# Principles of Different X-ray Phase-Contrast Imaging: A Review
## 2 Methods
### Grating Interferometer  
Figure 10 shows that in the grating interferometer, the first grating (G\({}_{1}\)) splits the incoming beam into two first-order diffractions. These two beams diffract downstream of the first grating, interfere with each other, and form linear periodic fringe patterns. The existence of a phase object causes displacement of the fringes. A second grating (G\({}_{2}\)) with the same periodicity and orientation as the fringes is inserted directly in front of the detector to read the fringes and obtain the refraction of the object. Thus, the fringes can be restored from the stepping readouts on the detector of G\({}_{2}\). To transform the phase modulation into intensity modulation with G\({}_{2}\), the distance between the first and second gratings is calculated from the Talbot effect. Therefore, this method is also called the \"Talbot interferometer\". The origin and development of X-ray grating interferometers until 2013 were thoroughly reported in a review by [PERSON] [89]; thus, we do not elaborate on this in the current review. However, this method also demands a highly coherent and high-brightness X-ray source, limiting its application to laboratory sources and commercial uses. In 2006, [PERSON] et al. introduced another grating G\({}_{0}\) into this method as this grating was placed immediately after the X-ray source. The G\({}_{0}\) grating creates an array of individually coherent, but mutually incoherent sources. The Talbot effects of these sources overlap with each other on the plane of G\({}_{2}\) due to the Lau effect [90], making this method suitable for incoherent and low brightness sources. The X-ray grating interferometer with G\({}_{0}\) is also named the \"Talbot-Lau interferometer\". The comparably simple alignment of instruments in the experimental setups allows for a large FOV when using the Talbot-Lau interferometer. This method is becoming one of the most popular X-ray phase-contrast images for biological samples. In 2014, [PERSON] et al. reported a hospital-installed X-ray phase-imaging machine based on a Talbot-Lau-type grating interferometer and successfully depicted the cartilage features in the joints of a human hand [91], as shown in Figure 11.  
In 2011, [PERSON] et al. integrated two-dimensional checkerboard designed gratings into this method. The results clearly showed the soft tissues and cartilage of a chicken wing sample [92]. In 2014, [PERSON] et al. employed a novel designed G\({}_{2}\) to avoid the stepping procedure of this method. Both physical phantom and biological samples were imaged. The results provided more information than conventional absorption images and presented better visibilities [93]. This approach decreased the dosage but brought a tradeoff to the resolution. In 2016, [PERSON] et al. performed X-ray Talbot-Lau interferometer CT with a laboratory source and obtained higher sensitivity than any other laboratory X-ray phase-contrast technique. A minimum refraction angle of 17 nrad was achieved [94]. In 2017, [PERSON] et al. obtained an X-ray tomogram with an exposure time under 10 ms using this method [95]. In 2018, [PERSON] et al. demonstrated time-resolved in vivo dark-field imaging of a breath cycle in a mechanically ventilated mouse. A time resolution of 0.1 s was achieved [96]. In 2020, [PERSON] et al. performed grating-interferometry-based mammography at a mean glandular dose of 1.6 mGy for a 5-cm-thick, 18%-dense breast, and an FOV of 26 \(\times\) 21 cm\({}^{2}\)[97]. In 2010, [PERSON] and [PERSON] introduced the mesh-based X-ray phase-imaging method that simultaneously obtained absorption and differential phase-contrast images [98]. This method requires no coherent sources and only simple alignment of a wired metal mesh, as shown in Figure 12.  
Figure 10: Sketch of the grating interferometer (Adapted with permission from [11], Copyright 2015 The Optical Society). Figure 11: (**a**) X-ray Talbot–[PERSON] phase-imaging system installed in a hospital and resultant (**b**) absorption image and (**c**) differential phase image.