## 3 Proposed System Concept Architecture
### Turbulence Compensation
#### 3.2.1 Adaptive Optics  
In adaptive optics, a device is used to reverse the distortions caused by turbulence. The deformable mirror (DM) is typically used for this purpose. In our research, we propose using LC-SLM. The key advantage of LC-SLMs lies in their high spatial resolution, which allows precise correction of fine-scale phase distortions [38]. This capability is critical in underwater optical systems, where complex turbulence-induced aberrations can significantly impact performance. Furthermore, LC-SLMs have been integrated with advanced Shack-Hartmann wavefront sensors, replacing traditional microlens arrays with programmable Fresnel lenses to enhance spatial resolution and dynamic range [39]. Moreover, unlike deformable mirrors, LC-SLMs operate entirely in the electrical domain, eliminating the need for mechanical changes [44]. This not only simplifies the system design but also enhances reliability and reduces the potential for mechanical failures. The absence of moving parts in LC-SLMs contributes to their durability and stability, particularly in environments where mechanical vibrations or stresses could impair performance. LC-SLM is controlled by a feedback loop containing a wavefront sensor and a controller. For several decades, the Shack-Hartmann wavefront sensor has been used in adaptive optics to detect and correct optical aberrations. This sensor uses a micro-lens array to split the incident light into smaller segments and focus each one onto a two-dimensional camera. The resulting pattern of focal points provides important information about the local wavefront inclination at each microlens. If the incoming wavefront is distorted, these spots will shift from their expected positions. By calculating the displacement of each spot relative to an ideal, aberration-free reference, the average wavefront slopes can be determined. Once these local slopes are measured, they are processed using a wavefront reconstruction algorithm, such as the modal or zonal approach, to determine the overall shape of the wavefront. This reconstructed wavefront provides a detailed map of the optical aberrations present in the system [46; 47]. The turbulence distortion can be expanded into Zernike polynomials, which are a set of basis functions. Zernike polynomials are among the most well-known and widely used functions in the adaptive optics field. The more Zernike modes can be removed by the adaptive optics system, the better the turbulence can be compensated and the better the communication performance [48; 49]. An adaptive optics system can be described mathematically by a filter function, which represents the removal of the spatial modes by the phase conjugation method. The filter function is derived from the Fourier transform of Zernike polynomials and is given by  
\[F_{\text{even}\,m,n}(\gamma\kappa,D,\phi) =2(n+1)\left[\frac{2J_{n+1}(\gamma\kappa D/2)}{\gamma\kappa D/2} \right]^{2}\,\cos^{2}(m\phi), \tag{14a}\] \[F_{\text{odd}\,m,n}(\gamma\kappa,D,\phi) =2(n+1)\left[\frac{2J_{n+1}(\gamma\kappa D/2)}{\gamma\kappa D/2} \right]^{2}\,\sin^{2}(m\phi),\] (14b) \[F_{m=0,n}(\gamma\kappa,D,\phi) =2(n+1)\left[\frac{2J_{n+1}(\gamma\kappa D/2)}{\gamma\kappa D/2} \right]^{2}, \tag{14c}\]  
where \(D\) is the receiver aperture diameter and \(J_{n+1}()\) are Bessel functions of the first order [24]. The parameter \(\gamma\) is given by  
\[\gamma=1-\left(\Theta+i\,\Delta\right)(1-z/L), \tag{15}\]with a special case involving a spherical wave \(\Theta=1\) and \(\Delta=0\). To integrate the effects of adaptive optics into our turbulence model, we modify the turbulence power spectrum by introducing the adaptive optics filter function. We define the corrected power spectrum as  
\[\Phi_{\text{new}}(\kappa)=\Phi_{\text{old}}(\kappa)\cdot\int_{0}^{2\pi}\bigl{[}1 -\sum_{m,n}F_{m,n}\bigl{(}\gamma\kappa,D,\phi\bigr{)}\bigr{]}\,d\phi. \tag{16}\]  
This expression is then applied to Equation (6) to recalculate the refractive index structure function.