Tomography

Short description: Imaging by sections or sectioning using a penetrative wave

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

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, cosmochemistry, 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.

## Contents

* 1 Types of tomography
* 1.1 Synchrotron X-ray tomographic microscopy
* 2 Volume rendering
* 3 History
* 4 See also
* 5 References
* 6 External links

## 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

Main article: Volume rendering

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.

## History

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

* Chemical imaging
* 3D reconstruction
* Discrete tomography
* Geometric tomography
* Geophysical imaging
* Industrial CT scanning
* Johann Radon
* Medical imaging
* MRI compared with CT
* Network tomography
* Nonogram, a type of puzzle based on a discrete model of tomography
* Radon transform
* Tomographic reconstruction
* Multiscale Tomography
* Voxels

## References

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. 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. doi:10.1016/S0006-3495(01)76077-8. PMID 11159465. Bibcode: 2001BpJ....80..986F.
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. doi:10.1364/AO.56.007385. PMID 29048060. Bibcode: 2017ApOpt..56.7385M.
6. ↑ Huang, S M; Plaskowski, A; Xie, C G; Beck, M S (1988). "Capacitance-based tomographic flow imaging system" (in en). Electronics Letters 24 (7): 418–19. doi:10.1049/el:19880283. Bibcode: 1988ElL....24..418H.
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" (in en). Proc. R. Soc. Lond. A 317 (1530): 319–340. doi:10.1098/rspa.1970.0119. ISSN 0080-4630. Bibcode: 1970RSPSA.317..319C.
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. https://archive.org/details/electrontomograp00fran_082.
9. ↑ Martin, Michael C; Dabat-Blondeau, Charlotte; Unger, Miriam; Sedlmair, Julia; Parkinson, Dilworth Y; Bechtel, Hans A; Illman, Barbara; Castro, Jonathan M et al. (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.
10. ↑ Cramer, A., Hecla, J., Wu, D. et al. Stationary Computed Tomography for Space and other Resource-constrained Environments. Sci Rep 8, 14195 (2018). [1]
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.[2]
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". Microwave and Optical Technology Letters 57 (12): 2917–2929. doi:10.1002/mop.29470. http://psasir.upm.edu.my/id/eprint/46731/1/Three dimensions localization of tumors in confocal microwave imaging for breast cancer detection.pdf.
13. ↑ Puschnig, P.; Berkebile, S.; Fleming, A. J.; Koller, G.; Emtsev, K.; Seyller, T.; Riley, J. D.; Ambrosch-Draxl, C. et al. (30 October 2009). "Reconstruction of Molecular Orbital Densities from Photoemission Data". Science 326 (5953): 702–706. doi:10.1126/science.1176105. PMID 19745118. Bibcode: 2009Sci...326..702P.
14. ↑ Donoghue, PC; Bengtson, S; Dong, XP; Gostling, NJ; Huldtgren, T; Cunningham, JA; Yin, C; Yue, Z et al. (10 August 2006). "Synchrotron X-ray tomographic microscopy of fossil embryos.". Nature 442 (7103): 680–3. doi:10.1038/nature04890. PMID 16900198. Bibcode: 2006Natur.442..680D.
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. https://www.degruyter.com/document/doi/10.1515/9783110589771-004.
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. http://chestjournal.chestpubs.org/content/24/6/663.abstract. Retrieved July 10, 2011.
18. ↑ Littleton, J.T.. "Conventional Tomography". A History of the Radiological Sciences. American Roentgen Ray Society. http://www.arrs.org/publications/HRS/diagnosis/RCI_D_c15.pdf. Retrieved 29 November 2014.

## External links

* Image reconstruction algorithms for microtomography

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Medical imaging (ICD-9-CM V3 87–88, ICD-10-PCS B, CPT 70010–79999)

X-ray/
Radiography|

| 2D|

| Medical:|

* Pneumoencephalography
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|

Industrial:|

* Radiographic testing

CT scan|

| Techniques:|

* General operation of CT
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* X-ray microtomography
* Electron beam computed tomography
* Cone beam computed tomography

|

Targets|

* Coronary
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Other|

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MRI|

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Ultrasound|

* Echocardiography
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Radionuclide|

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Full body:|

* Octreotide scan
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3D / ECT|

| SPECT (gamma ray):|

* Myocardial perfusion imaging

|

PET (positron):|

* Brain PET
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Optical/Laser|

* Optical tomography
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Thermography|

* non-contact thermography
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Target conditions|

* Acute stroke
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