Wheat stripe rust (WSR), caused by Puccinia striiformis, has been a major disease of wheat worldwide for centuries. P. striiformis f. sp. tritici (Pst), the causal pathogen of wheat stripe rust, has caused a dramatic, extensive, and serious magnitude of losses and the economic hardships endured [1, 2]. WSR on leaves appears as a mass of yellow to orange urediniospores erupting from pustules arranged in long, narrow stripes on leaves, usually between veins [3]. As the water and pigment levels in the infected tissue change, the infected tissue becomes brown and dry, and its cells are destroyed [4]. Chlorophyll is the most abundant photosynthetic pigment in leaves during plant growth; The decrease in its content causes changes in the reflectance spectrum to reflect environmental stress, disease, or vegetation aging [4, 5].

At present, there are many studies of spectral information on wheat stripe rust detection. Spectral information can discriminate WSR from healthy wheat [6–11]. In histological imaging, polarization imaging has good performance for image contrast enhancement in optical biopsy and cancer detection [12–14]. Polarization techniques can improve contrast in superficial tissue images by eliminating multiple scattered photons from deep layers [15]. Several studies proposed that polarization imaging can observe details in leaves that are not visible under standard lighting conditions [16, 17]. Savenkov et al. [18] performed polarization measurements of the transmission and reflection of oak leaves with a laser source. The Mueller matrix (MM) has been used to distinguish leaves that have different structures on the surface. The differences between the healthy and virus-infected wheat were characterized by the Mueller matrix (MM) [19]. Savenkov et al. [20] reported the polarization studies of barley leaves, and the distinction between different mutant lines was realized based on the MM.

Mueller matrix imaging (MMI) has been used in biomedical [21], agricultural [22], and other fields. The MMI technique allows quantifying the entirety of polarimetric properties, which is suitable for the highly scattered nature of bulk biological tissues [23]. MMI has great potential for the characterization of plant tissues, especially in leaves. Birefringence and dichroism are related to the structural properties of vine leaves through the MMI, whereas unpolarized intensity imaging produced little to no discernible contrast between these structures [24]. Kudenov et al. [25] identified barren and non-barren Zea maize hybrids and demonstrated the variations in retardance and diattenuation versus leaf canopy position by using a portable multi-spectral MMI. Thus, the multi-spectral MMI (MSMMI), which combines spectral information and MMI, has the potential the detect plant pathology, especially the detection of stripe rust, which is mainly infested on the leaf surface. To our knowledge, there are few MSMMI studies on agricultural disease detection, especially for WSR.

In this study, we propose an MSMMI system for WSR detection. Section 2 describes the principle of the MSMMI. Section 3 presents the way the sample was prepared and the details of the experiment setup. The variations in individual elements of the MM over the visible spectrum (430 to 690 nm) caused by Pst infection are discussed in Section 4. The conclusion is given in Section 5.

2.1. Mueller Matrix

The state of light can be specified by the Stokes vector and defined as [24]

where S₀ is the total power of the light. S₁ and S₂ represent the linear polarized components. S₃ indicates the circularly polarized components. I₀, I₄₅, I₉₀, and I₁₃₅ are intensities of light based on the angles of the coordinate system. I_L and I_R are intensities of left and right circularly polarized light. Incident light, denoted as S_in, passes through or is reflected by a sample. The output light S_out can be determined as

where M, with 4 × 4 elements, which relates a set of incident Stokes parameters to the exiting Stokes parameters for any type of sample, is MM. Each element of M represents all the polarization properties of a sample: Diattenuation, retardance, and depolarization [26].

2.2. Mueller Matrix Decomposition

The polarization decomposition is described as [27]

The sample MM, M_sample, can be decomposed into the product of a depolarizer MM M_∆, a retarder MM M_R and a diattenuator MM M_D. Based on these three MMs, the linear and circular diattenuation D_L and D_C, the linear and circular depolarization ∆_L and ∆_C, and the fast axis of retardance vector R can be solved. The details of measurement can be found in the Appendix.

2.3. Data Acquisition

As shown in Fig. 1, the MSMMI system consists of a polarization state generator (PSG) and a polarization state analyzer (PSA). The system can be built in the form of reflection or transmission depending on the properties of the sample. Due to the thickness of wheat leaves and the aim of observing the rust mainly on the surface, the reflective system was adopted. The incident light emitted by a monochromatic light source with adjustable wavelengths is affected by the sample after being polarized by the PSG. Then the light is analyzed by the PSA and captured by a focal plane array (FPA). The PSG and PSA both consist of a horizontal polarizer and a rotatable achromatic quarter-wave plate (AQWP). Two polarizers are labelled as P₁ and P₂. Two AQWPs are labelled as AQWP₁ and AQWP₂. In this study, the fast axis of AQWP₁ and AQWP₂ change 37 times in a 1:5 radio until AQWP₁ rotates 180°. From the data obtained by these 37 measurements, 4 × 4 MM images at the identical wavelength can be obtained. The process of data acquisition follows the method proposed by [28].

Figure 1. Schematic of the MSMMI system. PSG, polarization state generator; PSA, polarization state analyzer; P, polarizer; AQWP, achromatic quarter-wave plate; FPA, focal plane array; θ, the angle with respect to the fast axis of AQWP.

The relationship between the Stokes vector of incident light and output light in the system can be described by

where the MM of the polarizer with 0° polarization direction is

The MM of the AQWP M_AQWP is

where θ is the angle with respect to the fast axis of AQWP. Substituting Eqs. (5) and (6) to Eq. (4), it can be obtained that

where C₁ = cos(2θ₁); C₂ = cos(2θ₂); S₁ = sin(2θ₁); S₂ = sin(2θ₂); θ₁ and θ₂ are the angles with respect to the fast axis of AQWP₁ and AQWP₂, respectively. I_in and I_out are intensities of the incident light and outgoing light, which present the total light intensities of the S_in and S_out in Eq. (3). I_∆ is the difference between horizontal and vertical polarized components. The 16 elements from m₁₁ to m₄₄ are the elements of the sample Mueller matrix M_sample. The sample MM can then be reconstructed by solving Eq. (7) using approaches such as least square method [28].

3.1. Sample Preparation

The samples in this study were collected at Yangling (34°17’ N, 108°04’ E, altitude 519 m) in Shaanxi Province of China during the winter wheat cropping season (2022–2023). Each accession was planted in a single 1 m row with 30 cm spacing between rows. Artificial inoculations at Yangling were conducted in late March after flag leaf emergence. The spores of Pst were infected one month before sampling.

3.2. Experiment Setup

In this study, the MSMMI system shown in Fig. 1 was used to acquire a multi-spectral MM data cube with nine bands (430, 455, 480, 515, 550, 580, 610, 650, and 690 nm) with approximately 20 min. An LED (LB-L21-64-WDG-1; LBTEK, Hanam, Korea) and a set of optical filters (#66-637; Edmund Optics, NJ, USA) were used to generate the monochromatic waves. The two polarizers (GCL-05; Daheng New Epoch Technology Inc., Beijing, China) in this system are placed at a horizontal angle. The initial angles of both AQWPs (AQWP20-VIS; LBTEK) are horizontal. The two AQWPs mounted on turntables are synchronously controlled by a controller. By rotating the AQWP₁ in the PSG with an interval of 5°, the polarization state of the incident light changes accordingly. The controller controls the two turntables to rotate at a ratio of 1:5 each time while the FPA (MQ042MG-CM; Ximea, Münster, Germany) takes a measurement. With LabVIEW software, each rotation of the turntables takes time within 2 seconds, while the exposure time of the FPA is 400 ms. The AQWPs in the PSG and PSA rotate synchronously until the AQWP₁ in the PSG returns to the horizontal again.

A total of 37 valid measurements were obtained during the entire measurement. The incident light that is polarized modulated hits the sample at 40° to the FPA. Spectral measurement variations are affected by ambient lighting. To correct the effect of the differences between laboratory and natural light sources on the spectrum, the following calibration was implemented. A reflected mirror was measured as a sample to obtain reference multi-spectral MM data. For each pixel, the raw MMs were divided by the normalized reference curve corresponding to each MM element.

The true-color image of the infected wheat leaf sample takes Fig. 2(a) as an example for demonstration that is reconstructed by the multi-spectral data cube of m₁₁, via the CIE system [29]. More details about the reconstruction can be found in the Appendix. A multi-spectral data cube of m₁₁, as shown in Fig. 2(b), is obtained from the experiment. Multi-spectral images of a wheat leaf infested with Pst spores for one month are shown in Fig. 2(c). For the absorption peak of carotene and chlorophyll to be close to 480 and 690 nm [30], the incident light at 480 and 690 nm irradiated to the infected and the healthy area was absorbed. The infected area reflected more light than the healthy area, such as the m₁₁ image in Fig. 3.

Figure 2. Reconstructed results of m₁₁ for the sample. (a) True-color image of the sample (the highlighted area is the interest area enlarged follow), (b) multi-spectral data cube of m₁₁, and (c) multi-spectral images of m₁₁.

Figure 3. Mueller matrix (MM) images of the area of interest at 690 nm [Fig. 2(a)]. Color bar scale: the intensity of the MM (a.u.).

Compared with the true-color image, the affected area is insensitive to light with a wavelength of 430 to 515 nm. Significant differences between the healthy and infected areas are obvious when the wavelength is longer than 550 nm. Along with dehydration and deactivation in cells in the infected area, the chlorophyll content is significantly reduced [4]. The absorption of red and green light in the infected area is significantly reduced compared to the healthy area.

Biological samples such as leaves are depolarized [22]. When leaves were infected by the pathogens, the spores of Pst broke through the protection of the epidermal cells and destroyed the internal structure [4]. The MM images of the area of interest at 690 nm shown in Fig. 2(a) are depicted in Fig. 3. When the relatively smooth surface becomes rough, the scattering and depolarization of the incident light increase.

As for WSR destroying cells on the surface [4], the infected area became brighter than the healthy area in those elements of MM images related to depolarization and diattenuation. The infested area visible in m₁₁ is blurred in the other elements. The vein pattern on the surface is displayed, especially in m₁₂ (or m₂₁) and m₁₃ (or m₃₁), reflecting linear polarization information (including linear diattenuation, retardance, and depolarization). While m₁₂ (or m₂₁) and m₁₃ (or m₃₁) are structurally similar to m₁₁, especially in the visible veins, m₁₄ shows more differences between infected and healthy areas. Since m₁₄ implies the circularly polarized nature of the sample, the infected areas are less sensitive to circularly polarized light.

The decomposition results are shown in Fig. 4. It is seen that the differences between infected and healthy areas of a wheat leaf are distinguished in Figs. 4(b), 4(d), and 4(e), which is almost indistinguishable in the multi-spectral images in Fig. 2(c). As shown in Figs. 4(d) and 4(e), the areas with high pixel values are more severely infected, which represents a higher degree of depolarization. In contrast, the linear diattenuation of the infected area is lower than that of the healthy area. The circular diattenuation lacks sensitivity to the rust but shows specificity in vein patterns. The direction of the retardant fast axis of the leaf tissue is predominately horizontal (R ≈ π), showing noise and different angles in the leaf vein. The retardance R is insensitive to WSR. The area of rust can be observed in the linear diattenuation image and the linear depolarization image. The above images lack visibility into the extent of the lesion and the spores. It shows that the main factor affecting the linear diattenuation coefficient and the linear depolarization coefficient is whether the plant cells are damaged compared to Pst itself.

Figure 4. Mueller matrix decomposition result at 690 nm. (a) Reference image, (b) linear diattenuation (D_L), (c) circular diattenuation (D_C), (d) linear depolarization (Δ_L), (e) circular depolarization (Δ_C), and (f) retardance (R).

Fifty points were randomly selected from the reference and WSR samples, respectively. The total of 100 sampling points all avoided sampling the vein for distinctive spectropolarimetric features since the normal tissue and veins can be distinguished in the MM elements and decomposition components [16]. The means of the spectrum with positive and negative errors of the data are shown in Fig. 5. m₁₁ represents the non-polarized properties and describes the difference between healthy and infected leaf tissues. Healthy leaves have more absorption between 650 and 690 nm than the stripe rust area due to the presence of chlorophyll [30] and reflect less than the WSR tissues. Infected leaves absorb light better in other wavelength ranges than wavelengths longer than 550 nm. The values of m₁₂ and m₁₃ are higher in the infected area between 430 and 580 nm. Oppositely, healthy tissue has higher values in the range of 580 to 690 nm. m₄₁ and m₁₄ represent the induced fractional circular polarization and differential circular absorption. There are few differences in the numerical value between the healthy and infected data, while the opposite phenomenon is shown in the changing trend. The biggest difference occurs in the range of 480 to 580 nm. m₃₁, m₃₂, and m₃₃ show no significant difference in overall trend between the healthy and infected groups, but an obvious difference in magnitude, especially in the chlorophyll absorption band (550–690 nm). For all MM elements, there are differences between WSR samples caused by factors such as the degree of infection and the concentration of spores. It causes the range between positive and negative peaks to be greater for the infected sample than for the reference sample in addition to the influence of experimental error.

Figure 5. Multi-spectral 4 × 4 Mueller matrix element values for the healthy sample (green lines) and WSR sample (red line).

In conclusion, an MSMMI system was proposed in this work. The principle and theory of the MMI and MM decomposition were demonstrated. The MSMMI was used to identify WSR in the experiments.

According to the results, some significant and constructive conclusions can be drawn. In image analysis, linearly polarized images were more sensitive to WSR than circularly polarized images at each wavelength. Infected areas are visualized in linear diattenuation and linear depolarization images. There is less discrimination between healthy tissue and rust in circularly polarized images. In contrast, in the process of spectral analysis of MM elements, the linear polarization-related m₁₂, m₁₃, and other elements are similar in spectral trend, but there is a stable difference in magnitude. m₁₄ and m₄₁, which are dominated by circular polarization information, reflect differences in trends. Although m₁₄ and m₄₁ differ in trend, there is no significant difference in magnitude.

This study aims to investigate whether structure-sensitive polarized light data can distinguish yellow rust stains of WSR. This study demonstrates the potential application of MSMMI to phytopathology and offers new perspectives for disease detection under special conditions. Since WSRs of different severity were not differentiated in this study, there is a possibility to study more in the future.

The detailed calculation of the linear and circular diattenuation D_L and D_C, the linear and circular depolarization ∆_L and ∆_C, and the fast axis of retardance vector R is as follows [31].

The polarization decomposition is described as

The sample MM M_sample can be decomposed into the product of a depolarizer MM M_∆, a retarder MM M_R and a diattenuator MM M_D.

The diattenuation MM can be described by:

where the diattenuation vector D = (m₁₂, m₁₃, m₁₄)^T / m₁₁ and the m_D is given by

where E is a 3 × 3 identity matrix. There are the linear diattenuation D_L and the circular diattenuation D_c, which are defined as

The depolarization MM M_∆ can be described by:

where P = (m₂₁, m₃₁, m₄₁)^T / m₁₁ and m_∆ is

where λ₁, λ₂, and λ₃ are the eigenvalues of m_∆. The sign depends on the determinant of m′. The m′ = m_∆m_R, which can be defined by:

The depolarization ∆ can be defined as:

The linear depolarization ∆_L and the circular depolarization ∆_C can be defined as

According to Eqs. (A6) and (A7), M_R can be obtained. The fast axis of retardance vector R can be given by:

Based on the spectral data cube, the true-color images can be gotten according to the CIE 1931 RGB color space [31] using Eq. (A11):

where r(λ), g(λ), and b(λ) are the standardized CIE RGB color matching functions shown in Table A1. R, G, B are the three channels of a true color image. γ(λ) represents the spectral distribution of light stimulus, which can be seen equal to the multi-spectral data cube of m₁₁.

TABLE A1. CIE 1931 RGB color functions [29].

Wavelength (nm)	r¯ (λ)	g¯ (λ)	b¯ (λ)
430	3.109500e-001	2.730000e-002	1.467200e+000
450	2.596900e-001	5.212200e-002	1.374000e+000
480	9.194400e-002	1.390200e-001	7.559600e-001
515	2.927800e-002	6.081100e-001	1.091800e-001
550	4.363500e-001	9.949500e-001	8.782300e-003
580	9.163500e-001	8.700000e-001	1.806600e-003
610	9.923900e-001	5.030000e-001	4.288500e-004
650	2.786200e-001	1.070000e-001	2.423800e-005
690	2.218700e-002	8.210000e-003	1.313500e-006

The National Key Research and Development Project of China (2022YFD1900802); Key Research and Development Project of Shaanxi Province (2024NC-YBXM-215); Natural Science Foundation of Shaanxi Province (2024JC-YBQN-0051); Chinese Universities Scientific Fund, P. R. China (2452022382); the National Natural Science Foundation of China, P. R. China (12204380).

The authors declare no conflicts of interest.

All data generated or analyzed during this study are included in this published article.