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Fig.1: Basic principle of tomography: superposition free tomographic cross sections S1 and S2 compared with the (not tomographic) projected image P TomographyPrinciple Illustration.png
Fig.1: Basic principle of tomography: superposition free tomographic cross sections S1 and S2 compared with the (not tomographic) projected image P
Median plane sagittal tomography of the head by magnetic resonance imaging. Sagittal brain MRI.jpg
Median plane sagittal tomography of the head by magnetic resonance imaging.

Tomography is imaging by sections or sectioning that uses any kind of penetrating wave. The method is used in radiology, archaeology, biology, atmospheric science, geophysics, oceanography, plasma physics, materials science, astrophysics, quantum information, and other areas of science. The word tomography is derived from Ancient Greek τόμος tomos, "slice, section" and γράφω graphō, "to write" or, in this context as well, "to describe." A device used in tomography is called a tomograph, while the image produced is a tomogram.


In many cases, the production of these images is based on the mathematical procedure tomographic reconstruction, such as X-ray computed tomography technically being produced from multiple projectional radiographs. Many different reconstruction algorithms exist. Most algorithms fall into one of two categories: filtered back projection (FBP) and iterative reconstruction (IR). These procedures give inexact results: they represent a compromise between accuracy and computation time required. FBP demands fewer computational resources, while IR generally produces fewer artifacts (errors in the reconstruction) at a higher computing cost. [1]

Although MRI (magnetic resonance imaging), Optical coherence tomography and ultrasound are transmission methods, they typically do not require movement of the transmitter to acquire data from different directions. In MRI, both projections and higher spatial harmonics are sampled by applying spatially-varying magnetic fields; no moving parts are necessary to generate an image. On the other hand, since ultrasound and optical coherence tomography uses time-of-flight to spatially encode the received signal, it is not strictly a tomographic method and does not require multiple image acquisitions.

Types of tomography

Name Source of data Abbreviation Year of introduction
Aerial tomography Electromagnetic radiation AT 2020
Array tomography [2] Correlative light and electron microscopy AT 2007
Atom probe tomography Atom probe APT
Computed tomography imaging spectrometer [3] Visible light spectral imaging CTIS 2001
Computed tomography of chemiluminescence [4] [5] Chemiluminescence Flames CTC 2009
Confocal microscopy (Laser scanning confocal microscopy) Laser scanning confocal microscopy LSCM
Cryogenic electron tomography Cryogenic transmission electron microscopy CryoET
Electrical capacitance tomography Electrical capacitance ECT 1988 [6]
Electrical capacitance volume tomography Electrical capacitance ECVT
Electrical resistivity tomography Electrical resistivity ERT
Electrical impedance tomography Electrical impedance EIT 1984
Electron tomography Transmission electron microscopy ET 1968 [7] [8]
Focal plane tomography X-ray 1930s
Functional magnetic resonance imaging Magnetic resonance fMRI 1992
Gamma-ray emission tomography ("Tomographic Gamma Scanning") Gamma ray TGS or ECT
Gamma-ray transmission tomography Gamma ray TCT
Hydraulic tomography fluid flow HT 2000
Infrared microtomographic imaging [9] Mid-infrared 2013
Laser Ablation Tomography Laser Ablation & Fluorescent Microscopy LAT 2013
Magnetic induction tomography Magnetic induction MIT
Magnetic particle imaging Superparamagnetism MPI 2005
Magnetic resonance imaging or nuclear magnetic resonance tomography Nuclear magnetic moment MRI or MRT
Multi-source tomography [10] [11] X-ray
Muon tomography Muon
Microwave tomography [12] Microwave
Neutron tomography Neutron
Neutron stimulated emission computed tomography
Ocean acoustic tomography Sonar OAT
Optical coherence tomography Interferometry OCT
Optical diffusion tomography Absorption of light ODT
Optical projection tomography Optical microscope OPT
Photoacoustic imaging in biomedicine Photoacoustic spectroscopy PAT
Photoemission Orbital Tomography Angle-resolved photoemission spectroscopy POT 2009 [13]
Positron emission tomography Positron emission PET
Positron emission tomography - computed tomography Positron emission & X-ray PET-CT
Quantum tomography Quantum state QST
Single-photon emission computed tomography Gamma ray SPECT
Seismic tomography Seismic waves
Terahertz tomography Terahertz radiation THz-CT
Thermoacoustic imaging Photoacoustic spectroscopy TAT
Ultrasound-modulated optical tomography Ultrasound UOT
Ultrasound computer tomography Ultrasound USCT
Ultrasound transmission tomography Ultrasound
X-ray computed tomography X-ray CT, CATScan 1971
X-ray microtomography X-ray microCT
Zeeman-Doppler imaging Zeeman effect

Some recent advances rely on using simultaneously integrated physical phenomena, e.g. X-rays for both CT and angiography, combined CT/MRI and combined CT/PET.

Discrete tomography and Geometric tomography, on the other hand, are research areas[ citation needed ] that deal with the reconstruction of objects that are discrete (such as crystals) or homogeneous. They are concerned with reconstruction methods, and as such they are not restricted to any of the particular (experimental) tomography methods listed above.

Synchrotron X-ray tomographic microscopy

A new technique called synchrotron X-ray tomographic microscopy (SRXTM) allows for detailed three-dimensional scanning of fossils. [14] [15]

The construction of third-generation synchrotron sources combined with the tremendous improvement of detector technology, data storage and processing capabilities since the 1990s has led to a boost of high-end synchrotron tomography in materials research with a wide range of different applications, e.g. the visualization and quantitative analysis of differently absorbing phases, microporosities, cracks, precipitates or grains in a specimen. Synchrotron radiation is created by accelerating free particles in high vacuum. By the laws of electrodynamics this acceleration leads to the emission of electromagnetic radiation (Jackson, 1975). Linear particle acceleration is one possibility, but apart from the very high electric fields one would need it is more practical to hold the charged particles on a closed trajectory in order to obtain a source of continuous radiation. Magnetic fields are used to force the particles onto the desired orbit and prevent them from flying in a straight line. The radial acceleration associated with the change of direction then generates radiation. [16]

Volume rendering

Multiple X-ray computed tomographs (with quantitative mineral density calibration) stacked to form a 3D model. Image of 3D volumetric QCT scan.jpg
Multiple X-ray computed tomographs (with quantitative mineral density calibration) stacked to form a 3D model.

Volume rendering is a set of techniques used to display a 2D projection of a 3D discretely sampled data set, typically a 3D scalar field. A typical 3D data set is a group of 2D slice images acquired, for example, by a CT, MRI, or MicroCT scanner. These are usually acquired in a regular pattern (e.g., one slice every millimeter) and usually have a regular number of image pixels in a regular pattern. This is an example of a regular volumetric grid, with each volume element, or voxel represented by a single value that is obtained by sampling the immediate area surrounding the voxel.

To render a 2D projection of the 3D data set, one first needs to define a camera in space relative to the volume. Also, one needs to define the opacity and color of every voxel. This is usually defined using an RGBA (for red, green, blue, alpha) transfer function that defines the RGBA value for every possible voxel value.

For example, a volume may be viewed by extracting isosurfaces (surfaces of equal values) from the volume and rendering them as polygonal meshes or by rendering the volume directly as a block of data. The marching cubes algorithm is a common technique for extracting an isosurface from volume data. Direct volume rendering is a computationally intensive task that may be performed in several ways.


Focal plane tomography was developed in the 1930s by the radiologist Alessandro Vallebona, and proved useful in reducing the problem of superimposition of structures in projectional radiography.

In a 1953 article in the medical journal Chest, B. Pollak of the Fort William Sanatorium described the use of planography, another term for tomography. [17]

Focal plane tomography remained the conventional form of tomography until being largely replaced by mainly computed tomography in the late-1970s. [18] Focal plane tomography uses the fact that the focal plane appears sharper, while structures in other planes appear blurred. By moving an X-ray source and the film in opposite directions during the exposure, and modifying the direction and extent of the movement, operators can select different focal planes which contain the structures of interest.

See also

Related Research Articles

<span class="mw-page-title-main">Positron emission tomography</span> Medical imaging technique

Positron emission tomography (PET) is a functional imaging technique that uses radioactive substances known as radiotracers to visualize and measure changes in metabolic processes, and in other physiological activities including blood flow, regional chemical composition, and absorption. Different tracers are used for various imaging purposes, depending on the target process within the body. For example, 18
is commonly used to detect cancer, NaF18
is widely used for detecting bone formation, and oxygen-15 is sometimes used to measure blood flow.

<span class="mw-page-title-main">CT scan</span> Medical imaging procedure using X-rays to produce cross-sectional images

A computed tomography scan is a medical imaging technique used to obtain detailed internal images of the body. The personnel that perform CT scans are called radiographers or radiology technologists.

<span class="mw-page-title-main">Medical imaging</span> Technique and process of creating visual representations of the interior of a body

Medical imaging is the technique and process of imaging the interior of a body for clinical analysis and medical intervention, as well as visual representation of the function of some organs or tissues (physiology). Medical imaging seeks to reveal internal structures hidden by the skin and bones, as well as to diagnose and treat disease. Medical imaging also establishes a database of normal anatomy and physiology to make it possible to identify abnormalities. Although imaging of removed organs and tissues can be performed for medical reasons, such procedures are usually considered part of pathology instead of medical imaging.

<span class="mw-page-title-main">Single-photon emission computed tomography</span> Nuclear medicine tomographic imaging technique

Single-photon emission computed tomography is a nuclear medicine tomographic imaging technique using gamma rays. It is very similar to conventional nuclear medicine planar imaging using a gamma camera, but is able to provide true 3D information. This information is typically presented as cross-sectional slices through the patient, but can be freely reformatted or manipulated as required.

<span class="mw-page-title-main">Volume rendering</span> Representing a 3D-modeled object or dataset as a 2D projection

In scientific visualization and computer graphics, volume rendering is a set of techniques used to display a 2D projection of a 3D discretely sampled data set, typically a 3D scalar field.

<span class="mw-page-title-main">X-ray microscope</span> Type of microscope that uses X-rays

An X-ray microscope uses electromagnetic radiation in the X-ray band to produce magnified images of objects. Since X-rays penetrate most objects, there is no need to specially prepare them for X-ray microscopy observations.

<span class="mw-page-title-main">Tomographic reconstruction</span> Estimate object properties from a finite number of projections

Tomographic reconstruction is a type of multidimensional inverse problem where the challenge is to yield an estimate of a specific system from a finite number of projections. The mathematical basis for tomographic imaging was laid down by Johann Radon. A notable example of applications is the reconstruction of computed tomography (CT) where cross-sectional images of patients are obtained in non-invasive manner. Recent developments have seen the Radon transform and its inverse used for tasks related to realistic object insertion required for testing and evaluating computed tomography use in airport security.

<span class="mw-page-title-main">Iterative reconstruction</span>

Iterative reconstruction refers to iterative algorithms used to reconstruct 2D and 3D images in certain imaging techniques. For example, in computed tomography an image must be reconstructed from projections of an object. Here, iterative reconstruction techniques are usually a better, but computationally more expensive alternative to the common filtered back projection (FBP) method, which directly calculates the image in a single reconstruction step. In recent research works, scientists have shown that extremely fast computations and massive parallelism is possible for iterative reconstruction, which makes iterative reconstruction practical for commercialization.

<span class="mw-page-title-main">X-ray microtomography</span> X-ray 3D imaging method

In radiography, X-ray microtomography uses X-rays to create cross-sections of a physical object that can be used to recreate a virtual model without destroying the original object. It is similar to tomography and X-ray computed tomography. The prefix micro- is used to indicate that the pixel sizes of the cross-sections are in the micrometre range. These pixel sizes have also resulted in creation of it's synonyms high-resolution X-ray tomography, micro-computed tomography, and similar terms. Sometimes the terms high-resolution computed tomography (HRCT) and micro-CT are differentiated, but in other cases the term high-resolution micro-CT is used. Virtually all tomography today is computed tomography.

<span class="mw-page-title-main">Neuroimaging</span> Set of techniques to measure and visualize aspects of the nervous system

Neuroimaging is the use of quantitative (computational) techniques to study the structure and function of the central nervous system, developed as an objective way of scientifically studying the healthy human brain in a non-invasive manner. Increasingly it is also being used for quantitative studies of brain disease and psychiatric illness. Neuroimaging is a highly multidisciplinary research field and is not a medical specialty.

<span class="mw-page-title-main">Electron tomography</span>

Electron tomography (ET) is a tomography technique for obtaining detailed 3D structures of sub-cellular, macro-molecular, or materials specimens. Electron tomography is an extension of traditional transmission electron microscopy and uses a transmission electron microscope to collect the data. In the process, a beam of electrons is passed through the sample at incremental degrees of rotation around the center of the target sample. This information is collected and used to assemble a three-dimensional image of the target. For biological applications, the typical resolution of ET systems are in the 5–20 nm range, suitable for examining supra-molecular multi-protein structures, although not the secondary and tertiary structure of an individual protein or polypeptide. Recently, atomic resolution in 3D electron tomography reconstructions has been demonstrated.

<span class="mw-page-title-main">Tomosynthesis</span>

Tomosynthesis, also digital tomosynthesis (DTS), is a method for performing high-resolution limited-angle tomography at radiation dose levels comparable with projectional radiography. It has been studied for a variety of clinical applications, including vascular imaging, dental imaging, orthopedic imaging, mammographic imaging, musculoskeletal imaging, and chest imaging.

<span class="mw-page-title-main">Avizo (software)</span> Software for scientific and industrial data visualization and analysis

Avizo is a general-purpose commercial software application for scientific and industrial data visualization and analysis.

<span class="mw-page-title-main">Cone beam computed tomography</span>

Cone beam computed tomography is a medical imaging technique consisting of X-ray computed tomography where the X-rays are divergent, forming a cone.

<span class="mw-page-title-main">Phase-contrast X-ray imaging</span> Imaging systems using changes in phase

Phase-contrast X-ray imaging or phase-sensitive X-ray imaging is a general term for different technical methods that use information concerning changes in the phase of an X-ray beam that passes through an object in order to create its images. Standard X-ray imaging techniques like radiography or computed tomography (CT) rely on a decrease of the X-ray beam's intensity (attenuation) when traversing the sample, which can be measured directly with the assistance of an X-ray detector. However, in phase contrast X-ray imaging, the beam's phase shift caused by the sample is not measured directly, but is transformed into variations in intensity, which then can be recorded by the detector.

<span class="mw-page-title-main">Computed tomography imaging spectrometer</span> Method of capturing a multi-wavelength data cube

The computed tomography imaging spectrometer (CTIS) is a snapshot imaging spectrometer which can produce in fine the three-dimensional hyperspectral datacube of a scene.

<span class="mw-page-title-main">Focal plane tomography</span> Imaging technique using moving X-ray machines

In radiography, focal plane tomography is tomography by simultaneously moving the X-ray generator and X-ray detector so as to keep a consistent exposure of only the plane of interest during image acquisition. This was the main method of obtaining tomographs in medical imaging until the late-1970s. It has since been largely replaced by more advanced imaging techniques such as CT and MRI. It remains in use today in a few specialized applications, such as for acquiring orthopantomographs of the jaw in dental radiography.

<span class="mw-page-title-main">Operation of computed tomography</span>

X-ray computed tomography operates by using an X-ray generator that rotates around the object; X-ray detectors are positioned on the opposite side of the circle from the X-ray source.

Photon-counting computed tomography (PCCT) is a form of X-ray computed tomography (CT) in which X-rays are detected using a photon-counting detector (PCD) which registers the interactions of individual photons. By keeping track of the deposited energy in each interaction, the detector pixels of a PCD each record an approximate energy spectrum, making it a spectral or energy-resolved CT technique. In contrast, more conventional CT scanners use energy-integrating detectors (EIDs), where the total energy deposited in a pixel during a fixed period of time is registered. These EIDs thus register only photon intensity, comparable to black-and-white photography, whereas PCDs register also spectral information, similar to color photography.

<span class="mw-page-title-main">History of computed tomography</span> History of CT scanning technology

The history of X-ray computed tomography dates back to at least 1917 with the mathematical theory of the Radon transform In October 1963, William H. Oldendorf received a U.S. patent for a "radiant energy apparatus for investigating selected areas of interior objects obscured by dense material". The first clinical CT scan was performed in 1971 using a scanner invented by Sir Godfrey Hounsfield.


  1. Herman, Gabor T. (2009). Fundamentals of Computerized Tomography: Image Reconstruction from Projections (2nd ed.). Dordrecht: Springer. ISBN   978-1-84628-723-7.
  2. Micheva, Kristina D.; Smith, Stephen J (July 2007). "Array Tomography: A New Tool for Imaging the Molecular Architecture and Ultrastructure of Neural Circuits". Neuron. 55 (1): 25–36. doi:10.1016/j.neuron.2007.06.014. PMC   2080672 . PMID   17610815.
  3. Ford, Bridget K.; Volin, Curtis E.; Murphy, Sean M.; Lynch, Ronald M.; Descour, Michael R. (February 2001). "Computed Tomography-Based Spectral Imaging For Fluorescence Microscopy". Biophysical Journal. 80 (2): 986–993. Bibcode:2001BpJ....80..986F. doi:10.1016/S0006-3495(01)76077-8. PMC   1301296 . PMID   11159465.
  4. Floyd, J.; Geipel, P.; Kempf, A.M. (February 2011). "Computed Tomography of Chemiluminescence (CTC): Instantaneous 3D measurements and Phantom studies of a turbulent opposed jet flame". Combustion and Flame. 158 (2): 376–391. doi:10.1016/j.combustflame.2010.09.006.
  5. Mohri, K; Görs, S; Schöler, J; Rittler, A; Dreier, T; Schulz, C; Kempf, A (10 September 2017). "Instantaneous 3D imaging of highly turbulent flames using computed tomography of chemiluminescence". Applied Optics. 56 (26): 7385–7395. Bibcode:2017ApOpt..56.7385M. doi:10.1364/AO.56.007385. PMID   29048060.
  6. Huang, S M; Plaskowski, A; Xie, C G; Beck, M S (1988). "Capacitance-based tomographic flow imaging system". Electronics Letters. 24 (7): 418–19. Bibcode:1988ElL....24..418H. doi:10.1049/el:19880283.
  7. Crowther, R. A.; DeRosier, D. J.; Klug, A.; S, F. R. (1970-06-23). "The reconstruction of a three-dimensional structure from projections and its application to electron microscopy". Proc. R. Soc. Lond. A. 317 (1530): 319–340. Bibcode:1970RSPSA.317..319C. doi:10.1098/rspa.1970.0119. ISSN   0080-4630. S2CID   122980366.
  8. Electron tomography: methods for three-dimensional visualization of structures in the cell (2nd ed.). New York: Springer. 2006. pp.  3. ISBN   9780387690087. OCLC   262685610.
  9. Martin, Michael C; Dabat-Blondeau, Charlotte; Unger, Miriam; Sedlmair, Julia; Parkinson, Dilworth Y; Bechtel, Hans A; Illman, Barbara; Castro, Jonathan M; Keiluweit, Marco; Buschke, David; Ogle, Brenda; Nasse, Michael J; Hirschmugl, Carol J (September 2013). "3D spectral imaging with synchrotron Fourier transform infrared spectro-microtomography". Nature Methods. 10 (9): 861–864. doi:10.1038/nmeth.2596. PMID   23913258. S2CID   9900276.
  10. Cramer, A., Hecla, J., Wu, D. et al. Stationary Computed Tomography for Space and other Resource-constrained Environments. Sci Rep 8, 14195 (2018).
  11. V. B. Neculaes, P. M. Edic, M. Frontera, A. Caiafa, G. Wang and B. De Man, "Multisource X-Ray and CT: Lessons Learned and Future Outlook," in IEEE Access, vol. 2, pp. 1568-1585, 2014, doi: 10.1109/ACCESS.2014.2363949.
  12. Ahadi, Mojtaba; Isa, Maryam; Saripan, M. Iqbal; Hasan, W. Z. W. (December 2015). "Three dimensions localization of tumors in confocal microwave imaging for breast cancer detection" (PDF). Microwave and Optical Technology Letters. 57 (12): 2917–2929. doi:10.1002/mop.29470. S2CID   122576324.
  13. Puschnig, P.; Berkebile, S.; Fleming, A. J.; Koller, G.; Emtsev, K.; Seyller, T.; Riley, J. D.; Ambrosch-Draxl, C.; Netzer, F. P.; Ramsey, M. G. (30 October 2009). "Reconstruction of Molecular Orbital Densities from Photoemission Data". Science. 326 (5953): 702–706. Bibcode:2009Sci...326..702P. doi:10.1126/science.1176105. PMID   19745118. S2CID   5476218.
  14. Donoghue, PC; Bengtson, S; Dong, XP; Gostling, NJ; Huldtgren, T; Cunningham, JA; Yin, C; Yue, Z; Peng, F; Stampanoni, M (10 August 2006). "Synchrotron X-ray tomographic microscopy of fossil embryos". Nature. 442 (7103): 680–3. Bibcode:2006Natur.442..680D. doi:10.1038/nature04890. PMID   16900198. S2CID   4411929.
  15. "Contributors to Volume 21". Metals, Microbes, and Minerals - the Biogeochemical Side of Life. De Gruyter. 2021. pp. xix–xxii. doi:10.1515/9783110589771-004. ISBN   9783110588903. S2CID   243434346.
  16. Banhart, John, ed. Advanced Tomographic Methods in Materials Research and Engineering. Monographs on the Physics and Chemistry of Materials. Oxford ; New York: Oxford University Press, 2008.
  17. Pollak, B. (December 1953). "Experiences with Planography". Chest. 24 (6): 663–669. doi:10.1378/chest.24.6.663. ISSN   0012-3692. PMID   13107564. Archived from the original on 2013-04-14. Retrieved July 10, 2011.
  18. Littleton, J.T. "Conventional Tomography" (PDF). A History of the Radiological Sciences. American Roentgen Ray Society . Retrieved 29 November 2014.