# Imaging Liquid Water in a Polymer Electrolyte Fuel Cell with High-Energy X-ray Compton Scattering
## 2 Compton Scattering Imaging (CSI)  
The interaction of X-rays with matter includes the photoelectric effect, Thomson scattering, and Compton scattering [25]. The photoelectric effect varies greatly with the atomic number of substances and dominates the interaction when the incident X-ray energy is slightly above the electron binding energy. As the X-ray energy increases beyond the binding energy, the photoelectric effect decreases rapidly with the X-ray energy and thus Compton scattering becomes more easily detectable. Thomson scattering decreases as the scattering angle increases, while Compton scattering is almost constant over the whole scattering angle. Therefore, Compton scattering becomes dominant at high-energy X-rays around 100 keV and a large scattering angle of 90 degrees. Figure 1 shows the schematic of the CSI technique using a single-element X-ray detector. The intensity of Compton-scattered X-rays \(I_{\rm T}\) is given by  
\[I_{\rm T}=I_{0}t_{1}t_{2}\rho_{\rm e}V\frac{d\sigma_{\rm KN}}{d\Omega}, \tag{2}\]  
where \(I_{0}\) is the intensity of incident X-rays, \(t_{1}\) is the incident X-ray transmittance from the entrance surface to the position of the probing volume in an object, \(t_{2}\) is the scattered X-ray transmittance from the position of the probing volume to the exit surface, \(\rho_{\rm e}\) is the average electron density over the probing volume \(V\), and \(\frac{d\sigma_{\rm KN}}{d\Omega}\) is the Klein-Nishina differential cross section [25]. The probing volume \(V\) is defined by the two slits system for the incident and scattered X-rays with a scattering angle of 90 degrees. In an experiment, \(I_{0}\) is monitored so that \(I_{\rm T}\) depends on \(t_{1}\), \(t_{2}\), and \(\rho_{\rm e}\). When Compton scattering is dominant and the transmittances are constant, the detected intensity \(I_{\rm T}\) represents the average electron density \(\rho_{\rm e}\) after a calibration. Scanning the incident X-ray beams, an intensity map of Compton-scattered X-rays can be obtained. Since the electron density depends on constituent elements and compositions, the obtained images can display the internal structure of the object and the dynamical behavior of materials associated with chemical reactions. High-energy X-ray Compton scattering has been used as the basis for an imaging technique under an in situ or operando condition, fully utilizing the high penetration power of high-energy X-rays into substances. The technique of CSI with an X-ray tube [26] or a \(\gamma\)-ray source [27] was used to observe composition variations and was applied to medical diagnosis [28] and archaeological objects [29]. Because of the limited performance of these sources, however, the attained spatial resolution was sub-millimeter and the  
Figure 1: Schematic drawing of the Compton scattering imaging (CSI) technique. The intensity of Compton-scattered X-rays \(I_{\rm T}\) is given by Equation (2), where \(t_{1}\) and \(t_{2}\) are the transmittances for incident X-rays and Compton-scattered X-rays, and \(I_{0}\) is the intensity of incident X-rays. The probing volume \(V\) is defined by the two slits for the incident and Compton-scattered X-rays. measurements suffered from low counting rates. Recently, these drawbacks have been overcome by using synchrotron high-energy X-rays. Taking advantage of the intense, highly parallel X-ray beams, the spatial resolution of 70 \(\upmu\)m in a plane and 10 \(\upmu\)m in its normal direction have been achieved. In addition, the installation of a two-dimensional X-ray detector, combined with a pinhole (see Figure 2a), has enabled much faster, direct acquisition of cross-sectional images [23; 24]. Moreover, using a two-dimensional detector with an energy resolution, which can distinguish between Compton-scattered X-rays and fluorescent X-rays, a multimodal imaging is demonstrated in this work. Future research directions in the CSI technique are toward the further improvement of data acquisition efficiency and the higher spatial resolution.