Patent Number: 
Section: claims

1. A corrector for axial and off-axial beam paths of a particle-optical system, the corrector comprising:a first correction piece;a second correction piece disposed behind said first correction piece in a beam path on an optical axis, wherein each of said first and said second correction pieces comprises four successive multipole elements disposed symmetrically with respect to a center plane, wherein a first and a fourth multipole element of each of said first and said second correction pieces generate quadrupole fields and a second and a third multipole element of each of said first and said second correction pieces generate superposed magnetic and electric octupole fields and quadrupole fields, wherein quadrupole fields of all four multipole elements are successively rotated from one to the next through 90° to enable chromatic aberration correction using astigmatic intermediate images in said second and third multipole elements through interaction of said magnetic and electric fields as well as aperture aberration correction using said quadrupole fields and said octupole fields; anda central multipole element disposed in said center plane, said central multipole element generating an octupole field for eliminating an astigmatism of third order. 2. The corrector of claim 1, wherein twelve-pole fields are generated using said second and third multipole elements of said first correction piece and said central multipole element for correcting aberrations of fifth order. 3. The corrector of claim 2, wherein a star aberration of fifth order, a rosette aberration of fifth order, and an astigmatism of fifth order are each corrected with one of the twelve-pole fields. 4. The corrector of claim 1, wherein further octupole fields are generated for correcting an anisotropic coma of an objective lens using said multipole elements, said further octupole fields being rotated through 22.5° with respect to said octupole fields for correcting said aperture aberration, wherein the octupole field strengths are anti-symmetrical with respect to symmetry planes of said first and said second correction pieces and with respect to said center plane. 5. The corrector of claim 1, wherein at least said second and third multipole-elements of said first and second correction pieces and said central multipole element are twelve-pole elements which, by means of a controller, can generate differing, up to twelve-pole, fields, including superposition of different fields through a corresponding current and/or voltage load. 6. The corrector of claim 1, wherein two round transfer lenses are associated with the corrector on an objective side, a field setting of which can eliminate or substantially reduce aperture aberrations of fifth order and/or radial coma of third order. 7. The corrector of claim 6, wherein said quadrupole and octupole fields of said second and third multipole elements of said first and second correction pieces and said octupole field of said central multipole element are subjected to a readjustment, such that said field setting of said transfer lenses eliminates newly caused chromatic aberrations of first order and aperture aberrations of third order. 8. The corrector of claim 7, wherein twelve-pole fields of said second and third multipole elements of said first corrector and a twelve-pole field of said central multipole element can be readjusted to eliminate aberrations of higher order caused by said transfer lenses and said readjustment. 9. The corrector of claim 8, wherein chromatic aberrations of first order, aperture aberrations of third order, and aberrations of higher order caused by aberration corrections are eliminated through readjustment of said transfer lenses, said quadrupole fields of said first and second correction pieces, and said octupole fields of said first and second correction pieces and of said central multipole element and by subsequent readjustment of said twelve-pole fields of said first correction piece and of said central multipole element and then by readjustment of further octupole fields of all said multipole elements that generate quadrupole fields followed by iterative readjustment, in the above-mentioned sequence, for reducing aberrations caused by respective previous readjustments until those alternations are reduced to an amount that can be tolerated for a desired imaging. 10. The corrector of claim 1, wherein an image resolution of up to 10,000 image points along an image diameter can be obtained by allowing a small aperture aberration of fifth order. 11. A transmission electron microscope having correction of an electron beam using the corrector of claim 1.