## 2 Light Field Transmission Model
\(s\) represents the integral range of the exit pupil. Due to the phase modulation of the lens and the aperture's restriction on the light field, the transmittance function of the exit pupil can be expressed as follows:  
\[t_{l}(\xi,\eta)=P(\xi,\eta)\exp[\frac{jk_{0}}{2f}(\xi^{2}+\eta^{2})] \tag{8}\]  
Therefore, the outgoing light distribution of the exit pupil \(U_{l^{\prime}}(\xi,\eta)\) can be expressed as follows:  
\[U_{l^{\prime}}(\xi,\eta)=U_{l}(\xi,\eta)\cdot t_{l}(\xi,\eta) \tag{9}\]  
Similar to the process described in Equation (10), the propagation of the light field from the exit pupil to the target plane can be expressed as follows:  
\[ \begin{array}{l}U_{T,TX}(x_{i},y_{i})=\frac{\exp(jk_{0}d_{i})}{j\lambda d_{i }}\exp[\frac{jk_{0}}{2d_{i}}(x_{i}^{2}+y_{i}^{2})]\cdot\iint_{\xi}U_{l^{\prime }}(\xi,\eta)\times\\ \exp[\frac{jk_{0}}{2d_{i}}(\xi^{2}+\eta^{2})]\cdot\exp[-\frac{jk_{0}}{d_{i}}(x _{i}\xi+y_{i}\eta)]d\xi d\eta\end{array}  \tag{10}\]  
In the equation, \(x_{i},y_{i}\) denotes the coordinate at the target T-face, and \(d_{i}\) is the distance from the exit pupil to the T-face. When the target plane and the fiber emission plane are in an imaging relationship with respect to the lens, Equation (10) can be further simplified as follows:  
\[ \begin{array}{l}U_{T,TX}(x_{i},y_{i})=\frac{1}{\lambda^{2}d_{0}d_{i}}\cdot \iint_{\xi}G_{0}(\frac{\xi}{\lambda d_{0}},\frac{\eta}{\lambda d_{0}})\times \\ P(\xi,\eta)\exp[-\frac{jk_{0}}{d_{i}}(x_{i}\xi+y_{i}\eta)]d\xi d\eta\end{array}  \tag{11}\]  
In the equation, \(G_{0}(\frac{\xi}{\lambda d_{0}},\frac{\eta}{\lambda d_{0}})=FFT(U_{F,TX}(x,y))\). \(FFT\) represents the Fourier transform operator. The system's point spread function (PSF) is the Fourier transform of the \(P(\xi,\eta)\) as follows:  
\[h(x_{i},y_{i})=FFT\{P(\xi,\eta)\},f_{X}=\frac{x_{i}}{\lambda_{0}d_{i}},f_{Y}= \frac{y_{i}}{\lambda_{0}d_{i}}, \tag{12}\]  
Consequently, the complex amplitude light field distribution at the T-face can be expressed as follows:  
\[U_{T,TX}(x_{i},y_{i})=U_{g}(x_{i},y_{i})*\frac{1}{M}h(x_{i},y_{i}), \tag{13}\]  
In the equation, the symbol \({}^{*}\) represents the two-dimensional convolution operation. \(U_{g}(x_{i},y_{i})=\frac{1}{M}U_{F,TX}(\frac{x}{M},\frac{y}{M})\). \(M\) denotes the magnification factor between the object and the image obtained through geometric optical imaging. Through the aforementioned analysis and processing, we derived the expression for the light field distribution at the target plane. This result provides a mathematical framework to describe how the light field propagates through the optical system and forms the final distribution at the target plane. [PERSON]'s transformation system theory is employed to simulate the surface roughness state. The rough surface height function is generated by randomly producing a two-dimensional sequence and utilizing digital filtering techniques based on wide-sense stationary random processes [14]. It is assumed that the surface roughness modulates only the optical field phase, without affecting the spatial light intensity distribution. Consequently, the reflected light field from the rough surface can be expressed as follows:  
\[U_{T,RX}(x_{i},y_{i})=U_{T,TX}(x_{i},y_{i})\cdot\exp\{ik_{0}Z(x,y)\}, \tag{14}\]  
The process of light field transmission from the T-face to the F-face is analogous to the process from the F-face to the T-face described earlier. The received light field at the fiber end \(U_{F,RX}(x,y)\) can be determined as follows:  
\[U_{F,RX}(x,y)=U_{g}(x,y)*Mh(x,y), \tag{15}\]  
In the equation, \(U_{g}(x_{i},y_{i})=MU_{T,RX}(Mx_{i},My_{i})\), \(h(x,y)=FFT\{P(\xi,\eta)\}\), \(f_{X}=\frac{x}{\lambda_{0}f}\), \(f_{Y}=\frac{y}{\lambda_{0}f}\). In Equation (14), the backscattered optical field from the target surface is subject to phase modulation induced by surface roughness. Given the complex height variations of rough surfaces, the angular spectrum of the backscattered light spans a broad range.