## 2 Experimental Principle  
The optical phase conjugate is used to focus through a scattering medium. The basic principle is to realize the time reversal of the light by calculating the phase of the speckle light and taking the conjugate thereof, that is, returning along the original path. Usually, an ideal plane light wave is expressed as \(\text{A}\text{e}^{-|\phi}\) (ignoring the optical frequency term); after passing through the scattering medium,the amplitude and phase of the wavefront are modulated, and the speckle field formed on the latter plane is expressed as A\(\rho(x,y)\)e\({}^{-j(\phi+\varphi(x,y))}\). If we get \(\rho(x,y)\) and \(\varphi(x,y)\), we achieve phase and amplitude modulation of the light wave, so that the emitted light can be expressed as B\(\rho(x,y)\)e\({}^{-j(\phi+\varphi(x,y))}\), which means time reversal of the light wave can be achieved to suppress the scattering effect of the light. Theoretical analysis and practical research show that, compared with the combined modulation of phase and amplitude, only phase modulation also effectively suppresses the scattering effect [33]. In this paper, pure phase SLM is used, and we only study the phase modulation of the optical wave surface. The experimental setup designed in this paper is based on the off-axis holographic DOPC system (as shown in Figure 1), and the phase of the light field is extracted by the interference of the object light with angular difference and the reference light on the surface of the SLM [34]. As shown in Figure 1, the spatial coordinate system is established, which uses the intersection of the two planes light waves, \(\tilde{U}_{0}\) and \(\tilde{U}_{1}\), as the origin. It is assumed that the plane light wave \(\tilde{U}_{0}\) is injected at a specific angle with \(x\) and \(y\) axes, and \(\tilde{U}_{1}\) is perpendicular to the observation surface, the distance between the observation surface. If \(\tilde{U}_{1}\) is \(z\), then the ideal off-axis holographic interference intensity distribution \(U(x,y,z)\) is obtained on the observation surface. \[\overline{U}_{0}(x,y,z)=U_{0}(x,y,z)\exp\left(j\frac{2\pi}{\lambda}z\sqrt{1- \cos^{2}\alpha-\cos^{2}\beta}\right)\exp\left[j\frac{2\pi}{\lambda}(x\cos \alpha+y\cos\beta)\right] \tag{1}\]  
\[ \begin{array}{rl}\overline{U}_{1}(x,y,z)=U_{1}(x,y,z)\exp\left(j\frac{2\pi} {\lambda}z\right)\end{array}  \tag{2}\]  
\[ \begin{array}{rl}U(x,y,z)&=\left(\overline{U}_{0}+\overline{U}_{1}\right) \times\left(\overline{U}_{0}+\overline{U}_{1}\right)^{*}\\ &=U_{0}^{2}+U_{1}^{2}+2U_{0}U_{1}\cos\left[\frac{2\pi}{\lambda}\left(x\cos \alpha+y\cos\beta+z\sqrt{1-\cos^{2}\alpha-\cos^{2}\beta}-z\right)\right]\end{array}  \tag{3}\]  
We assume that \(\beta=\pi/2\), when \((\pi/2\lambda)x\cos\alpha+z(\sin 2\alpha)^{1/2}-z=2k\pi\), (\(k=Z\), \(Z\) represents a positive integer), we get the maximum value of \(U\); when \((\pi/2\lambda)x\cos\alpha+z(\sin 2\alpha)^{1/2}-z=(2k+1)\pi\), (\(k=Z\), \(Z\) represents a positive integer), we get the minimum value of \(U\). Thus, the spacing between adjacent bright (dark) stripes is expressed as:  
\[\Delta=\frac{\lambda}{\cos\alpha} \tag{4}\]  
In the actual experiment, the distance \(z\) is fixed and regarded as a constant omitted in the formula. Considering the two-dimensional plane only, we assume that the reference light is a uniform plane light whose initial phase is \(\psi\), and it is perpendicular to SLM plane; thus, the light field distribution on the SLM is expressed as:  
\[\overline{R}(x,y)=A(x,y)e^{-j\psi} \tag{5}\]  
Figure 1: Off-axis holographic interference. By making the object light on XY plane inject to the SLM plane at an angle \(\alpha\) with the \(X\)-axis direction, the object light wave surface is expressed as:  
\[\widetilde{O}(x,y)=B(x,y)e^{-j2\pi\xi x}e^{-j\phi(x,y)} \tag{6}\]  
where \(\xi=\cos\alpha/\lambda\) and \(\lambda\) is the wavelength of the light. We used a complementary metal oxide semiconductor (CMOS) camera to collect the light intensity information of the SLM surface.