Electrons are “point like” objects. They have mass, energy and momentum but don’t occupy any measurable volume of space. A beam of electrons can therefore be focused, usually with a magnetic field, so that all the electrons in the beam pass through a very small volume of space. The Heisenberg Uncertainty Principle determines the only limit to how small this volume can be.
This is the first physical principle of electron microscopes, the ability to focus a beam of electrons to pass through a small area.
The object you want to “look at” is placed in a plane where the electron beam is focused to a very small spot. At that point the electrons will either pass through an object, losing some energy as they do so, often in the form of x-rays, or they will be reflected or scattered from the surface of an object. All of these things can happen at the same time. If the electrons have enough energy, and they usually do, interaction with the surface of an object will result in secondary electron emission from that surface. All of these interactions can be detected with appropriate electronic instrumentation.
This is the second physical principle of electron microscopes, the ability of the electron beam to interact with an object in a detectable manner.
All of these interactions can be observed with appropriate instrumentation that detects the electrons or the effect of their interaction with the object. If the small electron beam spot is scanned through a small area of the object, like a television raster, usually by means of magnetic deflection coils, then the detected signal can be used to intensity modulate a CRT beam moving in synchronism with the scanning electron beam. This makes a wonderfully magnified image of a very small area on the surface, but the image generally needs further interpretation since it is not an image made with illumination from a light source, as in an optical microscope. For example, it is possible to detect characteristic x-ray energies representative of the element that interacted with the electron beam. If only these characteristic x-rays are used to intensity modulate the CRT display, then the display will present a magnified image showing the locations of that one element. A similar thing occurs for the secondary electrons emitted from the surface. If these are used to intensity modulate the CRT display, a “realistic” image of the surface is presented.
This is the third and final physical principle of the electron microscope, the ability to form a raster beam of focused electrons on a small area of an object that is then presented as a raster of a much larger area, thus providing magnification, for viewing and interpretation.
Of course with modern digital processing of the raster scan signals, sometimes the presentation of the image to the human eye is avoided altogether until a computer program has mashed the raw data into a more pleasing or understandable form. Electron microscope images are often pseudo-colored to represent different interactions of the focused electron beam with the object, but these are just bells and whistles that have nothing to do with the physics of how it works.