## 4 History of CXI Development  
The first crystal-based XIs, which were introduced in the 1960s, operated using an X-ray tube [2]. Subsequently, crystal-based XI operations were demonstrated in SR facilities. CXI was introduced as a phase shift detection method for PCXI [1]. Phase-contrast X-ray computed tomography (CT) [3,24], which enables highly sensitive three-dimensional non-destructive observation by combining CT with sample rotation, was devised in the 1990s and applied to the observation of biological soft tissues composed mainly of light elements [24,25]. However, the observation field of view of a CXI system using a monolithic crystal-based XI is limited by the diameter of the silicon ingot, which is the base material of the interferometer. Even with a 6-inch floating-zone (FZ) silicon ingot, it is not easy to enlarge the field of view to more than 30 mm\({}^{2}\). Furthermore, since the distance between the sample and the second crystal wafer (M) is less than 10 mm, if the temperature of the sample is greater than that of M, the wafer is heated, causing deformation of the interference pattern, which makes measurement impossible. This problem was overcome by the development of a CXI system using a two-crystal XI composed of two crystal blocks in the late 1990s. Nevertheless, monolithic crystal-based XIs are still being used for PCXI due to their easy operation, and fine three-dimensional observations of small biological samples have been performed using one at the SAGA Light Source (SR facility of saga prefecture in Japan) [26]. The relative displacement (position) and/or rotation between the crystal blocks must be stabilized within the order of X-ray wavelengths, i.e., with an accuracy of 0.1 nm or sub-nano radians, to operate a two-crystal XI. Research has shown that the number of axes requiring such extremely high accuracy depends on the separation configuration of the crystal blocks. The screw symmetric type requires only one axis to be precisely controlled (\(\sim\)10 picoradians, or prad) [20; 27]. Therefore, the screw symmetric two-crystal X-ray interferometer (STXI) was adopted for use in the CXI system. Figure 3 shows a schematic view of an STXI. The incident X-ray is divided into two beams at the first crystal wafer (S) of the first block by the Laue case of XRD. One beam is reflected by the second wafer (M1) of the first block, and the other is reflected by the first wafer (M2) of the second block. The two beams are superimposed on the second wafer (A) of the second block, generating two interference beams. Only one rotational movement between the crystal blocks is required to ensure sub-nano-radian accuracy for STXI operation. The relative rotation between the crystal blocks around the z-axis changes the path difference between the two beams, resulting in a phase difference \(\Delta p^{\prime}\):  
\[\Delta p^{\prime}=2\pi(l+t)d\theta/d \tag{5}\]  
where \(d\theta\) is the relative rotation between the blocks, \(d\) is the lattice spacing of the diffraction, \(l\) is the distance between the wafers on each block, and \(t\) is the thickness of each crystal wafer [20]. For example, for 17.8-keV X-rays and Si(220) diffraction (\(d\) = 0.192 nm), \(d\theta\) must be stabilized to within 20 prad to attain a phase fluctuation of \(\pi/20\) for an interferometer with \(l\) = 200 mm and \(t\) = 1 mm. STXI operation was first achieved using an X-ray tube in the 1970s [20]. Subsequently, STXI operation with a 5 \(\times\) 5-mm field of view was demonstrated in an SR facility [28]. This led to the earnest development of a CXI system using an STXI (ST-CXI) with a large field of view in the 1990s, supported by a large national budget (Special Coordination Funds of the Ministry of Education, Culture, Sports, Science, and Technology of the Japanese Government).