Reduce spherical aberration of doublet of combined quadrupole lenses (rectangular model)

The optimization calculations are made to find the optimum properties of doublet of combined quadrupole lens consist of electrostatic and magnetic lenses to produce reduce spherical aberration lens. The rectangular model is used and finds the properties of lens as the magnification and aberration coefficient. To find the optimum value of spherical aberration coefficient, the effect of both the excitation parameter of the lens, distance between of lenses and the effective wave length of the lens as active parameter to get the optimization.