The history of X-ray computed tomography (CT) traces back to Wilhelm Conrad Röntgen's discovery of X-ray radiation in 1895 and its rapid adoption in medical diagnostics. While X-ray radiography achieved tremendous success in the early 1900s, it had a significant limitation: projection-based imaging lacked depth information, which is crucial for many diagnostic tasks. To overcome this, additional X-ray projections from different angles were needed. The challenge was both mathematically and experimentally addressed by multiple scientists and engineers working independently across the globe. The breakthrough finally came in the 1970s with the work of Godfrey Hounsfield, when advancements in computing power and the development of commercial CT scanners made routine diagnostic applications possible.

Focal plane tomography

Early attempts to overcome the superimposition of structures inherent to projectional radiography involved methods in which the X-ray source and the detecting film moved simultaneously along specific trajectories. These techniques were based on principles of projective geometry, allowing a particular plane (or slice) to be "focused" during exposure while structures above and below the plane were blurred. This approach became known as planography or focal plane tomography. Key contributors to its development included the French physician André Bocage, Italian radiologist Alessandro Vallebona, and Dutch radiologist Bernard George Ziedses des Plantes.

In 1961, neurologist William Oldendorf proposed a notable approach to imaging structures inside the skull. He developed an experimental setup using a pencil beam and a rotating sample with slow linear motion perpendicular to the beam axis. This allowed him to record variations in radiodensity within a test sample containing aluminum and iron nails arranged concentrically around the center, mimicking the structure of a skull. Oldendorf's method can be considered a form of focal point tomography, as it sampled points on a specific line or trajectory, while objects outside the center of rotation appeared blurred. In 1963, he was granted a U.S. patent for a "Radiant energy apparatus for investigating selected areas of interior objects obscured by dense material". In recognition of his contributions, he shared the 1975 Lasker Award with Godfrey Hounsfield.

These early tomographic methods, relying solely on mechanical techniques, continued to evolve throughout the mid-20th century, steadily producing sharper images and allowing for greater control over the thickness of the examined cross-section. This progress was driven by the development of more complex, multidirectional devices capable of moving in multiple planes and achieving more effective blurring of out-of-focus structures. However, despite these advancements in focal plane tomography, its ability to image soft tissue remained highly limited due to poor contrast.

Mathematical solutions and first implementations

Integral Equations and Radon Transform

To reliably solve the problem of X-ray passage through a plane at various angles, it was necessary to formulate an integral equation that accounted for the setup's geometry. Given the line integrals of a function along multiple lines within the -plane, the goal was to reconstruct the original function . This kind of problem was solved by Johann Radon in 1917 who worked on integral transforms without having a certain practical application in mind. He became the eponym of the Radon transform and also provided its inverse solution needed for the image reconstruction.

Tetelbaum and Korenblum In 1957, Soviet scientists Semyon I. Tetelbaum and Boris I. Korenblum were the first to propose reconstructing the linear attenuation coefficient μ in a slice using angular radiographs. In their paper О методе получения объемных изображений при помощи рентгеновского излучения ("About a Method of Obtaining Volumetric Images by Means of X-Ray Radiation") they formulated the underlying integral equation and proposed a solution—without being aware of Radon's earlier work. As a practical implementation, they also proposed a collimated fan-beam setup, in which a narrow line was recorded on film while the sample's rotation was synchronized with the film's orthogonal movement relative to the imaging plane, recording what is today known as a sinogram directly onto the film. Additionally, they described an analog computing device, utilizing hardware available in the 1950s, capable of performing the reconstruction and displaying the results on a TV screen. They estimated that a 100 × 100 pixel matrix could be reconstructed in five minutes using an analog computing device with a frequency bandwidth of up to 1 MHz.

In his paper, Tetelbaum also proposed performing scans using different wavelength ranges (i.e., spectra of different energies) and utilizing the dependence of μ on energy to obtain a "colored image, which could provide, e.g. in medicine, additional diagnostic possibilities". According to their 1958 paper, such a device was under construction in their laboratory at the Kiev Polytechnic Institute. However, no experimental results were published after 1958, likely due to the unexpected death of Tetelbaum in November of that year. Since their papers were written in Russian and published in Soviet scientific journals, they remained largely unknown in the West.

Allan Cormack Meanwhile, Allan M. Cormack, a South African physicist working in the Radiology Department at the University of Cape Town, was also interested in obtaining cross-sections of the absorption coefficient of the body to optimize radiotherapy treatments. He described his motivation as follows:

He formulated the underlying integral equation and searched for its solutions in the mathematical literature. However, unable to find any references to Radon's work, he solved the problem independently and designed an experiment to validate his tomographic approach. The setup utilized a collimated gamma source and a Geiger counter, with both the source and detector moving linearly and scanning the sample with a pencil beam. For simplicity, he chose a sample consisting of a cylinder made of aluminum, encircled by a ring of wood, arranged symmetrically around the center of rotation. Due to this point symmetry, the recorded intensity pattern remained identical at all angles, making it sufficient to acquire data from just one angle to determine the linear attenuation coefficient within a plane of the sample. The results demonstrated a good agreement between the experimentally acquired data and the theoretical calculations. He published his results in two papers in 1963 and 1964, but received no feedback and chose not to pursue the project further until he learned about Hounsfield's work in 1972.

Godfrey Hounsfield In the late 1960s, British electrical engineer Godfrey N. Hounsfield, who was employed by EMI and had led the development of Britain's first commercially available all-transistor computer (EMIDEC 1100), began exploring aspects of pattern recognition. Since EMI had nearly doubled its profits from The Beatles' record sales, it began investing a substantial amount of money into funding bold and innovative research ideas. In 1967, Hounsfield was given the opportunity to work on his own project and proposed tackling the tomographic problem, drawing inspiration from his earlier radar research. Instead of detecting patterns in the periphery using radar, he wondered whether it would be possible to detect objects inside a structure by sending beams through it from different angles. With additional funding from the UK Government Department of Health and Social Security, Hounsfield began developing a pencil beam scanner similar to Cormack's setup, using an Americium gamma source. Early successful measurements on samples such as bottles, water-filled jars, and pieces of metal and plastic took up to nine days to complete, acquiring 28,000 data points, which then required over two hours to process on a high-speed computer. Unlike his predecessors, Hounsfield had access to significant computing power and applied an algebraic reconstruction technique, using the Kaczmarz method from numerical algebra. Encouraged by the promising results, he justified the investment in an X-ray tube, a generator, and more sensitive crystal detectors, which soon enabled a significant reduction in measuring time. In 1968, the first promising scans of bovine brain samples were obtained, where white and grey matter could be clearly differentiated. In the same year, UK Patent No. 1283915 for "A Method of and Apparatus for Examination of a Body by Radiation such as X or Gamma Radiation" was granted to Hounsfield.

When reaching out to radiologists at leading hospitals, Hounsfield was met with widespread indifference, and his proposals were often dismissed as unfeasible or of little practical value. However, he found a key collaborator in James Ambrose, a neuroradiologist at Atkinson Morley Hospital in London, after convincing him with an impressive image of a brain sample containing a tumor—supplied by Ambrose for a test scan. Over the following year, Hounsfield adapted his scanner for clinical in vivo application, designing it to keep the patient's head static while a rotating gantry moved the X-ray source and detector around it. The scanner was installed at Atkinson Morley Hospital, and on October 1, 1971, the first patient—a woman with a suspected brain tumor—was successfully examined. Over the following weeks, they successfully diagnosed brain diseases in several patients, aiding in surgical planning. When Ambrose presented these groundbreaking images at the British Institute of Radiology's Annual Congress in 1972, the conference participants were stunned. The clarity of the brain scans, revealing lesions, tumors, and hemorrhages, dispelled any skepticism and marked the beginning of a new era in radiology.

Hounsfield described the method, scanner design, and operation in his landmark 1973 paper, where he also introduced radiodensity units to which the reconstructed images were calibrated. Later, the eponymous Hounsfield scale was established, defining water as 0 HU and air as -1000 HU. For the introduction of computer tomography, the Nobel Prize in Physiology or Medicine was awarded jointly to Allan M. Cormack and Godfrey N. Hounsfield in 1979. The Nobel Committee stated in its announcement: "It is no exaggeration to state that no other method within x-ray diagnostics within such a short period of time has led to such remarkable advances in research and in a multitude of applications."

Commercial scanners After the public presentation of the first results in 1972 and the enthusiastic reception by the radiological community, several companies around the world began developing their own CT systems. Just five years later, no fewer than 17 companies were already active on the global market, offering commercial CT scanners. Progress was driven by innovations in various fields, including X-ray tube optimization, detector development, faster data processing, and advanced reconstruction algorithms. These technological advancements defined the different "generations" of CT scanners, ranging from the first to the fifth generation. In the long term, however, fan-beam CT devices using the rotate-rotate approach—known as third-generation scanners—have proven to be the most practical. Thanks to innovations such as rotating anode tubes, helical scanning, and slip ring technology, they continue to dominate the market today. Scanners with these developments have occasionally been classified as 6th generation by their manufacturers for marketing purposes, but the term has not become generally accepted.

First generation scanners