Method for eliminating first, second and third-order axial image deformations during correction of the third-order spherical aberration in electron optical systems

A method for eliminating first-, second- and third-order axial aberrations during correction of a third-order spherical aberration in electron optical systems with hexapoles, comprising the steps of:

• determining a value of a first-, second- and third-order axial image deformation coefficients behind an electron optical system in an image plane;
• changing focussing and, through super-positioning of a quadrupolar field, a first-order axial astigmatism with two-fold symmetry being thereby corrected;
• correcting a second-order axial coma and a second-order axial astigmatism with three-fold symmetry, the second-order axial coma being corrected via a method comprising the steps wherein two hexapoles are superimposed by a pair of quadrupolar fields of the same magnitude, in which products from a sign of a hexapole field from said two hexapoles and the sign from a respective said quadrupolar field superimposed on the hexapole field are opposed to each other, while the second-order axial astigmatism with three-fold symmetry is corrected via a method comprising the step of super-positioning an additional hexapole field;
• eliminating a third-order astigmatism with four-fold symmetry, wherein the off-axial deformation is one order higher, comprising the step that an optical axis is shifted until the off-axial fourth-order astigmatism fully compensates the axial astigmatism with four-fold symmetry;
• and,
• eliminating a third-order star deformation via a method wherein the off-axial deformation is one order higher, comprising the step of shifting a beam path perpendicularly relative to the optical axis until the fourth-order, off-axial star aberration, fully compensates the third-order axial star aberration,
• whereby after correction is performed, the first- and second-order deformations arising therefrom are eliminated with adjustment elements that do not, or only slightly, affect the third order.