Talk:Optical flat

I think that we should add a section or a link on how to use an optical flat, any takers? David Casale 12:54, 19 May 2010 (UTC) —Preceding unsigned comment added by David Casale (talk • contribs)

Stiction vs wringing

Seems like the author has the terms confused - winging flat surfaces together can cause sticktion - but wringing is not stiction.

Wringing is the forcing out of the air, which produces a vacuum force that holds the surfaces together, like a suction cup, making it difficult to pull them apart. This article never even touches on static friction (stiction) which makes it difficult to slide them relative to one another. The stiction, however, in enhanced by the wringing, forcing the surfaces harder together. Zaereth (talk) 06:02, 23 October 2014 (UTC)

The physics of wringing (to the extent that it is understood) is also discussed at gauge block > wringing. I added a cross-reference. — ¾-10 22:16, 23 October 2014 (UTC)

Thanks. That is helpful. Of course, the difference here being that flats are usually cleaned very thoroughly and allowed to wring naturally. (Usually, but not always.) Just set it on top of the test surface and watch it go. Maybe apply a little pressure to one side to set the direction of the wedge, but little effort should be required. Wringing should not be a problem if everything is flat and clean enough, but getting them apart again without scratching or breaking them is another story. (Not to mention you can get just as good if not better measurements, and a clearer picture of the surface, from initial wringing. The fully-wrung contour lines can be difficult to decipher sometimes.) Zaereth (talk) 22:42, 23 October 2014 (UTC)

Wringing doesn't appear to have anything to do with air pressure. Cody at Cody's Lab Published a video all about testing them in a vacuum chamber and under vacuum the wringing strength was not affected. Ksd275 (talk) 06:24, 3 December 2020 (UTC)

It does when testing with an optical flat. There is a slight wedge of air trapped between the surfaces. Without it, no fringes would form. This air likely exists in a vacuum chamber as well. It's impossible to get all of the air out, and even at pressures of a few micro-torr gases like oxygen and water vapor tend to cling strongly to the surface via adsorption. You can't read it on a gauge, but it becomes very apparent when building things like lightbulbs, flashtubes, or neon signs. If they put the surfaces together and then sucked the air out, it would not speed up wringing in the slightest. Zaereth (talk) 07:28, 3 December 2020 (UTC)

Stability due to viscosity section

The question of whether over long time periods glass "flows", is an interesting area of experimental physics. But I'm concerned that putting it in a section labeled "Stability", without including any of the other sources of instability of optical flats such as thermal expansion, raises issues of WP:UNDUE weight. Nontechnical people reading about optical flats for the first time, could easily get the impression that this is the main source of inaccuracy in optical flats - after all, it's the only one mentioned. So optical flats deform over time and have an 'expiration date'? "Gee, I guess I'd better throw out that set of flats in my uncle's optics laboratory, it's over 10 years old, bound to be inaccurate." I think this topic needs to be more clearly identified as experimental, and not a contribution to the error budget in engineering use of flats. --Chetvorno^TALK 02:41, 12 September 2013 (UTC)

Better still, the article could use a section on the accuracy and real, significant sources of error in optical flat work. Anyone feel up to that? --Chetvorno^TALK 02:50, 12 September 2013 (UTC)

Well I was trying to make the addition more related to what the source actually talks about, and to the article itself. However, because of the fact that these are primary sources, they have no actual cause, and for other reasons discussed at Talk:Glass, I would completely support its removal entirely ... at least until this becomes a well-established fact (or not) in secondary sources.

I do think it would be better for the article to add all of the things you discussed; perhaps info about the three-flat test method, on liquid flats, etc... Unfortunately, I don't have time right now. (I only tried to improve this because I had already looked at the sources.) Perhaps in a few months I can get back to it, but not right now. Zaereth (talk) 04:48, 12 September 2013 (UTC)

I almost did remove it, in response to your edit summary, but thought I'd test the waters first. By the way, I wouldn't just throw out your old flats. Perhaps recertification would be called for, but not every flat tested showed change. Only a very small number were tested, and, also, even a flat at $\lambda$/20 has a normal deviation of over 30 nanometers, so, even if it did change, it will probably be well within error margins for much longer than a decade.Zaereth (talk) 06:40, 12 September 2013 (UTC)

My sentence about throwing out old optical flats was meant to be satirical. I was suggesting that the Stability section might prompt uninformed people to throw out perfectly good flats. The point I'm trying to make is that optical flats are extremely widely used and the technology is very mature and well-studied. Optical flats have been certified and studied at metrology labs like the US NIST for 100 years. The technology for making glass and silica optical surfaces accurate to nanometers for telescope mirrors has been developed for 300 years. Astronomical telescope mirrors of silica, meters in diameter, weighing multiple tons, are routinely made to accuracies of λ/50 or more. For blue light that would be 8 nanometers. If viscous flow caused deformation in glass that was significant on an optical scale, the optics industry would be aware of it. The 5 meter, 14 ton mirror of the Hale telescope, accurate to 50 nm, has been studied closely for 60 years. If viscous deformation hasn't affected its performance, I don't think it is going to affect a little optical flat. --Chetvorno^TALK 11:40, 12 September 2013 (UTC)

I agree. The two studies on flats are far too small to give any definite answers, but are more along the lines of "look, see what happened to my flats..." but little else. It's a little dubious if you ask me. The question I have is, do you think this info should be cut from the article? If so say the word and I'll be happy to do it. (Keep in mind that I'm not the one who initially added it to this article, but feel a bit responsible, because I did deflect it here from the glass article. In any case, as it was originally written, it left out any relation to flats, but was trying to make a point about glass. That's why I made an attempt to try and improve it first.) Zaereth (talk) 16:17, 12 September 2013 (UTC)

λ/4 and all that.

@Zaereth: The whole explanation might need rephrasing, but I made a small change to improve it to "confusing" from "blatantly counterfactual". What is observed is the thickness of the gap between the two surfaces, which is the difference (or sum, depending on sign conventions) between their contours. Given a λ/4 surface and a λ/4 flat, it is extremely unlikely that their λ/4 errors will cancel and produce straight fringes as the original preposterous statement "a surface polished to a flatness of λ/4 will show straight fringes when tested with a λ/4 flat" promised. I weakened it to "might", but even that's extremely generous. The reason that using a λ/4 flat won't work is that half the curvature of the fringes you see will be due to the flat, and you don't know which half. (This is an oversimplification, as indeed sometimes the errors will cancel and you'll see no curvature where there should be some, but it's closer to the truth; in reality uncorrelated errors add in quadrature and you see √2 ≈ 1.4142× the error.)

I ended up making a more significant rephrasing that skips the whole thing and just says, basically, "you need a flat better than the surface you're testing or you get meaningless results". It still needs more work, as the whole bit about "the fringes to not exist within the gap' is, while technically true, not relevant. The fringes are produced by the gap and measure the gap, and the fact that they technically exist only above the gap isn't germane to the understanding of "precision and errors". 71.41.210.146 (talk) 18:31, 5 April 2017 (UTC)

The fact that the fringes don't exist in the gap is exactly why this phenomenon occurs. It explains why the fringes move in relation to the eye or pressure. If they were truly in the gap, the fringes would remain stationary and there wouldn't be these problems.

It doesn't matter if talking about λ/4, λ/10, λ/20, flats or better. It will even work with 4--6λ glass, provided that they will wring together. When the flatness of both surfaces are the same, the fringes will be straight. If allowed to fully wring, the fringes will widen until they disappear. If you don't believe me, check the sources or try it out yourself. (I had a hard time believing it myself until I took the photo of the two λ/10 flats.) The fact that it does happen cannot be disputed. The only place for debate is on how an why it happens. (In this instance, unlike with lasers, I find the classical explanation easier to understand than the quantum one, but that requires understanding how spherical waves of different radii interfere to form an image after being refracted (or diffracted) by a lens.)

The flat doesn't measure the contours of both surfaces. That's a misconception, cause by thinking about it intuitively rather than in the counterintuitive way that it actually happens. If they did, it would be much easier to determine absolute flatness. The contours on the flat are canceled out by the test surface, and the flat can only measure those contours which are greater than its own deviations. (This is why temperature changes within the flat can cause such trouble. They won't show up in the test except to reduce the accuracy of the reading, which you'd have no way of determining without a thermal camera.)

This information is found in the sources. For example, here, Edmund Industrial Optics says this: "This is a commonly asked question and the answer is dependent on what is being tested. If the surface that is being tested is flatter than λ/4, then a more precise flat will be required to show a change in the interference pattern. In this case, a λ/4 flat would exhibit straight parallel lines, but λ/10 or λ/20 flats would show enough curvature in the fringes to measure the surface accurately." If you have sources which contradict them, then please bring them to the table. Zaereth (talk) 19:54, 5 April 2017 (UTC)

@Zaereth: "It doesn't matter if talking about λ/4, λ/10, λ/20, flats or better. It will even work with 4–6λ glass, provided that they will wring together. When the flatness of both surfaces are the same, the fringes will be straight. If allowed to fully wring, the fringes will widen until they disappear. If you don't believe me, check the sources or try it out yourself. (I had a hard time believing it myself until I took the photo of the two λ/10 flats.)"

It will work fine with λ/10 flats. It might work with λ/4 flats. It will not work with 4λ glass unless the glass is so thin that the wringing forces distort the surfaces into alignment.

For example, suppose I have two smoothly convex λ/4 flats. (I.e. they're essentially perfect spheres, but λ/4 taller in the middle.) If I fully wring them together, the centers will be λ/2 closer together than the edges. This is one full fringe of Newton's rings which will never disappear no matter what the wringing.

Of course, real λ/4 flats have more complex figure errors, and are usually not right at the limit of their guaranteed tolerance. If they happen to match (e.g. one convex, one concave) to λ/8 or so, you'll see the fringes disappear. Much more than that, and there will be the remains of a fringe visible.

The Edmund optics ad copy is simply wrong. Being marketing material, it's not a particularly reliable source and if it were true then the three-flat method for testing (tons of refereed journal sources: [1][2][3], etc.) wouldn't work.

With a λ/4 flat, you can't make out errors smaller than λ/4, but that's not because the lines are straight. Rather, there will be slight curves left over, and you don't know where to place the blame for them.

Assuming perpendicular, coaxial illumination and viewing, the intensity of light of wavelength λ reflected from a Fizeau interferometer gap of thickness δ (that's wavelength in the gap; if it's filled with a material of refractive index η then λ = λ₀/η) will be modulated by cos²(4πδ/λ). The modulation won't be 100%, since the reflected intensities aren't exactly equal. This is also ignoring multiple reflections which turn a Fizeau interferometer into a Fabry-Perot interferometer and change the cos² function to increase the reflectivity away from the extrema (i.e. narrow the dark bands[4]) but don't change the fringe spacing.

"The contours on the flat are canceled out by the test surface, and the flat can only measure those contours which are greater than its own deviations."

This seems like a crazy mental model of "deviations", considering only their magnitude and completely neglecting the particular form of the figure errors. If the two surfaces have complementary form errors, then the errors cancel, and you measure nothing. Or they might add, and you measure twice the individual deviation.

In the common case that the flat and the test surface have uncorrelated guassian form errors, they add in quadrature.

The issue is that you can't accurately attribute the observed errors to one surface or the other; you're only measuring the sum. If one surface is good enough that its contribution can be assumed zero, this is straightforward. (E.g. the Raleigh water test].) If none are known good, you have to compare three references and do a three-cornered hat test. Measure A+B, B+C and C+A, and then you can solve for 2A=(A+B)+(C+A)−(B+C).

(While three is the minimum required to eliminate ambiguity, larger numbers allow an overdetermined solution which can be solved by least-squares fitting and checked for consistency.)

"If you have sources which contradict them, then please bring them to the table." I'm searching. However, it's a very specific claim, and my optics texts don't address that claim specifically; they just teach general principles which, when applied, contradict it. I'm searching for some more "practical" sources like metrology and precision machining texts,but that requires a trip to the library.

As I said, the most direct contradiction is the three-flat test. If two flats with errors of equal magnitude (but different shape) always produced undistorted fringes, then this test would never see errors. This plainly contradicts documented observations. 71.41.210.146 (talk) 19:46, 6 April 2017 (UTC)

Actually, it is very possible to do these tests with simple float glass. I'll take a photo tonight. Take a pair of windows, wet a lint-free tissue with acetone, sandwich it between the windows, then pull the tissue from between them. What you've done is replaced the air-wedge with a liquid-wedge made of acetone, which has much higher bonding potential than air. Now, the acetone will evaporate very quickly so it'll wring much faster than air, but you can get some good photos this way. When it fully wrings, it will do so very tightly. (You don't really need any special equipment, so I wasn't kidding when I recommended trying it. A few cheap λ/4 laser windows from ebay, a laser pointer and a frosted bulb is all you need.) My Coherent laser has a pair of λ/4 windows in it that I can use to take a photo the next time I clean them, or my old Edmund catalog at home has a wonderful photo (which unfortunately is copyrighted).

Please see this source, which gives some detail of the three-flat test. It says: "The errors of flatness of an optical surface are generally measured against a reference flat. What is in fact measured is the difference between the two surfaces. Considering that in general the reference flat is one order of magnitude flatter than the measured sample, all the differences are assigned to the latter. However, when measuring samples that are as flat as the reference, this cannot be done." That gives a basic description of how the test works, but books such as Introduction to Optical Metrology, by Rajpal S. Sirohi go into it much deeper.

For a standard optical-flat test, only those deviation which are greater than those on the flat appear. Everything else you can imagine as being "below sea-level." A better flat is required to change this zero-point. In this case, because the fringes don't exist in the flat itself, to make useful measurements a standard convention had to be adopted, which is called the parallel-plane separation theory. This depicts the fringes as layers of parallel-planes between the flat and the observer, separated by is distance of λ/2. Of course, that's not how it really works, because light waves are spherical, but the convention works for most measurements. Unfortunately, it only measures flatness in one direction (perpendicular to the wedge) so the flat must be rotated and tested again, and the results combined to get an actual reading.

For a three-flat test, you begin with three flats of known flatness, all equal in size and shape, but differing in flatness. In this test, you don't want any straight fringes, but the surfaces should be as parallel as you can get them, so that you're only analyzing 1 fringe. To avoid the problems associated with wringing and increase accuracy, the flats are measured some distance apart from each other, and aligned in the same way you would a Fabry-Perot interferometer. If the flats were the same in flatness there would be no indication of the actual topography, but since the flats differ in flatness, there will be contours evident in the fringe. When this surface is tested against the other flat, again there will be contours evident, but with slight differences from the first test. This difference represents the unknowns, or the difference in flatness between the three surfaces. To reduce these unknowns, the final two flats are tested against each other, which reduces these unknown variables to just three. By a process of extrapolation (basically mathematical guesswork), these three unknowns can then be filled in. Therefore, this is not an actual measurement but a process of reduction. However, this also gives an absolute flatness along only one axis (across the diameter), so the flats must be rotated and retested to give a result covering the entire surface. The test doesn't measure the flats anymore accurately but rather allows measurement of those unknown factors not shown by the flats. (Keep in mind that the image inverts in the field of depth, just like a mirror, which adds a whole other set of unknown variables.) Zaereth (talk) 23:20, 6 April 2017 (UTC)

A float-glass window on a piece of common plate glass @ 450nm

As promised, here is a photo of a float-glass optical window, with a flatness of 4--6λ (The same window pictured in the article, and on the antireflection coating article). It is sitting on top of a piece of common plate glass (taken from a picture frame) that measures 9--14λ using a λ/10 flat. When measuring with the float glass, the two are not added but subtracted, so the test only shows a flatness of 5--9λ. I hope that helps. User:Zaereth|Zaereth]] (talk) 07:19, 7 April 2017 (UTC)

@Zaereth: (Grrr, lost lengthy response in a browser crash. Grumble...)

I'm trying to figure out if we're actually disagreeing or not. I'm starting to suspect that we don't have any substantive disagreement but are talking past each other due to some earlier misunderstanding/miscommunication.

Your picture (than you very much!) shows what I expect: lots of strongly curved fringes. That's also what I was trying to say should be expected.

You wrote "It will even work with 4–6λ glass, provided that they will wring together. When the flatness of both surfaces are the same, the fringes will be straight. If allowed to fully wring, the fringes will widen until they disappear."

I took this to mean that "working" would consist of seeing straight fringes that would, over time, widen until they disappeared.

When I wrote "It will not work with 4λ glass", I meant that the fringes would not be straight and would not disappear when fully wrung.

That's what I see in your picture, so I feel vindicated. If you somehow interpreted me as predicting some other result (perhaps that I thought the fringes would not be visible in the first place?), there's a pretty major misunderstanding.

To be excruciatingly specific, I interpreted the original statement in the article and ES page as saying:

Given two λ/4 flats A and B, pressed together and illuminated with light of wavelength λ in the usual way, straight and evenly spaced fringes will be observed. This will occur regardless of the particular forms of A or B, so long as they each have a peak-to-valley deviation from flatness of no more than λ/4. If flat B is replaced by a λ/10 or λ/20 flat, (and, implicitly, flat A is far from perfect) curved fringes will be observed, showing the deviations from flatness of A.

Expanded out fully like that, it's easy to see that it's so wrong it contradicts itself. By definition, a λ/20 flat is also a λ/4 flat. Thus, using a λ/20 flat for B satisfies the conditions for the first half of the experiment, and predicts two contradictory observations: straight fringes, and curved fringes.

If you think the immediately preceding paragraph is nonsense and the statement above that is true, then we have a real, substantive disagreement. But perhaps you are defending a slightly different statement than the one I am attacking?

Are we diving into details of optics when it's actually a problem of ambiguous wording?

Thank you for your lengthy reply, suggested references, and so on. I had a whole section on the differences between Newton, Fizeau, and Fabry-Perot interferometers that I'd like to wait to re-write so we can perhaps focus on the original issue a bit.

What did you think I was saying would be seen in your window glass experiment?

71.41.210.146 (talk) 00:11, 8 April 2017 (UTC)

Sorry for the delay, but I've been away for the weekend. It wasn't so much an experiment as a demonstration. (Experiment implies an unknown outcome.) It's hard to argue in terms of pure theory when observable data contradicts the expected outcome. I think it was Maxwell who said (something like) If your experiment complies with the hypothesis, then you've made a measurement, but when it does not, you've made a discovery.

I dislike uploading photos unless they can have some encyclopedic value, and usually don't unless I see an article that could use them, but sometimes a picture really is worth a thousand words. I was in a rush when doing these, so I didn't take the time to cover the rest of the glass pane with black paper, to prevent over-reflection. The eye is so much better than a camera, and all the fringes appear crisp and clear. The camera tries to focus on the brightest spot, so it was difficult to get the fine fringes to come into perfect focus. I'll upgrade this photo to one that is in better focus when I get the chance. (Time is very limited right now.)

I revised my photo above to include the photo of the plate glass being tested with an optical flat, and one where I cut the plate glass into 1 inch squares and tested them against each other. (The problem with the plate glass is that it is too thin, so a little warping occurs just from the surface it is sitting upon, but I was aiming for a quick demonstration rather than a precise measurement.) Establishing that it indeed does occur in just such a way, that when the surfaces are both the same flatness and parallel across the wedge, straight fringes do occur, then how do we account for this discrepancy, seeing as that neither surface is perfectly flat? That can be accounted for if you picture each point on the flat as a series of waves, radiating from both surfaces. Regardless of surface shape, all waves are convex, and all converge while nearly perfectly overlapping each other, each with a radius that nearly matches the curvature of the lens of your eye. The wave become concave when they pass through the lens. It is the very minute differences between these waves that actually interfere to form the image, so it doesn't matter if either or both surfaces are concave, convex or a combination of both.

Light begins to act weird when thin films are involves, and the quantum theory gets even stranger. Let me ask another question, what do you suppose happens to all of the photons that were in the dark fringes? The answer is likened to one of the greatest mysteries of science, right up there with double-slit interferometry. Zaereth (talk) 21:52, 11 April 2017 (UTC)

@Zaereth: I have no quarrel with your experiment/demonstration distinction, but that's an example of what I was referring to: a difference of wording, not substance. As you say, it's a subjective distinction, based on the knowledge of the experimenter/demonstrator; there's no difference in the procedure.

"what do you suppose happens to all of the photons that were in the dark fringes?"

There's no mystery; they are transmitted rather than reflected. With low reflectivity surfaces, It's harder to see the fringes from the back due to worse contrast, but they're there, and reversed. 71.41.210.146 (talk) 03:17, 12 April 2017 (UTC)

Current image showing light traveling through optical flat is incorrect

The light traveling on the left side of the image, reflecting from the internal surface of the optical flat is showing 180° shift where it should not be. 2601:40C:4301:3726:81D2:3621:4DFE:7478 (talk) 01:40, 22 November 2023 (UTC)