Both analysis and synthesis approaches of optimization method are used in the present work to finding the optimum design of magnetic and electrostatic deflectors which give rise to the minimum spherical and chromatic aberration. In magnetic deflector calculations, the synthesis approach is used; the saddle yoke deflection coil is used as the source of magnetic field, then some axial field distribution models are to be used and new field distribution model to be suggested. The moving objective lens concept is included in the computation of deflection field. Deflection aberrations are minimized for each field distribution model by changing the shape of the deflection coil, where the length and angle are varied. By using the optimum axial field distribution for each case, the pole pieces design which give rise to these field distributions is to be found by using reconstruction method. In electrostatic deflector calculations, both analysis and synthesis approaches are used to find optimum design, which give rise to minimum aberrations. Firstly, the analysis approach is used to study some electrostatic deflector designs which consists of two parallel-plates, and the optimization is made by changing the geometrical shape of the deflector by varying the dimensions of the parallel-plates. Secondly, the synthesis approach is used to find minimum values for the aberration by means of the new axial field distribution that has been put forward in the present work for the electrostatic deflectors under investigation. The shape of the deflector is found by using the reconstruction method. Finally, the magnetic and electrostatic deflectors are to be assembled to give complete columns of deflection systems and plot the trajectories of the beam traversing them.