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I took the picture below with our microscope. It's a 8mm roller bearing, lighted from below with a parallel light bundel (white). The width of the yellowish light fringe is maybe 5 micron.

Originally I was hoping to make pictures with an accuracy of like 1 micron. But I'm afraid that was way too optimistic.

-First I would like to know if this is really a diffraction pattern?

-If yes, would a blue back light make the fringes smaller? What else could I do to increase quality?

-Is there a way to calculate the distance between the fringes and the "real" object position? On this website, I found a similar question, but I don't think those formulae are valid for this case (the calculated distances are like 0.3mm between fringes).

microscope image of ball bearing with difraction pattern

Thanks in advance,

Edit; the first back light I used did not have a pin hole, and the light beam was not focused at all. The resulting image in the microscope looked like this; (distance per pixel is the same)

rather vague diffraction pattern.

At first I was a bit disappointed when I saw all these fringes with the truly parallel light, but maybe it's a good thing to hit the limitations of the microscope (as Rod suggests below)?

MTH
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  • When you say the yellow fringe is $5{\rm \mu,m}$ wide, do you mean all the four or five cycles of fringing that can be seen, or that the widest yellow fringe is $5{\rm \mu,m}$ wide. If the latter, then $1{\rm \mu,m}$ is going to be well below the diffraction limit of your microscope. You're going to need at least 0.3NA optics, probably 0.5NA would be better. However, when you say "$1{\rm \mu,m}$ accuracy" do you mean that you need to see features of this size, or do you need to, say, locate a larger object to within $1{\rm \mu,m}$ accuracy. The latter is much easier than the former. – Selene Routley Jul 13 '17 at 11:35
  • The widest yellow fringe is 5 micron. About the accuracy; I would like to locate the filleted edge of an object within 1 micron to determine the exact location of a tangent line. – MTH Jul 13 '17 at 12:15
  • In that case (i.e. location rather than micron feature detection), then even with the fringes I should have thought that image processing should be able to locate the edge to well within a micron, given a reasonable smoothness model for the fillet shape. The signal to noise in this image is fantastic and, in fact, the fringes could be used to your advantage to enhance the location, using a theoretical model to decide exactly where in the fringe pattern the edge is. – Selene Routley Jul 13 '17 at 12:23
  • When I measured the diameter of the inner black feature, the result was maybe 10 micron too high. I could work with this as a constant offset. But I prefer to have a kind of formula for this. I tried googling this, but the closest I came was in the link in my post. I think that one is for a point light source and not parallel light. Could you maybe give a hint where I should look? – MTH Jul 13 '17 at 13:32
  • I have also added an other picture taken with a more diffuse back light, at first sight, that one looks better (less fringing). But somehow I feel that the first picture is better despite the large diffraction pattern. I don't have any experience to support this. What do you think? Thanks. – MTH Jul 13 '17 at 13:37
  • I'm pretty confident that if you could repeatably get those beautifully contrasting fringes, you could indeed use the formula in the other answer you found and linked to locate the edge accurately. If you can wait a day or so, I can turn my comments in an answer that will show you how to do this; in the meantime, take a look at my answer to a similar question which gives the equation of the wiggly curve and shows how to scale it for different distances from the object. – Selene Routley Jul 13 '17 at 14:05
  • Rod, that would be most helpful, I appreciate it a lot. But I'm still wondering if the Fresnel integral is valid in this case. Let's assume the parallel light beam is diameter 20mm, distance is 20cm and wavelength 500nm; then the Fresnel nr will be 1000. I think I need the Fraunhofer integral to solve this. But I must admit I don't know how to use that in practice. – MTH Jul 13 '17 at 14:20
  • I'll work through those figures for you tomorrow. – Selene Routley Jul 13 '17 at 14:24

3 Answers3

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Yes, definitely this is due to diffraction. But I'm surprised by the contrast and number of fringes you have with white light. Is the focus optimized? The fringes can become larger if the image plane is not on the object plane. Is the light really white? The yellow fringe is suspicious. If you can change the illumination, you can try to find a white light with flat and large spectrum, it will help to reduce the fringes. A real white light will be better than a blue light. If you use a more monochromatic light (even if not coherent as a laser), eg a LED, diffraction will increase. The best is a real white light which "washes out" the fringes (adding all the fringes of different dimensions at the different wavelengths).

scrx2
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    The yellow fringe (and the less visible blue fringe on the other side) are effects of chromatic aberration and are defects of the lenses, not the light source. – probably_someone Jul 12 '17 at 21:13
  • The back light is indeed not truly white as you suspect. I improvised it with a white LED and some lenses I had lying around. As a next step, I will use a real white light, and see if I can get my hands on a telecentric lens. Thanks for your advice! – MTH Jul 13 '17 at 08:02
  • edit: the telecentric lense is to create the white light beam / I can't change the microscope.. – MTH Jul 13 '17 at 10:19
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I can't add more than 2 pictures..

Edit2; I have done the same test with a blue back light, below the result. One picture is in focus (l), the other one slightly out of focus (r). At first sight, I would think monochromatic light gives better results. On the left picture, there is almost no diffraction visible and maybe the colour banding is more due to aberrations in the optics? Also, after some googling, I think the shape of the fringes is related to an "obscured airy pattern", wikipedia has some info about this. To be continued.. blue LED sharp blue LED out of focus

Edit; In the mean time, I found out why these pictures are so grainy and show different colours (<> LED back light is monochromatic) link

MTH
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After changing the back light to a blue LED and some extra test, I'm pretty sure the distances between the fringes of an obscured airy disc is the same as an Airy disc from a circular aperture. In the first picture I did some pixel counting, and the result was close enough.

Unlike with the white back light, It was also possible to get a much clearer picture without significant fringing. For the moment, I will first try which accuracy I can get working with the second picture.

I'm not confident such a noisy diffraction pattern could lead to more accurate results then the blue line a few pixels wide in the second picture. And it would save me a lot of work also.. (the location of the geometrical edge in the second picture is based on the first picture)

diffraction pattern obscured airy disc

enter image description here

MTH
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