Can the Nomura lens be free of spherical aberration?

Abstract

SummaryNomura has recently claimed that a combination of magnetic lenses can be found that is free of spherical aberration. Doubt is cast on this claim.Ever since 1936, when Scherzer showed that, subject to various conditions, the spherical aberration coefficient of electron lenses cannot change sign, sporadic attempts have been made to find round lenses for which this result is not true. The first and best known are those of Glaser (1940Glaser ( , 1956) and other claims have been made by Garg (1982, see Scherzer, 1982 and by S. Hosoki (see Davey & Hawkes, 1995); most recently, Nomura has entered the lists. He first claimed to have found a combination of round lenses free of spherical aberration at the meeting of EMAG in Oxford in 2003, but his paper was not accepted for publication in the Proceedings. Recently, an ostensibly aberration-free system was presented at EMC-2008 and is described in the Proceedings (Nomura, 2008). Our purpose here is to point out a flaw in his reasoning.It will be recalled that Scherzer showed that the integrand in the formula for the spherical aberration coefficient C s can be written as a sum of squared terms and that in order to establish this formula, several partial integrations were required. Each of these generates a new integral and an integrated term; for example, Until some justification for the claim that [h(z)...] zi zo = 0 has been made, we cannot accept that Nomura's configuration has the remarkable properties assigned to it. Uber denÖffnungsfehler der Elektronenlinsen, Bemerkungen zu vorstehender Erwiderung.

Aberration correction past and present

“…But in a corrigendum, Glaser (1956c) acknowledges that he has made a mistake in the calculation and, after correcting this, C s falls among the permitted values. At least one person remains incredulous today (Nomura 2008;Hawkes 2009). It is usual to regard a paper by Scherzer that appeared in 1947 as the next major event in the aberration correction saga.…”