Practical Electron Microscopy and Database

The magnification of electron microscopes is defined as the ratio of a specimen size and an image size recorded on a CCD camera or photo-film.

As discussed in Bell-Shaped Field in EMs, by introducing dimensionless coordinates y = r/a and x = z/a = cot φ (where we have the variable φ varying from π (z = −∞) to π/2 (z = 0) and then to 0 (z = +∞).), by following the theory of trajectories of electron in electron lenses, and by assuming a ray passing through a point P₀(y₀, φ₀) in front of the lens, a image point P₁(y₁, φ₁) can be theoretically obtained,

                 -------------------------- [4274a]

where,
       M -- Magnification
       ω -- Lens strength, given by,
                 ---------------------------------- [4274b]

Figure 4274. Rotationally symmetric magnetic fields and electron lenses.

Newton’s lens equation of light optics suggests Z₀Z₁ = f₀f₁. Further calculation based on bell-shaped field, we can obtain,

        -------------------------- [4274c]
         ------------------- [4274d]

We can see that the focal lengths f₀ and f₁ are not the same as the distances z(F₀) and z(F₁) of the foci from the lens center at z = 0, indicating that electron lenses cannot be treated as thin lenses. 

The magnification M in Equation 4274a can be re-written in terms of f and Z,

         M = f₀/Z₀ = Z₁/f₁ ------------------- [4274e]