The scan never saw the slice
A CT scanner does not look at a slice of you. It measures how X-rays dim along many lines through the body, and a computer solves for the densities that would cast those shadows.
Johann Radon had shown in 1917 that a function in a plane can be recovered from its integrals along lines, if you have enough lines. Godfrey Hounsfield, half a century later, built the machine that collects those integrals with X-rays and computes the function, which in a person is a map of how much each small volume absorbs. The first clinical scan, in 1971, took minutes and a computer the size of a cabinet. The mathematics is the same one in the scanner that finishes a chest in a second.
What you are shown is a reconstruction, with a chosen sharpness and a chosen tolerance for noise. Metal, motion, and a shortage of angles leave artefacts that are the equation complaining about its inputs. The dose is the price of the inputs. A prettier picture is not free, and a radiologist’s training includes knowing which shadows are the algorithm.
Caveats
- Modern machines are fast and the images look photographic. They are still solutions of a projection problem. The speed does not change the kind of thing the picture is.
- MRI, next door in the hospital and elsewhere in this library, is a different solution of a different measurement. It is not a CT done with magnets.
Sources
- 1Hounsfield G. N.. Computerized transverse axial scanning (tomography): Part 1. Description of system. The British Journal of Radiology 46, 1973.