tomographischen

Tomographischen, and the related adjective tomographisch, refer to tomography—the science and technique of creating cross-sectional, three-dimensional images of an object from two-dimensional projections taken from multiple directions. In German usage, tomographischen appears as an inflected form in phrases such as tomographischen Schnitten (tomographic slices) or in tomographischen Verfahren (tomographic methods).

Tomography relies on solving an inverse problem: measurements made from different angles are combined to estimate the internal structure of a specimen. A key mathematical concept is the Radon transform, which links a function describing the object to a set of projections. Reconstruction algorithms, including filtered backprojection and various iterative methods, convert projection data into tomographic images. Image quality depends on angular sampling, noise, resolution, and regularization to reduce artefacts.

There are several tomographic modalities. Computed tomography (CT) uses X-rays to produce cross-sectional images of the body or objects. Positron emission tomography (PET) and single-photon emission computed tomography (SPECT) detect gamma rays from radiotracers to visualize metabolic or functional processes. Optical tomography uses visible or near-infrared light to probe tissue properties, while ultrasound tomography relies on acoustic waves. In materials science and cultural heritage, tomography enables nondestructive imaging of internal features with X-ray or neutron sources.

Historical context emphasizes both mathematics and engineering. The Radon transform, established in 1917, provided the mathematical foundation, while practical medical CT emerged in the 1970s through work by Hounsfield and Cormack, earning them the Nobel Prize in 1979.

Limitations include radiation exposure for X-ray–based methods, computational demands, and potential artefacts from sparse data, motion, or beam hardening. Tomography remains a versatile tool across medicine, science, and industry for revealing internal structures noninvasively.