## 10 Novel Imaging Using CXI
### X-ray Thermography  
X-ray thermography [76] is a non-destructive method for visualizing the thermal distribution inside an object on the basis of the slight density changes caused by thermal expansion. The thermal expansion coefficient \(\alpha\) of solids and liquids at room temperature is very small and can be assumed constant regardless of temperature. Therefore, material volume \(V\) with changed temperature \(dT\) from original volume \(V_{0}\) can be approximated as  
\[V=V_{0}(1+\alpha dT)\]  
Figure 21: Photos of metal foils and corresponding phase maps, absorption maps, and \(Z_{\text{eff}}\) images. Average Zeff values were 16.4, 25.4, 27.9, and 28.8 for Al, Fe, Ni, and Cu foils, respectively [74]. Reproduced from ref. [74] with the permission of AIP Publishing.  
Figure 22: (a) \(Z_{\text{eff}}\) image and (b) photo of rusted iron plate. Orange circles indicate rusted areas [75].  
The relationship between \(V\) and density \(\rho\) (\(d\rho/dT=\alpha\rho\)) can be used to detect \(dT\) on the basis of the change in \(\rho\) (\(d\rho\)). Therefore, if \(\alpha\) is known, \(dT\) can be detected from d\(\rho\). However, since \(\alpha\) is very small (\(<\)10\({}^{-5}\)) and the sensitivity of conventional absorption-contrast CT is not so high, the temperature resolution is limited to several tens of degrees. In contrast, since the sensitivity of PCXI, especially when using CXI, is very high and the density resolution can exceed 1 mg/cm\({}^{3}\), the temperature can be measured with an accuracy of a few degrees.  
Figure 23 shows time-resolved projection images of thermal flow in heated water and the calculated images obtained using the finite element method under the same conditions [76]. The exposure time was 200 ms, and the fringe scanning method with three steps was used for quantitative phase-shift detection. Therefore, the time resolution (interval between image measurements) was 1.3 s, including the movement of the phase shifter.  
The results indicate that the temperature around the heater gradually increased after the heater was turned on (1.3 s) and that the high-temperature region gradually propagated as a band (heating band) to the upper area of the water cell. In the fifth image (3.9-5.2 s) and later images, the high-temperature band that reached the top surface extended horizontally (6.5-7.8 s). The spatial distribution of temperature and the speed of thermal propagation were in good agreement with the calculated images (right), so the water temperature could be accurately detected non-destructively with X-ray thermography with 1.3-s resolution.  
Figure 23: Time-resolved projection images of thermal flow in heated water (**left**) and images calculated using finite element method (**right**) [76].  
Figure 24 shows a schematic view of a sample cell and the three-dimensional (3D) temperature distribution of water heated using a heater [76]. A polypropylene tube (10-mm diameter) filled with water heated by a ceramic heater attached above the water was used as a demonstration sample. To measure the phase-contrast CT data, the tube was rotated inside an outer metal cell filled with water cooled by a heatsink. The exposure time and fringe scanning number were set to 1 s and 3, respectively. The projection number was 500 for a 180\({}^{\circ}\) rotation, and the total measurement time was 1 h and 15 min. The front half of the tube was digitally cut (making it transparent) to reveal the inside of the tube. The results indicate that the water in the upper region near the heater was hotter than that in other areas and that the temperature gradually decreased in accordance with the distance from the heater. Another example application is time-resolved visualization of heat propagation in aluminum plates and biological samples [77]. The results show that X-ray thermography should enable the development of novel ways to visualize thermal distribution and propagation inside objects non-destructively.