In the present work, a new analytical function has been proposed to represent the axial magnetic field strength for the symmetrical magnetic lenses. Thereby, the correspondence magnetic flux distribution, that is necessary, for determing the aberration integrals, can be deduced immediately. The effects of the geometrical and physical parameters as an optimization parameters on the objective focal properties and the pole piece configuration have been investigated. The results have shown, that new conclusions concerning comparison between the results of synthesis procedure with that of analysis procedure for the same initial conditions can be set up.