# Multi-Band Polarization Imaging in a Harsh Sea Fog Environment
## 4 Experimental Results and Analysis
### Analysis of the Effect of Optical Thickness on Polarization Imaging  
Due to the inconsistency of the medium concentration throughout the experiment, this part defines the sea fog environment at varying degrees of visibility via various optical thicknesses in order to visually depict the medium concentration. The Beer-Lambert equation may be used to determine the dependency of the transmittance ratio between transmitted and incident light intensity on optical thickness. If the value of the incident light intensity is \(I_{o}\), then the incident light intensity \(I\) may be represented as [17] after \(L\) distance of transmission in the medium. \[I=I_{o}\exp(-\mu_{e}L)=I_{o}\exp(-\tau) \tag{24}\]  
The optical thickness \(\tau=\mu_{e}L\), where \(\mu_{e}\) is the extinction coefficient, can be expressed as  
\[\mu_{e}=\rho C_{e}=\rho\pi r_{o}^{2}Q_{e} \tag{25}\]  
where \(Q_{e}\) is the extinction factor, which can be obtained from the Mie scattering calculation, \(\rho\) is the volume concentration of the transmission medium, \(r_{o}\) is the isomeric radius of the medium particles, and \(\pi r_{o}^{2}\) is the absorption cross section of the medium particles. Figure 10: Evaluation indexes of multi-band target polarization images in sea fog environment. Figure 9: Polarization contrast of multi-band targets. Therefore, bringing (24) into (25) yields the relationship between the transmittance \(T\) and the medium volume concentration \(\rho\) as follows:  
\[T=I/I_{o}=\exp(-\tau)=\exp(-\rho\pi r_{o}^{2}Q_{e}L) \tag{26}\]  
where the isomeric radius \(r_{o}\) of a single medium particle is constant and the extinction factor \(Q_{e}\) and the experimental light transmission distance \(L\) are constant; therefore, the right-hand side of the equation \(\pi r_{o}^{2}Q_{e}L\) is a constant. The above equation shows that the optical thickness \(\tau\) is proportional to the volume concentration \(\rho\), from which the optical thickness can be calculated. In this paper, the optical thickness of the sea spray was measured from 5:00 to 16:00 using a solar radiometer, and five sets of data were read for each time period and averaged. The optical thicknesses at different time periods are shown in Figure 11.  
In this section, imaging was performed when the optical thickness was 0.75, 0.61, and 0.52, mainly because the visual effect of sea fog with such optical thickness was obvious during the experiment. Figure 12 shows multi-band intensity images with optical thicknesses of 0.75, 0.61 and 0.52, respectively. As demonstrated in Figure 12, as the optical thickness rises, the polarization picture of each band gets blurrier, yet the polarization image produced may still reveal the edge contour with greater clarity. Since the difference between the visible target and the background is the basis and prerequisite for recognizing the target, and since each target surface has polarization characteristics, the polarization contrast between the target and background  
Figure 11: Optical thickness of sea spray from solar radiometer measurements. Figure 12: Multi-band images with different optical thicknesses (**a**). Intensity image; (**b**). Polarization image. can be obtained to compare the polarization characteristics of the target in a more intuitive manner; the polarization contrast is calculated as follows [18]:  
\[C_{DOP}=\frac{DOP_{T}-DOP_{B}}{DOP_{T}+DOP_{B}} \tag{27}\]  
where \(C_{DOP}\) is the polarization contrast between the target and the background, \(DOP_{T}\) is the polarization of the target, and \(DOP_{B}\) is the polarization of the background. Figure 13 shows the polarization contrast of multi-band images with different optical thicknesses of sea fog, where (a) is the polarization contrast of multi-band intensity images and (b) is the polarization contrast of multi-band polarization images.