Why can’t we see atoms in an optical microscope?

Question

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?

Answer 1

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).

Answer 2

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:

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:

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.

Answer 3

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.