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Digital methods of high precision have been developed for the calculation of electric fields and trajectories in electrostatic lenses and a computer program was written to apply these methods to the two-tube lens. The increased precision results from the use of nine-point formulas in the relaxation calculation of potentials in place of previously used five-point formulas and from the use of an improved predictor-corrector method for the calculation of trajectories. Trajectories obtained with these methods are sufficiently precise to determine third-order aberration coefficients.

journal of research of the national bureau of standards. section a. physics and chemistry

Accurate calculations of properties of the two-tube electrostatic lens. I. Improved digital methods for the precise calculation of electric fields and trajectories