Third-order asymptotic aberration coefficients of electron lenses. III. Formulas and results for the two-tube electrostatic lens.

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Abstract
The third‐order asymptotic aberration coefficients of round electrostatic electron lenses are formulated, following Hawkes, in a form independent of object and aperture positions. Six quantities are sufficient to specify completely the third‐order aberration properties of electrostatic electron lenses.Equations for these six quantities are derived in the form of integrals involving derivatives of the axial potential no higher than the second. Using these equations and our previously calculated potentials and first‐order trajectories we have computed the six aberrations coefficients for the two‐tube electrostatic lens for voltage ratios from 1.1 to 10 000. The results are believed accurate to better than 0.2%.
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