Talk:Coherence (physics)/Archive 1

Archive 1

Snakes, etc.

There is a problem with the pictures in this article, as has been noted. I'm not a real expert in this area, but I'm trying to figure out a better way to present this. As mentioned above, the diagram showing "incoherent" light is not really correct. If the phase relationship between those waves were to remain constant with time, then they would be coherent, as the interference pattern would not change. What we need is a second snapshot at a later time showing a different phase relationship, which would then demonstrate incoherence.

Also, diagrams somehow demonstrating spatial coherence would be good. Gwimpey 00:59, 14 May 2005 (UTC)

By definition, if the phase difference between two monochromatic waves varies with time, they have different frequencies (note that the definition of (angular) frequency is the rate of change of phase with time). So the only incoherent example is the third figure where the wavelengths are different. If the waves are not monochromatic they must each have a different range of frequencies if the waveforms are to vary in a different way with time. I have added some text to explain this.

So by definition, two waves of exactly the same frequency, travelling in exactly the same direction are always fully coherent, regardless of the phase difference between the waves (as shown in the second diagram).

Rnt20 14:22, 23 May 2005 (UTC)

polarization

The Poincare sphere link does not explain its application to polarization. Does the sphere represent the possible combinations of linear and circular polarization, as well as the degree of polarization? Did Poincare have more than one sphere named for him? David R. Ingham 21:24, 9 March 2006 (UTC)

Your right. There must be two Poincare spheres although it appears they are abstractly related. Yes, a vector in the Poincare sphere represents any combination of linear circular polarization as well the degree of polarization. I'll change the link to something more appropriate.--J S Lundeen 16:04, 10 March 2006 (UTC)

Figures

The figures don't display properly!!! 85.101.113.87 (talk) 21:46, 19 April 2006 (UTC)

Definition

I´ll try later to read all the previous comments. Anyway, the definition of coherence (the first line of the article) should not be based on interference considering it should be able to explain such phenomenon. And reading the interference article one finds that in the first sentences, it is kind of defined based on the concept of coherence, making the definitions circular and thus unsatisfactory. The article is quite confusing.--Wikiwert 04:36, 18 August 2007 (UTC)

Figure 10 is quite wrong

Take a look at figure 10 in the article. The different colors are supposed to represent different frequencies, but they all have the same period! (And for some reason different amplitudes...) This would be extremely confusing to a new student. In general, I believe all of the figures need some work. I agree with the previous comments about the misleading nature of the "squiggly snakes". If only I had the time to fix it myself... —Preceding unsigned comment added by 134.134.136.3 (talk) 01:32, 6 March 2008 (UTC)

The period is slightly different (at the center they are all in phase, but at the end not, or for another way to see it, you can count the maxima), and probably it is the correct superposition for the given pulse. But I agree that it is not very didactic: by shortening the pulse one could get frequencies that are not so similar to one another. --Danh (talk) 22:20, 6 March 2008 (UTC)

Definition

Should we specify that coherence should not be considered as approaching of the state to the coherent state? dima (talk) 02:12, 22 April 2008 (UTC)

State?

Coherence is the property of wave-like states that enables them to exhibit interference.

I think that sentence may make more sense to a physicist than to a layperson. For me, the big problem is "wave-like states". I understand that some thing in physics are "wave-like", but why "state"? What is a "state" in this context? Do you mean "phenomenon"? That last word may seem imprecise to the physicist, but I think it conveys a more coherent (no pun intended) picture to the layperson. --Isaac R (talk) 16:54, 2 June 2008 (UTC)

State is indeed used to say something like "phenomenon" and is very general (definition 6 of State (physics) is the nearest one). I agree that in the first sentence it should be replaced with something more understandable (even for a physicist it is not immediately clear). Does somebody have a word that sounds better than "phenomena" here?--Danh (talk) 09:08, 4 June 2008 (UTC)

How about "objects" or "entities"? Or instead of "wave-like states" just "waves"?--J S Lundeen (talk) 18:24, 4 June 2008 (UTC)

I changed the lead to simply use "waves", as suggested. (and made the lead shorter) MrZap (talk) 22:52, 6 June 2008 (UTC)

I rewrote the lead since it was too specific and started to contain inaccuracies and gave a separate section to the last paragraph. --Danh (talk) 19:29, 9 June 2008 (UTC)

Perfect coherent waves

The article doesn't explain in which case two waves are considered coherent and in which case not. For example, imagine two waves of the same frequency, just one billionth of a nanometer apart. are these waves already considered incoherent? I guess there is no laser in the world that exact to produce truly coherent waves of light. Thus, is there a percentage needed for phase relation to consider waves coherent? Thanks, --Abdull 16:36, 30 March 2005 (UTC)

By "billionth of a nanometer apart," what do you mean? Since two waves always add together to create a single wave that's weaker or stronger than the originals, in what way can they be "apart?" (If you're talking about the present misleading diagrams, then perhaps you've fallen for the misconception that light can behave like wiggling snakes with a space between the adjacent "snakes." Light acts nothing like this... yet these "wiggling snakes" diagrams appear widely in science articles and textbooks.) --Wjbeaty 05:59, 31 March 2005 (UTC)

It seems to me that some parts of the article make coherence look like a binary (yes/no) measurement. I believe it should be more of a continuum, where you can go continuously from coherent to incoherent. But coherence also depends on the time and/or spatial scale being considered. White light through the two arms of a Michelson interferometer can interfere completely in the end if the two arms are exactly the same length. Coherence will decrease continuously as the arm lengths are changed. Since coherence is normally measures over a finite time and/or space, the amount of coherence depends on the time scale or spatial scale of interest. It seems to me that the article doesn't explain those as well as it should. Gah4 (talk) 11:50, 11 May 2009 (UTC)

Optics

There is a statement "However, in optics one cannot measure the electric field directly as it oscillates much faster than any detector’s time resolution" that seems not quite true. Some years ago, it became possible to do frequency counting at optical frequencies, by measuring the difference frequency between two laser. That is, to get a voltage proportional to the difference between the electric fields of two light beams. Since that is similar to the way many 'direct' methods work, it seems that the statement isn't quite true. The ability to do optical frequency counting meant that time measurements could be done much with much more precision than previously. Without a corresponding change in the ability to measure distance, distance measurement was defined in terms of time and a defined (299792458m/s) speed of light. Gah4 (talk) 23:30, 10 August 2009 (UTC)

Things this article doesn't explain

Just imagine the sort of questions that a high school student might ask. How can a small slit in front of a light source produce coherence? Consider the source behind the slit. Each atom in the light source is working away independently and so photons arrive at the slit with every possible phase. How does the slit put them in phase? Somehow the photons get in step. What is the process? The width of the slit has to comparable with the wavelength of light. If so, how wide? Is the gap in the middle still big enough for most light to get through unaffected?

Consider the colours in a film of gasoline on water. One photon that was in phase with another interfers with another after reflecting off a different surface. This should only work if a significant proportion of the photons were in phase. How can the sun be considered as a coherent source in this instance? No coherence can occurs because the photons are emitted thousands of miles apart and so they will arrive with totally random phases. I guess the coloured bands are produced because the interference happens “within” the same photon ie it takes both paths.

The problem with many Wikipedia articles on physics is that they would put off any high school student who just wanted a clear explanation. It does not have to be over-simplified. Mathematics is all very well for the purists, but should always be kept to the end of an article, long after the hand-waving explanations. Please just think about the audience when you are writing. JMcC 10:03, 24 May 2006 (UTC)

To actual answer your nice simple question requires more quantum mechanics than I can get into here, and more than is usually taught in high school. For both the slit and gasoline, it is not different photons interfering with each other, but each photon interfering with itself. It still works (statistically) if only one photon goes through the slit or gasoline at a time. Now, say you take a light beam and split it with a half silvered mirror into two beams. Then using more mirrors put the two beams back together again. Even with white light, if you get the lengths equal you can get interference between the two beams. Again, it is not different photons interfering, but each photon interfering with itself. (You are not supposed to ask how one photon can go down two paths.) So, even white light has a coherence time and coherence length! On the other hand, I don't believe it should be up to this article to explain the quantum physics needed. Gah4 (talk) 23:44, 10 August 2009 (UTC)

Monochromatic etc.

I think monochromatic means "single frequency". Also I think the concepts of coherence or incoherence only apply to time harmonic waves. Waves with different frequencies can not be coherent, since they can not keep constant phase relationships with one another, thus no constructive or destructive interferences are possible . Monochromatic waves (waves with the same frequency) may be incoherent, provided the phases of the waves are random with each other, like the light from a hot tungsten filament. Please correct me if I am wrong.

Speckle pattern from a binary (double star) taken with the Nordic Optical Telescope. Note how each star has broken up into a pattern of speckles in a Rayleigh distribution.

The first point is a common misconception between temporal coherence (how monochromatic a light is) and the coherence between two or more signals (which is what is most commonly measured with optical instruments). The coherence between two signals is just a measure of how correlated they are to each other, and has nothing to do with their shape (it has nothing to do with whether the signals are sine waves, square waves, or any other shaped wave, like random noise). This is how it is possible for astronomical interferometers to measure the coherence of starlight, without requiring the starlight to consist of a sine wave (and in fact this is true of any imaging system -- the human eye works because white light combines coherently on the retina after passing through the lens, and this works even though the light source (the sun) does not produce pure sine waves -- if this wasn't true we would see uniform illumination in all directions, like a person with a cornea infection). A nice example of coherence is the "speckle pattern" that you get when observing white light from a star through the atmosphere (see image at right). This pattern is a coherence effect (it is a rayleigh speckle pattern) which is more commonly seen when you scatter laser light onto a surface (e.g. the reflection of a laser pointer), but in this case it is produced by many rays of white light combining coherently (to form what we call an image, in this case a speckled image of the star).

Tungsten lamps produce broad-band (non-monochromatic) light. You can filter this light to select a narrow range of wavelengths, and then the light you get will be exactly identical to the light you get from a (faint) laser having the same range of wavelengths (and the same spatial coherence -- i.e. coming from the same range of directions). There is no fundamental difference between the light from a tungsten filament and the light from a laser, apart from the range of frequencies and the angular size of the source typically being different (unless you use filters on the tungsten light to make the range of frequencies and angles the same). The biggest benefit of lasers is that they can be much brighter (and more convenient) than a temporally-coherent light source made using filters like Dennis Gabor's one described in the last paragraph of the article.

If a filtered filament light bulb has only a small range of frequencies (so it is almost, but not perfectly monochromatic), what you get out is a sine wave which varies randomly in phase (and amplitude) with time. The reverse is also true -- if you have a sine wave which varies randomly in phase with time, then by definition it is not monochromatic because a rate of change of phase with time is the same thing as a frequency shift (this is how frequency is actually defined!).

I hope this is helpful. Rnt20 12:02, 24 May 2005 (UTC)

This surely helps, thanks a lot. I understand that the tungsten lights are not monochromatic, what i said was wrong. I read the article and i want to make sure i understand it right. So coherence is a measure of how two signal sources are correlated and it has nothing to do with the shape of the waveform being sinusoidal or not, what do u mean by the word correlated? is it a measure of how similar the two waveforms are to each other, as the term correlation is usually defined? About the temporal coherence, in the article you say that the coherence time of a source is inversely proportional to its bandwidth, i am wondering if the temporal coherence is a different way to say the time duration of the signal or the pulse; It seems to me that u are saying wave sources with the same frequency are always coherent, but what about the phases of these different wave sources related to each other? If I have a filtered tungsten filament which gives out a single frequency light or light has only a small range of frequencies as u wrote above, then do u think the lights from different parts of the tungsten line segment will all be in phase with each other? what about the lights from a thousand such filtered light bulbs? I know nothing about optics or speckle patterns, but i know if a plane wave pass through a random medium, the wave front will develop wiggles and if i have a finite receiving aperture and if i scan the receiver over a plane i will get signal variations, i do a raster scan and i will get a spotty image. is that what u call speckle pattern?

Actually, I wasn't quite right (or not quite clear actually). I think the simplest explanation is probably something like:

If you measure the electromagnetic signal at two places (e.g. with two radio telescopes), and the signals are exactly identical then they are perfectly correlated, and are thus spatially coherent. With radio telescopes astronomers multiply the electric field measured at one telescope with the field measured at another, and then sum the result as a function of time, in a device unimaginatively called a correlator (see VLBI). If there is perfect correlation between the two signals, then the signals are coherent (and so there is spatial coherence between the two points in space). Note again that neither of these signals is necessarily a sine wave (although radio telescopes are normally restricted to a certain bandpass, perhaps covering a few GHz of frequency). Now the signals don't have to be correlated -- for example they could be anti-correlated (one being the opposite of the other) and they would still be coherent. The wave field used to describe electromagnetic waves is usually described in terms of complex numbers, so two anti-correlated signals are 180 degrees out of phase. In fact any other constant phase rotation is allowable, and the signals would still be coherent (actually this is a bit of a simplification, but it's sort-of correct). This is exactly how radio interferometry works for astronomy (again, see VLBI) -- how coherent the signals from the two telescopes are is called the fringe "visibility amplitude", and the average phase offset is called the "visibility phase" (e.g. the visibility phase would be 180 degrees if the signals were anti-correlated, or opposites of each other). Astronomical optical interferometry is the same, but it isn't possible to multiply the optical signals together, so a clever set of intensity measurements is done with different phase shifts, resulting in the same answer as if you'd multiplied the signals (see e.g. http://www.geocities.com/CapeCanaveral/2309/page2.html ).

If you have sine waves at both locations with the same wavelength, then they will be spatially coherent (because they look the same). If there is even the slightest difference in frequency (or any random changes in phase with time) then they won't be coherent with each other.

Now the other case of interest is when you measure the electromagnetic signal twice at the same place, but at two different times. Then you are measuring temporal coherence instead of spatial coherence, but otherwise it is all the same. Now the most common temporally coherent light is monochromatic light (or as monochromatic as you can make it) -- there you have a sine wave which looks the same at one time as it does at a later time, so it is temporally coherent. If the light is not quite monochromatic (the sine wave is changing gradually with time) then the coherence decreases when you reach a time delay corresponding to the "coherence time" of the source, which is inversely proportional to the bandpass (range of wavelengths). Of course a source doesn't have to be a sine wave to be temporally coherent, but it has to be some kind of repeating pattern, and a sine wave is the most obvious (and practically realisable) example. Temporal coherence of light sources is measured using a Michelson, or Fourier transform spectrometer (see http://scienceworld.wolfram.com/physics/FourierTransformSpectrometer.html). This device simply splits a light beam into two, delays one half by a variable length of time, and the recombines the light back into one beam. This allows you to directly measure the temporal coherence for any chosen time delay. This is normally done at a range of time delays, and then the plot of coherence vs time delay is Fourier transformed, which gives a spectrum of the light source (hence the name of this type of instrument).

--J S Lundeen 05:02, 22 January 2006 (UTC)

Non-linear optics pretty much does multiply optical signals. Gah4 (talk) 22:55, 15 October 2009 (UTC)

Recent change

Somebody has inserted an in-line comment:

<<The following is aimed at correcting the previous entry. It still needs reorganization. This was done to indicate what was corrected.>>

It would be better not to have such comments visible to the general readership. Could somebody with time and familiarity with the subject try to smooth over the reorganization issues? P0M (talk) 15:59, 21 April 2012 (UTC)

I took out the comments and the incorrect section (as I interpreted James R. Johnston). Some more smoothing and ref formatting is still required. --Danh (talk) 11:43, 23 April 2012 (UTC)

Polarization coherence

Dear all, I'm trying to figure out what the article means by the term "Polarization coherence". There's an entire section with that title, but the term itself is not explained or defined anywhere. Could somebody shed some light on this, or should that section (along with its title) be revised? --CoherenToweri (talk) 12:52, 14 September 2012 (UTC)

not a good topic?

the quantum coherence section includes the claim that a somewhat vague "this" isn't "a good topic for a description of quantum coherence". the fact that it is in such a description seems to imply that it is, at once, both a good and a bad topic for it. why, then, can't the cat have it both ways? k kisses 21:48, 11 October 2012 (UTC)

Untitled miscellany

Just a note on the comment about "the possibilities of macroscopic quantum coherence as illustrated by Schrödinger's cat thought experiment". Consider the wikipedia article about Schrödinger's cat: "Schrödinger did not wish to promote the idea of dead-and-alive cats as a serious possibility; quite the reverse". I suggest the entire line about the possibility of macroscopic quantum coherence be removed, unless a more appropriate citation discussing actual possibilities can be provided to replace the reference to Schrödinger's cat, which is so frequently misinterpreted by the layperson.65.110.153.151 (talk) 22:29, 20 September 2009 (UTC)

Just a comment that temporal coherence is not necessarily an indicator of bandwidth as laser can have a narrow band width and still have (in what might be called "sputtering") a short temporal coherence length. —Preceding unsigned comment added by 67.169.126.181 (talk) 21:11, 5 June 2008 (UTC)

Much of the page looks good, but I would like to see some description of the statistical nature of coherence. I think that helps resolve the spatial/temporal part of the discussion. Also, the perfect monochromatic wave with perfect coherence idea makes it harder to understand the coherence of real sources. Coherence length and coherence time require some amount of discussion of the statistical nature of coherence. Gah4 (talk) 21:15, 6 October 2008 (UTC)

The main problem with this article is that it is incoherent! Rnt20 10:39, 14 June 2005 (UTC)

I have begun a significant rewrite of this article along with new figures. My plan is to start with the broadest possible introduction to coherence. Then give examples of where it can be used. Then examples of types of coherence: temporal, spatial and polarization. Finally, I will end with quantum coherence. Over the coming weeks I will incorporate text from the current page and write the above sections. For now, the article is at http://en.wikipedia.org/wiki/User:J_S_Lundeen/Jeff%27s_Sandbox J S Lundeen 03:42, 3 July 2005 (UTC)

Okay, I have brought over the version I was constructing. When considering the changes please remember that coherence is a broad subject and not just applicable to light. --J S Lundeen 05:02, 22 January 2006 (UTC)

Keep coherence and decoherence separate. Quantum coherence is something beginners might want to learn about. Decoherence is a more advanced topic. — Preceding unsigned comment added by 181.194.114.186 (talk) 17:36, 17 November 2013 (UTC)

Quantum coherence - function meets object

This is funny: "Each electron's wave-function goes through both slits ...". How can a function (pure mathematics) go tough a slit (physical object)? Can someone fix this mess? --91.42.106.196 (talk) 11:23, 4 February 2014 (UTC)

If you want to get into wave functions, you have to get pretty far into quantum mechanics. There is a Feynman quote, "I think I can safely say that nobody understands quantum mechanics." Gah4 (talk) 23:39, 27 April 2015 (UTC)

It is definitely funny business. The trouble is that nobody knows what to call whatever emerges from the double slits. Photons are not being hacked in two like a piece of cheese being cut by a wire. A photon of a certain energy emerges from a laser and a photon of the same energy shows up on the detection screen. In between, nobody knows. Lately people involved in quantum cryptography have started talking about "sharp photons" that one is pretty sure have a single location (fuzzy though quantum factors may make that location be) and "unsharp photons" that seem to be going down both paths of an interferometer, through both slits of a double-slit diaphragm, etc. With a photon it seems more acceptable to ordinary intuition to see a wave going through two slits, just as a water wave could propagate through two gaps in a sea wall. But saying that an electron "goes both ways" through a double-slit device seems to create more cognitive dissonance. An electron has a wave aspect as well as a particle aspect, so it would seem as natural for the wave to propagate through both slits, but then what happens to the mass of the electron?

[The event-probability interpretation] of Gunn Quznetsov says that the electron does not exist in between "events" wherein there is an interaction with the environment, so by this account no thing goes anywhere. Only probability or maybe potentiality goes through the dual slits. I mentioned this idea to a physicist friend who said, basically, "Well, yes, this is another interpretation." When you take the interpretations away all you have left is the math. Math is an abstract model of the world, no? Models are not the real thing no mater whether they are made with balsa wood or with numbers in the mind.

Nobody that I know of has ever been able to "fix this mess," at least not without creating another mess. Sorry. P0M (talk) 23:43, 4 February 2014 (UTC)

There is a quote, for which I have never been able to find the source, paraphrasing as well as I can: "The worst pseudoscience foisted on students as actual science is the Copenhagen interpretation of quantum mechanics." There is no good explanation, but people try anyway. More and more experiments are showing that QM is right, and people (and general relativity) are wrong. Uncertainty explains the mass question above. When measured over a sufficiently small time, there is an energy (and so mass) uncertainty. That turns out to be exactly right to explain the two slit problem. Gah4 (talk) 23:39, 27 April 2015 (UTC)

References

Perfectly

I added 'perfectly' to the first sentence, which goes along with 'ideal' in the second. Seems to me a big problem with thinking about coherence is that real cases are not ideal or perfect, but are still coherent (enough). The light from diode lasers in CD players has a very short coherence length, for a laser, but that is fine for that application. It is easier to discuss when the answer is yes or no, not so easy when it is maybe. Nothing is perfectly (all time and all space) coherent. Gah4 (talk) 19:07, 9 May 2015 (UTC)

Comments

The present illustrations need work, since they reinforce a classic set of misconceptions. In truth, light waves do not act like narrow wiggling snakes. The "wiggling snakes" are actually e-field graphs, with the side-to-side motion being the graph of the strength of the e-field ...and not a transverse motion! And since light waves don't act like serrated threads as depicted, light waves cannot mesh together side by side as the illustrations suggest. The GRAPH of the e-field strength is not a light wave: we confuse the graph of e-field strength for a physical transverse motion.

A visual description of coherent versus incoherent light can be illustrated with two-dimensional fluid waves (e.g. photos of water wave patterns produced in ripple tanks.) To explain coherence/incoherence, we really should be using sphere waves or at least plane waves. Wiggly lines only illustrate waves on a rope, and to be accurate we'd have to compare two waves on ONE rope (or better: two plane waves on one water surface.) The present diagrams are essentially comparing waves found on several different ropes. I'll try to come up with some illustrations, watch [1] --Wjbeaty 02:03, 23 March 2005 (UTC)

I agree, it's better to have no pictures than misleading ones. And why should the waves in the second pictures be incoherent? They have all the same frequency and the difference of their phases is constant, so they can interfere. --

That's an issue I'm not clear on. Suppose we sequentially reflect some laser light from several frosted screens. Does an "incoherent wave" result? We could call the resulting wave "incoherent" on the grounds that it's not a plane wave or a sphere wave. Such a wave does not create line gratings or bullseye-shaped zoneplates when interfered, and it's useless in most applications requiring coherent light. Or... we could insist that the diffused wave is "coherent" because the phase difference between any two sampled points in the wave is not changing with time. --Wjbeaty 02:03, 23 March 2005 (UTC)

I agree. The figure captions were simply wrong -- as mentioned before, several monchromatic waves of exactly the same frequency are always coherent even if there are phase differences (as in the second diagram). The text specifically says that if you delay a truly monochromatic source (change its phase) it is still coherent with the original wave -- see temporal coherence paragraph, which contradicted the second figure caption completely (the caption said the opposite -- that if the phases are different, waves of the same frequency are incoherent). I have changed the captions, because they simply encouraged common misconceptions. I also added some text to emphasize that coherence and monochromaticity are not the same thing -- Young didn't have lasers and yet he produced coherent light beams (from non-monochromatic sunlight). And as far as the frosted screens are concerned, you are talking about reducing the spatial coherence by making the light come from multiple directions -- this doesn't apply to waves on a string which are all moving in exactly the same direction. Rnt20 14:14, 23 May 2005 (UTC)

I disagree. The pictures were a little misleading but the new captions are pointless. You might as well remove the pictures as they stand. I think you guys are missing a few things in your discussion. There are two main types of coherence, spatial and temporal. You seem to be concentrating on spatial coherence as tested in a Young's double-slit and used in Astronomy. But temporal coherence is the important quantity in other interfometers like the Mach-Zehnder. A truly monocromatic source is temporally coherent for all delays but doesn't need to have any spatial coherence at all. The opposite is also true which is why Young's experiment worked with sunlight. So in summary, the pictures were attempting to show temporal incoherence as opposed to spatial incoherence. For temporal coherence, the depiction of light as a squiggly line is sufficient. See degree of coherence for a more mathematical description of both. Still, the article does need some help. J S Lundeen 20:30, 3 June 2005 (UTC)

Indeed this is right. Monochromatic light is the most common example of highly temporally-coherent light, and would make a good example of this. Both of the first two figures show monochromatic light, so one could be removed. The text and ideas on this talk page need to be turned into a new article on coherence -- there are a lot of ideas further down. Rnt20 08:11, 4 June 2005 (UTC)

Yes, some of those ideas should be incorporated. But I think really, the article should be rewritten with a broader perspective of coherence. Coherence is a very fundamental concept and is used in acoustics, electrical engineering and especially in quantum physics. The article should begin with the broadest clearest introduction of coherence and what areas it is used in. Then the article should discuss specific examples like temporal and spatial coherence. It is only in this broader perspective that one can answer questions like "how close do two frequencies have to be before they are incoherent?" and apply the answer to every type of coherence. I have started writing something but it will take a while to finish. J S Lundeen 21:33, 6 June 2005 (UTC)

Other than a few picky details, I am surprised how good the article is.

I am wanting to work in the speckled look of lasers and some LEDs, somehow. That is perhaps the most often seen coherence. Some car tail lights have LEDs that are too uniform in composition, so they look speckley like supermarket lasers. David R. Ingham 20:59, 9 March 2006 (UTC)

The present illustrations need work, since they reinforce a classic set of misconceptions. In truth, light waves do not act like narrow wiggling snakes.

I fundamentally disagree with the objection expressed here. It is often convenient to visualize sections of vector bundles by magically projecting (rotating, in fact) slices of them into physical space, even though they don't live there and the geometric object that one visualizes is not the actual graph of the section. The reason I do this is because there is not enough space in 3 dimensions to visualize a higher-dimensional graph. Nonetheless, there is well-defined way to go back and forth between the visualized wiggle in R^3 and (portions of) the true graph of the E-field in R^6. You just un-rotate. But not using visualization abilities, rather using logic and formulas. 89.217.15.201 (talk) 14:36, 25 May 2015 (UTC)

Missing or vague definition

I'm bothered by the fact that "coherence" is not given a real definition in this article, only motivated with an incomplete definition.

(1) From the article:

The coherence of two waves expresses how well correlated the waves are as quantified by the cross-correlation function. The cross-correlation quantifies the ability to predict the phase of the second wave by knowing the phase of the first. As an example, consider two waves perfectly correlated for all times. At any time, phase difference will be constant. If, when combined, they exhibit perfect constructive interference, perfect destructive interference, or something in-between but with constant phase difference, then it follows that they are perfectly coherent.

The article states that coherence of wave u and wave v is defined via the cross-correlation between u and v.

I understand this to mean that u and v are random waves u = u(t,ω) and v = v(t,ω), where ω belongs to a probability space, and the cross-correlation at a given time t is

⟨u(t),v(t)⟩ = ∫u(t,ω) v(t,ω) dω.

It's also reasonable to assume that (u,v) is stationary (that is, u and v are jointly stationary), so that the cross-correlation is independent of t. In fact, this assumption is made in a slightly weaker form in the article on cross-correlation. You have to look down in the section entitled "Time-series analysis" — the defintion I've given here appears there, but is missing from the introduction.

This much I can reconstruct by dead reckoning, even though the mathematical definition is missing from this article. Perhaps someone would like to add the above definition to the current article under "Mathematical definition", if it is correct.

The problem I have is the following.

If the two waves have a phase difference of pi/2, then the cross correlation is 0. If their phase difference is pi, the cross-correlation is -1 (after normalizing by the intensity). If the phase difference is other number, the cross-correlation can be any number in between.

So I'm puzzled by the definition of "coherence". It isn't just given by the cross-correlation at some time t. In fact, if you want to use the cross-correlation to define it, you would have to introduce a delay τ, and then fish around with various choices of τ until you determine whether you can get the value of ⟨u(t),v(t+τ)⟩ / (⟨u^2⟩^(1/2) ⟨ v^2⟩^(1/2)) to come up to 1?

Is there a mathematical definition of "coherence" that performs this optimization over τ? Or are we just left with the verbal construct "the coherence is quantified by the cross-correlation", and the actual determination of coherence is done by gut feeling?

(2) Note that I am interpreting u and v as real-valued E-fields above, since the complex amplitude of E is not directly accessible. Indeed, the complex amplitude relies on a certain amount of integration, time-delay and/or Fourier transform of E even to be defined. Or do we simply assume that the complex amplitude is meant when we do the covariance ⟨uv⟩, and it is really a Hermitian inner product ⟨u,v⟩ = ∫ u(t,ω) bar(v(t,ω)) dω ? This would solve the τ-matching problem in the previous paragraph. If this approach is correct, the reference to the article cross-correlation is not adequate for the definitions in the current article, as there's no mention of "Hermitian" covariances in that article.

(3) A related difficulty is the repeated use (throughout the article) of "correlation" in an ambiguous sense.

As we know, correlation has two meanings: (a) a statistical correlation or covariance (a quadratic moment) (b) any kind of statistical dependence.

The "any statistical dependence" meaning is used informally all the time in the physics literature, but it's not really a good basis for a definition in the case at hand. "Coherence" really refers only to a covariance (a quadratic moment), even if the delay τ still has to be selected by the user. In the current article, we should really be using only the "covariance" definition. Yet we have sentences like this, where it appears we're using both meanings at once:

Spatial coherence describes the correlation (or predictable relationship) between waves at different points in space.

We seem to be using the two-point covariance definition when we talk of "the correlation between waves at different points in space", yet in the same breath we talk about "predictable relationship", which seems to require more information than just a 2-point correlation.

89.217.15.201 (talk) 17:32, 25 May 2015 (UTC)

You really should get a wikipedia account, but otherwise ... yes coherence is fuzzy. If you want to make a hologram, you need a light source with a coherence length larger than the size of the object. So, people say "coherent" when the coherence length is large enough, and "incoherent" when it isn't. It would be better to label each light source with a coherence length (and, after dividing by c, the coherence time), but that is too inconvenient. So, we end up with the fuzzy definition you see above. Gah4 (talk) 09:20, 27 May 2015 (UTC)

Lateral coherence

Having not thought about this in detail for some time, I started to read my Hecht "Optics" book. There is an important distinction between lateral spatial coherence and longitudinal spatial coherence. Lateral coherence (or lack thereof) comes from an extended source, and the difference in phase, even when the frequency is (almost) the same. This should also connect to spatial filtering, which is needed for good lateral coherence, especially in holography. Gah4 (talk) 09:45, 27 May 2015 (UTC)

Cohorence vs monochromatic light

This source says that coherent light has all waves in phase: http://www.differencebetween.com/difference-between-monochromatic-light-and-vs-coherent-light/

So what now? If the waves just need to have a stable phase relation, let's say phase shifted by 30°, as written in this article, then any monochromatic light would be coherent!?! --Felix Tritschler (talk) 11:21, 18 November 2016 (UTC)

The source is wrong. To start, coherence isn't true/false, but a continuum. No source is pure monochromatic (single frequency), unless it exists for all time, from before the universe began, until after it ends, though sometimes it is useful to consider one. A source with a single frequency has to have constant phase shift between different parts, or different times, and so is still 100%coherent. (Coherence time and length are infinite.) But real sources have either long or short coherence length and coherence time, and are considered coherent if the length is larger than the experiment, and time is appropriately long. For holography, the coherence length needs to be greater than the dimensions of the object of the hologram. Gah4 (talk) 19:40, 18 November 2016 (UTC)

You are contradicting yourself by saying that coherence isn't "true/false, but a continuum" and at the same time say that real sources (to which lasers belong!) "have either long or short coherence length". You made no point then why a monochromatic source of any kind wouldn't produce coherent light!

Lasers have a non-infinite coherence length and time and so there is no fundamental difference between a laser and any monochromatic light source.

--192.76.172.134 (talk) 00:41, 19 November 2016 (UTC)

There are no monochromatic (delta function in frequency) sources. There are sources with very narrow frequency bandwidth. And yes, if you make the bandwidth narrow enough, the coherence length increases. I don't see why you think it is a contradiction. Gah4 (talk) 01:08, 19 November 2016 (UTC)

Well, maybe I got that sentence wrong from you. But anyways, it seems that you agree that true monochromatic light is coherent (in time)! The fact that it is difficult (but not impossible) to produce "very" monochromatic light doesn't change this fact - monochromatism is a concept and it doesn't care about its feasibility!

It really seems that even experts in the field are unsure about what coherence is - e.g. a friend of mine who works in single-molecule science,a teacher at the university and others either think that coherent light needs to be in-phase or they insist that monochromatism and coherence are two different things (but they can't explain what the difference is). This is pretty amazing since this is such a basic concept.

--Felix Tritschler (talk) 16:13, 21 November 2016 (UTC)

The sections on Temporal Coherence and Spatial Coherence explain it pretty well. In much of physics, a word or description is used when something is close enough, but not exact. One might say frictionless, if the friction was close enough to zero for the experiment being done. In much of this article, monochromatic is used with such an approximation. Gah4 (talk) 02:05, 22 November 2016 (UTC)

Well, I read these sections and I cannot see how truly monochromatic light is not coherent. If we take e.g. a highly monochromatic light source, split it, collimate it and merge it again (or just collimate the light without splitting and merging), then any two photons of the resulting beam have a stable phase relation for a certain length and thus this beam is by definition coherent for this length. It is nowhere written that there can only be 2 phase-offsets. --Felix Tritschler (talk) 13:31, 23 November 2016 (UTC)

Truly monochromatic, one frequency, must exist from t=-∞ to t=+∞. That is from the Fourier connection between spectral width and duration. But yes, with good lasers it isn't hard to get a beam with a one meter coherence length. Big enough for many experiments. You can do holography with reasonable path lengths. Gah4 (talk) 14:52, 23 November 2016 (UTC)

Sure, but I didn't mean lasers. My point, as written above was that highly monochromatic light from any source has a certain coherence length. By definition the photons need to keep a stable phase relation and that is true for any highly monochromatic non-laser light as well (if it is aligned, then also spatial coherence, in addition to temporal coherence). --Felix Tritschler (talk) 14:42, 24 November 2016 (UTC)

So what now, is it so that there can be at most two different phase offsets or one or unlimited? I'm still confused. In the latter case, as indicated above, any monochromatic light would qualify as coherent which would confuse me. ::Felix Tritschler (talk) 17:37, 5 January 2017 (UTC)

Ok, never mind, I finally got it explained by a coworker: In collimated monochromatic light that's incoherent, any two photons always keep a stable phase relation along their path - but if you look at a cross section of this light beam, there are constantly photons passing it that have completely random phase relations if you observe this cross section over time, which is not the case for coherent light! ::Felix Tritschler (talk) 15:30, 6 January 2017 (UTC)

gradually

coherence dies gradually and finally the fringes disappear they gradually disappear for convenient coherence time and/or length. For very short coherence time/length, it won't be so gradual. For very long coherence time/length, you might not ever see them disappear, before something else happens. In the case of two slits, moving the slits apart moves the fringes together, so that even with good coherence, they will eventually get close enough that you can't see them by eye. Gah4 (talk) 21:52, 18 May 2017 (UTC)

Wave shape

There seems to be an (understandable) bias in this article towards interpreting "waves" as "light waves". But that is contrary to the article title.
Given the summary-definition: "two wave sources are perfectly coherent if they have a constant phase difference and the same frequency", I propose that additionally the shape of the waves is important. For example, in the context of the formal mathematical definition, I could have a square wave and a sinusoidal wave that are of identical frequency (and constant phase difference), but different shape and hence not coherent. Just because this is not applicable to light waves doesn't mean it should never be considered.
—DIV (137.111.13.48 (talk) 01:35, 13 September 2017 (UTC))

Yes coherence applies to other waves, but it is most often used for light waves. You can generalize to other electromagnetic waves, and then to other types of waves, such as sound waves or water surface waves. As for wave shape, it is usual to consider the Fourier components, but yes other shapes could be considered. I suspect most physicists consider it natural to use the Fourier components of the source. If you had a sine and square wave, the sine could be coherent with the fundamental of the square wave, or with one of the other harmonics. This could come up in non-linear optics, where you generate a third harmonic of a (sine) light wave in a non-linear material. You might consider the coherence of the third harmonics of two different light sources. Incoherence is a natural property of most light sources. Sound waves are more naturally coherent from many sources. Which wave sources were you wondering about? Gah4 (talk) 02:01, 13 September 2017 (UTC)

This article is horrible

I'm having real difficulty reading this article, and I'm familiar with the field. It simply assumes too much and many symbols used in the presented inline equations are not defined. —Preceding unsigned comment added by 58.107.215.254 (talk) 05:29, 23 October 2007 (UTC)

I agree - horrible may be kind - too much of this is about signaling virtuosity rather than making clear explanations. An example of an explanation featuring clarity of thought can be found here: https://www.rp-photonics.com/coherence.html I understand the math - most won't - and these concepts can and should FIRST be explained clearly without the math. Once the ideas have been clearly presented, the background math can be presented. Even then - "cross spectral density" is about the most confusing way to explain how narrow the frequency bandwidth is that you can come up with. How many words does it take to say that it requires a narrow frequency but there can be phase differences?

Not only that - after showing off a bit - the simple math for coherence time and length is missing.

Then the section on spacial coherence even fails to make it clear if this is normal or perpendicular to the path of the light.. Something like - "Spatial coherence means a strong correlation featuring a fixed phase relationship between the electric fields at different locations across the beam profile." might be a good start.. Instead we have garbage. — Preceding unsigned comment added by 108.243.106.82 (talk) 22:59, 2 January 2021 (UTC)

Fourier Theorem and Coherence of Light

I think the article promotes a general misconception about the association of the coherence time of light with the spectral bandwith over the Fourier theorem:

the Fourier theorem assumes actually that all superposing waves are locked in phase: for instance, the frequency spectrum of a rectangular pulse of duration T is given by the sinc-function sin(f*T/2)/(f*T/2) where f is the (angular) frequency. The pulse is exactly reconstructed if one superposes waves (ranging continuously in frequency from -infinity to +infinity) with this amplitude, but this is obviously only possible if all the sub-waves belonging to the individual frequencies f are locked in phase somehow. If the phases of the waves are however randomly uncorrelated, they could never produce the constructive and destructice interference required to reconstitute the rectangular pulse. The point here is that for all natural light sources the phases of the individual waves *are* randomly uncorrelated as they originate from statistically independent atomic emissions (i.e. the 'continuum' of the sun for instance is actually a spectrum consisting of many blended lines). So the Fourier theorem can not be applied here to obtain the coherence time of the signal from the shape of the spectrum. The coherence time is determined physically by the atomic decay times and/or collision times that are relevant for the radiation produced.

In this sense the paragraph about 'white light' in particular is incorrect in my opinion.

Thomas

Hi Thomas

Thanks for your comments. You misunderstanding is a very common one. White light and pulsed light with the same spectral bandwidth have the same coherence time. Coherence time has nothing to do with the phase relationship between different frequencies. Light pulses can not be any shorter than their coherence time, but they can be longer. Obviously, this needs to be made clearer in the article.--J S Lundeen 10:27, 1 April 2006 (UTC)

What should be made clearer in my opinion is the fact that the Fourier theorem implies that the whole spectrum is actually phase-locked and that thus the bandwidth/coherence_time relationship can not be applied to natural light.

Anyway, is there a reference for the statement that white light has a coherence time of only 10 periods or so? Is this merely a theoretical figure based on the spectral width of white light or has it been measured? And if the latter, how does one know that the coherence time is actually not determined by the length of the individual light pulses (as given by the individual atomic emissions) rather than the combined bandwidth. I found actually a reference where the coherence length of white light has been measured to be about 200 micrometers, which is subtantially more than the generally quoted value of a few micrometers (see http://www.iop.org/EJ/abstract/0143-0807/24/4/363 ).

Thomas

Hi Thomas. You are still misunderstanding this. The coherence time has NOTHING to do with the phase between different frequencies. It can always be applied (including natural light). The bandwidth-coherence time relationship involves the fourier transform of the "power spectrum" (the absolute squared of the E-field spectrum). The power spectrum is always real and positive - there is no phase in it. Let me reiterate - the coherence time only tells you about the spectrum of the light it does not tell you about its time-duration. As for the white-light coherence - I have measured it personally - as have many physics undergrads. The reference you give measures the coherence time of white light transmitted through a filter - in other words, after the filter it is no longer white, it has a smaller bandwidth and thus should have a longer coherence time. Time-duration is related to second-order coherence as measured in an autocorrelator.--J S Lundeen 18:31, 4 April 2006 (UTC)

I find it somewhat paradoxical when you are saying that the coherence time has nothing to do with the phase, when in fact coherence time is defined as the time over which a a predictable phase relationship is maintained.

Consider for instance a light source which emits individual light pulses of a number of different frequencies such that the pulses do not overlap at all but arrive at the measuring instrument one by one. Let's assume each of these pulses has a length of let's say 10^-8 sec. So even if the frequencies span the whole of the visible spectrum, it would be then clearly incorrect to say that the coherence time is 10^-14 sec when in fact each pulse maintains the phase for 10^-8 sec (and one should be able to easily demonstrate this for instance by producing a diffraction pattern at a slit; what you would simply observe here is all the diffraction patterns for each corresponding color at once, whereas with a coherence time of 10^-14 sec you should obviously not see any diffraction pattern at all).

Thomas

I thank you thomas for pointing out some the things that need to be made clearer in the article. There are different types of coherence - temporal coherence (and the coherence time) refers to the phase relationship (or correlation) between different times of the wave. This is a different phase than the one that appears between different frequencies in the wave - this type of coherence is called spectral coherence (or chromatic coherence). It is the spectral coherence that relates to the time duration of the light - light with little spectral coherence will have a longer duration than light with perfect spectral coherence. To reiterate, I didn't say the "coherence time" had nothing to do with phase" - I said it has nothing to do with the phase between frequencies (the spectral phase).

I can't address your example because I don't really understand what situation you are trying describe. I will try to change the article soon so that it is clearer. Hopefully, the next version will clear up some misunderstandings for you.--J S Lundeen 19:31, 5 April 2006 (UTC)

So the Fourier theorem actually provides a relationship between the spectral bandwidth and the *chromatic* coherence rather than the phase coherence. I think this is a very important point (as the example in my previous post above should make clear).

Thomas

In the meanwhile, I have treated the issue in more detail on my webpage http://www.physicsmyths.org.uk/fourier.htm ,which I hope further clarifies the topic( by all means, feel free to improve the Wikipedia article even further in this sense).

Thomas Smid 10:52, 9 February 2007 (UTC)

I would say that it depends. The coherence time and/or length doesn't only depend on the light source but how you are making the measurement. White light through the two arms of a Michelson interferometer could be considered completely coherent at the output if the arms are of equal length. Coherence time and distance should be considered together. Real measurements are made over finite times and distances, and that needs to be considered, as is the fact that coherence is a continuum. Gah4 (talk) 12:05, 11 May 2009 (UTC)

Two remarks: 1) the temporal coherence is defined as an integral over all times, so in Thomas' example the coherence time is 10^-14, because interference fringes would appear for 10^-8 sec and then change position so that after time-averaging the fringes are washed out. 2) talking about coherence, we deal with stochastic functions (also called random functions), so the Fourier relationship we should talk about is the Wiener-Khinchin theorem, and I think this would help to clarify Thomas' doubts. R.Coïsson 192.135.11.119 (talk) 10:06, 11 January 2011 (UTC)

Wow, over 10 years since I wrote that one. White light form an incandescent lamp is a collection of photons of different frequencies and phases generated by different parts of the filament. Each individual photons has some coherence length and time. If you put that through a Michelson interferometer, with equal length arms, they will interfere perfectly. (Don't think about photons going down one arm or the other. Each one goes down both arms.) Around the point of exact arm length, there are brown fringes averaged over the optical frequencies, and, as noted, a few fringes on either side. Gah4 (talk) 15:55, 14 January 2021 (UTC)

Correlation_and_dependence

There is a {{clarify}} related to correlation. It suggests that two waves with phase difference of pi/2 are not correlated. It seems that Correlation and dependence allows for a generalized correlation, but if you really want an expectation value of a product, consider the wave function as a complex value, and compute the expectation value <X Y*>. That is, the complex conjugate of one of them. That is the usual way in quantum mechanics. Gah4 (talk) 16:09, 14 January 2021 (UTC)