Basic principles of X-ray tomography - X-rays

X-rays cover a part of the spectrum of electromagnetic radiation with wavelength of roughly 10-9-10-11m, so about 1000 times shorter or 1000 times more energetic than visible light. The shorter wavelength permits to achieve a much higher resolution with X-rays than with light. Whereas visible light is usually reflected at solid surfaces, X-rays can penetrate much deeper into objects, which make X-rays particular interesting for the investigation of structures and materials. X-rays interact only weekly with most materials, in particular soft matter, and travel largely undisturbed through the object under investigation, which allows to image the internal structures of materials and organisms.

X-ray tube generated X-rays

In the old days since Röntgen's discovery of X-rays in 1895 X-ray tubes were the common source of X-rays and are still widely used in medical applications. The X-rays are generated by accelerating electrons in a strong electric field from a cathode source onto a metallic anode. When the electrons hit the metal target two types of interaction occur. Electrons with sufficiently high energy will knock out electrons from the inner shells of the metal-atoms. This electron-hole is filled up by electron in higher energy levels leading to the X-ray spectrum characteristic for the chemical element of the target. Lower-energy electron are slowed down by the strong electric field near the nuclei of heavy elements resulting in a continuous spectrum of electromagnetic radiation, the so called bremsstrahlung

Synchrotron generated X-rays

In a synchrotron x-rays are generated based on the same principle as the bremsstrahlung. The figure shows a sketch of a typical synchrotron (here based on the SOLEIL facility). Electrons are produced and emitted by an electron gun. They are first accelerated in a linear accelerator (linac) and then in a circular accelerator (booster ring) to reach the desired energy level. To produce (collimated) X-rays by means of the circulating electrons, they need to be (strongly) accelerated. This happend in the bendings magnets in the curved section and, for modern storage rings, in the straight sections by so-called insertion devices. Insertion devices apply an alternating magnetic field causing small undulations in the electron path, either in direction of the trajectory (undulators) or orthogonal to it (wigglers). The radiation produced by bending magnets and wigglers can cover a wide spectrum ranging from microwaves to hard x-rays. Undulators in contrast produce a distinct spectrum with very high intensities at certain energies. In all cases, the radiation is emitted tangential to the electron storage ring (synchrotron) to be used in tangentially arranged beamlines (where the experiments are being conducted) for diffraction, scattering or imaging experiments. The figure on the left shows a schematic layout of the experimental setup for phase contrast tomography. One characteristics of imaging beamlines is the long distance between the insertion device and the experimental hutch which guarantees a highly coherent beam. Together with the small beam size and high brilliance the imaging beamline at PETRA III for example can resolve details down to a size of 100nm.


Genealogy of synchrotrons and insertion devices

An important benchmark of the power and quality of a light source is its brilliance. This is a measure of not only the number of photons generated in a specific wavelength range but also the smallness of the light source and how tightly the beam is collimated. The greater the brilliance of the radiation, the larger the variety of experiments for which it can be used. Equally important, the amount of time required for the measurements strongly depends on the brilliance of the light source. Second-generation accelerators like DORIS III are fitted not only with bending magnets but also with special magnet structures – predominantly wigglers – that result in the generation of as much as a thousand times more light. Owing to the relatively large cross section of the electron beam in the accelerator, this type of source delivers a fairly broad light beam that is ideal for investigating samples several centimetres or milli­metres in size or even entire workpieces of the kind that is common in the field of materials research.

When it comes to smaller samples in the millimetre-to-micrometre­ range, or experiments necessitating highly colli­mated radiation, the light sources of the second generation no longer suffice. This is the realm of the third generation, the first representatives of which went into operation in the 1990s: storage rings that were custom-built for generating radiation­ and which, due to a small beam cross section in the accelerator and the systematic use of undulators, are able to produce light of a brilliance several orders of magnitude greater than their predecessors. Experiments at this type of light source attain a spatial resolution in the sub-micrometre range. Because a certain proportion of this highly brilliant radiation also displays coherent, laser­-like properties – i.e. its oscillations are exactly in phase with one another – it can also be used to conduct experiments that were impossible at second-generation sources.

In their attempts to attain ever higher brilliances and even synchrotron radiation with genuine laser properties, light source developers soon ran up against a fundamental problem. In a storage ring, electrons circulate for hours on end, emitting light several million times per second as they pass through the bending magnets, wigglers and undulators. Each time an electron emits a light particle, however, it is thrown slightly off track. For this reason, the particle beam can only be collimated to a certain degree. In a storage ring it is therefore close to impossible to produce a beam much finer than is already achievable at third-generation light sources. In other­ words, there seemed to be a limit to the maximum brilliance­ achievable. That is where Free Electron Lasers come into play.