# Exploring Frontiers of 4D X-ray Tomography
## 3 High-Speed X-ray CT
### With Sample Rotation
The advantage of this imaging is that it is more sensitive than X-ray absorption imaging as described in Section 2.1. With this imaging, the experimentally obtained refractive index decrement \(\delta\) for X-rays is taken as the physical quantity \(p(x,y)\) in Equation (1). The experimental setup (side view) is shown in Figure 5. Here, we used X-ray grating interferometry. As described in Section 2.1, this method uses gratings for X-rays (the two gratings in Figure 5), and it has the advantage that a white synchrotron radiation beam with high intensity and a relatively large area can be used. Figure 4: Non-destructive techniques for observing 3D internal structures of samples opaque to visible light. In grating interferometry [32], a self-imaging phenomenon called the Talbot effect [33; 34] is used. The Talbot effect occurs when a periodic object such as a grating is illuminated by light with a spatial coherence length comparable to or larger than the period of the object. The self-images generated downstream of the object are deformed when light is refracted by a sample located in front of or behind the object. From this deformation, we can obtain an image of the change in the propagation direction due to the refraction by the sample, which corresponds to the differential phase image for the sample. For the X-ray grating interferometer shown in Figure 5, we used a \(\pi\)/2-phase grating (G1) designed for an X-ray energy of 25 keV, whose lines are aligned in the horizontal direction. The grating was located at a distance of 44 m from the X-ray source with a full width at half maximum (FWHM) of 28.7 \(\upmu\)m, which, from the van-Cittert Zernike theorem [35], provides a spatial coherence length at G1 sufficiently larger than the period of G1 (5.3 \(\upmu\)m). Another 5.3 \(\upmu\)m-period grating (a 60 \(\upmu\)m-thick gold absorption grating (G2) was located on a self-image generated at a distance of 283 mm downstream of G1 to detect the deformation of the self-image as moire fringes. Both gratings were made of gold on 200 \(\upmu\)m-thick Si substrates. To achieve high-speed imaging, an indirect imaging-type X-ray detector was used that consists of a scintillator, a lens coupling system, and a high-speed camera. A scintillator is a material that converts X-rays into visible light [36]. The 40 \(\upmu\)m-thick single-crystal Ce:GAGG scintillator used in this experiment had a very short luminescence decay time of 53 ns and a large luminescence intensity [37]. As a high-speed camera, we used a CMOS camera (Photron FASTCAM Mini AX100), which is capable of capturing 1024 \(\times\) 1024 full-frame images at a maximum of 4000 frames per second. The effective pixel size at the sample position was 9.9 \(\upmu\)m, and the spatial resolution was 21 \(\upmu\)m.  
Figure 6 shows a 3D phase tomogram of a toothpick (piece of hardwood) as an example (3D CT reconstruction image of the refractive index decrement \(\delta\)) [29]. This 3D image was obtained on the basis of a fringe scanning method [38; 39; 40]: a three-step equal-sampling fringe scanning was performed by continuously moving G2 and rotating the sample. The speed of G2 was tuned so that it was moved by one period in the vertical direction while the sample was rotated through three turns. Since three projection images in the same projection angle are necessary for the three-step fringe scanning, 2.5 turns of the sample are required for CT reconstruction for the synchrotron beam. The sample was rotated at 33,850 rpm, so that the 3D image was captured in 4.43 ms. The projection images were captured at a frame rate of 127,500 frames per second (7.8 \(\upmu\)s per frame), and the 3D phase tomogram was obtained from 113 differential phase images by the filtered back-projection algorithm. Note that, for the projection images, the field of view was reduced to be 128 \(\times\) 64 pixels at the frame rate because there is generally a trade-off between the frame rate and the field of view of a high speed camera.