Phase-contrast X-ray imaging

The first to discover X-rays was Wilhelm Conrad Röntgen in 1895, where he found that they had the ability to penetrate opaque materials. He recorded the first X-ray image, displaying the hand of his wife. He was awarded the first Nobel Prize in Physics in 1901 "in recognition of the extraordinary services he has rendered by the discovery of the remarkable rays subsequently named after him". Since then, X-rays have been used as a tool to safely determine the inner structures of different objects, although the information was for a long time obtained by measuring the transmitted intensity of the waves only, and the phase information was not accessible. The principle of phase-contrast imaging was first developed by Frits Zernike during his work with diffraction gratings and visible light. The application of his knowledge to microscopy won him the Nobel Prize in Physics in 1953. Ever since, phase-contrast microscopy has been an important field of optical microscopy. The transfer of phase-contrast imaging from visible light to X-rays took a long time, due to slow progress in improving the quality of X-ray beams and the inaccessibility of X-ray lenses. In the 1970s, it was realized that the synchrotron radiation, emitted from charged particles circulating in storage rings constructed for high-energy nuclear physics experiments, may have been a more intense and versatile source of X-rays than X-ray tubes; this, combined with progress in the development of X-rays optics, was fundamental for the further advancement of X-ray physics. The pioneer work to the implementation of the phase-contrast method to X-ray physics was presented in 1965 by Ulrich Bonse and Michael Hart, Department of Materials Science and Engineering of Cornell University, New York. They presented a crystal interferometer, made from a large and highly perfect single crystal. Not less than 30 years later the Japanese scientists Atsushi Momose, Tohoru Takeda and co-workers adopted this idea and refined it for application in biological imaging, for instance by increasing the field of view with the assistance of new setup configurations and phase retrieval techniques. The Bonse–Hart interferometer provides several orders of magnitude higher sensitivity in biological samples than other phase-contrast techniques, but it cannot use conventional X-ray tubes because the crystals only accept a very narrow energy band of X-rays (ΔE/E ~ 10−4). In 2012, Han Wen and co-workers took a step forward by replacing the crystals with nanometric phase gratings. The gratings split and direct X-rays over a broad spectrum, thus lifting the restriction on the bandwidth of the X-ray source. They detected sub nanoradian refractive bending of X-rays in biological samples with a grating Bonse–Hart interferometer. and was based on the detection of "Fresnel fringes" that arise under certain circumstances in free-space propagation. The experimental setup consisted of an inline configuration of an X-ray source, a sample and a detector and did not require any optical elements. It was conceptually identical to the setup of Dennis Gabor's revolutionary work on holography in 1948. An alternative approach called analyzer-based imaging was first explored in 1995 by Viktor Ingal and Elena Beliaevskaya at the X-ray laboratory in Saint Petersburg, Russia, and by Tim Davis and colleagues at the CSIRO (Commonwealth Scientific and Industrial Research Organisation) Division of Material Science and Technology in Clayton, Australia. This method uses a Bragg crystal as angular filter to reflect only a small part of the beam fulfilling the Bragg condition onto a detector. Important contributions to the progress of this method have been made by a US collaboration of the research teams of Dean Chapman, Zhong Zhong and William Thomlinson, for example the extracting of an additional signal caused by ultra-small angle scattering and the first CT image made with analyzer-based imaging. An alternative to analyzer-based imaging, which provides equivalent results without requiring the use of a crystal, was developed by Alessandro Olivo and co-workers at the Elettra synchrotron in Trieste, Italy. and that, this notwithstanding, it still is fully quantitative. This self-imaging effect creates an interference pattern downstream of a diffraction grating. At a particular distance this pattern resembles exactly the structure of the grating and is recorded by a detector. The position of the interference pattern can be altered by bringing an object in the beam, that induces a phase shift. This displacement of the interference pattern is measured with the help of a second grating, and by certain reconstruction methods, information about the real part of the refractive index is gained. The so-called Talbot–Lau interferometer was initially used in atom interferometry, for instance by John F. Clauser and Shifang Li in 1994. The first X-ray grating interferometers using synchrotron sources were developed by Christian David and colleagues from the Paul Scherrer Institute (PSI) in Villingen, Switzerland and the group of Atsushi Momose from the University of Tokyo. In 2005, independently from each other, both David's and Momose's group incorporated computed tomography into grating interferometry, which can be seen as the next milestone in the development of grating-based imaging. In 2006, another great advancement was the transfer of the grating-based technique to conventional laboratory X-ray tubes by Franz Pfeiffer and co-workers, which fairly enlarged the technique's potential for clinical use. About two years later the group of Franz Pfeiffer also accomplished to extract a supplementary signal from their experiments; the so-called "dark-field signal" was caused by scattering due to the porous microstructure of the sample and provided "complementary and otherwise inaccessible structural information about the specimen at the micrometer and submicrometer length scale". At the same time, Han Wen and co-workers at the US National Institutes of Health arrived at a much simplified grating technique to obtain the scattering ("dark-field") image. They used a single projection of a grid and a new approach for signal extraction named "single-shot Fourier analysis". Recently, a lot of research was done to improve the grating-based technique: Han Wen and his team analyzed animal bones and found out that the intensity of the dark-field signal depends on the orientation of the grid and this is due to the anisotropy of the bone structure. They made significant progress towards biomedical applications by replacing mechanical scanning of the gratings with electronic scanning of the X-ray source. and time-resolved phase-contrast CT. Furthermore, the first pre-clinical studies using grating-based phase-contrast X-ray imaging were published. Marco Stampanoni and his group examined native breast tissue with "differential phase-contrast mammography", and a team led by Dan Stutman investigated how to use grating-based imaging for the small joints of the hand. Most recently, a significant advance in grating-based imaging occurred due to the discovery of a phase moiré effect by Wen and colleagues. It led to interferometry beyond the Talbot self-imaging range, using only phase gratings and conventional sources and detectors. X-ray phase gratings can be made with very fine periods, thereby allowing imaging at low radiation doses to achieve high sensitivity. ==Physical principle==

Conventional X-ray imaging uses the drop in intensity through attenuation caused by an object in the X-ray beam and the radiation is treated as rays like in geometrical optics. But when X-rays pass through an object, not only their amplitude but their phase is altered as well. Instead of simple rays, X-rays can also be treated as electromagnetic waves. An object then can be described by its complex refractive index (cf. In other words, in phase-contrast imaging a map of the real part of the refraction index can be reconstructed with standard techniques like filtered back projection which is analog to conventional X-ray computed tomography where a map of the imaginary part of the refraction index can be retrieved. To get information about the compounding of a sample, basically the density distribution of the sample, one has to relate the measured values for the refractive index to intrinsic parameters of the sample, such a relation is given by the following formulas: :\beta=\frac{\rho_a\sigma_a}{2k}, where is the atomic number density, the absorption cross section, the length of the wave vector and :\delta=\frac{\rho_ap}{k}, where the phase shift cross section. Far from the absorption edges (peaks in the absorption cross-section due to the enhanced probability for the absorption of a photon that has a frequency close to the resonance frequency of the medium), dispersion effects can be neglected; this is the case for light elements (atomic number Z\sigma_a=0.02[\text{barn}]\left (\frac{k_0}{k}\right )^3Z^4 where 0.02 is a constant given in barn, the typical unit of particle interaction cross section area, the length of the wave vector, the length of a wave vector with wavelength of 1 Angstrom and the atomic number. The valid formula under these conditions for the phase shift cross section is: :p=\frac{2\pi Zr_0}{k} where is the atomic number, the length of the wave vector, and the classical electron radius. This results in the following expressions for the two parts of the complex index of refraction: :\delta=\frac{\rho_ap}{k}=\frac{2\pi\rho_aZr_0}{k^2} :\beta=\frac{\rho_a\sigma_a}{2k}= 0.01[\text{barn}] \rho_a k_0^3 \left (\frac{Z}{k}\right )^4 Inserting typical values of human tissue in the formulas given above shows that is generally three orders of magnitude larger than within the diagnostic X-ray range. This implies that the phase-shift of an X-ray beam propagating through tissue may be much larger than the loss in intensity thus making phase contrast X-ray imaging more sensitive to density variations in the tissue than absorption imaging. Due to the proportionalities :\beta \propto k^{-4}, \delta \propto k^{-2} the advantage of phase contrast over conventional absorption contrast even grows with increasing energy. Furthermore, because the phase contrast image formation is not intrinsically linked to the absorption of X-rays in the sample, the absorbed dose can potentially be reduced by using higher X-ray energies. As mentioned above, concerning visible light, the real part of the refractive index n can deviate strongly from unity (n of glass in visible light ranges from 1.5 to 1.8) while the deviation from unity for X-rays in different media is generally of the order of 10−5. Thus, the refraction angles caused at the boundary between two isotropic media calculated with Snell's formula are also very small. The consequence of this is that refraction angles of X-rays passing through a tissue sample cannot be detected directly and are usually determined indirectly by "observation of the interference pattern between diffracted and undiffracted waves produced by spatial variations of the real part of the refractive index." ==Experimental realisation==

Crystal interferometry Crystal interferometry, sometimes also called X-ray interferometry, is the oldest but also the most complex method used for experimental realization. It consists of three beam splitters in Laue geometry aligned parallel to each other. (See figure to the right) The incident beam, which usually is collimated and filtered by a monochromator (Bragg crystal) before, is split at the first crystal (S) by Laue diffraction into two coherent beams, a reference beam which remains undisturbed and a beam passing through the sample. The second crystal (T) acts as a transmission mirror and causes the beams to converge one towards another. The two beams meet at the plane of the third crystal (A), which is sometimes called, the analyzer crystal, and create an interference pattern the form of which depends on the optical path difference between the two beams caused by the sample. This interference pattern is detected with an X-ray detector behind the analyzer crystal. By putting the sample on a rotation stage and recording projections from different angles, the 3D-distribution of the refractive index and thus tomographic images of the sample can be retrieved. These techniques can be used when the signal-to-noise ratio of the image is sufficiently high and phase variation is not too abrupt. X-ray interferometry is considered to be the most sensitive to the phase shift, of the 4 methods, consequently providing the highest density resolution in range of mg/cm3. A general limitation to the spatial resolution of this method is given by the blurring in the analyzer crystal which arises from dynamical refraction, i.e. the angular deviation of the beam due to the refraction in the sample is amplified about ten thousand times in the crystal, because the beam path within the crystal depends strongly on its incident angle. This effect can be reduced by thinning down the analyzer crystal, e.g. with an analyzer thickness of 40 m a resolution of about 6 m was calculated. Alternatively the Laue crystals can be replaced by Bragg crystals, so the beam doesn't pass through the crystal but is reflected on the surface. Another constraint of the method is the requirement of a very high stability of the setup; the alignment of the crystals must be very precise and the path length difference between the beams should be smaller than the wavelength of the X-rays; to achieve this the interferometer is usually made out of a highly perfect single block of silicon by cutting out two grooves. By the monolithic production the very important spatial lattice coherence between all three crystals can be maintained relatively well but it limits the field of view to a small size,(e.g. 5 cm x 5 cm for a 6-inch ingot) and because the sample is normally placed in one of the beam paths the size of the sample itself is also constrained by the size of the silicon block. Recently developed configurations, using two crystals instead of one, enlarge the field of view considerably, but are even more sensitive to mechanical instabilities. Another additional difficulty of the crystal interferometer is that the Laue crystals filter most of the incoming radiation, thus requiring a high beam intensity or very long exposure times. That limits the use of the method to highly brilliant X-ray sources like synchrotrons. According to the constraints on the setup the crystal interferometer works best for high-resolution imaging of small samples which cause small or smooth phase gradients. Grating Bonse-Hart (interferometry) To have the superior sensitivity of crystal Bonse-Hart interferometry without some of the basic limitations, the monolithic crystals have been replaced with nanometric x-ray phase-shift gratings. The first such gratings have periods of 200 to 400 nanometers. They can split x-ray beams over the broad energy spectra of common x-ray tubes. The main advantage of this technique is that it uses most of the incoming x-rays that would have been filtered by the crystals. Because only phase gratings are used, grating fabrication is less challenging than techniques that use absorption gratings. The first grating Bonse-Hart interferometer (gBH) operated at 22.5 keV photon energy and 1.5% spectral bandwidth. The incoming beam is shaped by slits of a few tens of micrometers such that the transverse coherence length is greater than the grating period. The interferometer consists of three parallel and equally spaced phase gratings, and an x-ray camera. The incident beam is diffracted by a first grating of period 2P into two beams. These are further diffracted by a second grating of period P into four beams. Two of the four merge at a third grating of period 2P. Each is further diffracted by the third grating. The multiple diffracted beams are allowed to propagate for sufficient distance such that the different diffraction orders are separated at the camera. There exists a pair of diffracted beams that co-propagate from the third grating to the camera. They interfere with each other to produce intensity fringes if the gratings are slightly misaligned with each other. The central pair of diffraction paths are always equal in length regardless of the x-ray energy or the angle of the incident beam. The interference patterns from different photon energies and incident angles are locked in phase. The imaged object is placed near the central grating. Absolute phase images are obtained if the object intersects one of a pair of coherent paths. If the two paths both pass through the object at two locations which are separated by a lateral distance d, then a phase difference image of Φ(r) - Φ(r-d) is detected. Phase stepping one of the gratings is performed to retrieve the phase images. The phase difference image Φ(r) - Φ(r-d) can be integrated to obtain a phase shift image of the object. This technique achieved substantially higher sensitivity than other techniques with the exception of the crystal interferometer. A basic limitation of the technique is the chromatic dispersion of grating diffraction, which limits its spatial resolution. A tabletop system with a tungsten-target x-ray tube running at 60 kVp will have a limiting resolution of 60 μm. Its setup consists of a monochromator (usually a single or double crystal that also collimates the beam) in front of the sample and an analyzer crystal positioned in Bragg geometry between the sample and the detector. (See figure to the right) This analyzer crystal acts as an angular filter for the radiation coming from the sample. When these X-rays hit the analyzer crystal the condition of Bragg diffraction is satisfied only for a very narrow range of incident angles. When the scattered or refracted X-rays have incident angles outside this range they will not be reflected at all and don't contribute to the signal. Refracted X-rays within this range will be reflected depending on the incident angle. The dependency of the reflected intensity on the incident angle is called a rocking curve and is an intrinsic property of the imaging system, i.e. it represents the intensity measured at each pixel of the detector when the analyzer crystal is "rocked" (slightly rotated in angle θ) with no object present and thus can be easily measured. Tomographic imaging with analyzer-based imaging can be done by fixing the analyzer at a specific angle and rotating the sample through 360° while the projection data are acquired. Several sets of projections are acquired from the same sample with different detuning angles and then a tomographic image can be reconstructed. Assuming that the crystals are normally aligned such that the derivative of the refractive index is measured in the direction parallel to the tomographic axis, the resulting "refraction CT image" shows the pure image of the out-of-plane gradient. For analyzer-based imaging, the stability requirements of the crystals is less strict than for crystal interferometry but the setup still requires a perfect analyzer crystal that needs to be very precisely controlled in angle and the size of the analyzer crystal and the constraint that the beam needs to be parallel also limits the field of view. Additionally as in crystal interferometry a general limitation for the spatial resolution of this method is given by the blurring in the analyzer crystal due to dynamic diffraction effects, but can be improved by using grazing incidence diffraction for the crystal. Due to its high sensitivity to small changes in the refraction index this method is well suited to image soft tissue samples and is already implemented to medical imaging, especially in Mammography for a better detection of microcalcifications Propagation-based imaging Propagation-based imaging (PBI) is the most common name for this technique but it is also called in-line holography, refraction-enhanced imaging or phase-contrast radiography. The latter denomination derives from the fact that the experimental setup of this method is basically the same as in conventional radiography. It consists of an in-line arrangement of an X-ray source, the sample and an X-ray detector and no other optical elements are required. The only difference is that the detector is not placed immediately behind the sample, but in some distance, so the radiation refracted by the sample can interfere with the unchanged beam. PBI can be used to enhance the contrast of an absorption image, in this case the phase information in the image plane is lost but contributes to the image intensity (edge enhancement of attenuation image). However it is also possible to separate the phase and the attenuation contrast, i.e. to reconstruct the distribution of the real and imaginary part of the refractive index separately. The unambiguous determination of the phase of the wave front (phase retrieval) can be realized by recording several images at different detector-sample distances and using algorithms based on the linearization of the Fresnel diffraction integral to reconstruct the phase distribution, but this approach suffers from amplified noise for low spatial frequencies and thus slowly varying components may not be accurately recovered. There are several more approaches for phase retrieval and a good overview about them is given in. Tomographic reconstructions of the 3D distribution of the refractive index or "Holotomography" is implemented by rotating the sample and recording for each projection angle a series of images at different distances. A high resolution detector is required to resolve the interference fringes, which practically limits the field of view of this technique or requires larger propagation distances. The achieved spatial resolution is relatively high in comparison to the other methods and, since there are no optical elements in the beam, is mainly limited by the degree of spatial coherence of the beam. As mentioned before, for the formation of the Fresnel fringes, the constraint on the spatial coherence of the used radiation is very strict, which limits the method to small or very distant sources, but in contrast to crystal interferometry and analyzer-based imaging the constraint on the temporal coherence, i.e. the polychromaticity is quite relaxed. Consequently, the method cannot only be used with synchrotron sources but also with polychromatic laboratory X-ray sources providing sufficient spatial coherence, such as microfocus X-ray tubes. A very important application of PBI is the examination of fossils with synchrotron radiation, which reveals details about the paleontological specimens which would otherwise be inaccessible without destroying the sample. Grating-based imaging Grating-based imaging (GBI) includes Shearing interferometry or X-ray Talbot interferometry (XTI), and polychromatic far-field interferometry (PFI). Since the first X-ray grating interferometer—consisting of two phase gratings and an analyzer crystal While the Talbot effect and the Talbot interferometer were discovered and extensively studied by using visible light it has been demonstrated several years ago for the hard X-ray regime as well. In GBI a sample is placed before or behind the phase grating (lines of the grating show negligible absorption but substantial phase shift) and thus the interference pattern of the Talbot effect is modified by absorption, refraction and scattering in the sample. For a phase object with a small phase gradient the X-ray beam is deflected by :\Delta \alpha=\frac{1}{k}\frac{\partial \phi(x)}{\partial x} where is the length of the wave vector of the incident radiation and the second factor on the right hand side is the first derivative of the phase in the direction perpendicular to the propagation direction and parallel to the alignment of the grating. Since the transverse shift of the interference fringes is linear proportional to the deviation angle the differential phase of the wave front is measured in GBI, similar as in ABI. In other words, the angular deviations are translated into changes of locally transmitted intensity. By performing measurements with and without sample the change in position of the interference pattern caused by the sample can be retrieved. The period of the interference pattern is usually in the range of a few micrometers, which can only be conveniently resolved by a very high resolution detector in combination with a very intense illumination ( a source providing a very high flux) and hence limits the field of view significantly . This is the reason why a second grating, typically an absorption grating, is placed at a fractional Talbot length to analyze the interference pattern. Using this approach, the spatial resolution is lower than one achieved by the phase-stepping technique, but the total exposure time can be much shorter, because a differential phase image can be retrieved with only one Moiré pattern. Single-shot Fourier analysis technique was used in early grid-based scattering imaging A technique to eliminate mechanical scanning of the grating and still retain the maximum spatial resolution is electronic phase stepping. It scans the source spot of the x-ray tube with an electro-magnetic field. This causes the projection of the object to move in the opposite direction, and also causes a relative movement between the projection and the Moiré fringes. The images are digitally shifted to realign the projections. The result is that the projection of the object is stationary, while the Moiré fringes move over it. This technique effectively synthesizes the phase stepping process, but without the costs and delays associated with mechanical movements. With both of these phase-extraction methods tomography is applicable by rotating the sample around the tomographic axis, recording a series of images with different projection angles and using back projection algorithms to reconstruct the 3-dimensional distributions of the real and imaginary part of the refractive index. The standard configuration as shown in the figure to the right requires spatial coherence of the source and consequently is limited to high brilliant synchrotron radiation sources. This problem can be handled by adding a third grating close to the X-ray source, known as a Talbot-Lau interferometer. This source grating, which is usually an absorption grating with transmission slits, creates an "array of individually coherent but mutually incoherent sources". As the source grating can contain a large number of individual apertures, each creating a sufficiently coherent virtual line source, standard X-ray generators with source sizes of a few square millimeters can be used efficiently and the field of view can be significantly increased. A great advantage of the usage of polychromatic radiation is the shortening of the exposure times and this has recently been exploited by using white synchrotron radiation to realize the first dynamic (time-resolved) Phase contrast tomography. A very common fabrication process for X-ray gratings is LIGA, which is based on deep X-ray lithography and electroplating. It was developed in the 1980s for the fabrication of extreme high aspect ratio microstructures by scientists from the Karlsruhe Institute of Technology (KIT). Another technical requirement is the stability and precise alignment and movement of the gratings (typically in the range of some nm), but compared to other methods, e.g. the crystal interferometer the constraint is easy to fulfill. The grating fabrication challenge was eased by the discovery of a phase moiré effect In PFI a phase grating is used to convert the fine interference fringes into a broad intensity pattern at a distal plane, based on the phase moiré effect. Besides higher sensitivity, another incentive for smaller grating periods is that the lateral coherence of the source needs to be at least one grating period. A disadvantage of the standard GBI setup is the sensitivity to only one component of the phase gradient, which is the direction parallel to the 1-D gratings. This problem has been solved either by recording differential phase contrast images of the sample in both direction x and y by turning the sample (or the gratings) by 90° or by the employment of two-dimensional gratings. Being a differential phase technique, GBI is not as sensitive as crystal interferometry to low spatial frequencies, but because of the high resistance of the method against mechanical instabilities, the possibility of using detectors with large pixels and a large field of view and, of crucial importance, the applicability to conventional laboratory X-ray tubes, grating-based imaging is a very promising technique for medical diagnostics and soft tissue imaging. First medical applications like a pre-clinical mammography study, show great potential for the future of this technique. Edge-illumination Edge-illumination (EI) was developed at the Italian synchrotron (Elettra) in the late '90s, as an alternative to ABI. It is based on the observation that, by illuminating only the edge of detector pixels, high sensitivity to phase effects is obtained (see figure). Also in this case, the relation between X-ray refraction angle and first derivative of the phase shift caused by the object is exploited: \Delta \alpha=\frac{1}{k}\frac{\partial \phi(x)}{\partial x} If the X-ray beam is vertically thin and impinges on the edge of the detector, X-ray refraction can change the status of the individual X-ray from "detected" to "undetected" and vice versa, effectively playing the same role as the crystal rocking curve in ABI. This analogy with ABI, already observed when the method was initially developed, Effectively, the same effect is obtained – a fine angular selection on the photon direction; however, while in analyzer-based imaging the beam needs to be highly collimated and monochromatic, the absence of the crystal means that edge-illumination can be implemented with divergent and polychromatic beams, like those generated by a conventional rotating-anode X-ray tube. This is done by introducing two opportunely designed masks (sometimes referred to as "coded-aperture" masks), one immediately before the sample, and one in contact with the detector (see figure). The purpose of the latter mask is simply to create insensitive regions between adjacent pixels, and its use can be avoided if specialized detector technology is employed. In this way, the edge-illumination configuration is simultaneously realized for all pixel rows of an area detector. This plurality of individual beamlets means that, in contrast to the synchrotron implementation discussed above, no sample scanning is required – the sample is placed downstream of the sample mask and imaged in a single shot (two if phase retrieval is performed). Although the set-up perhaps superficially resembles that of a grating interferometer, the underpinning physical mechanism is different. In contrast to other phase contrast X-ray imaging techniques, edge-illumination is an incoherent technique, and was in fact proven to work with both spatially and temporally incoherent sources, without any additional source aperturing or collimation. For example, 100 μm focal spots are routinely used which are compatible with, for example, diagnostic mammography systems. Quantitative phase retrieval was also demonstrated with (uncollimated) incoherent sources, showing that in some cases results analogous to the synchrotron gold standard can be obtained. results in a number of advantages, which include reduced exposure time for the same source power, reduced radiation dose, robustness against environmental vibrations, and easier access to high X-ray energy. Moreover, since their aspect ratio is not particularly demanding, masks are cheap, easy to fabricate (e.g.do not require X-ray lithography) and can already be scaled to large areas. The method is easily extended to phase sensitivity in two directions, for example, through the realization of L-shaped apertures for the simultaneous illumination of two orthogonal edges in each detector pixel. More generally, while in its simplest implementation beamlets match individual pixel rows (or pixels), the method is highly flexible, and, for example, sparse detectors and asymmetric masks can be used and compact and microscopy systems can be built. So far, the method has been successfully demonstrated in areas such as security scanning, biological imaging, paleontology and others; adaptation to 3D (computed tomography) was also demonstrated. Alongside simple translation for use with conventional x-ray sources, there are substantial benefits in the implementation of edge-illumination with coherent synchrotron radiation, among which are high performance at very high X-ray energies == Phase-contrast x-ray imaging in medicine ==

Four potential benefits of phase contrast have been identified in a medical imaging context: A quantitative comparison of phase- and absorption-contrast mammography that took realistic constraints into account (dose, geometry, and photon economy) concluded that grating-based phase-contrast imaging (Talbot interferometry) does not exhibit a general signal-difference-to-noise improvement relative to absorption contrast, but the performance is highly task dependent. Such a comparison is yet to be undertaken for all phase contrast methods, however, the following considerations are central to such a comparison: • The optimal imaging energy for phase contrast is higher than for absorption contrast and independent of target. • Differential phase contrast imaging methods such as, e.g., Analyser Based Imaging, Grating Based Imaging and Edge Illumination intrinsically detect the phase differential, which causes the noise-power spectrum to decrease rapidly with spatial frequency so that phase contrast is beneficial for small and sharp targets, e.g., tumor spicula rather than solid tumors, and for discrimination tasks rather than for detection tasks. • Phase contrast favors detection of materials that differ in density compared to the background tissue, rather than materials with differences in atomic number. For instance, the improvement for detection / discrimination of calcified structures is less than the improvement for soft tissue. • Grating-based imaging is relatively insensitive to spectrum bandwidth. It should also be noted, however, that other techniques such as propagation-based imaging and edge-illumination are even more insensitive, to the extent that they can be considered practically achromatic. and mammography, phase contrast imaging is beginning to be applied in real medical applications, such as lung imaging, imaging of extremities, intra-operative specimen imaging. In vivo applications of phase contrast imaging have been kick-started by the pioneering mammography study with synchrotron radiation undertaken in Trieste, Italy. ==References==