# Laser Spot Centering Algorithm of Double-Area Shrinking Iteration Based on Baseline Method
## 4 Results and Discussion
### Experiment  
We performed a specific practical experiment to further testify the validity of our proposed method. Figure 10a shows the experimental platform of the CCD-based laser beam measurement system built to acquire the laser spot. First, the laser light is generated by the GY-10 He-Ne laser which has better stability and reliability. Then, the attenuator is added to attenuate the laser beam energy incident on the photosensitive surface of the CCD camera in order for the CCD to receive energy without oversaturation to protect the CCD camera, considering that the energy of the laser beam may far exceed the saturation energy value of the CCD detector or even exceed the damage threshold of the CCD image element, which may damage the CCD device. The laser beam enters the lens after attenuation, which is used to ensure that the laser beam is within the measurable range. Finally, the beam is passed into the CCD camera, which completes the acquisition of the laser spot image. Table 1 presents the device parameters used for the experiment. We used a masking plate to mask the laser so that 10 consecutive background images were acquired for background noise baseline statistics. Then, we acquired the laser spot to obtain a 1626 \(\times\) 1236 pixel gray image. Since we cannot know the exact true spot center of the real acquired laser spot, multiple frames of spot images were acquired continuously for centering to perform stability analysis of the algorithm. Figure 10b shows that we continuously collected 10 frames of laser spot images displayed in pseudo-color in the same location. Table 2 displays the center positioning results of different algorithms for 10 consecutive laser spot image frames. Table 2 depicts that the location accuracy of several methods for comparison could reach the sub-pixel level. Figure 8: Iterative convergence process of spot area. Figure 9: Running time of different algorithms. After the corresponding denoising of the spot images, Table 3 shows the accuracy analysis and comparison of different center positioning algorithms in the x- and y-directions. The difference between the maximum positioning result and the minimum positioning result in the x and y directions was compared when centering 10 frames of spot images in succession. The results show that 0.204 and 0.189 pixels were reached for the Gaussian fitting method, 0.338 and 0.276 pixels were reached for the traditional centroid method, and 0.254 and 0.2 pixels were reached for the square-weighted centroid method, respectively. This shows that the fluctuation range of the center location results of these three methods exceeded 0.1 pixels. In comparison, the proposed method had the best results among other methods, regardless of whether it was the fluctuation range of the center positioning coordinates in the x-direction or y-direction, reaching 0.044 and 0.026 pixels, respectively, and the average standard deviation (SD) was even lower at 0.015 pixels on x and 0.01 pixels on y (Table 3), proving good stability. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Equipment Name** & **Equipment Parameter** & **Value** \\ \hline \multirow{3}{*}{Laser} & Type & GY-10 He–Ne \\  & Wavelength & 632.8 nm \\  & Power & 1.5 mw \\ \hline \multirow{3}{*}{CCD} & Type & BASLER ACA1600-20 GM \\  & Max resolution & 1626 \(\times\) 1236 \\  & Pixel size & 4.4 μm \(\times\) 4.4 μm \\ \cline{1-1}  & Output format & Mono 8-bit \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Device parameters used for the experiment.