon 06:38, 11 January 2007 (UTC)

[edit] Merge?

Someone has created the article Line moiré, which contains material that overlaps with this article. Perhaps they should be merged. On the other hand, that new article may be original research, as the references and external links are all to unpublished or self-published work by the same editor who created the article. Any merger should be done with care.--Srleffler 20:17, 12 March 2007 (UTC)

It's self-published, so definitely WP:OR. We should merge it here only if/when it gets published. On the other hand, the same material, maybe in less detail, can be found in other sources, so maybe someone wants to write a section based on w what can be found easily in online books, etc. The other article needs to be deleted. Dicklyon 16:53, 14 March 2007 (UTC)

This article is focuses on optical speedup offered by line moiré patterns (i.e. an accelerated fast movement of moiré bands when moving one of the layers). It presents a new simplified set of equations for achieving any desired optical speedup factor with curved line moiré patterns. The article should be further extended to present also rotational movements achieved with circular patterns. Except grid and line moiré patterns, there are also well known Glass patterns comprising random lines or dots, namely random line moiré and random dot moiré patterns. All these superimposition patterns have different behaviours and often require different mathematical approaches. These varieties should be taken into consideration when deciding whether a single article for moiré in general is sufficient or dedicating separate articles for moiré (in general), line moiré, micro-shape moiré (magnification effect of microscopic shapes, sometimes called band moiré), random dot Glass patterns [example], and random line Glass patterns [example] should be considered. Gabrielyan 17:59, 15 March 2007

You say that the article presents a new set of equations. This is precisely the problem. Wikipedia, by policy does not publish anything new. New research results must appear in a reliable (not self-published) publication before they can be presented here. The only references presented at line moiré are your self-published paper on ArXive, and your own websites. This is not sufficient. The best resolution of this would be for you to remove from the article everything that is your own original research until your paper is published in a journal. If that is the entire article, we can delete the article until the research is published. If the article contains some material that has been published, the article could be cut back to that material for now.--Srleffler 18:18, 15 March 2007 (UTC)

At this moment, the article contains only the portion of our research which should be considered as introductory and publicly known material. The purpose of such article was to distinguish at this moment line moiré as an autonomous part of the general phenomenon of moiré patterns (as it should be done also for the cases of random dot patterns, random line patterns, and micro-shape band moiré patterns). I suggest adding corresponding references... Gabrielyan

I agree it's probably publicly known; I've know about it for decades, possibly from some booklets from Edmund Scientific who used to sell moire kits (maybe still do). But since you wrote it, it would be best if you would find and add the references. Referring to your own work here is some combination of WP:COI and WP:OR, so not right. Dicklyon 23:49, 15 March 2007 (UTC)

I see that someone already improved the introduction of the article and made it more clear. I will take care of the references. Gabrielyan 09:41, 16 March 2007 (UTC)

The references are added Gabrielyan 20:16, 19 March 2007 (UTC)

Thanks. Proper referencing is a lot of work, but well worth it. Wikipedia policies aside, the article is much improved by having good references to the literature. By the way, I replaced many of your calls to {{cite book}} with {{cite journal}} or {{cite paper}}. Cite book is only for books. Cite journal is for papers and articles in periodical publications such as scientific journals or magazines. Cite paper is kind of a catch-all template for papers not published in a regular periodical. It's good for unpublished work, ArXive papers, and also for theses and the like.--Srleffler 20:47, 19 March 2007 (UTC)