A particle-optical corrector for correcting spherical aberrations of an electron microscope, thereby preventing a threefold axial astigmatism, an axial three-lobed aberration of fourth order and a sixfold axial astigmatism, wherein the corrector comprises:
- a first outer multipole element of length L′ for generating a first hexapole field;
- a second central multipole element of length L for generating a second hexapole field in a symmetry plane of the corrector;
- a third outer multipole element of length L′ for generating a third hexapole field, wherein said first outer multipole element and said third outer multipole element are identical and said first and said third hexapole fields have identical strengths, wherein a strength of said second hexapole field is selected with respect to strengths of said first and said third hexapole fields such that the threefold axial astigmatism vanishes, said strengths of said first and said third hexapole fields thereby being selected such that the corrector does not have the sixfold axial astigmatism;
- a first round lens doublet having a first doublet first round lens and a first doublet second round lens, wherein said first doublet second round lens is disposed closer to said symmetry plane than said first doublet first round lens, said first doublet second round lens having a first focal length, wherein said first doublet second round lens is disposed at a separation from said symmetry plane which is equal to said first focal length, said first doublet first round lens having a second focal length, wherein said first doublet first round lens is disposed at a separation from said first doublet second round lens which is equal to said first focal length plus said second focal length;
- a second round lens doublet having a second doublet first round lens and a second doublet second round lens, wherein said second doublet first round lens is disposed closer to said symmetry plane than said second doublet second round lens, said second doublet first round lens also having said first focal length, wherein said second doublet first round lens is disposed at a separation from said symmetry plane which is also equal to said first focal length, said second doublet second round lens also having said second focal length, wherein said second doublet second round lens is disposed at a separation from said second doublet first round lens which is equal to said first focal length plus said second focal length, wherein said first multipole element is separated from said first doublet first round lens by said second focal length plus an additional separation and said third multipole element is separated from said second doublet second round lens by said second focal length plus said additional separation, said additional separation being selected such that, for said lengths L and L′, the axial three-lobed aberration of fourth order vanishes, said length L of said second central multipole element thereby being selected relative to said lengths L′ of said first and third outer multipole elements in such a manner that an axial three-lobed aberration of sixth order vanishes for a given ratio between said first and said second focal lengths.