Correction of parasitic aberrations of hexapole corrector using differential algebra method

We demonstrate an application of the differential algebraic method in optimization of a hexapole corrector of spherical aberration for the transmission regime of the standard scanning electron microscope. We introduce the method by visualization of the effect of all correcting elements to illustrate the principle of the corrector. Special interest is given to parasitic aberrations and their correction using additional deflectors before and inside the corrector. They can alter the off-axial position and tilt of the beam in the hexapoles. The critical values of the parasitic aberration coefficients are calculated using a wave-optical method, which determines the stability of the deflection system, the lens doublet, and the hexapoles. The derived properties of the parasitic aberrations are used in an alignment procedure of the system with the corrector.