Tomographs don't produce ready-made pictures. They collect numerous 'shadows' — projections of innards from different angles or using various signals — and mathematically reconstruct a 3D picture from them. This idea came from an unexpected field: Joseph Fourier created his method for calculating heat flows, and today it underlies all of medical tomography. Doctors see tumors thanks to formulas that originally described cooling metal.
Different machines gather different 'shadows'. In CT, they measure the attenuation of X-rays — this is akin to determining density by the cast shadow. MRI picks up radio signals from hydrogen atoms in water molecules, as if 'listening' to the tissue's response to a magnetic field. PET and SPECT track radioactive tracers. Despite different physics, they all are solved with a common mathematical model and similar computational techniques.
Modern algorithms and powerful processors gather these 'shadows' in seconds, reducing radiation dose and procedure time. The fusion of physics, mathematics, and computer technology turns diagnostics into precise and safe routine.
The first CT scanner in 1971 took almost an hour to scan a head; today's tomographs do it in fractions of a second with less radiation.
The medical tricorder from 'Star Trek' isn't that far-fetched — it most likely also solves inverse problems by collecting projections of the human body.