2.4.2. Polarization of Vegetation

When light is reflected from the leaf surface, its spectral characteristics will be affected by the element composition of the leaf surface, and its polarization characteristics will be affected by the characteristics of the leaf surface [62]. Polarization [63] and multispectral imaging can provide complementary information for vegetation detection. However, few people currently propose to fuse the information of polarization and spectral imaging to obtain better vegetation detection results. Therefore, this paper introduces polarization into vegetation detection and integrates it with the vegetation index to improve the detection of the vegetation health status.

Stokes formula:

$$\mathbf{F} = \begin{bmatrix} \mathbf{I} \\ \mathbf{Q} \\ \mathbf{U} \\ \mathbf{V} \end{bmatrix} = \begin{bmatrix} \left< \mathbf{A}\_{\mathbf{x}} \,^2 + \mathbf{A}\_{\mathbf{y}} \,^2 \\ \left< \mathbf{A}\_{\mathbf{x}} \,^2 - \mathbf{A}\_{\mathbf{y}} \,^2 \right> \\ \left< 2\mathbf{A}\_{\mathbf{x}}\mathbf{A}\_{\mathbf{y}}\cos\gamma \right> \\ \left< 2\mathbf{A}\_{\mathbf{x}}\mathbf{A}\_{\mathbf{y}}\sin\gamma \right> \end{bmatrix} \approx \begin{bmatrix} \mathbf{S}\_0 \\ \mathbf{S}\_1 \\ \mathbf{S}\_2 \\ 0 \end{bmatrix} \tag{2}$$

Intensity of radiation: S0 is obtained by passing light waves through linear polarizers oriented at 0 degrees, S1 is obtained by passing light waves through linear polarizers oriented at 60 degrees, and S2 is obtained by passing light waves through linear polarizers oriented at 120 degrees.

The method for measuring linear Stokes parameters is shown in Figure 3 [64]. It should be noted that, in remote sensing measurements, the degree of circular polarization is usually very small, so we only describe the linear polarization state of the beam.

**Figure 3.** (**a**) Generation of polarized light with a polarized filter. (**b**) Fessenkovs Method to characterize Stokes vectors.

> Fessenkovs method was used to measure the Stokes parameters in the paper. Degree of Linear Polarization (DoLP):

$$\text{DoLP} = \frac{\sqrt{\text{S}\_1^2 + \text{S}\_2^2}}{\text{S}\_0} \tag{3}$$

Angle of Polarization (AOP):

$$\text{AOP} = \frac{1}{2} \tan^{-1} \left( \frac{\text{S}\_2}{\text{S}\_1} \right) \tag{4}$$

2.4.3. Fusion Algorithm for Nighttime Plant Detection

In view of the different polarization and spectral characteristics of healthy and stressed vegetation, in this paper, we propose a fusion algorithm to detect the vegetation with the spectral and polarization characteristics of diffuse and specular reflections of vegetation. The NDVI, DoLP and AOP are all calculated in the fusion algorithm to better detect the health status of plants in the night environment.

The schematic diagram of our method is shown in Figure 4. This algorithm can be summarized as follows: (1) Spectral and polarized images are preprocessed (normalization and filtering) and then co-registered together. (2) The NDVI was calculated with a F680-nm red spectral image and F760-nm infrared spectral image (Equation (1)). (3) The DoLP (Equation (3)) and AOP (Equation (4)) were calculated with 0, 60 and 120◦ polarized images. (4) The NDVI, DoLP and AOP images were fused, and the fused images were converted into HSV with RGB color mapping.

**Figure 4.** Schematic diagram of the proposed method.

> The images are combined following the conversion from HSV to RGB color maps:

$$
\sum \text{HSV} \to \text{RGB}\{\text{NDVI}, \text{DoLP}, \text{AOP}\} \tag{5}
$$

Based on the fusion image (NDAI) of the NDVI, DoLP and AOP, a new index, the night plant state detection index (NPSDI), was proposed.

The NPSDI formula (Equation (1)) is as follows:

$$\text{NPSDI} = \left(\frac{\text{R}\_{\text{(AOP)}} + \text{G}\_{\text{(NDAI)}} + \text{B}\_{\text{(DoLP)}}}{3 \times 255}\right) \tag{6}$$

R(AOP), G(NDAI) and B(DoLP) represent the intensity values of the R, G and B channels of the fused image, respectively.
