## 4 Experiments and Analysis
### Experimental Results  
#### 4.2.1 Long-Distance Maritime Target  
We acquired images under natural light conditions at the seaside for long-distance targets to verify the proposed method. Figure 8 presents the image of a \"lighthouse\" set against a sea-sky background at a distance of \(\sim\)1.5 km, captured under direct sunlight. Figure 9 depicts a seaside building from a distance of \(\sim\)200 m, wherein the sun was obscured but the sky was brightly illuminated. We employed the diffuse reflection theoretical model in Equation (6) and the proposed mixed light-based zenith angle solution model to reconstruct the zenith angle for both targets. Figure 10 displays the outline of a lighthouse. Despite some areas appearing relatively bright, owing to the strong direct sunlight, the basic shape of the lighthouse, including its tower body and the lantern room at the top, is clearly identifiable. This suggests that the depth map retains a certain level of detail, adequately conveying the outline and key features of the structure. Figure 6: Experimental setup. (**a**) Polarimetric camera; (**b**) lens; (**c**) camera and lens combination; (**d**) camera imaging page. Figure 7: The distribution of the polarization detector pixels. Figure 8: Polarized imaging of a seaside building. The polarization component of light (**a**) in the horizontal direction, (**b**) along the 45\({}^{\circ}\) direction, (**c**) in the vertical direction, and (**d**) along the 135\({}^{\circ}\) direction. Figure 9: Polarized imaging of the seaside structures. The polarization component of light (**a**) in the horizontal direction, (**b**) along the 45\({}^{\circ}\) direction, (**c**) in the vertical direction, and (**d**) along the 135\({}^{\circ}\) direction. Conversely, Figure 9(b) is more blurred, which increases the difficulty of discerning specific structures or objects. It exhibits a gradient effect that gradually darkens from the center outward. The central area of the image is slightly brighter but lacks clear edges and details, making it challenging to determine the target shape. Overall, the depth information provided by this image is very inaccurate, offering a vague sense of spatial depth and lacking recognizable details. Figure 10(a) demonstrates that the outline of the lighthouse is relatively clear, particularly the tower body. The top and bottom parts are quite distinct, and the overall structure exhibits a banded distribution. There is significant local depth variation, with a noticeable ripple-like structure near the top of the lighthouse. In the zoomed-in sections on the left and right sides of the lighthouse, finer surface details are displayed. The sides of the lighthouse are well restored, especially in the higher areas, with distinct detail. In the results reconstructed based on the diffuse reflection model, it is evident that the depth of the target surface is smoother compared to the reconstructed depth by our proposed method. Although the overall outline still resembles the shape of the lighthouse, the level of surface texture detail is not as pronounced as in Figure 10(a). In the zoomed-in sections, the surface structure is smoother. The reconstruction result in Figure 10(b) exhibits less prominent depth compared to the left side. Figure 10: A comparison of the reconstructed depth maps of the target. The depth map obtained using (**a**) the proposed method and (**b**) the diffuse reflection model. Figure 11: Reconstruction results of the target in Figure 8. The reconstruction results obtained using (**a**) the proposed method and (**b**) the diffuse reflection theoretical model. The brightness distribution in Figure 12a prominently depicts the cylindrical tower structure, with adequate representation of the brick texture in the middle of the tower body. The image reveals the brick structure of the lighthouse, displaying the depth variations in the gaps between the bricks.