1 Introduction

Photovoltaic(PV) modules are the core of the PV power generation system and play a decisive role in power generation efficiency. In actual use, there are dust, fallen leaves, bird dropping, and others coverings above the surface of PV modules, which reduce the output of the PV power generation system[1]. Researches show that air pollution has a significant impact on solar radiation. In recent years, PM2.5 and PM10 have become the main pollutants, which can significantly reduce the power generation efficiency of PV modules by changing the atmospheric composition and turbidity. On the one hand, the combination of suspended particles and water vapor in the atmosphere also affects the aerosol optical thickness in the process of atmospheric radiation transmission by scattering, absorbing and reflecting sunlight, and weakens the irradiance illustrated on the surface of PV modules and lowers the output power. On the other hand, PM2.5 and PM10 have strong adsorption capacity, which can cover the surface of PV modules and generate dust and dirt, thus blocking the radiation of sunlight on PV modules, further reducing power generation. Feng et al. [2] found that the output power of PV modules is directly proportional to the overall irradiance. Elminir [3] believed that air pollution will reduce the overall radiation by 9.3%—22% on sunny days. Mekhilef et al. [4] found that when the concentration of particulate matter in the air is high, the surface of PV modules is more prone to dust deposition. Dust deposition can reduce the output rate of PV modules, which is a natural phenomenon that adversely affects sol energy and affects PV module power generation by absorbing or reflecting solar radiation. Wind speed, humidity, rainfall, surface cleanliness of PV modules, inclination, soil type and surrounding vegetation all help dust adhere to the surface of PV modules. Compared with clean PV modules, the maximum power of dusty PV modules is reduced by 8.41%—20.1%, causing huge economic losses to PV power[5]. Adinoyi et al. [6] found that the size, quantity, chemical and physical characteristics of dust have an impact on the output characteristics of PV modules. Guo et al. [7] found that the daily power generation of PV modules lost 0.4%—0.8% due to dust deposition. Without monthly cleaning, PV power generation could lose 10%—24%. Li et al. [8] found that the PV power generation efficiency decreased by 19.23% on average and the average dust deposition density was 7.07 \({{\text{g}} \mathord{\left/ {\vphantom {{\text{g}} {{\text{m}}^{{2}} }}} \right. \kern-0pt} {{\text{m}}^{{2}} }}\) after the PV modules were exposed to dust for 11 days. Therefore, solar power plants usually use sweeping robots to sweep the coverings above PV modules, while the low recognition accuracy limits the sweeping robots to clean effectively due to the characteristics of the coverings not being fully understood.

In recent years, many scholars have conducted in-depth research on the detection of the coverings above PV modules. Chen et al. [9] proposed a coverings detection of PV array based on CenterNet, which can accurately identify and locate the types of coverings under different illumination directions, different occlusion degrees, and different distances. Xie et al. [10] proposed a PORNet algorithm to address the problem that single-resolution features are not sensitive enough to small-scale and low-density objects and evaluated the performance on the self-built fallen leaf occlusion dataset, with accuracy and recall improved by 9.21% and 15.79%, respectively. Wang et al. [11] proposed an abnormal shadow detection system based on YOLOv3 and Mask R-CNN for shadows caused by fallen leaves, bird droppings, and buildings, which achieves 94.5% accuracy for shadow classification. Li et al. [12] proposed a bird droppings detection method for PV modules based on transfer learning by collecting visible light images from UAVs, and the detection accuracy of bird dropping reached 96.75%. However, the above studies improve the detection accuracy of coverings from the aspect of algorithm optimization and have not studied the characteristics of coverings, so the detection accuracy still needs to be improved.

Based on physics knowledge, when the natural light shines on the object’s surface, due to the reflection of the object’s surface, partially polarized light will be obtained. Different objects or different states of the same object will produce different polarization states [13], so extracting polarization information in reflected light can distinguish objects that are difficult to distinguish in traditional light-intensity images. Vanderbilt et al. [14] found that the specular reflection of leaves is the main factor causing polarization. A single specular reflection of incident light occurs on the leaf surface, which is mainly influenced by the leaf surface and the observed geometric conditions. Therefore, the reflected light has obvious polarization characteristics and contains information on the leaf surface. The leaf is composed of cells and plant fibers, and the surface is uneven. The polarization characteristics of many microfacial elements are superimposed to obtain the polarization characteristics of the whole plane of the leaf, and the different polarization phase angles of each microfacet lead to the overall depolarization of the leaf [15]. However, the PV module has significant polarization characteristics because its surface of it is smooth glass. The polarization characteristics of the two are quite different, and this feature can be used as a basis for identifying fallen leaves on the surface of PV modules.

In this paper, based on the basic theory of polarization imaging, the research on the optical polarization characteristics of a fallen leaf, a typical covering on the surface of PV modules, is carried out. By setting up a polarization imaging experimental platform for PV modules, the effects of fallen leaf on the polarization characteristics of PV modules were studied where the wavelength of the incident light is 420 nm-546 nm and the observation angle of 0°—70°, the polarization characteristic parameters by which the fallen leaf can be distinguished from PV modules were given.

In the next section, we introduce the experimental samples, the composition of the experimental platform and the experimental steps. Section 3 shows the discussion and analysis of the experimental results. In Sect. 4, we summarize the research content of this paper.

2 Materials and Methods

2.1 Experimental samples

In this paper, photinia leaves and camphor leaves are selected as experimental subjects. Photinia leaves are long obovate, mucronate at the apex, subrounded at the base, with finely serrated and tough texture. Camphor leaves are ovate-elliptic, acute at the apex, and broadly cuneate at the base, with a microwave-like margin and a softer texture. In Fig. 1, leaf 1 and 2 are photinia leaves, leaf 3 and 4 are camphor leaves. Leaf 1 is red overall, leaf 2 is slightly red at the tip position and the rest is green, leaf 3 is green and leaf 4 is slightly yellowish.

Fig. 1
figure 1

Experimental samples. a Fallen leaf 1, b Fallen leaf 2, c Fallen leaf 3, d Fallen leaf 4

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The PV module model is DP60-270WE, as shown in Fig. 2(a). The multi-layer combination structure is shown in Fig. 2(b), formed by laminating the tempered glass panel, EVA adhesive film, crystalline silicon cells, and TPT backplane. The complete technical data of the PV module are shown in Table 1.

Fig. 2
figure 2

Experimental sample. a PV module, b multilayer composite structure

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Table 1 The complete technical data of the PV module
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2.2 Experimental platform

In this study, the time-sharing polarization imaging system is used as the image data acquisition system, mainly by adding a rotatable polarizer in front of the imaging detector to obtain the polarized light intensity images at different times and directions. Its working mode is sequential, and its advantage is the overall design is simple, without the need for accurate registration., as shown in Fig. 3.

Fig. 3
figure 3

Experimental platform

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The whole system consists of three main components: SALSA polarization camera, lens (SAMYANG AF35mm F1.4-22C), and laptop computer (Acer-N16Q2, Intel(R)Core i5-6200U 2.3 GHz) with polarization image acquisition software (SALSA Full Stokes Polarization Imaging 2.3.6).

Assuming that the Stokes vector of the optical signal entering the SALSA camera is \(S\), the images obtained at different azimuth angles can be analyzed:

$$S = \left[ {\begin{array}{*{20}c} {S_{0} } \\ {S_{1} } \\ {S_{2} } \\ {S_{3} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {I_{0} + I_{45} } \\ {I_{0} - I_{90} } \\ {I_{45} - I_{135} } \\ 0 \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {I_{90} + I_{135} } \\ {I_{0} - I_{90} } \\ {I_{45} - I_{135} } \\ 0 \\ \end{array} } \right]$$
(1)

where \(S_{0}\) denotes the total intensity of light, \(S_{1}\) denotes the intensity of linearly polarized light in the horizontal direction, \(S_{2}\) denotes the intensity of linearly polarized light in the diagonal direction, and \(S_{3}\) denotes the intensity of circularly polarized light, which in general has a very small component and can be ignored. \(I_{0}\),\(I_{45}\),\(I_{90}\),\(I_{135}\) denote the intensity of light passing through the polarizer with the directional angles of \(0^{ \circ }\),\(45^{ \circ }\),\(90^{ \circ }\),\(135^{ \circ }\), respectively.

The degree of polarization(DOP) represents the ratio of the light intensity of the polarized part of the beam to the whole light intensity.The angle of polarization(AOP) represents the angle between the light vector and the incident plane. The DOP and AOP can be calculated by Eqs. (2) and (3)[16].

$$DOP = \sqrt {S_{1}^{2} + S_{2}^{2} } /S_{0}$$
(2)
$$AOP = \frac{1}{2}\arctan \left( {S_{1} /S_{2} } \right)$$
(3)

2.3 Experimental procedure

Before the experiment, wipe the PV modules and fallen leaves with clean water and air dry them naturally. The angle between the PV module and the ground is 60°, and the SALSA camera is placed on the same horizontal line with the fallen leaves. To ensure clear and undistorted images, the lens is 3.2 m away from the surface of the PV module.

The SALSA camera comes with 6 bands of filters, including 420 nm, 435 nm, 450 nm, 488 nm, 510 nm, and 546 nm. Starting from the observation angle of 0°, the camera takes pictures every 10° up to the observation angle of 70°, totaling 8 observation angles. To reduce the error in the shooting, each observation angle was taken three times and averaged as the resultant image. The shooting time was from 9:00 a.m. to 12:00 p.m. on a clear day, and the shooting interval for each band was 20 min. The azimuthal and incident zenith angles of the sun were recorded assuming that the sun's position was constant at the time of the shooting, as shown in Table 2.

Table 2 Solar azimuth and Incident zenith angle
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3 Results and discussion

The size of the image taken by the SALSA polarization camera is 1040 \(\times\) 1040, in which the fallen leaves generally occupy only a part of the area, and the rest is the background area. To obtain only the effective area where the fallen leaves are located and reduce the influence of irrelevant background, the region of interest is cut from the original image with the smallest rectangle containing the fallen leaves, as shown in Fig. 4.

Fig. 4
figure 4

Schematic diagram of interesting area interception of polarization original image. a Original image, b interested area

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Polarization images include the DOP image, the AOP image, and Stokes parametric images. There is a significant difference in the polarization image when the observation angle is different, which is manifested by the different brightness of each pixel point. To describe this difference quantitatively, it is necessary to find the polarization of each pixel. It is not meaningful to compare each pixel point polarization value individually, and in this paper, the mean value of polarization of each pixel point in the region of interest is used as the polarization information of the falling leaves on the surface of the PV module [13].

This section analyzes the relationship between wavelengths and Stokes parameters, polarization degree, and polarization angle at 420 nm, 435 nm, 450 nm, 510 nm, and 546 nm bands for heather and camphor leaves on the surface of PV modules.

3.1 Spectral DOP analysis

Figure 5 shows the polarization curve of each band when the PV module is covered by leaves or not.

Fig. 5
figure 5

Spectral polarization analysis. a 0° observation angle, b 10° observation angle, c 20° observation angle, d 30° observation angle, e 40° observation angle, f 50° observation angle, g 60° observation angle, h 70° observation angle

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It can be seen from Fig. 5 that when the observation angle changes between 0° and 70°, the DOP difference of PV modules with or without fallen leaves is the largest at 420 nm and 546 nm; The specular reflection component of fallen leaves is unchanged, and the diffuse reflection component is greatly affected by the internal structure and physiological and biochemical characteristics of leaves [17, 18]. In the 420 nm wave band, although the surface of the PV module is relatively smooth compared with the fallen leaves surface, with obvious micromorphological differences, the physical and chemical characteristics of the two are different, and the DOP of the PV module is smaller than when it is sheltered by fallen leaves [19]; In the 546 nm wave band, due to the influence of chlorophyll, the diffuse reflection component will increase in the green wave band, leading to the increase of the unbiased component in the reflected light. Therefore, the DOP of the PV module is greater than that in the case of fallen leaves.

3.2 Effect of fallen leaf shading on the polarization characteristics of photovoltaic modules at different wavelengths

3.2.1 Effect of fallen leaves shading on the DOP of Photovoltaic Modules

As shown in Fig. 6, the DOP of PV modules at 420 nm and 546 nm is significantly different from that with fallen leaves, which is consistent with the above analysis. Whether or not there are fallen leaves covering the PV module, its DOP decreases first and then increases with the observation angle, and the minimum value is obtained at the observation angle of 30°. At 435 nm, 450 nm, 488 nm, and 510 nm, the influence of defoliation on the degree of polarization of photovoltaic modules is small. It can be seen that at 420 nm and 546 nm, within the observation angle of 0°—70°, the degree of polarization can be used to distinguish whether the photovoltaic modules are sheltered by fallen leaves.

Fig. 6
figure 6

Relationship between DOP and observation angle at different wavelengths. a 546 nm, b 510 nm, c 488 nm, d 450 nm, e 435 nm, f 420 nm

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3.2.2 Effect of fallen leaves shading on the AOP of Photovoltaic Modules

Figure 7 shows the AOP curves of each band.

Fig. 7
figure 7

Relationship between AOP and observation angle at different wavelengths. a 546 nm b 510 nm c 488 nm d 450 nm e 435 nm f 420 nm

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It can be seen from Fig. 7 that except for 546 nm, the AOP of PV modules in other wavebands increases with the increase of observation angle. From the perspective of the whole module, the AOP is little affected by fallen leaves, so it is not appropriate to use the polarization angle to distinguish whether there are fallen leaves on the surface of PV modules.

3.2.3 Effect of fallen leaves shading on the Stokes parameters of Photovoltaic Modules

Figures 8, 9, and 10 show the variation curves of Stokes parameters \(S_{0}\), \(S_{1}\) and \(S_{2}\) with wavelength for PV modules.

Fig. 8
figure 8

Relationship between \(S_{0}\) and observation angle at different wavelengths. a 546 nm b 510 nm c 488 nm d 450 nm e 435 nm f 420 nm

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Fig. 9
figure 9

Relationship between \(S_{1}\) and observation angle at different wavelengths. a 546 nm, b 510 nm, c 488 nm, d 450 nm, e 435 nm, f 420 nm

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Fig. 10
figure 10

Relationship between \(S_{2}\) and observation angle at different wavelengths. a 546 nm, b 510 nm, c 488 nm, d 450 nm, e 435 nm, f 420 nm

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\(S_{0}\) indicates the reflected light intensity received by the SALSA camera. As can be seen from Fig. 8, the incident light reflected the camera differs after refraction and absorption by different leaves due to the different color and chlorophyll content, and \(S_{0}\) changes with increasing observation angle, and the change curve is similar to a U-shaped curve. When observed at 0°, there is no leaf cover, the light is directly irradiated on the surface of the PV module and through a series of refraction and reflection, not absorbed by the fallen leaves, \(S_{0}\) is much larger than the value when there is leaf cover, so it can effectively distinguish between the fallen leaves and the PV module. It can be seen from Fig. 9 that the trend of \(S_{1}\) with observation angle is susceptible to wavelength, and \(S_{1}\) with or without leaf cover does not have regular differences with respect to different observation angles and wavelengths, so \(S_{1}\) is not suitable for distinguishing the presence or absence of leaf cover. In Fig. 10, \(S_{2}\) increases with increasing observation angle, and the curves of \(S_{2}\) with observation angle with and without leaf cover overlap, so \(S_{2}\) is also not suitable as a parameter to distinguish the presence or absence of leaf cover PV modules.

3.3 Discussion

At present, the electrical parameter measurement method is the main method to detect the covers on the surface of PV modules[20,21,22]. This method can better detect the presence of covers and the area of covers, but cannot determine their location. The cover detection method based on depth learning can locate the cover[9,10,11], but this method does not fully consider the physical characteristics of the cover, and the detection accuracy still needs to be improved. Starting from the polarization characteristics of the cover, this paper studied the impact of fallen leaves on the polarization characteristics of PV modules, and obtained the polarization characteristics parameters with the largest difference between the PV modules with and without fallen leaves, which can be used in the target detection algorithm in the future.

4 Conclusion

In this paper, we conducted an experimental study on the polarization characteristics of PV modules with leaf shading by incident light wavelength and observation angle and found that the effects of different types of leaf shading on the polarization characteristics of PV modules are similar for a given incident light wavelength and observation angle, and the main difference comes from the physiological characteristics of leaf shading. Among them, the DOP in the 420 nm band with leaf cover is smaller than that without leaf cover, while the opposite is true for the 546 nm band; At the observation angle of 0°, \(S_{0}\) without fallen leaves taken at 420 nm-546 nm is greater than that with fallen leaves. \(S_{1}\),\(S_{2}\) and AOP with or without fallen leaves have no regular difference concerning incident light wavelength and observation angle.

Restricted by the experimental conditions, this paper only studied the polarization characteristics of one kind of cover, and common covers also include dust and bird droppings. In the future, we can study the polarization characteristics of other common covers, and use these characteristics information in the target detection algorithm to achieve accurate detection of the cover.