four-fold astigmatism

The four-fold astigmatism, one of the third-order axial geometrical aberrations, is a parasitic aberration exhibiting four-fold symmetry. (Note that it is called a fourth-order aberration in terms of the wave aberration.) The four-fold astigmatism appears as a pattern with four-fold symmetry in a Ronchigram. In the case of a TEM equipped with a Cs corrector, prior to microscope observation, aberrations are measured and then the aberrations including the four-fold astigmatism are corrected by the automatic aberration correction function with the use of the deflectors of the Cs corrector.
It is possible to produce a four-fold astigmatism using magnetic octupole fields. In an octupole Cs corrector, the spherical aberration of the objective lens is corrected using the four-fold astigmatism by utilizing the fact that the four-fold astigmatism has the same order as that of the third-order spherical aberration of the objective lens to be corrected.

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