In the present paper, by means of the variational principle, the relativistic aberration theory for a combined electromagnetic foeusing-deflection system possessing a spherical cathode lens is studied. We have discussed the following general cases: electrons emitted from the cathode possess definite energy and angular initial distributions; the objective and image fields have finite curvatures; the cathode is situated in both magnetic and transversal electric fields. For these general cases the general formulae of aberration coefficients for first and third order transversal geometrical and chromatic aberrations on any ideal image plane are given in explicit form. The above-mentioned aberration coefficient formulae can be applied to the following eases: either the wide electron beam system or the narrow electron beam.system; either the relativistic or the non-relativistic electron optical system; either the cathode or the screen having the spherical or the planar shapes. In the present work, the electron trajectories are described in the complex form. The aberrations are expressed in the matrix form, and are thus suitable for computer computations.
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