# Principles of Different X-ray Phase-Contrast Imaging: A Review
## 2 Methods
### Crystal Interferometer  
In 1965, [PERSON] and [PERSON] proposed a crystal interferometer that used diffraction patterns to show the difference in the beam paths [PERSON] (2018). Figure 9 suggests that the instrument used in the crystal interferometer was a perfect crystal (silicone, for instance), which had two grooves, so that the crystal was separated into splitter, mirror, and analyzer. The splitter splits the incident monochromatic X-ray beam into two coherent waves. After convergence using the mirror, the two waves formed a diffraction pattern on the analyzer, which showed the difference in the beam paths caused by refraction from the object. Because the entire interferometer was fabricated from an entire crystal, no extra alignment was needed except for setting the incident angle of the X-ray beam under Bragg conditions.  
Figure 9: Sketch of (**a**) the crystal interferometer instrument and (**b**) its wave paths.  
In 1995, [PERSON] and [PERSON] obtained high contrast X-ray phase images of a slice of a rat cerebellum, and the phase-retrieval techniques were explained [78]. In 2002, [PERSON] et al. revealed clear vessels that were larger than 0.03 mm in diameter of the liver from rats and a rabbit using this method, whereas no vessel could be seen in the absorption image and only 0.1-mm-diameter vessels could be seen under almost the same X-ray dose, similar to those in the iodine-loaded acrylic microspheres [79]. In 2003, [PERSON] et al. applied the method with a 60 \(\times\) 30 mm FOV with a synchrotron source. The visibility of the interference pattern averaged 50%. Phase imaging of rat liver vessels was performed where blood vessels with a diameter of approximately 50 \(\upmu\)m could be seen [80]. In 2004, [PERSON] et al. presented in vivo phase-contrast X-ray computed tomography (CT) images of cancer implanted in nude mice using this method [81]. In 2011, [PERSON] et al. revealed the portal vein, capillary vessel area, and hepatic vein of live rats using this method [82]. All these experiments were performed with synchrotron sources owing to the requirement for highly coherent incident X-ray beams. In 2013, [PERSON] et al. used this method to obtain an elemental map of an object by calculating the ratio of absorption and phase-contrast images. The results showed that aluminum, iron, nickel, and copper foils were clearly distinguished [83]. In 2014, [PERSON] et al. investigated the X-ray optical anisotropy of 5 CB type liquid crystals using this method. The values of refractive indices for the specimen were measured [84]. In 2016, [PERSON] et al. demonstrated crystal interferometer-based phase-contrast CT with brain tumors. The results clearly show the tumor's various pathological features [85]. In 2018, [PERSON] et al. developed a phase-contrast X-ray laminography using this method. Images of an old flat slab of limestone from the Carnic Alps depicting fusulinids in the Carboniferous period were obtained with 3 mg cm\({}^{-3}\) density resolution [86].  
In 2002, [PERSON] reviewed the principle and some demonstrations of the method [87]. In 2014, [PERSON] reviewed various configurations of this method [88].  
Because the splitter, the mirror, and the analyzer are graved on one crystal, there is no need to align these three instruments. However, this limits the size of the object. If larger samples are illuminated, two or three independent crystals are needed for the splitter, the mirror, and the analyzer [80]. For this, a precise alignment is required to obtain the diffraction pattern. This method provides high visibility and contrast for biological samples, especially when combined with the CT technique.