six-fold astigmatism

"Six-fold astigmatism" is one of the fifth-order parasitic aberrations having six-fold symmetry. ("Two-fold astigmatism," which is conventionally called "astigmatism" has two-fold symmetry.) In the case of a current Cs corrector of the two-stage three-fold-field type, a six-fold astigmatism is generated as a combination of the aberrations of the three-fold fields in the two stages. The six-fold astigmatism is the largest aberration when the third-order spherical aberration, parasitic aberrations up to the fourth order and the fifth-order spherical aberration are successfully corrected. Thus, the aberration-corrected range is restricted by the six-fold astigmatism. A Ronchigram clearly shows a hexagonal shape pattern at its peripheral part, when the Cs corrector is incorporated in the illumination system. Two aberration correctors that can correct the six-fold astigmatism have been developed. One is an aberration corrector of a three-stage three-fold-field type composed of dodecapoles. This corrects the six-fold astigmatism by making the vector sum of the astigmatism produced in each three-fold field to be zero. Another is an aberration corrector of a two-stage three-fold-field type composed of hexapoles. This corrects the six-fold astigmatism using that of the opposite sign produced by the combination of the effect of the transfer lens and the three-fold field through optimizing the length of the hexapoles.

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