Stigmator

A stigmator is a component of electron microscopes that reduces astigmatism of the beam by imposing a weak electric or magnetic quadrupole field on the electron beam.

Background

Quadrupole field created by four wires. The principle of a stigmator is that the current through each of the wires would be adjusted to change the shape of the beam.

For early electron microscopes - between the 1940s and 1960s^[1] - astigmatism was one of the main performance limiting factors.^[2] Sources of this astigmatism include misaligned objectives, non-uniform magnetic fields of the lenses, which was especially hard to correct, lenses that aren't perfectly circular and contamination on the objective aperture.^[3][4][5] Therefore, to improve the resolving resolution, the astigmatism had to be corrected.^[6] The first commercially used stigmators on electron microscopes were installed in the early 1960s.^[1]

The stigmatic correction is done using an electric or magnetic field perpendicular to the beam.^[7] By adjusting the magnitude and azimuth of the stigmator field, asymmetric astigmatization can be compensated for.^[5] Stigmators produce weak fields compared to the electromagnetic lenses they correct, as usually only minor correction are necessary.^[8]

Number of poles

Stigmators create a quadrupole field, and thus have to consist of at least four poles, but hexapole,^[9] octopole and dodecapole stigmatizors are also used, with octopole stigmators being the most common.^[10][11] The octopole (or higher order of poles) stigmatizers also produce a quadrupole field, but use their additional poles to align the imposed field with the direction of the stigmatization ellipticity.^[3]

Types

Magnetic stigmator

The magnetic stigmator is a weak cylindrical lens that can correct the cylindrical component of the beam. It can consist of metal rods which induce a magnetic field, which are inserted with their long axis towards the beam center. By retracting or extending the rods, the astigmatism can be compensated.^[12]

Electromagnetic

Electromagnetic stigmators are stigmators that are integrated with the lenses and directly deform the magnetic field of the lens(es). These were the first types of stigmators to be used.^[9][12]

Automatic stigmators

In most cases, the astigmatism can be corrected using a constant stigmator field which is adjusted by the microscope operator. The main cause of astigmatism, the non-uniform magnetic field produced by the lenses, usually does not change noticeable during a TEM session. A recent development are computer-controlled stigmators, which usually use the Fourier transform of the image to find the ideal stigmator setting. The Fourier transform of an astigmatic image is usually elliptically shaped.^[13] For a stigmatic image, it is round, this property can be used by algorithms to reduce the astigmatic aberration.^[4]

Multiple stigmator systems

Normally, one stigmator is sufficient, but TEMs normally contain three stigmators: one to stigmatize the source beam, one to stigmatize real-space images, and one to stigmatize diffraction patterns. These are commonly referred to as condensor, objective, and intermediate (or diffraction) stigmators.^[14] The use of three post-sample stigmators is proposed to reduce linear distortion^[15]

See also

• Anastigmat, a photographic lens completely corrected for the three main optical aberrations

References

1. Jon Orloff (24 October 2008). Handbook of Charged Particle Optics, Second Edition. CRC Press. p. 130. ISBN 978-1-4200-4555-0.
2. Peter W. Hawkes (6 November 2013). The Beginnings of Electron Microscopy. Elsevier Science. ISBN 978-1-4832-8465-1.
3. Jon Orloff (24 October 2008). Handbook of Charged Particle Optics, Second Edition. CRC Press. p. 292. ISBN 978-1-4200-4555-0.
4. Batten, C. F. (2000). Autofocusing and astigmatism correction in the scanning electron microscope (Doctoral dissertation, Faculty of the Department of Engineering, University of Cambridge).
5. Elizabeth M. Slayter; Henry S. Slayter (30 October 1992). Light and Electron Microscopy. Cambridge University Press. p. 240. ISBN 978-0-521-33948-3.
6. Hillier, James; Ramberg, E. G. (1947). "The Magnetic Electron Microscope Objective: Contour Phenomena and the Attainment of High Resolving Power". Journal of Applied Physics. 18 (1): 48. Bibcode:1947JAP....18...48H. doi:10.1063/1.1697554. ISSN 0021-8979.
7. Anjam Khursheed (2011). Scanning Electron Microscope Optics and Spectrometers. World Scientific. ISBN 978-981-283-667-0.
8. Peter W. Hawkes; E. Kasper (24 April 1996). Principles of Electron Optics: Basic Geometrical Optics. Academic Press. pp. 517–. ISBN 978-0-08-096241-2.
9. Riecke, W.D. (11 November 2013). Magnetic Electron Lenses. Springer Science & Business Media. p. 269. ISBN 978-3-642-81516-4.
10. P. Rai-Choudhury (January 1997). Handbook of Microlithography, Micromachining, and Microfabrication: Microlithography. IET. p. 154. ISBN 978-0-85296-906-9.
11. Peter W. Hawkes (6 November 2013). The Beginnings of Electron Microscopy. Elsevier Science. p. 369. ISBN 978-1-4832-8465-1.
12. Saul Wischnitzer (22 October 2013). Introduction to Electron Microscopy. Elsevier Science. pp. 91–92. ISBN 978-1-4831-4869-4.
13. Rudnaya, M.E.; Van den Broek, W.; Doornbos, R.M.P.; Mattheij, R.M.M.; Maubach, J.M.L. (2011). "Defocus and twofold astigmatism correction in HAADF-STEM". Ultramicroscopy. 111 (8): 1043–1054. doi:10.1016/j.ultramic.2011.01.034. ISSN 0304-3991. PMID 21740867.
14. B.G. Yacobi; L.L. Kazmerski; D.B. Holt (29 June 2013). Microanalysis of Solids. Springer Science & Business Media. p. 81. ISBN 978-1-4899-1492-7.
15. Bischoff, M., Henstra, A., Luecken, U., & Tiemeijer, P. C. (2013). U.S. Patent No. 8,569,693. Washington, DC: U.S. Patent and Trademark Office.