# Image Dehazing Enhancement Strategy Based on Polarization Detection of Space Targets
## 5 Image Dehazing Method Based on Full Polarization Information Inversion and Image Fusion
### Basic Principle of Image Dehazing Based on Full Polarization Information Inversion  
The atmospheric light radiation intensity and the space target radiation light intensity are expressed by polarization configuration, as shown in the Equations (9) and (10):  
\[I^{air}(x,y)=S^{air}_{0\_{lp}}(x,y)+S^{air}_{0\_{inp}}(x,y)+S^{air}_{0\_{cp}} (x,y) \tag{9}\]  
\[I^{target}(x,y)=S^{target}_{0\_{lp}}(x,y)+S^{target}_{0\_{inp}}(x,y) \tag{10}\]  
\(S^{air}_{0\_{lp}}(x,y)\), \(S^{air}_{0\_{inp}}(x,y)\), \(S^{air}_{0\_{cp}}(x,y)\) are the linearly polarized part of the skylight, the unpolarized part of the skylight, and the circularly polarized part of the skylight, respectively. \(S^{target}_{0\_{lp}}(x,y)\) and \(S^{target}_{0\_{inp}}(x,y)\) are the linearly polarized part of the reflected light of space targets and the unpolarized part of the reflected light of space targets, respectively. Since the transmittance of light under different polarization states is different, the transmittance of linearly polarized light, unpolarized light, and circularly polarized light can be expressed as \(t_{\rm{fp}}\), \(t_{\rm{inp}}\), and \(t_{\rm{cp}}\), respectively. Based on the physical model of atmospheric degradation, the transmission model of skylight and space target light can be expressed as:  
\[I^{air}(x,y)=A(x,y)[1-t_{lp}(x,y)-t_{unp}(x,y)-t_{cp}(x,y)] \tag{11}\]  
\[I^{target}(x,y)=I^{target}(x,y)[t_{lp}(x,y)+t_{unp}(x,y)] \tag{12}\]  
\(A(x,y)\) is the intensity of the skylight, and \(I^{target}(x,y)\) is the radiation intensity of the space target. The intensity of radiation received by the detector can be expressed as transmittance in different polarization states:  
\[S_{0}(x,y)=J^{target}[t_{lp}(x,y)+t_{unp}(x,y)]+A(x,y)[1-t_{lp}(x,y)-t_{unp}( x,y)-t_{cp}(x,y)] \tag{13}\]Assuming that the circularly polarized information is known, the transmittance of the linearly polarized and unpolarized portions can be expressed as shown in Equation (14):  
\[t_{lump}(x,y)=t_{lp}(x,y)+t_{lump}(x,y) \tag{14}\]  
So, the expression of the radiant intensity of the space target is  
\[J^{\text{target}}(x,y)=\frac{S_{0\_Lump}^{air}(x,y)-A(x,y)[1-t_{lump}(x,y)]}{ t_{lump}(x,y)} \tag{15}\]  
According to Equation (15), in order to restore the scene light, it is necessary to estimate the \(t_{\text{lump}}\) in the atmospheric light, which can be expressed as:  
\[t_{lump}(x,y)=1-\frac{S_{0\_Lump}^{air}(x,y)}{A(x,y)}=1-\frac{S_{0\_Lump}^{ air}(x,y)}{A(x,y)}+\frac{S_{0\_cp}^{air}(x,y)}{A(x,y)} \tag{16}\]  
According to the definition of linear polarization, the expression of \(S_{0}^{air}(x,y)\) derived from Equation (16) can be used as:  
\[S_{0}^{air}(x,y)=\frac{Dolp_{\text{target}}(x,y)S_{0}(x,y)-\Delta I(x,y)}{Dolp _{\text{target}}(x,y)-Dolp_{air}(x,y)} \tag{17}\]  
Substituting Equation (17) into Equation (16), the expression of linear polarization and unpolarized light transmittance is obtained:  
\[t_{lump}(x,y)=1+\frac{S_{0\_cp}^{air}(x,y)}{A(x,y)}-\frac{Dolp_{\text{target} }(x,y)S_{0}(x,y)-\Delta I(x,y)}{A(x,y)[Dolp_{\text{target}}(x,y)-Dolp_{air}(x,y)]} \tag{18}\]  
Finally, by substituting the above formula into Equation (15), the expression of the radiation intensity of the space target is obtained, which can be expressed as:  
\[I^{target}(x,y)=S^{target}_{0\_{lp}}(x,y)+S^{target}_{0\_{inp}}(x,y) \tag{10}\]0  
Equation (19) is the image restoration model of the method based on full polarization information inversion. It can be seen that in the process of dehazing the polarization image of space targets, the variables that need to be resolved include skylight intensity \(A(x,y)\), differential radiation intensity \(\Delta I(x,y)\), the degree of linear polarization of skylight \(Dolp_{air}(x,y)\), the radiation intensity of circularly polarized light \(S_{0}^{cp}(x,y)\), and the degree of linear polarization of space targets \(Dolp_{target}(x,y)\).