Improved fifth-order geometric aberration coefficients of electron lenses

Abstract

In this paper, fifth-order geometric aberrations of round electron lenses have been restudied. Improved analytical formulae of the aberration coefficients were derived by the computer algebra software-Mathematica-and their correctness verified by cross-checking with numerical integration and differential algebraic techniques for a given electromagnetic lens.

The correction of electron lens aberrations

“…The fifth and even higher order geometrical aberrations and the chromatic aberrations of third order were analysed and a full list of formulae for the fifth order aberration coefficients of round lenses in reasonably usable form at last became available (Liu [113]; but see Hawkes [61], in which these expressions are reproduced with corrections furnished by the author). The two leading software Fig.…”

First- and third-order chromatic aberrations in Glaser magnetic lens for object magnetic immersion

“…The numerical results of third- and fifth-order aberrations of a given electromagnetic lens computed through the DA technique are shown to be in excellent agreement with those evaluated using electron optical aberration integrals. From his work, one can conclude that the DA technique is concise, efficient, and precise for electron optical aberration analysis and the code COSY INFINITY he used, has been proven to be an excellent computer code for such purposes [ [5] , [6] , [7] , [8] , [9] , [10] ].…”