Optical Microscopy
* History: Introduced by Antony van Leeuwenhoek (NL) in 1671.
* Characteristics: Visible and near UV photons, relatively long λ; Resolution about 2000 Å; 2003, Improved to less than 20 nm using "near-field Raman microscopy" [@ Hartschuh et al PRL(03)].
@ General references: Imhof & Vanden Bout AJP(03)may [laser-based, RL]; Tsang Opt(15)-a1411 [fundamental quantum limits].
@ Beating the diffraction limit: Müller & Enderlein PRL(10) + Blom & Widengren Phy(10) [image scanning microscopy]; Chu et al PRL(14).

X-Ray Diffraction Microscopy > s.a. X-Rays.
* History: Introduced by Max Laue in 1912 and used by Lawrence Bragg in 1913.
* Characteristics: Medium-hard X-rays with energies up to about 10 KeV; Resolution about 500–700 Å.
* Advantages: Good quality images at atomic or near-atomic scales.
* Disadvantages: A macroscopic crystal or oriented fiber sample has to be used, due to the low coherent scattering cross-section and the need to get a reasonably simple image.

Soft X-Ray Microscopy > s.a. X-Rays.
* History: Introduced in the 1950s.
* Advantages: Avoids the difficulties with the above methods.

Electron Microscopy
* History: Introduced by Ernst Ruska and Max Knoll (Berlin) in 1932.
* Characteristics: Uses electrons of energy 5–2000 KeV.
* Disadvantages: Specimen subjected to cellular disassembly and dehydration, and decoration with heavy atoms, to avoid the problems related to the high electron-water cross-section and to improve the contrast.
@ References: Alem et al PRB(09) + Klie Phy(09) [new resolution standard]; Marks Phy(13) [unexpected barrier to better resolution].

Scanning Tunneling (Electron) Microscopy
* History: Discussed in 1978, and introduced in 1981 (by Binnig and Rohrer); The first generation used magnetic levitation (with superconducting bowl) to avoid vibrations; Later used eddy-current damping; 1996, Four generations by now; 2004, Crystal imaged on sub-Å scales by exploiting a technique to correct aberrations.
* Idea: One positions the tip of an extremely sharp needle (best so far is 3 atoms) so close to a surface that the wavefunctions of electrons in the tip overlap those those of electrons in the surface, and a tunneling current is established, which is extremely sensitive to tip-surface separation.
* Characteristics: Allows to study surfaces at an atomic scale, with a lateral resolution of 1 Å, and a height corrugation accuracy of 0.01 Å; Initially limited to conductors, and under a vacuum, now these limitations partly overcome (1996).
@ General references: Binnig & Rohrer SA(85)aug; Golovchenko Sci(86)apr; Chen 93; Nellist et al Sci(04)sep + pw(04)sep [aberration correction].
@ Use for placing atoms: Meyer et al PRL(96) + pn(96)sep.
@ Watching single atoms move: Molinàs-Mata et al PRL(98); Kavanagh Phy(09) [aberration-corrected transmission electron microscopes]; van Houselt & Zandvliet RMP(10) [time-resolved STM].

Acoustic Microscopy
* History: Proposed by Sergei Y Sokolov (USSR) in 1949; Serious work on it started in the late 1960s.
* Characteristics: Resolution 200 Å.
@ References: Briggs & Kolosov 09.

Other Types and References
* Field ion microscopy: The first to achieve atomic resolution; Non scanning, uses a sharp tungsten needle, and gives an image of atoms on its tip.
* Ion beam microscopy: Can analyze masses of atomic species that come from a specimen during sputtering; Resolution 400 Å.
* Microtomography: Developed in 1987; Essentially 3D X-ray microscopy; Resolves micron-sized structures inside (dead) solid objects.
@ Atomic force microscopy: Binnig et al PRL(86) + focus Phy(12); Wickramasinghe SA(89)oct; Rugar & Hansma PT(90)oct; news pw(04)jun [100-pm resolution]; Stomp et al PRL(05)cm + pw(05)jan [electrons, 50 nm resolution]; Eaton & West 10; Bonson et al AJP(11)feb [working model]; news BBC(11)mar [imaging of single molecule].
@ Field-emission microscopy: news SA(09)dec [images of electron orbitals].
@ Other types: Cybulski et al PLOS(14)-a1403 [foldscope, an rigami-based paper microscope].

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