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I know, the answer to this question may seem obvious: The resolution/magnification of an optical microscope is limited by the minimum wavelength one uses. This is due to the diffraction limit.

However, there are different types of optical microscopes. The classical type shines light on a sample and looks at the reflection. It is clear to me why the resolution is limited by the diffraction limit in this case.

A second type is the fluorescence microscope. There the single atoms do send out photons. It is stated (at least on the german Wikipedia page) that this type of optical microscopy is also limited by the diffraction limit, but why?

My question in short:

Why is a fluorescence microscope limited by the diffraction limit if single atoms send out photons? Shouldn’t the resolution be that of a single atom, at least when the detector is sensitive enough?

Qmechanic
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Lockhart
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  • The diffraction limit is not a hard limit. One can localize single atoms on scales far below the diffraction limit (typically five times smaller or better). If a Wikipedia article says otherwise, then somebody needs to rewrite that Wikipedia article. It's simply not correct. This article gets it right(er): https://en.wikipedia.org/wiki/Super-resolution_microscopy – FlatterMann Apr 03 '23 at 19:24
  • @FlatterMann the technique that you cite allows increase of resolution that is still a fraction of optical wave length - hundreds or thousands of times bigger than atoms. – Roger V. Apr 03 '23 at 19:28
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    @RogerVadim The question was not if one can optically resolve the structure of atoms. It was about the resolution limit for all I can tell and microscopes are not limited by the classical diffraction limit in cases in which we can assume point emitters. – FlatterMann Apr 03 '23 at 19:32
  • @FlatterMann It is true that the title of the question, Why can’t we see atoms in an optical microscope?, does not quite correspond to the content. – Roger V. Apr 03 '23 at 20:16
  • @RogerVadim Neither does the classical diffraction limit correspond to the actual resolution that one can achieve with optical instruments. It was always a very simple minded estimate that may be somewhat correct for unstructured (random?) patterns, but I doubt even that. It is certainly not a good estimate for typical image data, neither in biology nor in astronomy. You are, of course, correct that atoms don't have structure in the optical, but not because of microscopes. They are dipole emitters and that's that. – FlatterMann Apr 03 '23 at 21:37
  • https://www.newscientist.com/article/2161094-a-single-atom-is-visible-to-the-naked-eye-in-this-stunning-photo/ seems relevant but I don't know enough about the specifics to be sure – Pete Kirkham Apr 05 '23 at 00:00
  • Yeah, it's unclear if the question is about seeing atoms, or about resolution limits for fluorescence microscopes. The key about (1) seeing atoms and (2) superresolution techniques, is that, either the sources are farther apart from eachother than the resolution limit or only a small fraction of sources are emitting at any moment in time so that, at every moment in time, all the sources that ARE emitting are further apart than the diffraction limit. – Jagerber48 Apr 08 '23 at 15:58

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The size of atoms is about 1 Angstrom ($=10^{-10}$meters), whereas the wavelength of electromagnetic waves in the optical range is several hundred nanometers ($~10^{-7}$ meter) - about a thousand times larger. In other words, atoms due to their small size are are below diffraction limit - this applies to any type of optical microscope, since we cannot distinguish the light coming from different parts of an atom.

Atoms can be seen in electronic microscope, atomic force microscope, scanning tunneling microscopy, or using X-ray. One can also observe light emitted by single molecules - via technique called single molecule spectroscopy - but we still cannot see their shape.

Remark:
From the comments it appears that some people seem to associate the diffraction limit with a particular types of microscopy or spectroscopy. To avoid ambiguity, let me restate it in different terms: it is hard to measure an object with a measuring stick that is a thousand times bigger than the object measured.

Example
The famous image below was created from xenon atoms (each point is an atom) and visualized using scanning tunneling microscopy in 1989 (see here).
enter image description here

Roger V.
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  • Thank you for the answer. I still don’t understand how the conclusion is made that ‚because the wavelength of light is larger then that of an atom, we cannot distinguish single atomsˋ. How can I imagine this qualitatively? – Lockhart Apr 07 '23 at 07:22
  • @Lockhart I tried to capture it by this sentence: it is hard to measure an object with a measuring stick that is a thousand times bigger than the object measured. How do you imagine visualizing an atom? - in any optical-like technique light is reflected from different parts of an object, and we perceive it as rays coming from different points. If the object is so small, we cannot talk about rays anymore, and cannot distinguish light coming from different parts of it. The solution is to use either much shorter wave-length (X-rays, electrons) or using something other than conventional imaging. – Roger V. Apr 07 '23 at 07:42
  • Scanning electron microscopy, atomic force microscopy and other techniques mentioned in the comments are essentially touching atom by an object that is smaller than the atom itself and then presenting the results as a pseudo-image. – Roger V. Apr 07 '23 at 07:44
  • Thanks. Maybe I am thinking to much in pictures, but let’s imagine the following: We have a surface and one atom at the surface emits a wave. The wavelength may be normal to the surface (the propagation direction of the wave), not parallel to it. So I can understand why we would have problems to distinguish atoms which are in layers above each other, but why can’t we distinguish atoms laying next to each other on the surface? I hope you can understand what I am trying to say. – Lockhart Apr 07 '23 at 10:00
  • @Lockhart Let me first remark that you are shifting the goalposts a bit: instead of seeing the atom (i.e., its shape, internal structure, etc.) you are no talking about seeing light coming from different atoms. If they are close (much closer than the light wavelength) then the same logic applies, as described above - they are too close. One could add that when atom emits light, the light does not emerge from one infinitesimal point - rather there are electric and magnetic fields originating in a rather large region of space around the atom. – Roger V. Apr 07 '23 at 10:05
  • I did mention though single molecule spectroscopy in my answer - we can see light coming from a single atom/molecule, and we can distinguish atoms/molecules, e.g., by the polarization or frequency of the light they emit - but this doesn't mean that we see them. More precisely - we "see them" in the same sense as we see stars - we see them as points where light comes from, but we can't distinguish their structure, even with a telescope. – Roger V. Apr 07 '23 at 10:06
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Maybe my question was a bit misleading, because I think the answers that I got do not really answer what I wanted to know. However, I did some digging and found out what I wanted to know:

There are two different heuristic approaches to determining the diffraction limit:

  1. The Abbe Limit which limits the resolution if we directly shine light on a system and look at the reflection.
  2. The Rayleigh Limit which limits the resolution of an object that can also emit light by itself, like in a fluorescence microscope.

The reason for the Rayleigh limit is the following: Every microscope, also a perfect one, has an aperture, like a hole where light goes through. This aperture may just be determined by the diameter of the lens. By diffraction at this aperture an Airy disk is formed, which looks like that:

enter image description here

The size of the Airy disk depends on the wavelength of the light used. If there are two atoms, there are two Airy disks. If they are close together, both structures can not be distinguished anymore:

enter image description here

However, this quite a heuristic argument. One person may distinguish the two objects, another one would not. However, to do quantitative calculations we have to define a limit where these objects are indistinguishable. This definition is somewhat arbitrary.

Lockhart
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  • Whether two sun-resolution objects are resolvable (with a certain statistical confidence) depends on (1) the resolution (the size of the microscopes point spread function) (2) the spacing between the objects and (3) the signal to noise for the recorded signal. Two nearby objects can be resolved if the signal to noise is very high. – Jagerber48 Apr 08 '23 at 22:16
  • @Jagerber48 When you say ‚signal to noise‘, do you mean for example the uncertainty emerging of a non-perfect microscope? Because even when one has a perfectly built microscope the Rayleigh limit would be applicable. – Lockhart Apr 09 '23 at 06:56
  • no, I mean amplitude noise on the detected image. Often arising from optical shot noise in each pixel – Jagerber48 Apr 09 '23 at 12:38
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The resolution for a linear optical microscope is set by the far field diffraction limit which is a few hindered nanometers for the optical wavelengths of many atomic transitions. This means that microscope can’t produce distinct spots for point sources closer to each other than the microscope Resolution. However, if the individual atoms are separated from each other by distances greater than the resolution limit then they can indeed be observed in an optical microscope. Such feats are performed routinely in cold atoms labs in which individual atoms are trapped using a variety of cooling and trapping techniques. This story is exemplery.

Jagerber48
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