Stigmator

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For early electron microscopes - between the 1940s and 1960s{{cite book|author=Jon Orloff|title=Handbook of Charged Particle Optics, Second Edition|url=https://books.google.com/books?id=y0FF19lud5YC|date=24 October 2008|publisher=CRC Press|isbn=978-1-4200-4555-0|page=130}} - astigmatism was one of the main performance limiting factors.{{cite book|author=Peter W. Hawkes|title=The Beginnings of Electron Microscopy|url=https://books.google.com/books?id=QEHgBAAAQBAJ&pg=PA369|date=6 November 2013|publisher=Elsevier Science|isbn=978-1-4832-8465-1}} 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.{{cite book|author=Jon Orloff|title=Handbook of Charged Particle Optics, Second Edition|url=https://books.google.com/books?id=y0FF19lud5YC|date=24 October 2008|publisher=CRC Press|isbn=978-1-4200-4555-0|page=292}}Batten, C. F. (2000). Autofocusing and astigmatism correction in the scanning electron microscope (Doctoral dissertation, Faculty of the Department of Engineering, University of Cambridge).{{cite book|author1=Elizabeth M. Slayter|author2=Henry S. Slayter|title=Light and Electron Microscopy|url=https://books.google.com/books?id=LlePVS9oq7MC|date=30 October 1992|publisher=Cambridge University Press|isbn=978-0-521-33948-3|page=240}} Therefore, to improve the resolving resolution, the astigmatism had to be corrected.{{cite journal|last1=Hillier|first1=James|last2=Ramberg|first2=E. G.|title=The Magnetic Electron Microscope Objective: Contour Phenomena and the Attainment of High Resolving Power|journal=Journal of Applied Physics|volume=18|issue=1|year=1947|pages=48|issn=0021-8979|doi=10.1063/1.1697554|bibcode=1947JAP....18...48H }} The first commercially used stigmators on electron microscopes were installed in the early 1960s.

The stigmatic correction is done using an electric or magnetic field perpendicular to the beam.{{cite book|author=Anjam Khursheed|title=Scanning Electron Microscope Optics and Spectrometers|url=https://books.google.com/books?id=pLO1gT9owEIC&pg=PA47|year=2011|publisher=World Scientific|isbn=978-981-283-667-0}} By adjusting the magnitude and azimuth of the stigmator field, asymmetric astigmatization can be compensated for. Stigmators produce weak fields compared to the electromagnetic lenses they correct, as usually only minor correction are necessary.{{cite book|author1=Peter W. Hawkes|author2=E. Kasper|title=Principles of Electron Optics: Basic Geometrical Optics|url=https://books.google.com/books?id=yXsqpL70wQMC&pg=PA517|date=24 April 1996|publisher=Academic Press|isbn=978-0-08-096241-2|pages=517–}}

Stigmators create a quadrupole field, and thus have to consist of at least four poles, but hexapole, octopole and dodecapole stigmatizors are also used, with octopole stigmators being the most common.{{cite book|author=P. Rai-Choudhury|title=Handbook of Microlithography, Micromachining, and Microfabrication: Microlithography|url=https://books.google.com/books?id=-kbT328H1XQC&pg=PA154|date=January 1997|publisher=IET|isbn=978-0-85296-906-9|page=154}}{{cite book|author=Peter W. Hawkes|title=The Beginnings of Electron Microscopy|url=https://books.google.com/books?id=QEHgBAAAQBAJ&pg=PA369|date=6 November 2013|publisher=Elsevier Science|isbn=978-1-4832-8465-1|page=369}} 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.

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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.{{cite book|author=Saul Wischnitzer|title=Introduction to Electron Microscopy|url=https://books.google.com/books?id=SZM4BQAAQBAJ&pg=PA91|date=22 October 2013|publisher=Elsevier Science|isbn=978-1-4831-4869-4|pages=91–92}}

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.{{cite book|title=Magnetic Electron Lenses|url=https://books.google.com/books?id=_QP8CAAAQBAJ&pg=PA269|date=11 November 2013|publisher=Springer Science & Business Media|isbn=978-3-642-81516-4|page=269|first=W.D.|last=Riecke}}

==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.{{cite journal|last1=Rudnaya|first1=M.E.|last2=Van den Broek|first2=W.|last3=Doornbos|first3=R.M.P.|last4=Mattheij|first4=R.M.M.|last5=Maubach|first5=J.M.L.|title=Defocus and twofold astigmatism correction in HAADF-STEM|journal=Ultramicroscopy|volume=111|issue=8|year=2011|pages=1043–1054|issn=0304-3991|doi=10.1016/j.ultramic.2011.01.034|pmid=21740867}} For a stigmatic image, it is round, this property can be used by algorithms to reduce the astigmatic aberration.

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.{{cite book|author1=B.G. Yacobi|author2=L.L. Kazmerski|author3=D.B. Holt|title=Microanalysis of Solids|url=https://books.google.com/books?id=MygDCAAAQBAJ&pg=PA81|date=29 June 2013|publisher=Springer Science & Business Media|isbn=978-1-4899-1492-7|page=81}} The use of three post-sample stigmators is proposed to reduce linear distortionBischoff, M., Henstra, A., Luecken, U., & Tiemeijer, P. C. (2013). U.S. Patent No. 8,569,693. Washington, DC: U.S. Patent and Trademark Office.

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

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