## 3 Results and Discussion  
Table 2 shows the TEM and X-ray absorption images obtained using STXM at the energies 285.4 eV (Is\(\rightarrow\)\(\pi\)\(\pi\)) and 292.0 eV (1s\(\rightarrow\)\(\sigma\)\({}^{\rm\alpha}\)) of the cross sections of the PAN- and pitch-based CFs. The red and blue arrows in Table 2 indicate the X-ray polarization directions of LH and LV, respectively. Each STXM image consists of 150 \(\times\) 150 pixels (1 pixel = 40 nm) and 200 \(\times\) 200 pixels (1 pixel = 40 nm) for the PAN- and pitch-based CFs, respectively. With respect to the PAN-based CFs, the contrast (optical density, OD) in X-ray absorption images at 285.4 eV (b,c in Table 2) and 292.0 eV (d,e in Table 2) was independent of the direction of the X-ray polarization. Here, OD is defined as  
\[\rm{OD}\equiv\mu(E)t=\ln\frac{I_{0}}{I} \tag{1}\]  
where \(\mu\)(E) is the absorption coefficient, \(t\) is the sample thickness, and \(I_{0}\)(\(E\)) and \(I\)(\(E\)) are the incoming and transmitted X-ray intensities, respectively. Note that \(I_{0}\)(E) is the intensity of the X-ray that directly enters the detector without passing through the sample during the measurement. In the PAN-based CFs, the OD images at \(E\) = 285.4 eV in b,c in Table 2 were independent of the direction of X-ray polarization. Similarly, the OD images at \(E\) = 292.0 eV in d,e in Table 2 were independent of the direction of the X-ray polarization. This is because the \(\sigma\)-orbital has no spatial anisotropy, while the \(\pi\)-orbital forms a uniaxial orbit. Therefore, even in X-ray absorption at the carbon \(K\)-edge, the absorption peak intensity derived from the \(\pi\)-orbital is anisotropy not observed in that of the \(\sigma\)-orbital [15]. In general, OD is proportional to cos\({}^{2}\theta\) when the angle between the vector of the \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**STEM**} & \multicolumn{1}{c}{**STXM (OD)**} \\ \cline{2-3} \multicolumn{1}{c}{} & **LH** & **LV** & **LH** & **LV** \\ \hline \hline \multicolumn{1}{c}{} & **LH** & **LV** & **LH** & **LV** \\ \hline \hline \end{tabular}
\end{table} 
Table 2: (**a**), (**f**) TEM (bright field) images of the cross sections of the PAN- and pitch-based CFs, respectively; (**b–e**), (**g–j**) optical density (OD) images obtained using STXM at the energies 285.4 eV (1s\(\rightarrow\)\(\pi\)\({}^{\rm\alpha}\)) and 292 eV (1s\(\rightarrow\)\(\sigma\)\({}^{\rm\alpha}\)) with linear horizontal (LH) and linear vertical (LV) polarized beams. (**f**) is rotated to align with other X-ray absorption images (**g–j**). polarized electric field of the X-rays and the direction of the orbit is \(\theta\)[15; 16; 17; 18; 19]. These results, depicted in b,c in Table 2, are similar to those reported in earlier studies [19]. Thus, it is suggested that the domain sizes within the cross section of the PAN-based CFs are less than the spatial resolution of STXM (i.e., 50 nm). In contrast, in the pitch-based CFs, the OD images at \(E=285.4\) eV shown in g,h in Table 2 were dependent on the polarization direction and showed an opposite contrast between the LH and LV polarizations. However, the OD images at \(E=292.0\) eV, shown in i,j in Table 2, were independent of the direction of the X-ray polarization. Due to the symmetry of the \(\sigma\)-orbital, there is no polarization dependence. It was suggested that the pitch-based CFs consisted of \(\pi\)-orbital-oriented domains whose sizes are approximately 100 nm-1 \(\upmu\)m, which is greater than the spatial resolution of STXM (i.e., 50 nm). Note that we consider that even a detailed observation of a single fiber section can have a representative discussion because there is no significant difference among fibers within the range (1-10 mm\({}^{2}\)) that can be seen with scanning electron microscopy (SEM) or optical microscopy. In addition, for other research projects, we have performed STXM measurements of some types of PAN- and pitch-based CFs.