Method for three-dimensional reconstruction of plasma emission spectrum intensity based on path length weight

Abstract

The application provides a plasma emission spectrum intensity three-dimensional reconstruction method based on a path length weight matrix, calculates the integral path length average value of light rays emitted from four vertexes of each plasma image and passing through a space voxel as the contribution degree of the voxel to the pixel; the contribution degree is used as a weight coefficient to construct a weight projection matrix; the relationship between the gray value vector of the plasma image pixel and the emission spectrum intensity of the voxel is established according to the weight projection matrix, and the emission spectrum intensity of the voxel is solved to realize the three-dimensional reconstruction of the plasma emission spectrum intensity. The application considers the refraction factor when the light rays pass through the camera lens and the influence of the gap between the voxels, and the three-dimensional path length information when the projection light rays pass through the unit voxel is used in the calculation, so that the weight projection matrix is more accurately calculated, and the three-dimensional reconstruction of the plasma emission spectrum intensity is more accurate.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of three-dimensional reconstruction, and particularly relates to a plasma emission spectrum intensity three-dimensional reconstruction method based on path length weight BACKGROUND

[0002] The plasma emission spectrum intensity reflects the form and spatial density distribution of the plasma, and plays an important role in plasma welding, ICP plasma wind tunnel, etc. The single-wavelength plasma emission spectrum intensity can also be used to invert the plasma electron temperature and electron density, and the three-dimensional distribution of the plasma emission spectrum intensity can be used to invert the three-dimensional spatial distribution of the plasma physical parameters.

[0003] The three-dimensional reconstruction technology of the emission spectrum intensity based on the light-emitting ability of the plasma itself is also called emission spectrum tomography technology. At present, the commonly used sensor is a CCD or CMOS pixel array, that is, a digital camera. The methods adopted by researchers mainly include surface tomography method and volume tomography method. The surface tomography method is derived from the early CT (Computed Tomography) method, which assumes that the light does not refract and converge when passing through the camera lens (the characteristic of X-ray), and the geometric model is a parallel projection model. It is an approximate method in the stage when researchers do not have a deep understanding of the geometric model of camera imaging. This model cannot be established when the camera is close to the object and the focal length is small.

[0004] The volume tomography method considers the difference between the imaging model of the camera and the X-ray imaging model of the CT machine. The imaging of the camera for visible light, infrared and ultraviolet light is a pinhole imaging model. When the light passes through the lens in front of the camera image sensor array, the light will refract and converge. The volume tomography method divides the space into several voxel units, and the emission spectrum intensity of each voxel is approximately constant. Each voxel is projected to the image plane according to the light propagation direction, that is, the energy is propagated to the image pixel. Each image pixel receives different energy and forms different gray scales. The different energy is different in size, which is called weight matrix, and represents the energy contribution of each voxel in the space to each pixel in the image.

[0005] The calculation of the weight matrix is a difficult and important point in the tomographic method. The existing literature (Zhou Z, Tian D, Wu Z, et al. 3-D reconstruction of flame temperature distribution using tomographic and two-color plyometric techniques [J]. IEEE Transactions on Instrumentation and Measurement, 2015, 64(11): 3075-3084.); Zhong Zhou et al. proposed to regard the unit voxel as a spherical shape for the three-dimensional reconstruction of the emission spectrum intensity, wherein the weight coefficient is calculated using the angle between the principal axis and the sphere. This method does not involve the pinhole imaging principle of the camera in actual use, and the calculated weight matrix is not very accurate due to the gap influence between the spherical voxels.

[0006] The existing literature (Goyal A, Chaudhry S, Subbarao P M V. Direct three dimensional tomography of flames using maximization of entropy technique [J]. Combustion and flame, 2014, 161(1): 173-183.) proposes to use a coarse square beam model when performing three-dimensional reconstruction of the flame, but this model considers that the light rays will not be refracted when passing through the camera lens, and the calculation process is complex.

[0007] The existing literature (Deng Zhun. Three-dimensional reconstruction of flame intensity field based on emission spectrum tomography method [D]. Xi'an University of Electronic Science and Technology, 2019. DOI: 10.27389 / d.cnki.gxadu.2019.000935.) proposes a weight coefficient algorithm based on the projection area. This calculation method is relatively simple because it only uses the two-dimensional area of the projection light, but the actual projection light projection is not only two-dimensional information, so the weight matrix calculated by this method lacks spatial information. SUMMARY

[0008] In order to solve the above problems existing in the prior art, the present application provides a three-dimensional reconstruction method of plasma emission spectrum intensity based on path length weight. The technical problems to be solved by the present application are realized by the following technical solutions:

[0009] The three-dimensional reconstruction method of plasma emission spectrum intensity based on path length weight provided by the present application comprises:

[0010] Step 1: calibrate the internal and external parameters of the camera;

[0011] Step 2: use the calibrated camera and the synchronous trigger device to shoot the plasma images at the same time;

[0012] Step 3: calculate the average integral path length of the light rays emitted from the four vertices of the pixel through the space voxels in each plasma image;

[0013] Step 4: take the average integral path length of the light rays emitted from the four vertices of the pixel through the voxels as the contribution of the voxels to the pixel;

[0014] Step 5: take the contribution as the weight coefficient to construct the weight projection matrix;

[0015] Step 6: according to the weight projection matrix, establish the relationship between the gray value vector of the pixel of the plasma image and the emission spectrum intensity of the voxel, and solve the emission spectrum intensity of the voxel to realize the three-dimensional reconstruction of the plasma emission spectrum intensity.

[0016] Optionally, before the step 3, the plasma emission spectrum intensity three-dimensional reconstruction method based on path length weight further comprises:

[0017] graying, distortion correction and image filtering are performed on the plasma images;

[0018] The gray value of each plasma image is converted into the gray value of the pixel.

[0019] Optionally, the gray value i of the pixel p is h The emission spectrum intensity of each voxel is integrated along the light ray L to obtain, which is expressed as:

[0020]

[0021] wherein the light ray L passes through n voxels, and the emission spectrum intensity values of the voxels are x1, x2, …, xn respectively; n the path lengths of the light ray L passing through the voxels are l1, l2, …, ln respectively; n and the distance from the pixel p to the first voxel is l0; the gray value vector I of the pixel is composed of the gray values.

[0022] Optionally, the step 3 comprises:

[0023] Step 31: according to the geometric relationship between the three-dimensional coordinate point in the world coordinate system and the two-dimensional projection point on the projection plane, determine the relationship between the pixel coordinate system and the image coordinate system;

[0024] Step 32: According to the relationship between the pixel coordinate system and the image coordinate system, and the relationship between the camera coordinate system and the world coordinate system, the coordinates of the pixel in the world coordinate system are obtained;

[0025] Step 33: The homogeneous coordinates of the pixel on the image plane in the world coordinate system are connected with the three-dimensional homogeneous coordinates of the camera optical center in the world coordinate system, to obtain the path of the light ray from each pixel of the plasma image passing through the spatial voxel;

[0026] Step 34: The integral path lengths of the four paths passing through each voxel in space are calculated, and the average of the four integral path lengths is obtained to obtain the integral path length of the voxel corresponding to the pixel.

[0027] Optionally,

[0028] The relationship between the pixel coordinate system and the image coordinate system is

[0029]

[0030] wherein the coordinates of the pixel p in the pixel coordinate system are (u, v) T , the two-dimensional coordinates in the image coordinate system are (x, y) T , the three-dimensional coordinates in the camera coordinate system are (X c , Y c , Z c ) T , and the coordinates in the world coordinate system are (X w , Y w , Z w ) T , dx and dy are the physical sizes of the pixel in the horizontal and vertical directions, respectively;

[0031] The relationship between the coordinates of the pixel in the world coordinate system is

[0032]

[0033] wherein f is the focal length of the camera, the three-dimensional coordinates of the pixel in the camera coordinate system are (X c , Y c , Z c ) T =(x, y, f) T , R is the rotation matrix of the camera coordinate system relative to the world coordinate system, t is the translation matrix of the camera coordinate system relative to the world coordinate system, (u0, v0) T , the focal length f, R, and t can be obtained by camera calibration;

[0034] The integral path length of the pixel to the voxel is

[0035]

[0036] wherein, the vertex coordinate of the left lower corner of the pixel is (u, v), the vertex coordinate of the left upper corner of the pixel is (u, v+1), the vertex coordinate of the right upper corner of the pixel is (u+1, v+1), and the vertex coordinate of the right lower corner of the pixel is (u, v+1).

[0037] Optionally, the contribution degree of each voxel to each pixel is:

[0038] w hk =l hk

[0039] wherein, w hk represents the contribution of the kth voxel to the hth pixel, l hk represents the integral path length of the light ray L passing through the hth pixel in the kth voxel.

[0040] Optionally, the relationship between the weight projection matrix, the gray value vector of the pixel of the plasma image and the emission spectrum intensity of the voxel in step 6 is:

[0041] WX=I

[0042] I is the gray value vector of the pixel of the two-dimensional image, W is the projection weight matrix, X is the emission spectrum intensity matrix of the voxel, and is the unknown to be solved.

[0043] The present application has the following beneficial effects:

[0044] The present application provides a plasma emission spectrum intensity three-dimensional reconstruction method based on path length weight, which shoots the plasma images at the same time through the calibrated camera and the synchronous trigger device; calculates the average value of the integral path length of the light ray passing through the space voxel from the four vertexes of the pixel in each plasma image, calculates the contribution degree of the voxel to the pixel; takes the contribution degree as the weight coefficient, constructs the weight projection matrix; establishes the relationship between the gray value vector of the pixel of the plasma image and the emission spectrum intensity of the voxel according to the weight projection matrix, solves the emission spectrum intensity of the voxel, so as to realize the three-dimensional reconstruction of the plasma emission spectrum intensity. The present application considers the refraction factor when the light ray passes through the camera lens and the influence of the gap between the voxels, and utilizes the three-dimensional path length information when the projection light ray passes through the unit voxel in the calculation, so that the present application can more accurately calculate the weight projection matrix, and thus can more accurately perform the three-dimensional reconstruction of the plasma emission spectrum intensity.

[0045] The present application will be further described in detail below in combination with the drawings and embodiments. BRIEF DESCRIPTION OF DRAWINGS

[0046] Figure 1is a flowchart of a method for three-dimensional reconstruction of plasma emission spectrum intensity based on path length weight provided by an embodiment of the application;

[0047] Figure 2 is an integral intensity diagram provided by an embodiment of the application;

[0048] Figure 3 is a schematic diagram of the geometric relationship between a three-dimensional coordinate point and a two-dimensional projection point on a projection plane in a world coordinate system provided by an embodiment of the application;

[0049] Figure 4 is a schematic diagram of integral path length calculation provided by an embodiment of the application;

[0050] Figure 5 is a schematic diagram of a projection matrix model based on path length weight provided by an embodiment of the application;

[0051] Figure 6 is a uv plane diagram for projection weight calculation provided by an embodiment of the application. DETAILED DESCRIPTION

[0052] The application will be further described in detail below with reference to specific embodiments, but the embodiments of the application are not limited thereto.

[0053] As shown in Figure 1 , the application provides a method for three-dimensional reconstruction of plasma emission spectrum intensity based on path length weight, which comprises the following steps:

[0054] Step 1: calibrate the internal and external parameters of a camera;

[0055] Step 2: use the calibrated camera and a synchronous triggering device to shoot plasma images at the same time;

[0056] The application then performs grayscale, distortion correction and image filtering on the plasma images, and converts the grayscale values of each plasma image into the grayscale values of image elements.

[0057] Referring to Figure 2 , the plasma to be reconstructed is a self-luminous flow field, and the space where the plasma is located is divided into multiple unit cubic voxels, and each unit cubic voxel is regarded as a point light source. The light rays emitted by each point light source are not affected by other factors in the propagation process, and the absorption and refraction between the light rays emitted by each point light source are ignored, i.e., the plasma to be reconstructed satisfies the point light source symmetry and the optical thinness, and the grayscale value i h of the image element p obtained by the camera is regarded as the linear integral result of the emission spectrum intensity of each point light source on the light propagation path.

[0058] As shown in Figure 2As shown, assuming that the emission spectrum intensity of each voxel is uniformly distributed, the spatial voxel is projected onto the image pixel by the camera, the gray value of the image pixel is related to the emission spectrum intensity of the voxel, and is also related to the spatial geometric position of the pixel and the voxel, the mapping relationship is called the weight projection matrix, and the following equation can be established:

[0059] WX=I (1)

[0060] Wherein, I is a two-dimensional image pixel gray value vector, is a known quantity; X is the emission spectrum intensity matrix of the voxel, is an unknown quantity to be solved; W is the projection weight matrix, that is, the contribution value of each voxel to each unit pixel, which is determined by the geometric relationship between the three-dimensional unit voxel and the image pixel. The gray value vector I of the pixel is composed of gray values.

[0061] Step 3: Calculate the average value of the integral path length of the light ray emitted from the four vertices of each plasma image pixel through the spatial voxel;

[0062] As an optional embodiment of the application, the step 3 comprises:

[0063] Step 31: According to the geometric relationship between the three-dimensional coordinate point in the world coordinate system and the two-dimensional projection point on the projection plane, the relationship between the pixel coordinate system and the image coordinate system is determined;

[0064] Step 32: According to the relationship between the pixel coordinate system and the image coordinate system, the relationship between the camera coordinate system and the world coordinate system, the coordinates of the pixel in the world coordinate system are obtained;

[0065] Step 33: The homogeneous coordinates of the pixel in the world coordinate system on the image plane are connected with the three-dimensional homogeneous coordinates of the camera optical center in the world coordinate system, and the path of the light ray emitted from the four vertices of each plasma image pixel through the spatial voxel is obtained;

[0066] Step 34: Calculate the integral path length of the four light rays through the spatial voxel, and take the average value of the four integral path lengths to obtain the integral path length of the pixel corresponding to the voxel.

[0067] Suppose that the light ray L passes through n voxels, and the emission spectrum intensity values of these voxels are x1, x2, …, x n The path lengths of the light ray L through the voxel grid are l1, l2, …, l n , and the distance from the pixel p to the first voxel is l0, according to the light intensity integral model, the gray value i h of the unit pixel p is obtained by integrating the emission spectrum intensity of each voxel along the light ray L, then

[0068]

[0069] According to formula (1), the essence of the projection weight matrix is to calculate the contribution of the emission spectrum intensity of each voxel to the gray value of each pixel, that is, the proportion of the energy of the voxel allocated to the pixel.

[0070] Step 4: Shoot a light ray through the average integral path length of the voxel to the four vertices of the pixel as the contribution of the voxel to the pixel;

[0071] According to formula (2), the integral path length l of the light ray L through the voxel k represents the contribution of the voxel k to the pixel i h , that is

[0072] w hk = l hk (3)

[0073] where w hk represents the contribution of the kth voxel to the hth pixel, that is, the weight coefficient, and l hk represents the integral path length of the light ray L through the hth pixel in the kth voxel.

[0074] The integral path length l is solved by the following method.

[0075] Figure 3 The geometric relationship between the three-dimensional coordinate point in the world coordinate system and the two-dimensional projection point on the camera projection image plane is shown in the figure, wherein O0-uv is the pixel coordinate system, O1-xy is the image coordinate system, O2-X C Y C Z C is the camera coordinate system, and O3-X w Y w Z w is the world coordinate system. The image plane is perpendicular to the principal axis of the camera and intersects the principal point (u0, v0) T , the camera optical center C coincides with the origin O2 of the camera coordinate system, and the distance between the image plane and the optical center C is the focal length f.

[0076] Let the coordinates of the pixel in the pixel coordinate system be (u, v) T , the two-dimensional coordinates in the image coordinate system be (x, y) T , the three-dimensional coordinates in the camera coordinate system be (X c , Y c , Z c ) T , and the coordinates in the world coordinate system be (X w , Y w , Z w ) T . The relationship between the pixel coordinate system and the image coordinate system is

[0077]

[0078] where dx and dy are the physical size of the pixel in horizontal and vertical direction respectively.

[0079] The pixel is located on the image plane of the camera, which is located on the Z C plane in the camera coordinate system, where f is the focal length of the camera. Then the three-dimensional coordinates of the pixel in the camera coordinate system (X c , Y c , Z c ) T = (x, y, f) T . According to the relationship between the camera coordinate system and the world coordinate system, the coordinates of the pixel in the world coordinate system are obtained as

[0080]

[0081] where R is the rotation matrix of the camera coordinate system relative to the world coordinate system, t is the translation matrix of the camera coordinate system relative to the world coordinate system, (u0, v0) T , focal length f, R, t in formula (4) (5) can be obtained by camera calibration.

[0082] According to formula (5), the homogeneous coordinates of the pixel on the image plane in the world coordinate system are recorded as P = (X w , Y w , Z w , 1) T , the three-dimensional homogeneous coordinates of the camera optical center in the world coordinate system are C, and the line connecting the two points is L, and the surface planes of the cubic voxel are π1 to π6, and the straight line L intersects the surface of the cubic voxel at two points A and B, as shown in Figure 4 .

[0083] If P and C are expressed using homogeneous coordinates, the straight line L connecting the two points P and C can be expressed by a 4x4 skew-symmetric homogeneous matrix

[0084] L = PC T - CP T (6)

[0085] Let the six surface planes of the unit voxel be π i (i = 1, 2,..., 6), then the six intersection points M i

[0086] M i = Lπ i , i = 1, 2,..., 6 (7)

[0087] It is known that only two of the six intersection points are located on the surface of the unit voxel, and let the two points be A and B, then the distance between A and B is

[0088] l=dist(A,B) (8)

[0089] The above distance is calculated for each voxel in space and each pixel in projection.

[0090] The above method regards the coordinates of the pixel as a point on the image plane, but in practice, the pixel is a sensor with a certain area, so it is proposed to calculate the integral path length of the light rays passing through the four vertices of the pixel in the voxel, as shown in the (a) of Fig. Figure 5 , instead of calculating the integral path length of the light rays passing through the center point of the pixel, as shown in the (b) of Fig. Figure 5 .

[0091] Let the coordinates of the lower left corner of the pixel be (u, v), as shown in Fig. Figure 6 . The integral path lengths of the light rays passing through the four vertices of the pixel in the voxel are calculated, and their average is taken as the integral path length l(p) of the pixel to the voxel, that is,

[0092]

[0093] The integral path length between the kth voxel and the hth pixel is calculated by formula (9), and the weight coefficient between each voxel and pixel in the weight matrix can be obtained according to formula (3).

[0094] Step 5: Construct a weight projection matrix by taking the contribution as the weight coefficient.

[0095] Step 6: According to the weight projection matrix, the relationship between the gray value vector of the plasma image pixel and the emission spectrum intensity of the voxel is established, and the emission spectrum intensity of the voxel is solved to realize the three-dimensional reconstruction of the plasma emission spectrum intensity.

[0096] After obtaining the weight projection matrix, the formula (1) is solved to obtain the emission spectrum intensity X of the voxel, so that the three-dimensional reconstruction of the plasma emission spectrum intensity is realized.

[0097] The application provides a plasma emission spectrum intensity three-dimensional reconstruction method based on path length weight, which comprises the following steps: calibrating the internal and external parameters of a camera; using the calibrated camera and a synchronous trigger device to shoot plasma images at the same time; calculating the average integral path length of light rays from four vertices of a pixel in each plasma image; taking the corresponding integral path length as the contribution of the voxel to the pixel; taking the contribution as a weight coefficient to construct a weight projection matrix; establishing the relationship between the gray value vector of the pixel of the plasma image and the emission spectrum intensity of the voxel according to the weight projection matrix, and solving the emission spectrum intensity of the voxel, so as to realize the three-dimensional reconstruction of the plasma emission spectrum intensity. The application takes into account the refraction factor when the light rays pass through the camera lens and the influence of the gap between the voxels, and uses the three-dimensional path length information of the projection light rays when passing through the unit voxel during the calculation, so that the weight projection matrix is calculated more accurately, and the three-dimensional reconstruction of the plasma emission spectrum intensity is more accurate.

[0098] In addition, the terms "first", "second", "third", etc. are used only to describe the purpose and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first", "second", etc. can explicitly or implicitly include one or more of the features. In the description of the application, the meaning of "a plurality of" is two or more, unless otherwise specifically limited.

[0099] Although the application is described herein in conjunction with various embodiments, other variations of the disclosed embodiments can be understood and implemented by those skilled in the art by viewing the drawings, disclosure and appended claims during the implementation of the claimed application. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "one" does not exclude a plurality.

[0100] The above is a further detailed description of the application in conjunction with specific preferred embodiments, and cannot be considered as limiting the specific implementation of the application to these descriptions. For those skilled in the art, without departing from the concept of the application, a number of simple deductions or substitutions can be made, which should be considered as falling within the protection scope of the application.

Claims

1. A method for three-dimensional reconstruction of plasma emission spectrum intensity based on path length weight, characterized in that, The application relates to a kind of plasma emission spectrum intensity three-dimensional reconstruction method based on path length weight, which comprises the following steps: Step 1: calibrating the internal and external parameters of a camera; Step 2: using the calibrated camera and a synchronous trigger device to shoot plasma images at the same time; Step 3: calculating the average integral path length of light rays emitted from the four vertices of each pixel in each plasma image through space voxels; Step 4: taking the average integral path length of light rays emitted from the four vertices of each pixel through voxels as the contribution of voxels to the pixel; Step 5: taking the contribution as a weight coefficient to construct a weight projection matrix; Step 6: establishing the relationship between the gray value vector of the pixel of the plasma image and the emission spectrum intensity of the voxel according to the weight projection matrix, and solving the emission spectrum intensity of the voxel to realize the three-dimensional reconstruction of the plasma emission spectrum intensity. The step 3 comprises the following steps: Step 31: determining the relationship between the pixel coordinate system and the image coordinate system according to the geometric relationship between the three-dimensional coordinate point in the world coordinate system and the two-dimensional projection point on the projection plane; the relationship between the pixel coordinate system and the image coordinate system is wherein the coordinates of the pixel p in the pixel coordinate system are (u, v) T , and the two-dimensional coordinates in the image coordinate system are (x, y) T , and the three-dimensional coordinates in the camera coordinate system are (X c , Y c , Z c ) T , and the coordinates in the world coordinate system are (X w , Y w , Z w ) T , and dx and dy are the physical sizes of the pixel in the horizontal and vertical directions, respectively; Step 32: obtaining the coordinates of the pixel in the world coordinate system according to the relationship between the pixel coordinate system and the image coordinate system and the relationship between the camera coordinate system and the world coordinate system; the relationship between the coordinates of the pixel in the world coordinate system is wherein f is the focal length of the camera, the three-dimensional coordinates (X c , Y c , Z c ) of the image element in the camera coordinate system, and (x, y) is the two-dimensional coordinates of the image element in the image plane. T = (x, y, f ) T R is the rotation matrix of the camera coordinate system relative to the world coordinate system, t is the translation matrix of the camera coordinate system relative to the world coordinate system, and (u0, v0) T , the focal length f, R, and t can be obtained by camera calibration. Step 33: connecting the homogeneous coordinates of the pixel on the image plane in the world coordinate system with the three-dimensional homogeneous coordinates of the camera optical center in the world coordinate system to obtain the path of light rays emitted from the four vertices of each pixel in each plasma image through space voxels; Step 34: calculating the integral path length of the four paths through each voxel in space, and taking the average of the four integral path lengths to obtain the integral path length of the corresponding voxel of the pixel; the integral path length of the pixel to the voxel is Wherein, the left lower corner vertex coordinate of the pixel is , the left upper corner vertex coordinate of the pixel is , the right upper corner vertex coordinate of the pixel is , and the right lower corner vertex coordinate of the pixel is .

2. The method of claim 1, wherein, Before the step 3, the plasma emission spectrum intensity three-dimensional reconstruction method based on path length weight further comprises the following steps: graying, distortion correction and image filtering are performed on the plasma image; the gray value of each plasma image is converted into the gray value of the pixel.

3. The method of claim 2, wherein, Gray value i of a pixel p h The emission spectrum intensity of each voxel is integrated along the light ray L and is expressed as: Wherein, the light L passes through n voxels, and the emission spectral intensity values of the voxels are x1, x2, …, x n n respectively, the path lengths of the light L in the voxels are l1, l2, …, ln respectively n , and the distance from the pixel p to the first voxel is l0; the gray value vector of the pixel is the gray value composition.

4. The method of claim 1, wherein, The contribution of each voxel to each pixel is wherein, represents the contribution of the kth voxel to the hth pixel, represents the integrated path length of the light ray L through the hth pixel within the kth voxel.

5. The method of claim 3, wherein, In step 6, the relationship between the weight projection matrix, the gray value vector of the pixel of the plasma image and the emission spectrum intensity of the voxel is is a two-dimensional image pixel gray value vector, is a projection weight matrix, is a voxel emission spectrum intensity matrix, and is an unknown to be solved.

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