Today, I am busy operating the atom-probe here at Oxford.
There are a number of texts and figures on the internet describing the basic principles of APT [1,2], so I am not going to reinvent the wheel here. However, I always like to know a little bit about the historical development of a technique, because the circumstances leading to it's invention often teach us a lot about the science involved and problems to expect. This is also true in this case. As it happens I already wrote a short introduction (including the above image) in my DPhil thesis ...
"In his PhD thesis, which initially was a general study of field electron emission , Erwin Muller designed the rst eld electron microscope , which consisted of a needle specimen in an evacuated glass tube and a phosphor screen. In 1951 the addition of hydrogen as imaging gas and the reversion of the polarity of the tip from negative to positive, led him to the invention of the first field ion microscope . M uller reported,
"Das Feldionenmikroskop ermoglicht zum ersten Male eine Abbildung mit genugendem Auflosungsvermogen, um das atomare Gitter sichtbar zu machen."
English: The field ion microscope allows for the first time a projection with sufficient resolution to make the atomic lattice visible. He also suggested cooling the tip and discusses possibilities to decrease the necessary desorption field strength. This was the first time that imaging gas atoms, field ionised by electrons tunnelling through the free space between the ion and the surface of the needle, were made visible and revealed the atomic structure of a tungsten tip surface .
The strength of the field, F, on the apex of the needle is given by
F = V/krt
where V is the applied voltage, rt is the radius of the tip and k a numerical constant (k = 2-5) , dependent on the shape of the needle. As it was now possible to achieve a field large enough to cause desorption of positively-charged ions, it did not take long before Muller reported the eld evaporation of other elements . Finally the addition of a mass spectrometer led to the construction of a prototype 1D atom-probe in 1967. At this time an aperture was used to only allow atoms from selected regions to enter the mass spectrometer and be analysed. A high voltage pulse on the needle is superimposed on the standing voltage to stimulate field evaporation, so that the time of flight could be measured accurately.
If the voltage at the needle is V0 and the charge of the evaporating ion is n x e with e being the elementary charge, the electrostatic potential energy of the ion at the tip can be expressed as Epot = neV0. The kinetic energy at the detector is approximately Ekin = 1/2m d^2/t^2 if m is the mass of the ion, d the distance to the detector and t the time of flight. This approximation is correct, if we assume a grounded counter electrode directly in front of the tip, so that the ions reach their final speed instantly . With the laws of energy conservation it follows that
neV0 = 1/2m d^2/t^2.
From this it is easy to see that the mass-to-charge ratio is proportional to the square of the time-of-flight t^2:
m/n = 2eV0 t^2/d^2.
This way single selected atoms could be identied for the first time.
This concept was picked up by Cerezo et al., who added a position sensitive detector and constructed the first fully operational 3D atom-probe in 1988 . Several improvements to the technique have been implemented and become commercially available since. Tsong et al. showed that field ionization and eld evaporation can also be photon-stimulated  and laser field ion microscopes and atom-probes were implemented.
The addition of a local electrode has improved mass resolution and field of view and requires lower applied voltages to achieve sucient eld strengths for ion evaporation. It also allows the examination of multi tip coupons, as sucient evaporation elds are only achieved for one tip at a time [11,12]. A disadvantage of the local electrode is that material from fractured specimens can contaminate the electrode, which will then start
field evaporating itself. Therefore these electrodes have to be easily exchangeable in a sensible set-up.
The Local-Electrode Atom-Probe
Although the Cameca LEAP 3000X HR (TM)  (the instrument I am using at Oxford) looks a lot more complicated than the simple apparatus Erwin Muller designed, the basic principle remains the same. Atoms and molecules are eld evaporated and eld ionised from a thin, needle specimen. This can be achieved by traditional voltage pulsing or laser pulsing. As mostly less-conductive oxides were studied in this thesis, laser-pulsing was used throughout. The ions are accelerated in the field of an exchangeable local electrode. They pass the reflectron, which further improves mass resolution. The time-of-flight is recorded when the ions hit a MicroChannel Plate which locally amplies the signal at the point of ion impact before it is detected with a position sensitive detector. With a thorough knowledge of the instrument geometry and an estimate of the field at the tip it is possible to reconstruct the sample in 3D."
 K Kruska, DPhil thesis: Understanding stress corrosion cracking mechanisms, Oxford University 2012
 M Drechsler. Erwin Muller and the early development of field emission microscopy. Surface science, 70:1-18, 1978.
 E W Muller. Zeitschrift fur technische Physik, 17:412, 1936.
 E W Muller. Das Feldionenmikroskop. Zeitschrift fur Physik, 131:136-142, 1951.
 E W Muller. Feldemission. In Ergebnisse der exakten Naturwissenschaften, volume 27 of Springer Tracts in Modern Physics, pages 290-360. Springer Berlin / Heidelberg, 1953. 10.1007/BFb0110808.
 M K Miller. Atom-probe Tomography : Analysis at the Atomic Level. Kluwer Academic/ Plenum Publishes, 2000.
 A Cerezo, T J Godfrey, and G D W Smith. Application of a position-sensitive detector to atom-probe microananlysis. Review of Scientic Instruments, 59:862-866, 1988.
 T T Tsong, J H Block, M Nagasaka, and B Viswanathan. Photon stimulated field ionization. The Journal of Chemical Analysis, 65:2469-2470, 1976.
T F Kelly, V Patrick, P P Camus, D J Larson, and L M Holzman S S Bajikar. On the many advantages of local-electrode atom probes. Ultramicroscopy, 62:29-42, 1996.
T F Kelly, P P Camus, D J Larson, L M Holzman, and S S Bajikar. Us patent 5,440,124, 1995.