This paper deals with the generalization of the theory of third order aberrations of an electrical deflection system under the situation as the electron beam is originally immersed in an electric field. The formulae of third order electrical deflection aberration coefficients in an arbitrary plane have been derived. It can be applied to either sequential deflection systems or superimposed deflection yokes. By means of mathematical manoeuvres, the formulae are simplified and made easy for calculation. In order to obtain high precision, the first and second order derivatives of the field E0(z) have been eliminated. In accordance with our previous work, the nomenclature and calculating procedure are kept the same as before, so we can adopt the same computing scheme.Finally, we have described the relations between the patterns of the raster distortion, astigmatism, field curvature, coma, and the corresponding deflection aberration coefficients for a small electron beam which is initially point-focused on the image screen. These relations may also be applied to the third order magnetic deflection aberrations.
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