Tomography is

imaging Imaging is the representation or reproduction of an object's form; especially a visual representation (i.e., the formation of an image). Imaging technology is the application of materials and methods to create, preserve, or duplicate images. ...

by sections or sectioning that uses any kind of penetrating

wave In physics, mathematics, and related fields, a wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities. Waves can be periodic, in which case those quantities oscillate repeatedly about an equilibrium (res ...

. The method is used in

radiology Radiology ( ) is the medical discipline that uses medical imaging to diagnose diseases and guide their treatment, within the bodies of humans and other animals. It began with radiography (which is why its name has a root referring to radiat ...

archaeology Archaeology or archeology is the scientific study of human activity through the recovery and analysis of material culture. The archaeological record consists of artifacts, architecture, biofacts or ecofacts, sites, and cultural landscap ...

biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...

atmospheric science Atmospheric science is the study of the Atmosphere of Earth, Earth's atmosphere and its various inner-working physical processes. Meteorology includes atmospheric chemistry and atmospheric physics with a major focus on weather forecasting. Climat ...

geophysics Geophysics () is a subject of natural science concerned with the physical processes and physical properties of the Earth and its surrounding space environment, and the use of quantitative methods for their analysis. The term ''geophysics'' som ...

oceanography Oceanography (), also known as oceanology and ocean science, is the scientific study of the oceans. It is an Earth science, which covers a wide range of topics, including ecosystem dynamics; ocean currents, waves, and geophysical fluid dynamic ...

plasma physics Plasma ()πλάσμα
, Henry George Liddell, R ...

, materials science,

cosmochemistry Cosmochemistry (from Greek κόσμος ''kósmos'', "universe" and χημεία ''khemeía'') or chemical cosmology is the study of the chemical composition of matter in the universe and the processes that led to those compositions. This is done ...

astrophysics Astrophysics is a science that employs the methods and principles of physics and chemistry in the study of astronomical objects and phenomena. As one of the founders of the discipline said, Astrophysics "seeks to ascertain the nature of the h ...

quantum information Quantum information is the information of the state of a quantum system. It is the basic entity of study in quantum information theory, and can be manipulated using quantum information processing techniques. Quantum information refers to both th ...

, and other areas of

science Science is a systematic endeavor that builds and organizes knowledge in the form of testable explanations and predictions about the universe. Science may be as old as the human species, and some of the earliest archeological evidence for ...

. The word ''tomography'' is derived from

Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages (), the Archaic peri ...

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 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 ...

, such as

X-ray computed tomography An X-ray, or, much less commonly, X-radiation, is a penetrating form of high-energy electromagnetic radiation. Most X-rays have a wavelength ranging from 10 picometers to 10 nanometers, corresponding to frequencies in the range 30 ...

technically being produced from multiple

projectional radiograph Projectional radiography, also known as conventional radiography, is a form of radiography and medical imaging that produces two-dimensional images by x-ray radiation. The image acquisition is generally performed by radiographers, and the images ...

s. Many different

reconstruction algorithm 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 ...

s exist. Most algorithms fall into one of two categories:

filtered back projection In mathematics, the Radon transform is the integral transform which takes a function ''f'' defined on the plane to a function ''Rf'' defined on the (two-dimensional) space of lines in the plane, whose value at a particular line is equal to the ...

(FBP) and

iterative reconstruction 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 recons ...

(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. Although MRI (

magnetic resonance imaging Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio wave ...

optical coherence tomography Optical coherence tomography (OCT) is an imaging technique that uses low-coherence light to capture micrometer-resolution, two- and three-dimensional images from within optical scattering media (e.g., biological tissue). It is used for medical ...

and

ultrasound Ultrasound is sound waves with frequency, frequencies higher than the upper audible limit of human hearing range, hearing. Ultrasound is not different from "normal" (audible) sound in its physical properties, except that humans cannot hea ...

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

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

angiography Angiography or arteriography is a medical imaging technique used to visualize the inside, or lumen, of blood vessels and organs of the body, with particular interest in the arteries, veins, and the heart chambers. Modern angiography is performe ...

, combined CT/

MRI Magnetic resonance imaging (MRI) is a medical imaging technique used in radiology to form pictures of the anatomy and the physiological processes of the body. MRI scanners use strong magnetic fields, magnetic field gradients, and radio waves ...

and combined CT/

PET A pet, or companion animal, is an animal kept primarily for a person's company or entertainment rather than as a working animal, livestock, or a laboratory animal. Popular pets are often considered to have attractive appearances, intelligence, ...

Discrete tomography Discrete tomography Herman, G. T. and Kuba, A., Discrete Tomography: Foundations, Algorithms, and Applications, Birkhäuser Boston, 1999 Herman, G. T. and Kuba, A., Advances in Discrete Tomography and Its Applications, Birkhäuser Boston, 2007 fo ...

and Geometric tomography, on the other hand, are research areas 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. 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.

Volume rendering

Volume rendering is a set of techniques used to display a 2D projection of a 3D discretely

sampled Sample or samples may refer to: Base meaning * Sample (statistics), a subset of a population – complete data set * Sample (signal), a digital discrete sample of a continuous analog signal * Sample (material), a specimen or small quantity of so ...

data set A data set (or dataset) is a collection of data. In the case of tabular data, a data set corresponds to one or more database tables, where every column of a table represents a particular variable, and each row corresponds to a given record of the ...

, typically a 3D

scalar field In mathematics and physics, a scalar field is a function (mathematics), function associating a single number to every point (geometry), point in a space (mathematics), space – possibly physical space. The scalar may either be a pure Scalar ( ...

. A typical 3D data set is a group of 2D slice images acquired, for example, by a CT,

, or

MicroCT X-ray microtomography, like tomography and X-ray computed tomography, uses X-rays to create cross-sections of a physical object that can be used to recreate a virtual model ( 3D model) without destroying the original object. The prefix ''micro- ...

scanner. These are usually acquired in a regular pattern (e.g., one slice every millimeter) and usually have a regular number of image

pixel In digital imaging, a pixel (abbreviated px), pel, or picture element is the smallest addressable element in a raster image, or the smallest point in an all points addressable display device. In most digital display devices, pixels are the smal ...

s in a regular pattern. This is an example of a regular volumetric grid, with each volume element, or

voxel In 3D computer graphics, a voxel represents a value on a regular grid in three-dimensional space. As with pixels in a 2D bitmap, voxels themselves do not typically have their position (i.e. coordinates) explicitly encoded with their values. Ins ...

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 A camera is an Optics, optical instrument that can capture an image. Most cameras can capture 2D images, with some more advanced models being able to capture 3D images. At a basic level, most cameras consist of sealed boxes (the camera body), ...

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 RGBA stands for red green blue alpha. While it is sometimes described as a color space, it is actually a three-channel RGB color model supplemented with a fourth ''alpha channel''. Alpha indicates how opaque each pixel is and allows an image to ...

(for red, green, blue, alpha)

transfer function In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a function (mathematics), mathematical function that mathematical model, theoretically models the system's output for ...

that defines the RGBA value for every possible voxel value. For example, a volume may be viewed by extracting

isosurface An isosurface is a three-dimensional analog of an isoline. It is a surface that represents points of a constant value (e.g. pressure, temperature, velocity, density) within a volume of space; in other words, it is a level set of a continuous fu ...

s (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 Marching cubes is a computer graphics algorithm, published in the 1987 SIGGRAPH proceedings by Lorensen and Cline, for extracting a polygonal mesh of an isosurface from a three-dimensional discrete scalar field (the elements of which are sometime ...

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 In radiography, focal plane tomography is tomography (imaging a single plane, or slice, of an object) 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 ac ...

was developed in the 1930s by the radiologist

Alessandro Vallebona Alessandro is both a given name and a surname, the Italian form of the name Alexander. Notable people with the name include: People with the given name Alessandro * Alessandro Allori (1535–1607), Italian portrait painter * Alessandro Baricco ...

, and proved useful in reducing the problem of superimposition of structures in

projectional radiography Projectional radiography, also known as conventional radiography, is a form of radiography and medical imaging that produces two-dimensional images by x-ray radiation. The image acquisition is generally performed by radiographers, and the images ...

. In a 1953 article in the medical journal ''Chest'', B. Pollak of the

Fort William Sanatorium Fort William Sanatorium was a tuberculosis hospital or sanatorium in Fort William, Ontario, today part of the city of Thunder Bay. It opened in 1935 as a tuberculosis treatment centre for settlers, adding 20 government-funded beds for Indigenous pat ...

described the use of planography, another term for tomography. Focal plane tomography remained the conventional form of tomography until being largely replaced by mainly

computed tomography A computed tomography scan (CT scan; formerly called computed axial tomography scan or CAT scan) is a medical imaging technique used to obtain detailed internal images of the body. The personnel that perform CT scans are called radiographers ...

in the late 1970s. 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.

References

External links

*
Image reconstruction algorithms for microtomography
{{Authority control Medical imaging