Quadrupoles in Electron Lens Design

If the spherical aberration functions C₄ and C₃ are known, the distortion may hence be derived immediately. If, furthermore, the lens is symmetric, then C₄ = C₀ and C₃ = C₁ and so

$\begin{array}{l}C=C_4{m}^4+C_3{m}^3+C_2{m}^2+C_{3}m+C_4\left(\text{symmetric lens}\right)\\ D=-C_{4}m+\left(3f-2C_3\right)/8\end{array}$

  (94)

In practice, some of the coefficients C_i may not be required. In projector lenses, the magnification is normally high and hence m is small; we have

$C_s=C\simeq C_0\left(\text{projector}\right).$

  (95)

In probe-forming lenses, the spherical aberration is characterized by C_s′ = M⁴C_s [see Eqs. (72) and (74)]. We now have

$C_s^{\prime }={\mathit{CM}}^4=C_4+C_3$