Why do diffraction limits exist? My question does not deal with standard derivations of diffraction. I have no doubt that I can follow standard derivations for diffraction phenomena. Actually, I have probably been shown these before, it's just been so long that I forget them.
My question deals with thinking about diffraction phenomenon from the quantum/particle perspective. I was thinking about why processes such as photolithography, e-beam lithography, electron microscopes, or even optical microscopes should be limited wavelength.
In all of these processes we are firing a bunch of elementary particles at a target. We know that the wave-like properties of these particles disappear when an 'observation' takes place. My understanding is that 'observation' really means interaction. So once these particles interact with the target they should lose their wave-like qualities and behave like particles. Since they are then localized in space, this would give infinite resolution. Obviously there is something wrong with this way of thinking. So to remedy this I was thinking that maybe the loss in resolution arises when the particle reflects back to the detector. During this journey it would return to wave-form and in a sense lose the information of where it reflected from.
Hope that at least made enough sense for someone to explain where it is wrong.
 A: You mention the contrast: the propagation of elementary particles is described with wave mechanics, but the transfer of energy is localized.
There is for instance the 1989 demonstration, achieved at Hitachi labs, of a double slit experiment with electrons.
(See also: a short history of double slit experiments )
(Scanned version of the 1989 article itself: Demonstration of single-electron buildup of an interference pattern In these scanned pages the images of the buildup are too dark. For the buildup see the images on the Hitachi website.)

The luminosity was set very low, so that the buildup could be observed.
From the paper describing the demonstration:
"Electrons are detected by a two-dimensional position sensitive electron-counting system."
So the event of triggering a detection cell is localised. The registration of the detections is accumulated and the accumulated data are presented on a computer screen.
The pattern of points gradually becomes denser. As the density increases the distribution approaches ever closer to the luminosity distribution that is expected of wave interference.

So:
Sure: the individual events of an electron triggering a detection cell are sharp. However, there is no way of precisely aiming the electrons. No matter what you do, the distribution of detection cells being triggered occurs in accordance with wave mechanics.
A: It’s all fields, forget particles. Particles is a misnomer. What are called particles in quantum field theory are actually quantized excitations in quantum fields. The quantized fields obey wave equations and diffractions limits follow from wave equations.
A: Assuming numerical aperture of 1, diffraction limited resolvable feature diameter of microscope is $$ d = \lambda/2.$$
Like you can't push a basketball through the $1~mm$ hole,- without disintegrating your ball, similarly you can't reflect waves from a spot a lot less in diameter than a wavelength,- because it simply will not fit there. You will not know from a scattered and gathered wave,- which parts of it was scattered from which surface spots. It does not carry such information.
Or another analogy with ball,- try to scatter basketball from a needle tip,- will you succeed ? Most probably ball will release air out, or depending on the the material from which ball is made - will break needle apart, or will go straight though it, but in any scenario it can be said that likely you can't probe needle "reflectance" with a basketball. You can only probe things which are more or less comparable in size with a basketball.
