A study of first- and third-order chromatic aberrations for electrostatic round lenses

In this paper the first- and third-order chromatic aberrations of electrostatic round lenses have been studied based on the electron optical-canonical aberration theory. The present work uses the Hamiltonian function expansion method to derive all analytical expressions of the first- and third-order chromatic aberration coefficients instead of the generalized integration transformation method. Its advantage is that it is much simpler. An application to bi-potential immersion lens has been illustrated. It is hoped that this work would be helpful for investigating high-order electron optical aberrations in rotationally symmetric lenses, including geometric aberrations.