page_title: Phase-contrast X-ray imaging
section_title: Grating Bonse-Hart (interferometry)
hierarchical_section_title: Phase-contrast X-ray imaging / Experimental realisation / Grating Bonse-Hart (interferometry)
caption_attribution_description: English: Drawing of a grating Bonse-Hart interferometer depicting how it creates interference fringes.
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: 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. Another constraint is that the x-ray beam is slitted down to only tens of micrometers wide. A potential solution has been proposed in the form of parallel imaging with multiple slits.
caption: Drawing of a grating Bonse-Hart interferometer.
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