The theoretical basis of Computed Tomography (CT) finds its origins in 1917, when the Austrian mathematician Johan Radon (16 December 1887 – 25 May 1956) proved that an n-dimensional object can be reconstructed from its (n-1)-dimensional projections . However, only in the second half of the century the mathematical basis for the actual CT image reconstruction was presented in two papers by Allan M. Cormack (Feb. 23, 1924 – May 7, 1998) [2, 3] in 1964 and 1965, respectively.
The first CT scanner
The first CT scanner was invented in 1972 by Godfrey N. Hounsfield (August 28, 1919 – August 12, 2004), an English electrical engineer of Electrical and Musical Instruments (EMI) Laboratories, England. It took several hours to acquire the raw data for a slice and days to reconstruct a single image from this raw data. The first EMI-Scanner was installed in Atkinson Morley Hospital in Wimbledon, England, and the first patient brain-scan was done in 1972. By 1975 Hounsfield had constructed the first full-body CT scanner . The invention was of such importance that Cormack and Hounsfield were awarded with the Nobel Prize in Physiology or Medicine in 1979. The “Hounsfield scale” still remains the standard measurement of radiodensity in CT scans.
Godfrey N. Hounsfield (left) and Allan M. Cormack (right) (from http://www.nobelprize.org)
Hounsfield’s CT prototype (image from http://en.wikipedia.org/wiki/File:RIMG0277.JPG)
The advent of microCT
In the early 1980s the application of the CT technology was extended from the clinics to the research field. Higher resolution and longer exposure time could be used, as for research applications patient’s safety was not an issue. The first X-ray microtomography system was conceived and built by Jim Elliott in the early 1980s. The first published X-ray microtomographic images were reconstructed slices of a small tropical snail, with pixel size about 50 micrometers . Feldkamp et al.  were first to build a microCT scanner for the evaluation of the three-dimensional micro-structure of trabecular bone. Only in 1994, with the presentation of the first commercially available bone microCT scanner [7, 8], this technique started to become a standard in bone research. Nowadays, in-vivo and in-vitro microCT scanners are available from several manufacturers (see the post “Who are the microCT scanner manufacturers?“).
From x-ray to synchrotron radiation
With the advent of third generation synchrotron radiation facilities, microCT with resolutions of 1 μm and even better became feasible. This allowed bone researchers to study osteocyte lacunae, intrabone vasculature, or micro-cracks and micro-fractures. With the ongoing development of CT systems, this technique became available on many different levels of resolution, while always using the exact same physical working principle.
Swiss Light Source (SLS) synchrotron facility
Future developments in microCT will include improving the systems with respect to speed, increasing the spatial resolution, and developing new imaging modes. A very promising imaging mode is phase contrast microCT, in which photon absorption and phase shift can be measured simultanously. This method allows a high contrast of soft tissue, which opens the microCT field to a large number of new applications. Speed improvement can be obtained with Free-Electron Lasers (FEL), the 4th generation of X-ray light sources offering novel experimental capabilities in diverse areas of science by providing very intense and tightly focused beams of x-rays with pulses as short as 10 femtoseconds (1 femtosecond= 1 quadrillionth of a second, that is approximately the duration of a molecular vibration) and wavelengths down to 0.1 nanometer. Free-electron lasers can produce much more brilliant, i.e. more tightly focused and intense, light beams than the most advanced synchrotron light sources. This higher brilliance is crucial for experiments with very small samples.
Image from http://www.psi.ch/swissfel/
In late 2010, at the Sincrotrone Trieste Laboratory in Italy, the seeded-FEL source FERMI@Elettra has started commissioning. SwissFEL, Switzerland’s X-ray free-electron laser, and other FEL facilities are currently being built (more info on light source facilities worldwide here) and will drive the development of a novel source for the generation of femtosecond pulses.
Fermi@Elettra facility in Trieste, Italy
 Radon J, Über die Bestimmung von Funktionen durch ihre Integralwerte längs bestimmter Mannigfaltigkeiten. Ber Verb Sächs Akad Wiss Leipzig Math-Nat Kl, 1917, 69:262–277.
 Cormack AM, Representation of a function by its line integrals with some radiological applications. J Appl Phys, 1963, 34:2722–2727.
 Cormack AM, Representation of a function by its line integrals with some radiological applications. II. J Appl Phys, 1964, 35:2908–2913.
 Hounsfield GN, EMI scanner. Proc the Roy Soc London Series B Biol Sci, 1977, 195:281–289.
 Elliott JC and Dover SD, X-ray microtomography. J. Microscopy, 1982, 126:211-213.
 Feldkamp LA, Goldstein SA, Parfitt AM, et al., The direct examination of threedimensional bone architecture in vitro by computed tomography. J Bone Miner Res, 1989, 4:3–11.
 Müller R, Rüegsegger P, Morphological validation of the 3D structure of non-invasive bone biopsies. Abstracts 10th Int. Workshop on Bone Densitometry. Bone Miner, 1994, 25:8.
 Rüegsegger P, Koller B, Müller R, A microtomographic system for the nondestructive evaluation of bone architecture. Calcif Tissue Int, 1996, 58:24–29.