## 3 Results and Discussion
Notably, the position of the 1122 cm\({}^{-1}\) band is related to the fictive temperature (\(T_{f}\)). As shown in Figure 5, after the peak deconvolution of the 1122 cm\({}^{-1}\) band using a Gaussian function, the radial fictive temperature (\(T_{f}\)) of the glass sample was calculated using Equation (3) to characterize the structural changes in the quartz glass [19]. \[v_{1}=1114.5+(11603.51/T_{f}) \tag{3}\]  
where \(v_{1}\) represents the measurement position of the 1122 cm\({}^{-1}\) spectral band with an error value of \(\pm 0.3\). \(T_{f}=1253\) cm\({}^{-1}\) is obtained according to Equation (3). The calculated \(T_{f}\) value was 1253 K. Figure 6 illustrates the variation of the \(T_{f}\) values along the radial direction before and after homogenization (with a test point position at 40 mm). As depicted in Figure 6, for homogenized quartz glass, \(T_{f}\) values at the edge are higher than those at the center, attributed to the higher cooling rate at the edge compared to the center during the cooling process after a high-temperature homogenization. However, the differences in the fictive temperatures at various radial positions of the homogenized quartz glass are relatively small, indicating a more uniform structure throughout the quartz glass. This uniformity is also related to the distribution state of hydroxyl groups and their impact on structural relaxation. For optical quartz glass, hydroxyl groups disrupt the integrity of the silica network structure, leading to an increase in the \"non-bridging oxygen\" content and greater disorder in the silica network. An uneven distribution of hydroxyl content within quartz glass can result in anisotropy, affecting light refraction and absorption when passing through these local regions, manifesting as differences in optical homogeneity in test results. Therefore, to improve the optical homogeneity of the glass, hydroxyl groups must be uniformly  
Figure 5: Infrared reflectance spectra of quartz glass. Figure 6: Value of \(T_{f}\) along radius of quartz glass before and after homogenization. distributed in the vertical plane through which light passes. The hydroxyl content of samples can be measured using the transmission spectrum of quartz glass. The hydroxyl content in quartz glass can be calculated using the hydroxyl absorption peak at a 2730 nm wavelength according to Equation (4) [20]:  
\[C=96.5\frac{1}{d}\log(\frac{I_{0}}{I}) \tag{4}\]  
where C is the hydroxyl content in the sample (ppm) with an error of \(\pm 0.02\), \(d\) is the sample thickness (mm), \(I_{0}\) is the distance from the baseline to the zero line at 2730 nm (mm), and I is the distance from the absorption peak to the zero line at 2730 nm (mm). Figure 7 shows the UV-visible transmission spectra of the quartz glass before and after homogenization. Using Equation (4), it can be seen that the hydroxyl content of the quartz glass prepared in this experiment was only 4.11 ppm, and the hydroxyl content of the quartz glass prepared by the CVD process was 1108 ppm. According to the literature, the hydroxyl content of quartz glass prepared by the CVD method is 880 ppm according to [PERSON] et al. [21] and 1200 ppm according to [PERSON] et al. [22]. Comprehensively, the hydroxyl content of the quartz glass prepared in this paper is much lower than that from the CVD process, which may be due to the difference in the heat source of the preparation process. The CVD process uses hydrogen and oxygen as the heat source, and the reaction between the hydrogen and oxygen generates water, so that the hydroxyl group of the quartz glass prepared by the CVD process has a high content of the hydroxyl group. In addition, the hydroxyl content before homogenization was 4.11 ppm, and, after homogenization, it decreased to 2.64 ppm. The homogeneity improved significantly by 35% after the high-temperature treatment.