## 3 Experiment and Discussion
### Focusing through the Scattering Media Based on the Automatic Optimized Method for DOPC System
(**a,b**) The phase pattern of a negative United States Air Force (USAF) target and image obtained by CCD1; (**c**) the image subtraction in the case of inaccurate alignment; (**d**) the image subtraction in the case of fine-tuned alignment. The magenta part in Figure 3c,d are the the images loaded by the SLM; The green image is the CCD1 image. shown in Figure 4c; the full width at half maximum (FWHM) of the focal spot decreased from 35.4 to 19.7 \(\upmu\)m. It is smaller than the 21.4 \(\upmu\)m in the \(\Delta\)-xyz modes. Comparing Figure 4e,f, it can be concluded that the Zernike modes can not only compensate for the misalignment parameters in the three displacement axes but also suppress the aberration of the system by decreasing the noise around the focal spot. The comparison of optimization abilities under the three methods is shown in Table 1. Obviously, the compensation quality of DOPC is greatly optimized by Zernike modes in the automatic optimized method, which is better than the \(\Delta\)-xyz modes. Moreover, we use circular polynomials as Zernike modes, which are widely employed in circular pupils. When applying them to a rectangular area, such as the SLM, they might not compensate for the optical aberrations at the corners [46]. Using rectangular polynomials [46; 47] might further improve the compensation effect. For further exploration of the optimized capability of the automatic optimized method, we used intensity fitness as the fitness function of MPGA. Intensity fitness is defined as the comparison between \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **Correlation Coefficient (\(\gamma\))** & **PBR** & **FWHM** \\ \hline Initial DOPC & 0.41 & 310 & 34.5 \(\upmu\)m \\ \(\Delta\)-xyz modes & 0.73 & 16,300 & 21.4 \(\upmu\)m \\ Zernike modes & 0.78 & 54,000 & 19.7 \(\upmu\)m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of optimization abilities under three methods. Figure 4: Experimental results of the automatic optimized method for DOPC in focusing through scattering media. (**a**) Focus pattern without DOPC compensation; (**b**) Zernike coefficients of the Zernike compensation phase in this experiment, searched via the MPGA; (**c**) line profiles of the central row of focal spots in initial DOPC, in \(\Delta\)-xyz modes, and in Zernike modes; (**d**) initial DOPC focus pattern before the MPGA optimization process; (**e**) DOPC focus in \(\Delta\)-xyz modes with the MPGA optimization process; (**f**) DOPC focus pattern in Zernike modes with the MPGA optimization process; (**g**) initial conjugate compensation phase pattern of the scattering field; (**h**) conjugate compensation phase pattern in \(\Delta\)-xyz modes with the MPGA optimization process; (**i**) conjugate compensation phase pattern in Zernike modes with the MPGA optimization process. the maximum intensity of the focus and the maximum intensity of the target focus. The results of intensity fitness are compared with Figure 4f, representing the correlation coefficient. During the optimization in the two cases, we recorded the typical normalized intensity and the correlation coefficient curves of the OPC focus with generation, as shown in Figure 5a,b. The normalized intensity is defined as the ratio of peak intensity of the current focal spot and the maximum intensity 65,535, which depends on the bit depth of the camera; it decreased from 0.77 to 0.55, and the correlation coefficient (\(\gamma\)) decreased from 0.78 to 0.68. Figure 5c shows the line profiles of the central row of the focal spot; the FWHM of intensity fitness was about 23.3 \(\upmu\)m, which is worse than the FWHM of 19.7 \(\upmu\)m in Figure 4f. Additionally, the PBR was about 20,400 with intensity fitness. The comparison of optimization abilities in two fitness functions is shown in Table 2. This method with Zernike modes can raise the correlation coefficient to above 0.7. Thus, for a correlation coefficient of less than 0.7, this method is available for compensation improvement.