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[[File:HrtemMg.png|thumb|High-resolution image of [[magnesium]] sample.]]
'''High-resolution transmission electron microscopy''' is an imaging mode of specialized [[transmission electron microscope]]s that allows for direct imaging of the atomic structure of samples.<ref>{{cite book |title=Experimental high-resolution electron microscopy |last=Spence |first=John C. H | author-link = John C. H. Spence |year=1988 |orig-year=1980 |publisher=Oxford U. Press |location=New York |isbn=978-0-19-505405-7 }}</ref><ref>{{cite journal|last1=Spence|first1=J. C. H.|author-link1 = John C. H. Spence|title=Imaging dislocation cores - the way forward|journal=Phil. Mag.|date=2006|volume=86|issue=29–31|pages=4781–4796|doi=10.1080/14786430600776322|bibcode = 2006PMag...86.4781S |s2cid=135976739|display-authors=etal}}</ref> It is a powerful tool to study properties of materials on the atomic scale, such as semiconductors, metals, nanoparticles and sp<sup>2</sup>-bonded carbon (e.g., graphene, C nanotubes). While this term is often also used to refer to high resolution scanning transmission electron microscopy, mostly in high angle annular dark field mode, this article describes mainly the imaging of an object by recording the two-dimensional spatial wave amplitude distribution in the image plane,
|journal= Microscopy and Microanalysis |volume=14 |issue=5 |pages=469–477 |doi=10.1017/S1431927608080902 |pmid=18793491 |bibcode=2008MiMic..14..469K |s2cid=12689183 }}</ref> At these small scales, individual atoms of a crystal and [[Crystal defect|
One of the difficulties with high resolution transmission electron microscopy is that image formation relies on phase contrast. In [[phase-contrast imaging]], contrast is not intuitively interpretable, as the image is influenced by aberrations of the imaging lenses in the microscope. The largest contributions for uncorrected instruments typically come from defocus and astigmatism. The latter can be estimated from the so-called Thon ring pattern appearing in the Fourier transform modulus of an image of a thin amorphous film.
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The interaction of the electron wave with the crystallographic structure of the sample is complex, but a qualitative idea of the interaction can readily be obtained. Each imaging electron interacts independently with the sample. Above the sample, the wave of an electron can be approximated as a plane wave incident on the sample surface. As it penetrates the sample, it is attracted by the positive atomic potentials of the atom cores, and channels along the atom columns of the crystallographic lattice (s-state model<ref>{{cite journal|last=Geuens|first=P|author2=van Dyck, D|title=The S-state model: a work horse for HRTEM.|journal=Ultramicroscopy|date=Dec 2002|volume=3-4|issue=3–4|pages=179–98|doi=10.1016/s0304-3991(02)00276-0|pmid=12492230}}</ref>). At the same time, the interaction between the electron wave in different atom columns leads to [[Bragg diffraction]]. The exact description of dynamical scattering of electrons in a sample not satisfying the [[weak phase object approximation]], which is almost all real samples, still remains the holy grail of electron microscopy. However, the physics of electron scattering and electron microscope image formation are sufficiently well known to allow accurate simulation of electron microscope images.<ref>{{cite journal |title=Computed crystal structure images for high resolution electron microscopy|author=O'Keefe, M. A., Buseck, P. R. and S. Iijima|volume=274|year=1978|pages=322–324| doi= 10.1038/274322a0 | journal=Nature | issue=5669 | bibcode=1978Natur.274..322O|s2cid=4163994}}</ref>
As a result of the interaction with a crystalline sample, the '''electron exit wave''' right below the sample ''φ<sub>e</sub>('''x''','''u''')'' as a function of the spatial coordinate '''''x''''' is a superposition of a plane wave and a multitude of diffracted beams with different in plane [[Spatial frequency|spatial frequencies]] '''''u''''' (spatial frequencies correspond to scattering angles, or distances of rays from the optical axis in a diffraction plane). The phase change ''φ<sub>e</sub>('''x''','''u''')'' relative to the incident wave peaks at the location of the atom columns. The exit wave now passes through the imaging system of the microscope where it undergoes further phase change and interferes as the '''image wave''' in the imaging plane (mostly a digital pixel detector like a CCD camera).
===The phase contrast transfer function===
The phase [[contrast transfer function]] is a function of limiting apertures and [[Aberration in optical systems|aberrations]] in the imaging lenses of a microscope. It describes their effect on the phase of the exit wave ''φ<sub>e</sub>('''x''','''u''')'' and propagates it to the image wave. Following ''Williams and Carter'',<ref>{{cite book |title=Transmission electron microscopy: A textbook for materials science |last=Williams |first=David B. |author2=Carter, C. Barry |year=1996 |publisher=Plenum Press |location=New York |isbn=978-0-306-45324-3 |url-access=registration |url=https://archive.org/details/transmissionelec0002will }}</ref>
: <math>CTF(u)=A(u)E(u)2\sin(\chi(u))</math>
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*[http://www.tf.uni-kiel.de/matwis/amat/def_en/kap_6/backbone/r6_3_4.html High Resolution Transmission Electron Microscopy Overview]
==
{{reflist|2}}
{{Electron microscopy}}
[[Category:Electron microscopy techniques]]
[[Category:Scientific techniques]]
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