Fifth-order 6-fold Astigmatism & its Corrections
- Practical Electron Microscopy and Database -
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This book (Practical Electron Microscopy and Database) is a reference for TEM and SEM students, operators, engineers, technicians, managers, and researchers.


The 6-fold astigmatism |A6| in double hexapole (or dodecapole) systems is given by [2],

          Fifth-order 6-fold Astigmatism ------------------------ [2239]

          f0 -- The focal length of the objective lens;
          M -- The (de)magnification for (S)TEM between the corrector and the objective lens;
          Cs -- The original spherical aberration coefficient of the objective lens;
          z -- The multipole length.

The effect of A6 astigmatism is more critical at low accelerating voltages than at high voltages because the focal length at low voltages is much smaller than that at high voltages.

Two main methods for compensating for the A6 have been proposed. Müller et al. optimized the hexapole length for the compensation [1]. The A6 astigmatism generated by the first and second hexapoles is successfully cancelled out by the one from the combination of third-order aberrations of the transfer lenses and the 3-fold astigmatism introduced by the hexapole elements. Sasaki et al. proposed a delta corrector [2 - 4], consisting of a triple dodecapole system, to compensate for the positive A6 (generated by the first and second dodecapoles) with a negative A6 (from the second and third dodecapoles).







[1] Müller H, Uhlemann S, Hartel P, and Haider M (2006) Advancing the hexapole Cs-corrector for the scanning transmission electron microscope. Microsc. Microanal. 12: 442–455.
[2] Sawada H, Sasaki T, Hosokawa F, Yuasa S, Terao M, Kawazoe M, Nakamichi T, Kaneyama T, Kondo Y, Kimoto K, and Suenaga K
(2009) Correction of higher order geometrical aberration by triple 3-fold astigmatism field. J. Electron Microsc. 58: 341–347.
[3] Sawada H, Sasaki T, Hosokawa F, Yuasa S, Terao M, Kawazoe M, Nakamichi T, Kaneyama T, Kondo Y, Kimoto K, and Suenaga K
(2010) Higher-order aberration corrector for an image-forming system in a transmission electron microscope. Ultramicroscopy, doi:10.1016/j.
[4] Takeo Sasaki, Hidetaka Sawada, Fumio Hosokawa, Yuji Kohno, Takeshi Tomita, Toshikatsu Kaneyama, Yukihito Kondo, Koji Kimoto, Yuta Sato, and Kazu Suenaga, Performance of low-voltage STEM/TEM with delta corrector and cold field emission gun, Journal of Electron Microscopy 59(Supplement): S7–S13 (2010).





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