Magnification of Electron Microscopes
- Practical Electron Microscopy and Database -
- An Online Book -  


This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.



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,

                image point -------------------------- [4274a]

       M -- Magnification
       ω -- Lens strength, given by,
                strength parameter of the lens ---------------------------------- [4274b]

Rotationally Symmetrical Electron Lenses

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,

       focus of EMs -------------------------- [4274c]
        focus of EMs ------------------- [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]



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