## 2 Principle of Phase-Contrast X-ray Imaging  
X-rays are electromagnetic waves with short wavelengths, and when an X-ray passes through a sample, its amplitude (intensity) decreases and its phase simultaneously changes (shifts), as shown in Figure 1a. In the hard X-ray region (X-ray energy \(>\) 10 keV), the cross-section of the phase shift for light elements (the real part of the complex refractive index) is more than 1000 times greater than the cross-section of the amplitude (the imaginary part of the complex refractive index) (Figure 1b). Therefore, PCXI, which visualizes phase shifts, is extremely sensitive compared with conventional absorption-contrast X-ray imaging, which visualizes intensity changes [1]. PCXI thus enables fine observation of biomedical soft tissues and organic materials such as polymers without the need to use a contrast agent and with low radiation exposure due to the short measurement time.  
Since current X-ray detectors cannot directly detect the phase shift, it is necessary to convert the phase shift into detectable X-ray intensity changes. So far, four major PCXI methods have been developed for a large field of view.  
1. Crystal-based X-ray interferometry (CXI), which uses a crystal-based XI to detect phase shifts by using the superposition of waves [1; 3].
2. Diffraction-enhanced imaging (DEI), in which the refraction of X-rays generated by the sample (proportional to the spatial derivative of the phase shift) is detected on the basis of the X-ray diffraction (XRD) of an analyzer crystal placed downstream of the sample [4].
3. Grating-based (Talbot) interferometry (GXI), in which the refraction of X-rays produced by the sample is detected with a grating interferometer (i.e., a Talbot interferometer) [5].  
Figure 1: Principle of phase-contrast X-ray imaging: (**a**) schematic view of absorption and phase shift of X-rays and (**b**) sensitivity ratio of phase- and absorption-contrast imaging against atomic number.  
Propagation-based imaging (PI), which detects phase shifts from the Fresnel fringes (a second-order derivative of the phase shifts) generated at a sufficient distance from the sample [6]. The density resolution, spatial resolution, and temporal resolution of each method are completely different due to differences in the detection principles and X-ray device used (Table 1) [7].  
CXI detects the phase shift by using the superposition of waves, so its sensitivity is about ten times higher than that of the other methods, which detect the spatial deviation of the phase shift [8; 9]. This method is thus suited for visualizing tiny density differences (\(<\)mg/cm\({}^{3}\)) in biological soft tissues caused by disease or aging, for example. DEI has a wide dynamic range of density and is thus suitable for observing biological samples with large density differences, including bone and calcification. The spatial resolution of PI is the highest because it does not require an X-ray device, which causes image blurring. Therefore, it is suitable for the microscopic observation of small samples. These three methods require monochromatic, high-intensity, and parallel X-rays, and in many cases, observations are performed at synchrotron radiation (SR) facilities. In contrast, GXI does not have the noteworthy sensitivity and spatial resolution of the other methods, but it can use quasi-monochromatic and divergent X-rays, and can achieve sufficient intensity with a classical X-ray tube. For this reason, a small PCXI system with X-ray tubes has been developed for laboratories, hospitals, and factories [10]. Furthermore, fast GXI combined with high-intensity quasi-monochromatic SR has also been developed [11; 12], and observations requiring high temporal resolution, such as laser ablation [13], were performed. In addition, an edge illumination imaging method (in which the refraction angle due to the sample is detected by a grating (solar slit) installed downstream of the sample) that can use quasi-monochromatic and divergent X-rays, as well as GXI, has also been developed [14].