Correction of misalignment aberrations of a hexapole corrector using the differential algebra method

Overcoming the limitations of the Schertzer theorem is a long story in electron microscopy. Although the basic principle of a spherical aberration (C3) correction was suggested as early as in 1947 the first experimental correctors of spherical aberration were only realized in the last decade of the 20th century. The recent multipole correctors are designed for high-energy\nTEM or STEM, where the corrector system enables reaching the atomic resolution. On the other\nhand, the corrector for low-energy SEM has been developed but this type of corrector must also contain chromatic aberration (Cc) correction to reduce the effect of the non-zero energy width. Recently, the energies of SEM reach 30 keV and transmission mode (TSEM) is a standard part of the instrument. Standard resolution in TSEM is about 0.6 nm and it is limited by C3. Reaching atomic resolution with this set-up is not a real expectation because of its instability, but the resolution of about 0.2 nm would increase the field of applications. Corrector for these type of instruments should be (a) simple, compact and cheap (b) only spherical aberration of the third,\noptionally the fifth order must be corrected (c) effect of the chromatic aberration may be reduced by energy filtering. We studied design based on Rose’s hexapole corrector