## 3 Phase Contrast Imaging Techniques on Conventional Systems
### Grating Interferometry  
Grating-based imaging (GI) is an X-ray PCI technique based on the use of grating interferometers. Such gratings are usually made of Au or Si and typically measure around 5 cm; they have periods of a few microns. It has been successfully adapted from visible-light grating interferometry [37]. Fairly recent, this technique has become popular in many fields because of its good adaptability to conventional X-ray tubes. The principle of GI is a phenomenon called the Talbot effect (observed in 1836 by the English inventor [PERSON]), where a periodic wave repeats its pattern at a certain distances in the Fresnel regime. Figure 5 presents a GI set-up on a conventional source. An X-ray grating interferometer consists of two gratings (G1 and G2); a detector; and in the case of conventional X-ray source, an additional grating G0 that acts as a collimator creating multiple small X-ray sources. G1 is usually a phase grating, and G2 is an absorption grating. G1 is used to split the beam, creating periodic interference patterns varying with distance. This interference pattern is called the \"Talbot carpet\", as shown in Figure 6. The interference pattern created from the waves re-emitted through G1 gives periodic peaks of intensity at characteristic distances. The detector is placed at one of these characteristic distances, usually where the intensity peaks are higher. When the sample is placed in the beam, these interference patterns will be distorted due to attenuation, refraction and scattering. When placing an attenuation grating in front of the detector with the same period as the original interference pattern, the phase variations are translated into intensity variations, as the peaks of intensity no longer fall in the space between two bars of G2. Taking several acquisitions with several positions of the gratings allows one to retrieve the precise refraction angles and the attenuation and spreading of the dark field. Figure 5: Grating interferometer imaging set-up. A beam from a very coherent source or from a source collimated by a G0 grating is emitted towards the sample. A grating G1 placed before or after the sample creates a Talbot carpet interference pattern. The grating G2 filters the peaks of intensity that have been deviated from the axis before the detector. Several acquisitions are required with various positions of G1 and G2. There are two types of interferometers: the most common is a 1D interferometer that consists of gratings made up of parallel lines and the 2D grating interferometer designed with two-dimensional patterns [38]. Besides this latter proof of feasibility, it is difficult to find real application of these 2D interferometers. The fabrication of a gratings interferometer is a very challenging task and is a very active field of research [39; 40; 41], which is not the purpose of this review. In 2006, [PERSON] et al. [42] demonstrated the possibility of using the method on conventional sources, and a new field was born with tens of teams around the world working on this set-up. Albeit presenting a good sensitivity, this technique requires complex experimental set-ups difficult and is expensive to manufacture, especially for large fields of view. However, recent advances have shown impressive results on human patients using grating interferometry dark-field imaging [9; 43; 44]. Even more recently, the same team published the first results on the implementation of the technique on a clinical CT scanner [45]. This proof of concept on phantoms still needs to be optimized in order to reduce the acquisition time for clinical routine. Despite the set-up's precision requirement and stability, it was proven that, given the means and materials, it was possible to implement it on a tomography set-up.