## 3 Experiment and Discussion
### Focusing through the Scattering Media Based on the Automatic Optimized Method for DOPC System  
Based on the automatic optimized method mentioned above, the optimization ability of compensation on OPC focusing was verified, and the experimental results are shown in Figure 4. Figure 4a shows the image by CCD2 when the phase of the SLM was set to 0, which means the DOPC system was not used. At the same time, the conjugate beam propagated back to the transmission through scattering medium was an unmodulated plane wave. After carefully aligning the system conventionally, the initial OPC focus through the SM can be obtained, as shown in Figure 4d. Figure 4g shows the conjugate phase loaded in the SLM. Instead of initiating the MPGA positions completely randomly, here, we designated the initial position as the initial OPC focus. The correlation coefficient was chosen as the fitness function. We compared the compensation effect of only optimizing misalignment parameters \(\Delta\)x, \(\Delta\)y, and \(\Delta\)z (misalignment parameters in the three displacement axes), with Zernike polynomial optimization. Here, the two situations can be simplified and defined as the \(\Delta\)-xyz modes and Zernike modes, respectively. After the above optimization process by MPGA, the final optimal compensation phase of the two modes loaded into the SLM can be written as  
\[\varphi_{op_{-}\Delta\text{-xyz}}(\Delta\text{x},\Delta y,\Delta z) =\varphi_{0}+2\pi\left\{\left[f_{x}(x-\Delta\text{x})+f_{y}(y- \Delta y)\right]+\frac{\Delta z}{\lambda}\sqrt{\left[1-\left(\lambda f_{x} \right)^{2}-\left(\lambda f_{y}\right)^{2}\right]}\right\}, \tag{8}\]  
\[\varphi_{op_{-}Zernike}(\rho,\theta)=\varphi_{0}+\left[ \begin{array}{c}z_{1} \rho\cos\theta+z_{2}\rho\sin\theta+z_{3}\big{(}2\rho^{2}-1\big{)}\\ +z_{4}\rho^{2}\cos 2\theta+z_{5}\rho^{2}\sin 2\theta+z_{6}\big{(}3\rho^{2}-1 \big{)}\rho\cos\theta\\ +z\big{(}3\rho^{2}-1\big{)}\rho\sin\theta+z_{8}\big{(}6\rho^{4}-6\rho^{2}+1 \big{)}\end{array} \right], \tag{9}\]  
where \(\Delta\)x, \(\Delta y\), \(\Delta z\) are misalignment parameters in the three displacement axes. \(f_{x}\) and \(f_{y}\) are spatial frequency; \(\lambda\) is the wavelength; \(\varphi_{0}\) is the initial conjugate phase of the scattering field; the origin of \((\rho,\theta)\) is selected in the center of the SLM panel.\(z_{1}\): tilt of X; \(z_{2}\): tilt of Y; \(z_{3}\): focus; \(z_{4}\): focus and astigmatism of \(0^{\circ}\); \(z_{5}\): focus and astigmatism of \(45^{\circ}\); \(z_{6}\): coma and tilt of X; \(z_{7}\): coma and tilt of Y; \(z_{8}\): spherical and focus. In \(\Delta\)-xyz mode, the final OPC focus was acquired, as shown in Figure 4e. The peak-to-background ratio (PBR) [31; 32] of the OPC focus increased from the original 310 to 16,300, which is defined as the ratio of the peak intensity of the OPC focus to the mean intensity of the speckle pattern when a random phase map is loaded in the SLM. The correlation coefficient is a statistical index used to reflect the degree of correlation between the ideal focus and the OPC focus. The value of \(\gamma\) increased from the original 0.41 to 0.73. In the Zernike modes, after the optimization step was completed, the final OPC focus was acquired, as shown in Figure 4f. The Zernike coefficients of the global compensation phase from the MPGA in this experiment are given in Figure 4b. The PBR of the OPC focus increased from the original 310 to 54,000; it increased 174 times that of the initial OPC focus. It achieved about 3.3 times the enhancement of compensation effect compared with the \(\Delta\)-xyz modes. The correlation coefficient (\(\gamma\)) with Zernike modes increased from the original 0.41 to 0.78, which has a higher interrelationship than the 0.73 score of the \(\Delta\)-xyz modes. The line profiles of the central row of the focal spot are  
Figure 3: Pixel alignment of the DOPC system.