# Exploring Frontiers of 4D X-ray Tomography
## 2 High-Speed X-ray CT  
### X-ray Imaging  
X-rays have been used for imaging for more than 120 years since their discovery by [PERSON] in 1895 [3]. The advantage of hard X-rays lies in their high penetration and straight propagation, both of which are due to the weak interaction of X-rays with matter. The former is due to the low absorption of X-rays, which makes it possible to observe the interior of an object. The latter is due to the fact that X-rays are only slightly refracted by matter, which not only facilitates the interpretation of projection images but also led to the success of CT in visualizing the interior of objects in three dimensions. X-ray imaging and CT are now widely used as indispensable tools in various fields ranging from medical diagnosis to non-destructive testing. In general, improving the resolution is an eternal issue in imaging technology. We have to consider spatial resolution, which determines the size that can be spatially resolved, temporal resolution, which determines the sampling interval at which data can be collected, and density resolution, which determines how much difference in density can be distinguished. There is generally a trade-off relationship among them. For example, to improve the temporal resolution by a factor of 100 while keeping the sensitivity of the optical system constant, we must set the spatial resolution to 10 times lower by increasing the pixel area by a factor of 100. Likewise, if we want to increase the temporal resolution by a factor of 10 while maintaining the spatial resolution, we need to increase the sensitivity of the optical system by an absolute factor of 10. Thus, to improve the temporal resolution while maintaining the spatial resolution, it is necessary to improve the sensitivity of the imaging system. Using the phase shift of X-rays caused by an object provides a solution to improving the sensitivity. In classical electromagnetism, X-rays are described as electromagnetic waves, i.e., transverse waves of electric and magnetic fields, characterized by phase, amplitude, frequency, and direction of polarization. When X-rays pass through an object, the intensity of the transmitted X-rays decreases due to the attenuation of the amplitude. A conventional X-ray image is an image of the contrast caused by this attenuation. In addition, when X-rays pass through an object, the phase of the X-rays also shifts, as shown in the left of Figure 1. Imaging carried out using the phase shift of X-rays is called \"X-ray phase-contrast imaging\" [4; 5]. This phase shift can also be understood as the deformation of the wavefront caused by the refraction of X-rays by an object and is therefore also called \"X-ray refraction-contrast imaging\". In principle, the use of X-ray phase shifts can improve sensitivity by several orders of magnitude compared with imaging methods that use X-ray absorption. This is mainly due to the fact that the cross section of the elastic scattering of X-rays by electrons (Thomson scattering) is larger than that of photoelectric absorption. As shown in the right pad of Figure 1, the phase shift cross section is several orders of magnitude larger than the absorption cross section for a given energy, especially for light elements with small atomic numbers. By taking quantitative X-ray phase-contrast images from various directions, the so-called phase CT can be realized. In this case, what is reconstructed in the CT is a physical quantity corresponding to the deviation \(\delta\) of the refractive index from 1 (refractive index decrement) for X-rays, which is proportional to the density of electrons per unit volume, except in special cases where the energy of X-rays used is close to an absorption edge. The refractive index decrement \(\delta\) is about \(10^{-5}\) to \(10^{-6}\), which is so small that X-rays are hardly refracted, but it can be detected by special methods as described below.