# Geometric Parameter Self-Calibration Based on Projection Feature Matching for X-Ray Nanotomography
## 3 Experiment
### Nanotomography Experimental Section  
To verify the proposed method results in the actual data, a nanotomography device developed by the Intelligent Imaging Processing Laboratory in Zhengzhou, Henan Province, China, was used. Scanning parameters: voltage 60 Kv, exposure time 15 s, detector size 1065 pixel \(\times\) 1030 pixel, pixel size 75 um. A projection was scanned at 3-degree intervals under a circular scan trajectory, and 120 chip-projection data were scanned. The chip data calibration parameters are shown in Table 4. The calibration result is shown in Figure 8. In the figure, we can see that the three methods all show good correction effects, and the general image information can be recovered well. The method of [PERSON] et al. still exhibits a slight ghosting phenomenon at the edge of the image. The RANSAC method and the method in this paper produce a clearer edge in the correction results. The Variance function [25] and the Tenengrad function [26] were also used to evaluate the image quality. The Variance function is a function that evaluates the image sharpness through the image variance, where a clear image has a larger grayscale difference than a blurred image, and the image quality is better. The Tenengrad function is a gradient-based image-sharpness evaluation function where the sharper the edge of the image, the larger the value of the function. The evaluation results are shown in Figure 9b, and we calculate the percentage improvement by averaging the two evaluation functions. Compared with Xiao and RANSAC, it increased by 22.7% and 5.8%, respectively. \begin{table}
\begin{tabular}{c c c} \hline \hline  & \(\mathbf{u}_{0}\) (Pixel) & \(\mathbf{\eta}\) (\({}^{\circ}\)) \\ \hline Parameters Calculated by [PERSON] & 523.00 & \(-\)0.152 \\ \hline Parameters Calculate by RANSAC & 523.47 & \(-\)0.059 \\ \hline Parameters Calculated by our method & 523.93 & \(-\)0.014 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The calibration parameters in the Chip data compared with Xiao, RANSAC and our method. Figure 8: The Chips data reconstruction results with different parameters. (**a**) Misaligned parameters. (**b**) Parameters calculated using [PERSON] et al.’s method. (**c**) RANSAC feature-point screening results. (**d**) Parameters calculated by our proposed method. We also scanned ants in a circular scan trail at 0.25-degree intervals for a total of 1440 slice projection data. Other scanning parameters were the same as chip data. Different methods were used to carry out the contrast experiment of nanotomography system parameter calibration. FDK algorithm is used for 3D reconstruction. The ant's data calibration parameters are shown in Table 5. Figure 10 shows the ant data subjected to different methods of calibrating parameters to reconstruct the 2D image slices. All three methods exhibited improved results compared with the uncorrected results, and the blurring and ghosting are suppressed to some extent. The method described in this paper recovers the ant head structure more clearly. The planar maps of two positions in Figure 11 also illustrate the excellent correction results achieved by this method. The results of the two evaluation functions are shown in Figure 11, which are 25.2% and 14.4% higher than Xiao and RANSAC, respectively. The blurring and ghosting caused by geometric artifacts are significantly suppressed. Figure 11: Graphs showing the numerical analysis results for image quality reconstruction. (**a**) The pixel value of the green line (I) position inside the red box in Figure 10. (**b**)The pixel value of the green line (II) position inside the red box in Figure 10. (**c**) Normalized evaluation results for Variance and Tenengrad. Figure 10: The Ants data reconstruction results with different parameters. (**a**) Misaligned parameters. (**b**) Parameters calculated using [PERSON] et al.’s method, (**c**) RANSAC feature-point screening results. (**d**) Parameters calculated using our proposed method. (**a**-**I**–**d**-**t**) is an enlarged view of the I position of (**a**–**d**).