Methods of noise suppression and decomposition in mixture Mueller partial array measurement

Abstract

The present invention relates to a method for noise suppression and decomposition in mixed Mueller matrix measurement, and proposes a theoretical model of scattering noise. A new method is proposed for Mueller matrix measurement, noise processing, complex depolarization calculation, polarization imaging, etc. of complex mixed scattering media, which solves the problem of random scattering noise in polarization measurement and polarization imaging of scattering media.

Description

Technical Field

[0001] The invention relates to a method for suppressing and decomposing noise in mixture Mueller partial array measurement, belonging to the technical field of mixture polarization. Background Art

[0002] The study of polarization of mixtures is a hot topic in the study of Mueller depolarization, which has attracted widespread attention from researchers. In the study of Foldyn et al., the components in the mixture were regarded as ideal non-depolarized substances, and the depolarization of the mixture was caused by the linear superposition of the Mueller matrix. When polarized light is irradiated on the interface of the grating, depolarization is related to the complex grating structure. In the patent number: 202210688992.6, the patent name is: Mixture Mueller Matrix Vector Synthesis Method and System Based on Similarity Parameters, the composition of the mixture is an ideal isotropic depolarized material. At present, most studies focus on ideal models and ignore the factors of non-uniform depolarization caused by multiple scattering, and few studies analyze the intrinsic polarization relationship between the mixture and the component. In actual research, it is found that when the component of the mixture is a rough scattering medium, its multiple scattering effect is more complicated, and it is difficult to explain the complex depolarization mechanism using existing methods and research. Therefore, it is necessary to conduct a more comprehensive and in-depth study on complex mixed scattering media to explain the complex depolarization mechanism.

[0003] For a mixture of two components, its depolarization is related to the incoherent superposition of reflected light at the interface of the two substances, defective optical elements, non-periodic structures, the spectral resolution of the instrument itself, etc. Therefore, it is necessary to comprehensively consider the surface structure of the substance, component composition, spectral resolution, multiple scattering and other factors.

[0004] When the target medium is a rough mixed material, it is affected by multiple scattering and reflection effects, so some traditional methods are difficult to apply. Summary of the invention

[0005] In order to solve the above technical problems, based on previous research, the present invention provides a method for noise suppression and decomposition in mixture Mueller partial array measurement, and its specific technical solution is as follows:

[0006] A method for noise suppression and decomposition in mixture Mueller partial array measurement, the specific process is:

[0007] The average light intensity detected by one pixel on the detector CCD is:

[0008]

[0009] In the formula, K DRepresents the area of ​​a pixel, a=1,2,3,...,N represents different pixels. For different polarized incident light, it is assumed that the light intensity detected by each pixel is the linear superposition of the target signal and the random scattered signal. The dynamic range of the scattered light is different.

[0010]

[0011] In the formula, l represents different polarization states, Indicates signal strength. represents the scattering intensity, Represents the light intensity of a pixel;

[0012] Then the Stokes vector of the outgoing light is

[0013]

[0014] It is expressed as:

[0015] S' u +S' v =(M u +M v )S (4)

[0016] According to formula (4), the error of scattered light intensity is transmitted to the Mueller matrix through the Stokes vector of the outgoing light; since the dynamic range of random scattering is large, its dynamic range is only related to the intensity;

[0017]

[0018] Formula (5) represents the integral of the noise matrix of all different levels of scattering intensity, i represents the scattering intensity level. In general, if the target matrix M is to be solved u The threshold segmentation method is used for light intensity. However, due to the large dynamic range of scattering, it is difficult to find a suitable threshold to remove all scattering noise. The coherence matrix of the target signal is expressed as:

[0019] H=H U +H V (6)

[0020]

[0021] In the formula, γ i is the weight coefficient; Formula (8) represents the integral of the coherence matrix corresponding to all matrices of different scattering intensities

[0022]

[0023] Eigenvalue λ of formula (8) i (i=1,2,3,4) are all equal to 0.5, and their η i=0(i=2,3,4), so using η i = 0 or a specific threshold value to determine H i And random noise is removed to obtain the coherence matrix, Mueller matrix, polarization and depolarization parameters of the target signal.

[0024] Furthermore, for scattering media, due to measurement system errors and multiple scattering, the Mueller matrix is ​​not an ideal Mueller-Jones matrix. The actual measured Mueller matrix needs to be processed for noise and error analysis. The error and decomposition error of the Mueller matrix are estimated and analyzed using the least squares method.

[0025]

[0026] Where V A 、V B Respectively represent the row vector form of Mueller matrix A and B, Convert the Mueller matrix into a vector for processing. In the formula, ||.|| represents the 2-norm of the residual R, and the coefficients satisfy ω A +ω B =1, the least square method is used to calculate the decomposition coefficient to reduce the experimental error;

[0027] Converting the Mueller matrix into a row vector form facilitates the calculation of linear fitting coefficients, accurately evaluates the errors of different data points, and performs data correction and error estimation.

[0028] The beneficial effects of the present invention are:

[0029] In traditional research, the components of the mixture are usually regarded as ideal non-depolarized substances, and the components are ideal isotropic depolarized substances. The depolarization of the mixture is caused by the linear superposition of the Mueller matrix. For a mixture of two components, its depolarization is related to the incoherent superposition of reflected light on the interface of the two substances, defective optical elements, non-periodic structures, and the spectral resolution of the instrument itself. Therefore, it is necessary to comprehensively consider the surface structure, component composition, spectral resolution, multiple scattering and other situations of the substance. In actual research, it is found that when the component of the mixed substance is a rough scattering medium, its scattering effect is more complicated, the intensity of the random scattering signal is not high, and the dynamic range of the scattering noise is large. It is difficult to accurately measure the Mueller matrix of the mixture using existing methods and explain the complex depolarization mechanism. At the same time, due to the influence of noise, the contrast between different components in the mixture is low and it is difficult to distinguish, which greatly limits the research of Mueller polarization technology on complex mixtures. Therefore, it is necessary to invent a new method for measuring the Mueller matrix of complex mixed scattering media, noise processing, complex depolarization calculation, polarization imaging, etc., which solves the problem of random scattering noise in polarization measurement and polarization imaging of scattering media.

[0030] The present invention takes into account that when the target medium is a rough mixed material, it is affected by multiple scattering and reflection effects, and proposes a new method based on the Mueller matrix decomposition and polarization of the rough mixture. In practical applications, these characteristic parameters are used to perform polarization imaging for verification.

[0031] The invention suppresses noise and improves experimental accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is a sample diagram of a mixture in an embodiment of the present invention,

[0033] Figure 2 is a linear fitting coefficient diagram in an embodiment of the present invention,

[0034] Where (a) is the coefficient ω of graphite A , (b) is the coefficient ω of polypropylene B ;

[0035] Figure 3 is the mixture intensity image in the embodiment of the present invention,

[0036] Among them, (a) is the intensity image, (b) is the three-dimensional distribution;

[0037] Figure 4 is a three-dimensional morphological image of the mixed material in an embodiment of the present invention,

[0038] Wherein, (a) is graphite, (b) is polypropylene;

[0039] Figure 5 is the eigenvalue image in the embodiment of the present invention,

[0040] Where (a) is λ 1 , (b) is λ 2 , (c) is λ 3 , (d) is λ 4 ;

[0041] Figure 6 is an IPPs image in an embodiment of the present invention,

[0042] Where (a) is P 1 , (b) is P 2 , (3) is P 3 , (4) is P 4 ;

[0043] Figure 7 is the graphite IPPs image in the embodiment of the present invention,

[0044] Among them, (a) is P1, (b) is P2, (3) is P3, and (4) is P4;

[0045] Figure 8 is the relative polarization degree image in the embodiment of the present invention,

[0046] Among them, (a) is the depolarization coefficient, (b) is (c) (d) DETAILED DESCRIPTION

[0047] The present invention will now be described in further detail with reference to the accompanying drawings. These drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the components related to the present invention.

[0048] Combination Figure 2 It can be seen that in most cases, the surface of the medium is rough. For rough multiple scattering media, the noise is mainly random scattering noise. Therefore, this patent proposes a theoretical model of scattering noise to solve the problem of random scattering noise in polarization measurement and polarization imaging of scattering media.

[0049] The average light intensity detected by one pixel on the detector CCD is:

[0050]

[0051] In the formula, K D Represents the area of ​​a pixel, a=1,2,3,...,N represents different pixels. For different polarized incident light, it is assumed that the light intensity detected by each pixel is the linear superposition of the target signal and the random scattered signal. The dynamic range of the scattered light is different.

[0052]

[0053] In the formula, l represents different polarization states, Indicates signal strength. represents the scattering intensity, Represents the light intensity of a pixel.

[0054] Then the Stokes vector of the outgoing light is

[0055]

[0056] It can be expressed as:

[0057] S' u +S' v =(M u +M v )S (4)

[0058] According to formula (4), the error of scattered light intensity is transmitted to the Mueller matrix through the Stokes vector of the outgoing light. Since the dynamic range of random scattering is large, its dynamic range is only related to the intensity.

[0059]

[0060] Formula (5) represents the integral of the noise matrix of all different levels of scattering intensity, i represents the scattering intensity level. In general, if the target matrix M is to be solved u A threshold segmentation method can be used for light intensity. However, due to the large dynamic range of scattering, it is difficult to find a suitable threshold to remove all scattering noise. The coherence matrix of the target signal can be expressed as

[0061] H=H U +H V (6)

[0062]

[0063] In the formula, γ i is the weight coefficient. Formula (8) represents the integral of the coherence matrix corresponding to all matrices of different scattering intensities:

[0064]

[0065] Eigenvalue λ of formula (8) i (i=1,2,3,4) are all equal to 0.5, and their η i =0(i=2,3,4). Therefore, we can use η i = 0 or a specific threshold value to determine H i And random noise is removed to obtain the coherence matrix, Mueller matrix, polarization and depolarization parameters of the target signal.

[0066] In order to verify the patented method, a mixture sample was selected for experiment. The mixture in the experiment was a mixture of graphite and polypropylene. Unlike the patent number: 202210688992.6, the patent name is: Research on the vector synthesis method and system of the mixture Mueller matrix based on similarity parameters, the mixture sample increases the roughness of graphite and polypropylene, so that the two are in full contact and the surface level height is basically the same. The refractive index of graphite is 2.8, and the refractive index of polypropylene is 1.5. The three-dimensional morphology and roughness of the sample were tested using the white light interferometer (SuperView W1) produced by Zhongtu Instruments, the surface structural characteristics of the mixture were analyzed, and the 0.96*0.96mm area in the center of the sample was divided into three equal parts for line roughness evaluation. The instrument parameters are: resolution of 1024×1024; step height measurement: accuracy of 0.3%, repeatability of 0.08%; Z-direction resolution: 0.1nm; roughness RMS repeatability: 0.005nm. Objective lens: 10X eyepiece: 0.5X.

[0067] Error analysis and data correction

[0068] For scattering media, due to measurement system errors and multiple scattering, the Mueller matrix is ​​not an ideal Mueller-Jones matrix. The actual measured Mueller matrix needs to be processed for noise, error analysis, etc. This embodiment uses the least squares method to estimate and analyze the error and decomposition error of the Mueller matrix.

[0069]

[0070] V A 、V B Respectively represent the row vector form of Mueller matrix A and B, Convert the Mueller matrix into a vector. In the formula, . represents the 2-norm of the residual R, and the coefficient satisfies ω A +ω B = 1. The least square method is used to calculate the decomposition coefficient and reduce the experimental error.

[0071] Converting the Mueller matrix into a row vector form facilitates the calculation of linear fitting coefficients, accurately evaluates the errors of different data points, and performs data correction and error estimation.

[0072]

[0073]

[0074] from Figure 2 It can be found that ω A ,ω B The slopes of the two straight lines are 0.3451 and 0.6549 respectively, R 2 It is close to 1, indicating that the fitting result is accurate and reliable. There are two points with large errors in the figure, corresponding to M in the Mueller matrix of the mixture. 11 、M 34 This is mainly caused by random scattering on the surface, which reduces the light intensity entering the detector. According to the fitting equation in the curve, the mixture is calculated The theoretical value is 1.15e -4 Therefore, the M of the mixture Mueller matrix element 11 The maximum relative error is -6.7%, which is mainly due to the fact that the first element of the Mueller matrix reflects the total scattering intensity of the medium, and a small amount of random scattering is not detected by the detector. Figure 2 It can be found that the relative errors of different elements of the Mueller matrix are different. The Mueller matrix of a mixture is easily disturbed by random scattering during calculation. Using the method in this chapter, it is easy to identify the "bad points" in the data and perform error estimation and denoising.

[0075] Polarization imaging of mixed materials

[0076] like Figure 3 (a) is a mixed coded image obtained from 36 images. There is an arc-shaped dividing line in the center of the mixed material, which is caused by the gap between the two materials during processing and assembly. The left side of the dividing line is graphite, and the right side is polypropylene. Figure 3 (b) in the figure shows the three-dimensional distribution of the intensity image. The experiment found that due to the different scattering of the rough surface of the sample, the intensity distribution of the outgoing light is not an ideal Gaussian pattern. The edges of the mixture image are obviously diffused, and the scattered photons reduce the resolution and contrast of the imaging. The contrast between graphite and polypropylene is 1.52. The grayscale image shows that there is a difference in the intensity of scattered light on the surface of the two substances, and the surface distribution is uneven. Therefore, it is difficult to directly use intensity information to distinguish between the two substances.

[0077] The three-dimensional morphology of the surfaces of the two materials is as follows Figure 4 As shown in the figure, the graphite surface is distributed in regular stripes, the polypropylene surface is a random distribution structure of irregular surface particles, and the surface average roughness (R a ) are 7.19um and 2.59um respectively. This is related to the physical properties and processing of graphite materials. Graphite has a layered structure and has obvious regularly distributed stripes during processing. Polypropylene has a random surface structure composed of organic particles.

[0078] The eigenvalue image of the mixture is as follows Figure 5 As shown. Figure 5 In (a), the image shows that the reflection of the two samples is relatively uniform. Figure 5 In (c)-(d), the scattering effect of graphite is very small, so there is almost no surface texture and detail information of polypropylene in the image. i (i=2,3,4) It can be seen that polypropylene has greater light scattering and depolarization effects than graphite.

[0079] Figure 6 This is the IPPs image of the mixture. It can be seen from the IPPs image that the noise at the edge of the image is basically suppressed. Figure 6 The contrasts of graphite and polypropylene in (a)-(d) are 1.50, 2.03, 1.68, and 1.72, respectively, and images with different contrasts are obtained.

[0080] The Mueller matrix reflects the macroscopic polarization characteristics of the material, and cannot reflect the details of the surface of the material. The polarization image can reflect the details of the surface structure of the material. In actual polarization imaging, due to the uneven distribution of the signal intensity of the scattered light, the large dynamic range, and the small contrast, it is difficult to directly separate the two materials using the intensity information, but they can be distinguished by using the difference in their polarization scattering properties. Since the contrast is relatively close, the dynamic range of the scattering intensity is large. According to the difference in scattering and depolarization of the two materials, the appropriate threshold can be selected to segment and extract the image, and the method of this patent can be used to separate the two materials. Used as threshold for image segmentation. Figure 7 for The IPPs image of graphite was extracted using a threshold value of 0.25, achieving complete segmentation.

[0081] exist Figure 7 In the figure, the graphite IPPs images have different contrast and clarity, and the IPPs images of polypropylene almost disappear completely because their values ​​are close to 0.

[0082] The depolarized image is Figure 8 As shown, in Figure 8 The depolarization coefficient image in (a) shows that the depolarization of graphite is smaller than that of polypropylene. This is mainly because the roughness of polypropylene is greater than that of graphite, and its surface scattering is stronger than that of graphite. Figure 8 In (b), the image of graphite is extracted, while the image of polypropylene almost disappears completely. The main reason is that under linear polarized light, the scattering difference of the graphite surface is much greater than that of polypropylene, while its depolarization coefficient is smaller than that of polypropylene. According to Table 1, the scattering difference of graphite surface is much greater than that of polypropylene. For polypropylene 12.68. Figure 8 As shown in (c), polypropylene almost disappears because its depolarization degree is close to the average depolarization degree in the 45° polarization state, while the depolarization degree of graphite is slightly larger than the average. Figure 8 (d) is the depolarized image under circular polarized light. Since its value is negative, an absolute value operation is performed on it. The image is Figure 8 Similar to (a) in . Figure 8 It can be seen that the parameters of depolarization are sensitive to the inhomogeneous structure of rough surface materials and can reflect the large dynamic range of depolarization related to scattering. Therefore, this method can effectively improve the contrast of polarization images and be applied to target decomposition, material classification, target recognition, etc.

[0083] Table 1 Mueller matrix decomposition results of mixed substances

[0084]

[0085] The similarity parameter of the Mueller Jones matrices of graphite and polypropylene calculated from Table 1 is cosθ, which is 0.9503, SD is 0.9751, and the depolarization coefficient caused by the superposition of the Mueller Jones matrices is 0.0168. Because the Mueller Jones matrices of the two substances have a high similarity, the depolarization degree caused by the linear superposition of the Mueller Jones matrices of the two substances is small, the decomposition coefficient of graphite is 0.4255, and the decomposition coefficient of polypropylene is 0.5745. The depolarization matrix of the mixture can be expressed as

[0086]

[0087] In the formula, the theoretical value of the depolarization coefficient of the mixture caused by scattering is 0.3489. According to the above error analysis and data correction method, the Mueller matrix element of the mixture is corrected, because M 11 The error is the largest, and other errors are ignored. The Mueller matrix of the mixed substance becomes

[0088]

[0089] The depolarization coefficient of the Mueller matrix in formula (33) after element correction is 0.3715. Considering the depolarization effect caused by the superposition of the Mueller-Jones matrices of the two substances, the total depolarization coefficient of the mixture is 0.3657, and the relative error between the two is 1.6%. The experimental error is reduced after calibration. Therefore, at an incident angle of 45 degrees, the depolarization of the mixed substance is mainly caused by multiple scattering of the rough surfaces of graphite and polypropylene.

[0090] Based on the above ideal embodiments of the present invention, the relevant staff can make various changes and modifications without departing from the technical concept of the present invention through the above description. The technical scope of the present invention is not limited to the contents of the specification, and its technical scope must be determined according to the scope of the claims.

Claims

1. A method for noise suppression and decomposition in mixture Mueller partial array measurement, characterized in that: The specific process is: the average light intensity detected by one pixel on the detector CCD is: In the formula, K D Represents the area of ​​a pixel, a=1,2,3,...,N represents different pixels. For different polarized incident light, it is assumed that the light intensity detected by each pixel is the linear superposition of the target signal and the random scattered signal. The dynamic range of the scattered light is different. In the formula, l represents different polarization states, Indicates signal strength, represents the scattering intensity, Represents the light intensity of a pixel; Then the Stokes vector of the outgoing light is It is expressed as: S u '+S' v =(M u +M v )S (4) According to formula (4), the error of scattered light intensity is transmitted to the Mueller matrix through the Stokes vector of the outgoing light; since the dynamic range of random scattering is large, its dynamic range is only related to the intensity; Formula (5) represents the integral of the noise matrix of all different levels of scattering intensity, i represents the scattering intensity level. In general, if the target matrix M is to be solved u The threshold segmentation method is used for light intensity. However, due to the large dynamic range of scattering, it is difficult to find a suitable threshold to remove all scattering noise. The coherence matrix of the target signal is expressed as: H=H U +H V (6) In the formula, γ i is the weight coefficient; Formula (8) represents the integral of the coherence matrix corresponding to all matrices of different scattering intensities Eigenvalue λ of formula (8) i All are equal to 0.5, where i = 1, 2, 3, 4; η i =0, where i = 2, 3, 4, so using η i = 0 or a specific threshold value to determine H i And random noise is removed to obtain the coherence matrix, Mueller matrix, polarization and depolarization parameters of the target signal.

2. The method for noise suppression and decomposition in mixture Mueller partial array measurement according to claim 1, characterized in that: For scattering media, due to measurement system errors and multiple scattering, the Mueller matrix is ​​not an ideal Mueller-Jones matrix. The actual measured Mueller matrix needs to be processed for noise and error analysis. The error and decomposition error of the Mueller matrix are estimated and analyzed using the least squares method. Where V A 、V B Respectively represent the row vector form of Mueller matrix A and B, Convert the Mueller matrix into a vector for processing. In the formula, ||.|| represents the 2-norm of the residual R, and the coefficients satisfy ω A +ω B =1, the least square method is used to calculate the decomposition coefficient to reduce the experimental error; Converting the Mueller matrix into a row vector form facilitates the calculation of linear fitting coefficients, accurately evaluates the errors of different data points, and performs data correction and error estimation.

Images