Advances in Electronics and Electron Physics, Vol. 76 by Peter W. Hawkes (Ed.)

By Peter W. Hawkes (Ed.)

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B. In addition to geometrical aberrations, there are errors known as chromatic aberrations, by analogy with light optics. These arise from the fact that the effect of an electrical field on high-energy particles is not as strong as on low-energy particles, so that if a beam consists of particles of different energies, a point image in the Gaussian plane looks like a spot of finite size. C. There are other factors responsible for poor focusing, for example, mechanical defects in electron lenses, external field, and electrode contamination.

A similar derivation can be drawn for the y projection. By grouping the identical power terms of transverse shifts in the object and aperture planes in Eq. (89), we shall obtain a general expression for the aberration broadening. For the Gaussian image plane it has the form2 = 'Yi + B 2 x x B y i + GlxxixO + G Z x y i x O + G 3 x x B y B y 0 + E L x x B x i + E2xxByi + E 3 x y B x O y 0 + Dlxxi + D Z x x O y O2, Blxx; + B 2 y x i Y B + GlyyiyO + G 2 y x i y 0 + G 3 y x B y B x 0 + ElyyBy; + E2yyBxi + E 3 y x B x O y 0 + DlyY: + &yXiYO.

YA. YAVOR If the particle beam is not planar, it is necessary to also analyze the yprojections of the trajectories. Three situations are likely to occur. 1. The partial solution y,(z) does not become zero at any value z . In this case the beam emerging from a point z = z,, in the plane z = z i x is converged into a line parallel to the y-axis and is known as a line image; this is one-directional focusing. The line-image length is defined by the product 2 ~ rnaxYa(zix). d 2. The function y,(z) becomes zero at the point z = ziy # zix.

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