# Multi-Band Polarization Imaging in a Harsh Sea Fog Environment
## 2 Multi-Band Polarization Imaging Principle
### Polarization Image Evaluation Index  
The polarization picture including polarization information is generated by applying theoretical knowledge to the intensity image, and the assessment of the resulting polarization image is a crucial aspect of the study. This study will employ the standard approach of image assessment index to analyze the quality of polarization photographs, focusing primarily on subjective evaluation and objective evaluation. (1) Subjective evaluation  
People are often the topic of picture quality assessment, and subjective evaluation is the more prevalent method, which is mostly based on the evaluator's perception of the image's integrity and clarity. Image fidelity refers to the difference between the processed image and the original image, whereas clarity is the amount of information the human eye extracts from a picture. However, the human eye lacks sufficient knowledge about the picture, and the subjective sentiments of various evaluators and the appraisal of the image's virtues and demerits may vary, so it cannot be objectively appraised. In order to describe the influence of polarized pictures, objective assessment indices are used. (2) Objective evaluation  
Objective assessment entails calculating a certain numerical index using a specified method in order to arrive at a quantitative evaluation of the picture. Objective assessment provides the benefits of high certainty and efficacy and is resistant to subjective human  
Figure 3: LCVR phase delay characteristic curve. influence. In order to analyze the findings of polarization photographs objectively, the following three metrics are used. * Information entropy (EN)  
Information entropy may be used to quantify the amount of information included in a picture, and a rise in the information entropy value of an image signifies an increase in the amount of information contained in that image [13]. The resulting image's information entropy is determined by the following equation. \[EN=-\sum_{i=0}^{n}p_{i}\log_{2}p_{i} \tag{19}\]  
where \(n\) represents the entire number of gray levels and \(p_{i}\) represents the proportion of pixels having a gray value of \(i\) to the total number of pixels. EN may be used to assess the amount of information contained in a picture, with bigger numbers indicating higher quality and more data. * Average gradient (AG)  
The average gradient, which not only measures the blurriness of the picture but also reflects the contrast of the image's features, characterizes the image's clarity [14]. When there are more layers in a picture, the average gradient value increases, and the image's sharpness improves. The definition of the mean gradient is as follows: where \(M\times N\) is the picture size and \(P(i,j)\) is the pixel value at \((i,j)\). \[AG=\frac{1}{(M-1)(N-1)}\sum_{i=1}^{M-1}\sum_{j=1}^{N-1}\left[\frac{\left[F(i +1,j)-F(i,j)\right]^{2}+\left[F(i,j+1)-F(i,j)\right]^{2}}{2}\right]^{\frac{1} {2}} \tag{20}\]  
where \(F\) is the processed image. The average gradient shows the contrast of the image features, with a bigger AG value indicating a more distinct and high-quality image. * Standard deviation (STD)  
The standard deviation of an image reveals the degree of dispersion of the image's grayscale mean and may also be used to assess the image's contrast [15]. The greater the STD value, the greater the contrast of the image. The following equation defines the standard deviation. \[STD=\sqrt{\frac{\sum_{i=1}^{M}\sum_{j=1}^{N}\left(P(i,j)-\bar{P}\right)^{2}}{M \times N}} \tag{21}\]  
where \(\bar{P}\) is the average grayscale of the image and is determined by the following equation:  
\[\bar{P}=\frac{1}{M\times N}\sum_{i=1}^{M}\sum_{j=1}^{N}P(i,j) \tag{22}\]  
The link between the value of the evaluation indexes and the evaluation effects may be observed more clearly in Table 1, which displays the objective assessment effects based on image attributes.