page_title: Phase-contrast X-ray imaging
section_title: Grating-based imaging
hierarchical_section_title: Phase-contrast X-ray imaging / Experimental realisation / Grating-based imaging
caption_attribution_description: English: Diagram of Electronic Phase Stepping (EPS). The source spot is moved electronically, which leads to movement of the sample image on the detector.
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: 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—was built, various slightly different setups for this method have been developed; in the following the focus lies on the nowadays standard method consisting of a phase grating and an analyzer grating. (See figure to the right).
  The XTI technique is based on the Talbot effect or "self-imaging phenomenon", which is a Fresnel diffraction effect and leads to repetition of a periodic wavefront after a certain propagation distance, called the "Talbot length". This periodic wavefront can be generated by spatially coherent illumination of a periodic structure, like a diffraction grating, and if so the intensity distribution of the wave field at the Talbot length resembles exactly the structure of the grating and is called a self-image. It has also been shown that intensity patterns will be created at certain fractional Talbot lengths. At half the distance the same intensity distribution appears except for a lateral shift of half the grating period while at certain smaller fractional Talbot distances the self-images have fractional periods and fractional sizes of the intensity maxima and minima, that become visible in the intensity distribution behind the grating, a so-called Talbot carpet. The Talbot length and the fractional lengths can be calculated by knowing the parameters of the illuminating radiation and the illuminated grating and thus gives the exact position of the intensity maxima, which needs to be measured in GBI. 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
  where k 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.
  The analyzer grating does normally have the same period as the interference fringes and thus transforms local fringe position into signal intensity variation on the detector, which is placed immediately behind the grating.
  In order to separate the phase information from other contributions to the signal, a technique called "phase-stepping" is used. One of the gratings is scanned along the transverse direction term xg; over one period of the grating, and for different positions of the grating an image is taken. The intensity signal in each pixel in the detector plane oscillates as a function of xg. The recorded intensity oscillation can be represented by a Fourier series and by recording and comparing these intensity oscillations wi
caption: Diagram of Electronic Phase Stepping (EPS). The source spot is moved electronically, which leads to movement of the sample image on the detector.
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