I am trying to understand what numerical aperture and extraction field means in a scanning electron microscope. From what I understand numerical aperture is used to set the Depth of Focus which is generally the permitted focus range. Is Extraction field is voltage difference between the Objective Lens and the specimen? I am not sure how extraction field plays a part in resolution or the focus. Thanks for helping me out!
Numerical aperture in electron microscopy has a very similar meaning to that in optical microscopy. However, unlike optical microscopy there is only vacuum in the path of the beam so the lens doesn't have an index of refraction. In optical microscopes we define Numerical Aperture: NA = n*sin(theta) where n is the index of refraction. In electron microscopes, we just say the convergence angle = theta. Controlling the convergence angle in an SEM is done by changing the current through the lenses, or changing an aperture that is collimating the beam. Increasing the convergence angle means the focal point moves closer to the objective lens and the sample has to be moved up to be in focus. This generally provides better resolution. Thus, people often don't even bother describing the convergence angle in an SEM, but just say the working distance is 5 mm (for example).
The extraction field is the electric field around the electron emitter which aids in allowing the electrons to overcome the work function of the electron emitter material. Once the electrons leave the extraction system, they are usually accelerated further in order to pass through the optical system. If you have an image that you acquire at "10 keV" this is usually the accelerating voltage and not the extraction voltage (which may be just a few hundred volts or up to several keV.)
Generally speaking, the extraction voltage influences the resolution by allowing electrons to enter the optical system from a larger or smaller portion of the electron emitter, and thus with a wider/narrower range of angles and energies. If you adjust your extraction system to emit electrons only from the very tip of the emitter, then the beam will be more collimated and your resolution will improve at the cost of your beam current. This will mean that you will have to acquire longer to achieve the same signal to noise in your image.
90% of the time, the resolution of the instrument is not the limiting factor at all. It is the interactions of the beam with the sample that really limit your resolution. For example, operating at 20 keV will mean that electrons will bounce around within several microns in your sample and re-emit nearby. Thus, an electron beam with a FWHM of 1 nm will practically never produce an image with 1 nm resolution at a voltage like 20 keV.
I hope this clears things up!