# Design and Experiment of High-Resolution Multispectral Polarization Imaging System
###### Abstract  
This paper addresses the objectives in a complex context: the polarization mathematical and physical model of the basic components of the target/background is constructed by simulation modeling. The image fusion experiment is carried out based on a two-dimensional wavelet transformation. A high-resolution polarization imaging instrument was developed, and static experiments were carried out with polarization, infrared, and visible cameras. The result shows that using polarization imaging detection technology to detect physical evidence targets in complex backgrounds can effectively improve target contrast. It can enrich the target information, improve image quality, and improve target detection accuracy.  
polarimetric imaging; image fusion; high-resolution Article Design and Experiment of High-Resolution Multispectral Polarization Imaging System  
Qiang [PERSON] superposition of all elements' mirror reflection components \(\mathrm{dL_{r,s}}\) and diffuse reflection components \(\mathrm{dL_{r,d}}\):  
\[\mathrm{dL_{r}}=\mathrm{dL_{r,s}}+\mathrm{dL_{r,d}} \tag{1}\]  
The specular reflection of a single element is calculated by the Fresnel formula. The direction's micro-bins are randomly distributed, and the included angle distribution between its normal direction and the macroscopic normal distribution of the surface is Gaussian distribution: \(\mathrm{dL_{r,s}}\).  
\[\mathrm{P(\theta)}=\frac{\exp\left(-\frac{\tan^{2}(\theta)}{2\sigma^{2}} \right)}{2\pi\sigma^{2}\cos^{3}(\theta)} \tag{2}\]  
where \(\theta\) is the angle between the macro surface normal and the original micro surface normal, and \(\sigma\) is the roughness.  
The diffuse reflection component is given by:  
\[\mathrm{dL_{r,d}}=\mathrm{aL_{i}cos\theta_{i}} \tag{3}\]  
where a is the diffuse reflection coefficient, which is obtained by experimental measurement [1, 2, 3]. \(\theta_{i}\) is the amplitude brightness of the incident light and the angle between the incident light and the macro normal.  
Different scholars have made targeted revisions to the TS model, making its adaptability better [4, 5]. In pBRDF, a polarization correction model based on the TS model, diffuse reflection is regarded as complete Lambert scattering, which is unpolarized, while specular reflection will produce a polarization effect. If shadow and shading factors are considered at the same time, the reflection attenuation caused by the geometric relationship of adjacent micro-bins is defined according to the bidirectional reflection function BRDF:  
\[\mathrm{f}=\frac{\mathrm{dL_{r}}}{\mathrm{dE_{i}}} \tag{4}\]  
where \(\mathrm{L_{r}}\) is the brightness of the outgoing light and \(\mathrm{E_{i}}\) is the incident light intensity. Therefore, we can get the polarization BRDF--pBRDF that the microelements are equi-sawtooth, the normal direction of the bin is Gaussian, and the shielding factor g is as follows:  
\[\mathrm{f_{j,k}}(\theta_{i},\theta_{r},\phi_{r},-\phi_{i})=\frac{\mathrm{G\cdot P (\theta)}}{4\cos(\theta)\cos(\theta_{r})\cos(\theta_{i})}\mathrm{M_{j,k}}( \theta_{i},\theta_{r},\phi_{r},-\phi_{i})+\frac{\mathrm{a}}{\mathrm{d}\omega_ {i}} \tag{5}\]  
where \(\theta_{i}\) and \(\theta_{r}\) are the angles between the incident light and the outgoing light and the macro normal, respectively, \(\mathrm{P(\theta)}\) is the Gaussian distribution function, \(\mathrm{M_{j,k}}(\theta_{i},\theta_{r},\phi_{r},-\phi_{i})\) are the 16 Mueller matrix elements characterizing the polarization characteristics of the surface reflection process, and \(\phi_{r}\) and \(\phi_{i}\) are the azimuth angles of the incident and outgoing light, respectively.