Paul Lauterbur, at the State University of New York at Stony Brook, develops in 1973 the fundamental principle that turns nuclear magnetic resonance — a physical phenomenon known since the 1940s and used in chemistry to analyze molecular structures — into a technique capable of generating images of the interior of the human body. Lauterbur introduces spatially varying magnetic field gradients, so that the resonance signal emitted by the hydrogen atoms in bodily water depends on their exact position, allowing a two- or three-dimensional spatial image of tissues to be reconstructed instead of a single overall chemical signal. Peter Mansfield, at the University of Nottingham, independently and almost simultaneously develops mathematical methods to analyze the signal using mathematical transforms that drastically speed up the image-reconstruction process, and also designs ultra-fast acquisition techniques that would make real-time magnetic resonance imaging possible decades later. Unlike the computed tomography of Cormack and Hounsfield, which uses potentially harmful ionizing radiation, magnetic resonance imaging uses no ionizing radiation at all, while also offering much superior contrast between different types of soft tissue — muscle, fat, nervous tissue — with no radiological risk, becoming a medical diagnostic tool in massive use in neurology, oncology, and orthopedics.