Transmission electron microscope beam focusing

[artis]

So I'm reading up on this device and what I get is that in all electron guns once the electrons are emitted they would tend to repel one another so in order to make the beam focused instead of spread out across, one uses magnetic fields in the electron microscope,
So after the focused beam hits and travels through the target thin layer it is then "refocused" at the other side in order to make the otherwise small beam point now spread out over a film or window on which the fine little details could get enlarged for visual viewing. So far so good? Here is what I don't get. an electron traveling perpendicularly to a B field has the Lorentz force exerted upon it which causes it;'s deflection perpendicularly to both the field and it's trajectory, in vacuum free space it makes it spiral.

So let's say the electron came out from the think target layer at a particular spot, now it would fly downwards to hit the (phosphor ?) on the screen forming a pixel of information that it carries , but the secondary magnetic lens deflects the electron and it hits the screen at some random place, if this happens for each electron how come a picture be formed that represents the material?Also is it not the case that each electron has slightly different kinetic energy after it has come out from the layer of target material that it has been shot through? So having a different kinetic energy each electron would be deflect slightly differently in the magnetic lens?

 

[berkeman]

Can you give some links to what you are reading? I believe that a transmission electron microscope would mainly use electric fields to focus the e- beam, and magnetic fields would only be used for a scanning electron microscope's raster deflection (but I could be wrong).

https://en.wikipedia.org/wiki/Electron_microscope

 

[artis]

https://en.wikipedia.org/wiki/Transmission_electron_microscopy@berkeman Well I've read multiple sources , cannot find them all but mostly I see that both TEM and SEM use magnetic coils/fields as lenses both for the focusing before the sample as well as the defocusing after the sample. the difference might be that for TEM one can only change the beam diameter and physically move the sample while in a SEM one can raster the beam using additional coils much like in a CRT I believe.
Also they use apertures with hole to "cleanse" the beam of electrons that are spread too far outward.

But my main question still stands, because even though the electron beam can be focused down to sub mm diameters and due to wavelength differences zoom in better than optical light but I think the basic principle should hold true that just as each photon is reflected from a specific parts of the sample also each electron is coming through from a specific place in the sample and that electron then represents a single pixel on the screen it hits,

The thing I can't understand is the lens after the sample because each electron coming through the sample is then once more "spiralled" while spread out at the same time. So how can the electron hit the screen representing the same spot it went through the sample?

Only way I can imagine this is that the speed of the electrons is fast and the focusing B field is strong so their gyro radius is very very small , maybe even so small that it can be considered almost as a straight line?
I'm guessing here obviously but that is how far I can see this.