page_title: Phase-contrast X-ray imaging
section_title: Crystal interferometry
hierarchical_section_title: Phase-contrast X-ray imaging / Experimental realisation / Crystal interferometry
caption_attribution_description: English: Drawing of Crystal interferometer (Phase-contrast X-ray imaging technique)
context_page_description: Phase-contrast X-ray imaging or phase-sensitive X-ray imaging is a general term for different technical methods that use information concerning changes in the phase of an X-ray beam that passes through an object in order to create its images. Standard X-ray imaging techniques like radiography or computed tomography rely on a decrease of the X-ray beam's intensity when traversing the sample, which can be measured directly with the assistance of an X-ray detector. In PCI however, the beam's phase shift caused by the sample is not measured directly, but is transformed into variations in intensity, which then can be recorded by the detector.
  In addition to producing projection images, PCI, like conventional transmission, can be combined with tomographic techniques to obtain the 3D distribution of the real part of the refractive index of the sample. When applied to samples that consist of atoms with low atomic number Z, PCI is more sensitive to density variations in the sample than conventional transmission-based X-ray imaging. This leads to images with improved soft tissue contrast.
context_section_description: 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.
  In contrast to the methods below, with the crystal interferometer the phase itself is measured and not any spatial alternation of it.
  To retrieve the phase shift out of the interference patterns; a technique called phase-stepping or fringe scanning is used: a phase shifter (with the shape of a wedge) is introduced in the reference beam. The phase shifter creates straight interference fringes with regular intervals; so called carrier fringes. When the sample is placed in the other beam, the carrier fringes are displaced. The phase shift caused by the sample corresponds to the displacement of the carrier fringes. Several interference patterns are recorded for different shifts of the reference beam and by analyzing them the phase information modulo 2π can be extracted. This ambiguity of the phase is called the phase wrapping effect and can be removed by so-called "phase unwrapping techniques". These techniques can be used when the signal-to-noise ratio of the image is sufficiently high and phase variation is not too abrupt.
  As an alternative to the fringe scanning method, the Fourier-transform method can be used to extract the phase shift information with only one interferogram, thus shortening the exposure time, but this has the disadvantage of limiting the spatial resolution by the spacing of the carrier fringes.
  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. But due to its high sensitivity, the fringes created by a strongly phase-shifting sample may become unresolvable; to overcome this problem a new approach called "coherence-contrast X-ray imaging" has been developed recently, where instead of the phase shift the change of the degree of coherence caused by the sample is relevant for the contrast of the image.
  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 μm a resolution of about 6 μm 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 impor
caption: Drawing of crystal interferometer
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