Fifth-order asymptotic geometric aberrations of electron lenses.

In this article the analytical expressions of the fifth-order asymptotic geometric aberrations of electron lenses are derived by Mathematica. The process of the derivation is analogous to the method described in "Principles of Electron Optics" by P.W. Hawkes and E. Kasper. All the analytical formulae for asymptotic aberration coefficients in polynomials in the reciprocal magnification are numerically cross-validated with the differential algebraic (DA) method. The results indicate that the derived formulae are doubtless correct.