By passing light (left) or even electron streams (right) through a regular, crystalline structure we create an interference pattern that gives us information about the structure of the crystal (but never pictures of individual atoms).
The picture on the left (left) is a pattern created by DNA (species unimportant).
The picture on the right is created by an electron beam passing through some simple mineral or salt.
Carbon-14 is continuously generated in the upper atmosphere when stray neutrons bombard atmospheric nitrogen (which is what most of the atmosphere is).
The reason carbon dating works is that the fresh carbon-14 gets mixed in with the rest of the carbon in the atmosphere and, since it’s chemically identical to regular carbon, gets worked into whatever is presently absorbing atmospheric carbon.
These techniques are still in use today (are relatively cheap), but since 1981 we’ve also had access to the Scanning Tunneling Electron Microscope (STM).
However, despite the images it creates, the STM isn’t taking a photograph either.
When the scales are so small that light behaves more like a wave than a particle, then we just use its wave properties (what else can you do?
If you get a heck of a lot of identical copies of a thing and arrange them into some kind of repeating structure, then the structure as a whole will have a very particular way of interacting with waves.
The STM sees the world the way a blind person on the end of a tiny robotic arm sees the world.
The STM is basically a needle with a point that is a single atom (literally, it is the pointiest thing possible) which it uses to measure subtle electrical variations (such as a stray atom sitting on what was otherwise a very flat, clean surface).
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