Computed tomography camera layout optimization method with limited projection angle

Abstract

The invention provides a computer tomography camera layout optimization method with a limited projection angle, and belongs to the technical field of chemiluminescence computer tomography. Comprising the following steps: S1, system modeling: establishing a mathematical relationship between a target flow field and a projection thereof; s2, reconstructing a flow field through an inversion algorithm; performing chromatography reconstruction by using a classic algebraic reconstruction technology ART algorithm; s3, a computer tomography camera layout optimization method of a limited projection angle; constructing a target function as an effective predictor of a reconstruction error; the maximization problem is globally optimized and solved by using a simulated annealing SA algorithm; and realizing an optimal solution by adopting a simulated annealing algorithm. By optimizing the pitch angle and the azimuth angle of the camera, capturing of effective projection information is remarkably increased. And camera layout optimization is carried out by adopting a simulated annealing algorithm, so that the system can flexibly adapt to a dynamic environment. According to the method, the morbidity of a weight matrix is effectively reduced, the calculation complexity is reduced, and the reliability of a measurement result is enhanced.

Description

Technical Field

[0001] The invention provides a computer tomography camera layout optimization method with limited projection angle, belonging to the technical field of chemiluminescence computer tomography. Background Art

[0002] Computed tomography of chemiluminescence (CTC) is an important technology for obtaining three-dimensional flow characteristics in combustion and fluid fields. CTC captures two-dimensional projections from multiple angles and reconstructs the three-dimensional flow field within the volume of interest (VoI) using a mathematical inversion algorithm. It is widely used in combustion diagnosis, gas detection, and high-temperature flow field analysis. This technology can accurately provide information on the temperature field and chemical distribution in the combustion area, providing support for a deep understanding of the combustion process and the optimization of combustion equipment.

[0003] Although current chemiluminescence computed tomography (CTC) technology can provide high temporal and spatial resolution three-dimensional flame structure measurements, in actual operation, especially in complex environments such as supersonic wind tunnels, only a limited number of high-speed cameras can be deployed due to limited optical channels. Traditional camera layouts (such as uniform distribution along a circular plane) cannot fully capture useful information in the scene, resulting in unsatisfactory reconstruction quality of volume tomography. Summary of the invention

[0004] The present invention aims to solve the problem of how to achieve high-quality volumetric tomography in complex flow and combustion diagnosis under limited projection angle conditions. By combining CTC technology with fiber optic endoscope, a camera layout optimization method is proposed to maximize the angle of the weight matrix subspace, reduce correlation, improve imaging accuracy, and verify its stability under changes in flame direction.

[0005] The specific technical solution is:

[0006] A method for optimizing the layout of a computer tomography camera with a limited projection angle comprises the following steps:

[0007] S1. System modeling: Establish the mathematical relationship between the target flow field and its projection;

[0008] The region of interest VOI of the flow field is discretized into a rectangular area, and the world coordinate system X is established. w -Y w -Z w , the origin of the coordinate system is established at the upper left corner of the VOI; the camera coordinate system X c -Y c -Z cEstablished at the optical center of the lens, the image plane defines the pixel coordinate system uov; the perspective projection transformation establishes the relationship between the geometric position in the physical space and the pixel position in the image, and the next point P in the world coordinate system is established through the rigid body transformation w (X w , Y w , Z w ) and the camera coordinate system point P c (X c , Y c , Z c )

[0009]

[0010] in They are the rotation matrix and translation matrix from the world coordinate system to the camera coordinate system, r ij and t i Represents the matrix element; the rotation matrix can also be determined by the pitch angle α, yaw angle β, and roll angle γ; this relationship is expressed as:

[0011]

[0012] A point P in the camera coordinate system c (X c , Y c , Z c ) is transformed to the pixel coordinate system uov:

[0013]

[0014] Where: (f x , f y ) is the focal length of the camera in the x and y directions, dx, dy represent the physical size of a single pixel, τ is the skew coefficient in the pixel coordinate system, indicating whether the two coordinate axes of the pixel coordinate system are strictly orthogonal, (u 0 , v 0 ) represents the coordinates of the camera's principal point.

[0015] The pitch angle α, yaw angle β, roll angle γ and translation matrix T determine the position of the camera. In this process, the Zhang Zhengyou calibration method is used to calibrate the internal and external parameters of the camera to obtain the above parameters.

[0016] The part of interest in the flame area is divided into voxels in the x, y, and z directions, and the signal inside each voxel is considered to be uniform. Assuming that the flow field to be measured is a continuous function f(x, y, z), its projection on the imaging plane can be described as:

[0017] p(s, t) = ∫ V f(x,y,z)·w(x,y,z;s,t)dV (4)

[0018] Where p(s, t) is the signal intensity at the sth pixel of the projection image taken at the tth angle; w(x, y, z; s, t) represents the contribution of f(x, y, z) to the image point p(s, t), and V is the volume of the entire flow field to be measured. If the flow field to be measured is discretized into voxels of the same size, then Equation 4 can be approximately expressed as:

[0019]

[0020] Where j and N represent the voxel index and the total number of voxels respectively, w(x j ,y j , z j ) represents the position of voxel j within the voxel; w(x j ,y j , z j ; s, t) represents f(x j ,y j , z j ) is the contribution weight of the s-th pixel on the t-th angle projection image; p s，t is the weighted sum of all voxel signals; the equation is expressed in matrix form as:

[0021]

[0022] Projection vector of the flow field to be measured is obtained through experimental measurement, W is calculated through the imaging model, and the projections at multiple angles are obtained. and the weight matrix W, which together form a system of equations. The solution to this system of equations is the flow field to be measured. The distribution of .

[0023] S2. Inversion algorithm to reconstruct the flow field;

[0024] The classical algebraic reconstruction technique ART algorithm is used for tomographic reconstruction. The mathematical description of ART is as follows:

[0025]

[0026] Where k represents the number of iterations, w in represents the contribution rate of the nth voxel to the i-th pixel, and λ is the relaxation factor, which usually ranges from 0 to 2.

[0027] In each iteration, ART modifies the current solution according to each equation; each equation represents a hyperplane, and the modification process is to make a vertical projection between the current solution and the line / plane corresponding to the equation; each row of the weight matrix is i A subspace is defined; the core idea of ​​ART iteration is to make the solution gradually approach the intersection of these subspaces through projection.

[0028] S3. Optimization method of computer tomography camera layout with limited projection angle;

[0029] S3.1 construct an objective function as an effective predictor of reconstruction error;

[0030] The weight corresponding to each projection of CTC is in matrix form. The weight represents the effective constraint information obtained by the projection. Equation (6) is determined by the weight matrix. The angle between the two subspaces using the weight matrix columns is defined as:

[0031] θ ij =f(W i , W j ) (8)

[0032] where θ ij represents the subspace angle between any two weight matrices. Geometrically, this angle is the angle between two hyperplanes embedded in a higher dimensional space. The camera layout optimization problem is transformed into a maximization problem, whose cost function is defined as, for example, θ ij The objective function Fobj of the optimization problem is defined as:

[0033] Fobj=min(θ ij ) (9)

[0034] Where min() returns the minimum value. Take the minimum angle of the subspace between any matrices to maximize the objective function Fobj. The weight matrix W is completely calculated by the camera calibration parameters and position. W is determined by the external parameters including the rotation matrix and the translation matrix. The cameras are distributed on the same sphere and the camera is facing the VOI. The translation matrix T is a constant value and the roll angle T = 0. The α and β that determine the camera position are introduced as variables into the optimization objective function. The maximization problem is solved by global optimization using the simulated annealing SA algorithm.

[0035] S3.2 Simulated annealing algorithm implementation:

[0036] Initial algorithm parameters, including the upper and lower bounds of the variable pitch angle α, yaw angle β, and initial solution α 0 , β 0 , initial temperature T 0 And the attenuation coefficient The variable boundary conditions ensure the effectiveness of optimizing the camera distribution under finite projection angles. Set the value range of α to (0, 2 / 3π) and the value range of β to (0, 1 / 4π) to simulate finite projection angles. During the optimization process, the angle θ between any two weight matrix subspaces is calculated from the initial position. ij, and obtain the initial value of the objective function Fobj_0. Generate a set of new solutions based on the initial position, and calculate the new objective function value Fobj_new. If Fobj_new>Fobj_0, accept the new solution, otherwise accept the new solution with probability exp(-ΔF / T), which is called the Metropolis criterion. In each cycle, record the optimal solution and the corresponding objective function value Fobj_T, generate a new solution from it, and calculate the new objective function value. Repeat the number of cycles before lowering the temperature T each time to ensure a global search for the optimal solution. Achieve temperature reduction, where A constant belonging to (0, 1). When Fobj_T remains unchanged or insignificant between several consecutive temperature states, that is, it is less than a positive integer, or when the maximum number of cycles is reached, the algorithm terminates.

[0037] The technical solution provided by the present invention has the following technical effects:

[0038] 1. Improve the accuracy of 3D reconstruction: This invention significantly increases the capture of effective projection information by optimizing the pitch angle and azimuth angle of the camera. This optimization process effectively reduces the reconstruction error, making the 3D flow field reconstruction results obtained from limited projection angles more accurate, especially in complex flow and combustion environments.

[0039] 2. Enhanced adaptability to dynamic scenes: The simulated annealing algorithm is used to optimize the camera layout, allowing the system to flexibly adapt to dynamic environments. This means that in the case of high-speed combustion or large changes in the flow field, the system can still maintain high reconstruction accuracy and stability.

[0040] 3. Reduce computational complexity: Compared with the traditional layout method, the present invention effectively reduces the pathological nature of the weight matrix and reduces computational complexity. This makes the CTC system more efficient in real-time imaging and rapid reconstruction, and can meet the needs of rapid response experiments.

[0041] 4. Improve system stability: By optimizing the camera position, the introduction of redundant information in the reconstruction process is reduced, and the stability of the imaging system in various experimental environments is improved. The optimized layout makes the reconstruction results more consistent under different experimental conditions and enhances the reliability of the measurement results. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is a linear imaging model diagram of this embodiment;

[0043] Figure 2 This is a schematic diagram of the ART algorithm iteration of this embodiment;

[0044] Figure 3 This is a Gaussian flow field diagram containing eddy currents in this embodiment;

[0045] Figure 4 This is a schematic diagram of the distribution of a quarter spherical camera in this embodiment;

[0046] Figure 5 This is a diagram of the model simulation results of this embodiment;

[0047] Figure 6 This is an optimized flow chart of this embodiment;

[0048] Figure 7 is the objective function and reconstruction error curve diagram of this embodiment;

[0049] Figure 8 This is a diagram of the deflected flame model of this embodiment;

[0050] Fig. 9 This is a comparison diagram of the random 100 model optimization distributions and uniform distributions in this embodiment;

[0051] Fig.10 This is a realistic diagram of the optimized camera distribution for this embodiment. DETAILED DESCRIPTION

[0052] The specific technical solution of the present invention is explained in conjunction with embodiments.

[0053] A method for optimizing the layout of a computer tomography camera with a limited projection angle comprises the following steps:

[0054] S1. System modeling: Establish the mathematical relationship between the target flow field and its projection;

[0055] The region of interest VOI of the flow field is discretized into a rectangular area, and the world coordinate system X is established. w -Y w -Z w , the origin of the coordinate system is established at the upper left corner of the VOI; the camera coordinate system X c -Y c -Z c Based on the optical center of the lens, the image plane defines the pixel coordinate system uov, such as Figure 1 As shown. ; The perspective projection transformation establishes the relationship between the geometric position in the physical space and the pixel position in the image, and the rigid body transformation establishes the next point P in the world coordinate system w (X w , Y w , Z w ) and the camera coordinate system point P c (X c , Y c , Z c )

[0056]

[0057] in They are the rotation matrix and translation matrix from the world coordinate system to the camera coordinate system, r ij and t i Represents the matrix element; the rotation matrix can also be determined by the pitch angle α, yaw angle β, and roll angle γ; this relationship is expressed as:

[0058]

[0059] A point P in the camera coordinate system c (X c , Y c , Z c ) is transformed to the pixel coordinate system uov:

[0060]

[0061] Where: (f x , f y ) is the focal length of the camera in the x and y directions, dx, dy represent the physical size of a single pixel, τ is the skew coefficient in the pixel coordinate system, indicating whether the two coordinate axes of the pixel coordinate system are strictly orthogonal, (u 0 , v 0 ) represents the coordinates of the camera's principal point.

[0062] The pitch angle α, yaw angle β, roll angle γ and translation matrix T determine the position of the camera. In this process, the Zhang Zhengyou calibration method is used to calibrate the internal and external parameters of the camera to obtain the above parameters.

[0063] The part of interest in the flame area is divided into voxels in the x, y, and z directions, and the signal inside each voxel is considered to be uniform. Assuming that the flow field to be measured is a continuous function f(x, y, z), its projection on the imaging plane can be described as:

[0064] p(s, t) = ∫ V f(x,y,z)·w(x,y,z;s,t)dV (4)

[0065] Where p(s, t) is the signal intensity at the sth pixel of the projection image taken at the tth angle; w(x, y, z; s, t) represents the contribution of f(x, y, z) to the image point p(s, t), and V is the volume of the entire flow field to be measured. If the flow field to be measured is discretized into voxels of the same size, then Equation 4 can be approximately expressed as:

[0066]

[0067] Where j and N represent the voxel index and the total number of voxels respectively, w(x j ,y j, z j ) represents the position of voxel j within the voxel; w(x j ,y j , z j ; s, t) represents f(x j ,y j , z j ) is the contribution weight of the s-th pixel on the t-th angle projection image; p s，t is the weighted sum of all voxel signals; the equation is expressed in matrix form as:

[0068]

[0069] Projection vector of the flow field to be measured is obtained through experimental measurement, W is calculated through the imaging model, and the projections at multiple angles are obtained. and the weight matrix W, which together form a system of equations. The solution to this system of equations is the flow field to be measured. The distribution of .

[0070] S2. Inversion algorithm to reconstruct the flow field;

[0071] The classical algebraic reconstruction technique (ART) algorithm is used for tomographic reconstruction. Compared with other algorithms, it is relatively easy to implement and can obtain high-quality reconstruction results even in the presence of noise. The mathematical description of ART is as follows:

[0072]

[0073] Where k represents the number of iterations, w in represents the contribution rate of the nth voxel to the i-th pixel, and λ is the relaxation factor, which usually ranges from 0 to 2. Figure 2 The ART algorithm iteration diagram is shown in Figure 1. In each iteration, ART modifies the current solution according to each equation. Each equation represents a hyperplane (or a line in two dimensions), and the modification process is to make a vertical projection between the current solution and the line / plane corresponding to the equation. Each row of the weight matrix W i A subspace is defined. The core idea of ​​ART iteration is to gradually approach the intersection of these subspaces through projection. The larger the angle between the subspaces, the more effective the projection is and the faster the convergence is. If these subspaces are close to parallel to each other (i.e. the angle is small), the algorithm will converge more slowly because the correction amplitude of the projection is small.

[0074] S3. Optimization method of computer tomography camera layout with limited projection angle;

[0075] S3.1 construct an objective function as an effective predictor of reconstruction error;

[0076] The weight corresponding to each projection of CTC is in matrix form. The weight represents the effective constraint information obtained by the projection. Equation (6) is determined by the weight matrix. The greater the difference between the weight matrices, the more effective information the camera captures. In a geometric sense, the subspace defined by each weight matrix corresponds to a hyperplane. In the ART algorithm, the goal of the optimization problem is to maximize the correlation between the weight matrices calculated by any two cameras. Specifically, the larger the subspace angle between the weight matrices, the greater the distance between the two hyperplanes, thereby improving the effectiveness of the projection. In this case, the ART algorithm can converge to the intersection faster through an iterative correction process. The correlation is measured using the angle between the two subspaces of the weight matrix columns, defined as

[0077] θ ij =f(W i , W j ) (8)

[0078] where θ ij represents the subspace angle between any two weight matrices. Geometrically, this angle is the angle between two hyperplanes embedded in a higher dimensional space. The camera layout optimization problem is transformed into a maximization problem, and its cost function can be defined as, for example, θ ij The angle θ between the subspaces of the two matrices is ij There is a small value, then the two corresponding cameras provide very similar spatial information, and one of the cameras is redundant. Therefore, the objective function Fobj of the optimization problem can be defined as:

[0079] Fobj=min(θ ij ) (9)

[0080] Where min() returns the minimum value. Take the minimum angle of the subspace between any matrices to maximize the objective function Fobj. The weight matrix W is completely calculated from the camera calibration parameters and position. Once the camera is selected, the internal parameters are determined. Therefore, W is determined by the external parameters including the rotation matrix and the translation matrix. Cameras are usually distributed on a sphere so that the distance between the camera and the center of the VOI is equal to the radius of the sphere, so that the translation matrix T is a constant. In addition, in general, in order to facilitate subsequent data processing and comparison, it is hoped that the flame projection obtained will remain upright and the roll angle γ is set to 0. Finally, α and β, which determine the camera position, are introduced as variables into the optimization objective function. Subsequently, the maximization problem can be solved using the simulated annealing (SA) algorithm (global optimization).

[0081] S3.2 Simulated annealing algorithm implementation:

[0082] Figure 6The flowchart shown provides a detailed description of the simulated annealing algorithm for the finite projection angle problem. The initial algorithm parameters include the upper and lower bounds of the variable pitch angle α, the yaw angle β, the initial solution α 0 , β 0 , initial temperature T 0 And the attenuation coefficient The variable boundary conditions ensure the effectiveness of optimizing the camera distribution under limited projection angles. The value range of α is set to (0, 2 / 3π) and the value range of β is set to (0, 1 / 4π) to simulate limited projection angles. This is because Figures 3 to 5 It shows that the reconstruction accuracy curve is symmetrically shaped like "W" as the camera pitch angle β increases. During the optimization process, the angle θ between any two weight matrix subspaces is calculated from the initial position. ij , and obtain the initial value of the objective function Fobj_0. Generate a set of new solutions based on the initial position, and calculate the new objective function value Fobj_new. If Fobj_new>Fobj_0, accept the new solution, otherwise accept the new solution with a certain probability exp(-ΔF / T), which is called the Metropolis criterion. In each cycle, record the optimal solution and the corresponding objective function value Fobj_T, generate a new solution from it, and calculate the new objective function value. Repeat a certain number of cycles before lowering the temperature T each time to ensure the global search for the optimal solution. Through Achieve temperature reduction, where A constant belonging to (0, 1), here we set When Fobj_T remains unchanged or insignificant between several consecutive temperature states, that is, it is less than a positive integer (10 -5 ), or when the maximum number of cycles is reached, the algorithm terminates.

[0083] This embodiment implements the above optimization process within a limited projection field of view range of 0-120°.

[0084] Step 1: System initialization: At the beginning of the experiment, a high-speed camera is selected to combine with 7 fiber-optic image bundles, and the initial positions are evenly distributed on a hemispherical surface. The camera's pitch angle (β) and azimuth angle (α) are initially set to 0°, the initial temperature T is 100, and the attenuation coefficient t is 0.95.

[0085] Step 2: Set the projection range: Limit the effective projection range of the camera to between 0° and 120° to adapt to the limitations of the optical channel in the actual environment.

[0086] Step 3: Weight matrix calculation: Perform a preliminary measurement of the projection signal of each camera and calculate the weight matrix corresponding to each projection. These weight matrices are used to describe the contribution of voxels to pixels and provide necessary information for subsequent image reconstruction.

[0087] Step 4: Optimization process: Apply simulated annealing algorithm to optimize the camera's pitch and azimuth angles. During the optimization process, set the boundary conditions of the pitch and azimuth angles to ensure that the camera always stays within the range of 0° to 120°. Record the objective function value and corresponding reconstruction error of each iteration, and decide whether to accept the new solution according to the Metropolis Criterion.

[0088] Step 5: Final layout deployment: After multiple iterations, the final camera position distribution is obtained, which can effectively reduce the reconstruction error. The optimized camera positions are fixed and deployed in the CTC measurement system.

[0089] Step 6. Result verification: Use the optimized camera layout to image the flame and obtain projection data from multiple angles. Use the ART algorithm to reconstruct the image and analyze the relationship between the reconstruction accuracy and the objective function. The experimental results show that the optimized layout significantly reduces the reconstruction error, especially when the flame rotates 90°, the reconstruction quality remains stable.

[0090] The flow field is reconstructed using projections from seven cameras in different directions. Figure 7 In the figure, the evolution of the objective function (the blue curve with a solid triangle) is plotted as a function of T reduction. For ease of comparison, the objective function is inverted and normalized. The solid red curve is the evolution of the reconstruction error under the corresponding objective function. Figure 3 Reconstruction of asymmetric flow field containing eddies. As T decreases, the algorithm becomes less and less likely to accept new solutions with smaller function values ​​and gradually converges to the global solution. Therefore, the inverse objective function value decreases with T. Figure 7 The relationship between the objective function and the reconstruction error is shown as the annealing temperature T decreases. Overall, the reconstruction error and the objective function value change trend are basically consistent. It can be seen that the objective function Fobj can be used as an effective predictor of the reconstruction error.

[0091] To further verify our method, we use the set of solutions output when the algorithm terminates as the final camera position distribution. Looking only at the horizontal direction, the camera position is evenly distributed, with angles of 0°, 20°, 40°, 60°, 80°, 100°, and 120°. The optimization result is consistent with our previous conclusion that the uniform distribution has the smallest reconstruction error. Then, we randomly generate one hundred models to test the reconstruction error of the two cases of optimized distribution and circular plane uniform distribution. The results are plotted on Fig. 9 In fact, by changing Figure 8 The deflection size and direction of the flame are used to generate the first 50 random models, and the flame model is rotated 90° to generate another 50 random models. Fig. 9The blue line in the middle triangle and the red line in the diamond represent the results of the optimized distribution and the uniform distribution, respectively. For all models, the reconstruction error curve of the optimized camera distribution is always below the uniform distribution error curve. More noteworthy is that when the flame is rotated 90°, the reconstruction error curve of the uniform distribution shows an upward trend, while the reconstruction error corresponding to the optimized distribution remains basically unchanged. It can be seen that under the limited projection angle space, the reconstruction quality of this optimization method in which the cameras are arranged in two orthogonal directions is not sensitive to the flame morphology, and not only the reconstruction error is smaller, but also the stability is higher.

[0092] Fig.10 Arrange the on-site physical map based on the optimization results of the example.

[0093] The experimental device of this embodiment includes:

[0094] Fiber optic bundle clamp: fix the fiber optic image bundle and lens.

[0095] Fiber optic imaging bundle: transmits the projection signal of the flame area to the sensor of the high-speed camera to generate image data.

[0096] Lens: A lens is installed in front of each fiber optic imaging bundle to improve the clarity and resolution of the captured image.

[0097] High-speed camera: It is placed on the top of the device and is specially used to capture the dynamic characteristics of high-speed flowing flames.

[0098] Bunsen burner: used to generate flame in combustion experiments as the flow field to be measured.

Claims

1. A method for optimizing the layout of computed tomography cameras with limited projection angles, characterized in that: The following steps are involved: S1. System modeling: Establish the mathematical relationship between the target flow field and its projection; S2. Reconstruct the flow field using the inversion algorithm; use the classical algebraic reconstruction technique ART algorithm for tomographic reconstruction; S3. Optimization method for computer tomography camera layout with limited projection angles; constructing an objective function as an effective predictor of reconstruction error; solving the maximization problem globally using the simulated annealing SA algorithm; achieving the optimal solution using the simulated annealing algorithm.

2. The method for optimizing the layout of a computer tomography camera with a limited projection angle according to claim 1, characterized in that: S1 specific method is: The region of interest VOI of the flow field is discretized into a rectangular area, and the world coordinate system X is established. w -Y w -Z w , the origin of the coordinate system is established at the upper left corner of the VOI; the camera coordinate system X c -Y c -Z c Established at the optical center of the lens, the image plane defines the pixel coordinate system uov; the perspective projection transformation establishes the relationship between the geometric position in the physical space and the pixel position in the image, and the next point P in the world coordinate system is established through the rigid body transformation w (X w , Y w , Z w ) and the camera coordinate system point P c (X c , Y c , Z c ) in They are the rotation matrix and translation matrix from the world coordinate system to the camera coordinate system, r ij and t i Represents the matrix element; the rotation matrix can also be determined by the pitch angle α, yaw angle β, and roll angle γ; this relationship is expressed as: A point P in the camera coordinate system c (X c , Y c , Z c ) is transformed to the pixel coordinate system uov: Where: (f x , f y ) is the focal length of the camera in the x and y directions, dx, dy represent the physical size of a single pixel, τ is the skew coefficient in the pixel coordinate system, indicating whether the two coordinate axes of the pixel coordinate system are strictly orthogonal, (u0, v0) represents the principal point coordinates of the camera; The pitch angle α, yaw angle β, roll angle γ and translation matrix T determine the position of the camera. In this process, the Zhang Zhengyou calibration method is used to calibrate the internal and external parameters of the camera to obtain the above parameters. The part of interest in the flame area is divided into voxels in the x, y, and z directions, and the signal inside each voxel is considered to be uniform; let the flow field to be measured be a continuous function f(x, y, z), and its projection on the imaging plane is described as: p(s,t)=∫ V f(x,y,z)·w(x,y,z;s,t)dV (4) Where p(s, t) is the signal intensity at the sth pixel of the projection image taken at the tth angle; w(x, y, z; s, t) represents the contribution of f(x, y, z) to the image point p(s, t), and V is the volume of the entire flow field to be measured; the flow field to be measured is discretized into voxels of the same size, then Equation 4 is expressed as: Where j and N represent the voxel index and the total number of voxels respectively, w(x j ,y j , z j ) represents the position of voxel j within the voxel; w(x j ,y j , z j ; s, t) represents f(x j ,y j , z j ) is the contribution weight of the s-th pixel on the t-th angle projection image; p s，t is the weighted sum of all voxel signals; the equation is expressed in matrix form as: Projection vector of the flow field to be measured is obtained through experimental measurement, W is calculated through the imaging model, and the projections at multiple angles are obtained. and the weight matrix W, which together form a system of equations. The solution to this system of equations is the flow field to be measured. The distribution of .

3. The method for optimizing the layout of a computer tomography camera with a limited projection angle according to claim 2, characterized in that: The specific method of S2 is: The classical algebraic reconstruction technique ART algorithm is used for tomographic reconstruction. The mathematical description of ART is as follows: Where k represents the number of iterations, w in represents the contribution rate of the nth voxel to the i-th pixel, λ is the relaxation factor, ranging from 0 to 2; In each iteration, ART modifies the current solution according to each equation; each equation represents a hyperplane, and the modification process is to make a vertical projection between the current solution and the line / plane corresponding to the equation; each row of the weight matrix is i A subspace is defined; the core idea of ​​ART iteration is to make the solution gradually approach the intersection of these subspaces through projection.

4. The method for optimizing the layout of a computer tomography camera with a limited projection angle according to claim 3, characterized in that: The specific method of S3 is: S3.1 construct an objective function as an effective predictor of reconstruction error; The weight corresponding to each projection of CTC is in matrix form; the weight represents the effective constraint information obtained by the projection; the angle between the two subspaces of the weight matrix column is used to measure the correlation, which is defined as: θ ij =f(W i ,W j ) (8) where θ ij represents the subspace angle between any two weight matrices; geometrically, this angle is the angle between two hyperplanes embedded in a higher-dimensional space; The camera layout optimization problem is transformed into a maximization problem, whose cost function is defined as ij The average value or weighted sum of; the objective function Fobj of the optimization problem is defined as: Fobj=min(θ ij ) (9) Among them, min() returns the minimum value; take the minimum angle of the subspace between any matrices to maximize the objective function Fobj; the weight matrix W is completely calculated by the camera calibration parameters and position; W is determined by external parameters including the rotation matrix and the translation matrix; the cameras are distributed on the same sphere and the camera is facing the VOI, the translation matrix T is a constant value, and the roll angle γ=0; α and β that determine the camera position are introduced as variables into the optimization objective function; the maximization problem is solved by global optimization using the simulated annealing SA algorithm; S3.2 Simulated annealing algorithm implementation: Initial algorithm parameters, including the upper and lower bounds of the variable pitch angle α, yaw angle β, initial solution α0, β0, initial temperature T0, and attenuation coefficient The variable boundary conditions ensure the effectiveness of optimizing the camera distribution under limited projection angles; the value range of α is set to (0, 2 / 3π) and the value range of β is set to (0, 1 / 4π); during the optimization process, the angle θ between any two weight matrix subspaces is calculated from the initial position. ij , and obtain the initial value of the objective function Fobj_0; generate a set of new solutions based on the initial position, and calculate the new objective function value Fobj_new; if Fobj_new>Fobj_0, accept the new solution, otherwise accept the new solution with probability exp(-ΔF / T), which is called the Metropolis criterion; record the optimal solution and the corresponding objective function value Fobj_T in each cycle, generate a new solution in it, and calculate the new objective function value; repeat the number of cycles before lowering the temperature T each time to ensure the global search for the optimal solution; through Achieve temperature reduction, where A constant belonging to (0,1). When Fobj_T remains unchanged or insignificant between several consecutive temperature states, that is, it is less than a positive integer, or when the maximum number of cycles is reached, the algorithm terminates.

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