Abstract: A new geometric figure of the three dimensional coordinate for studying the first order lateral aberration radius ip cathode lenses has been suggested. The multi-energy point spread function (PSF) considering angular distribution and initial energy distribution for the cathode lenses has vividly been depicted and the expressions of normalized multi-energy PSF at arbitrary image plane have also been given, in which both the various parameters and the limits of different integrals have a clear and definite physical and mathematical meaning. Some practical examples for determining multi-energy PSF in the sharp focusing systems and proximity focusing systems have also been described