A method, system, device and storage medium for three-dimensional reconstruction of a radiation field

Abstract

The application discloses a kind of radiation field three-dimensional reconstruction method, system, equipment and storage medium, belong to nuclear radiation detection and three-dimensional environment perception technical field, method includes: obtaining the three-dimensional point cloud data and visual image data of target environment, constructs and includes the multi-material voxel map of geometric structure, material category and equivalent thickness;Establish radiation forward transmission model based on voxel space, calculate the theoretical response value of detector according to radioactive source parameter and multi-material voxel map, obtain the measured radiation response value of detector, and construct objective function based on theoretical response value and measured radiation response value, solve the optimal radioactive source parameter by optimization algorithm, and then reconstruct the three-dimensional radiation field distribution of full space.The application realizes high-precision, interpretable three-dimensional radiation field reconstruction and visualization under complex shielding environment.Solve the problem that radiation propagation physical model and space environment model are separated in the prior art, lack unified representation framework and lack voxel-level material and thickness information.

Description

Technical Field

[0001] This invention belongs to the field of nuclear radiation detection and three-dimensional environmental perception technology, specifically relating to a method, system, device and storage medium for three-dimensional reconstruction of radiation fields. Background Technology

[0002] Accurately obtaining the location, intensity, and radiation distribution of radioactive sources in the environment is crucial for nuclear facility inspections, radioactive source searches, nuclear emergency response, nuclear decommissioning environmental mapping, and radiation monitoring in complex scenarios. Existing radiation detection methods typically rely on radiation detectors to obtain count rate, dose rate, or energy spectrum information, and combine this with a positioning system to estimate radioactive sources or map radiation fields.

[0003] After radiation is emitted from a radiation source, it is affected by factors such as distance attenuation, material absorption, obstruction, and scattering during propagation, ultimately forming the observed values ​​of the detector. Therefore, the radiation reconstruction problem is essentially an inverse problem combining the laws of physical propagation and the constraints of the space environment. Meanwhile, with the development of visual perception, convolutional neural networks, laser point cloud modeling, and SLAM technology, the three-dimensional geometry, obstacle locations, obstacle thicknesses, and material types of complex environments can be estimated through image-point cloud fusion. This provides the conditions for introducing real-world environmental constraints into radiation reconstruction.

[0004] However, most existing radiation reconstruction methods focus primarily on the radiation measurements themselves, failing to adequately utilize environmental material differences and geometric thickness information, making it difficult to accurately depict the propagation process of radiation in complex environments. Therefore, there is an urgent need for a method to construct three-dimensional radiation maps that can uniformly integrate physical information of the radiation field, spatial environment information, material identification information, and point cloud thickness information.

[0005] The existing technology has the following main problems: 1) Separation of physical model and spatial environment model: Existing radiation source reconstruction methods usually focus on modeling the relationship between radiation measurement values ​​and source location, while underutilizing the three-dimensional structure of the environment such as walls, equipment, and shielding objects, resulting in the radiation propagation path not accurately corresponding to the actual environment.

[0006] 2) Separation of spatial and physical information: There is a lack of a unified representation framework that deeply integrates environmental geometry, material properties, and radiation propagation laws. Existing models struggle to quantify the local effects of different materials on the radiation field while simultaneously reconstructing it.

[0007] 3) Lack of voxel-level material and thickness information: Existing voxel maps (such as occupancy grid maps) usually only store geometric occupancy information and cannot identify and record the specific material and equivalent thickness of the shielding at the voxel granularity, which limits the accuracy of radiation source terms and radiation field reconstruction. Summary of the Invention

[0008] To address the aforementioned shortcomings in the prior art, this invention provides a method, system, device, and storage medium for three-dimensional reconstruction of radiation fields, which solves the problems of separation between the radiation propagation physical model and the spatial environment model, lack of a unified representation framework, and missing voxel-level material and thickness information in the prior art.

[0009] To achieve the above-mentioned objectives, the technical solution adopted by this invention is: a three-dimensional reconstruction method for a radiation field, comprising the following steps: S1. Acquire 3D point cloud data and visual image data of the target environment; S2. Perform voxelization on the 3D point cloud data to generate a 3D voxel mesh, and perform semantic segmentation and material identification on the visual image data. Map the identified material category information to the corresponding voxels to form a multi-material voxel map. Combine the geometric information of the point cloud within the voxel to calculate the equivalent thickness of each voxel along a specific direction. S3. Establish a forward radiation transfer model based on voxel space. The forward radiation transfer model uses the activity, energy spectrum and position of the radiation source as parameters. Based on the material type and equivalent thickness of each voxel through which the line connecting the radiation source and the detector passes in the multi-material voxel map, calculate the theoretical response value of the radiation particles after material attenuation to reach the detector. S4. Obtain the measured radiation response value of at least one detector, construct an objective function based on the measured radiation response value and the theoretical response value, solve the optimal radiation source parameters through optimization algorithm iteration, and reconstruct the three-dimensional radiation field distribution of the whole space based on the optimal radiation source parameters and multi-material voxel map.

[0010] Furthermore, S2 includes the following sub-steps: S21. Transform the 3D point cloud data to the world coordinate system, divide the space into a 3D voxel grid according to the preset voxel resolution, count the number of points in each voxel, and determine whether the number of points is greater than the preset point cloud number threshold. If yes, mark the voxel as occupied; otherwise, mark the voxel as idle or unknown, thus forming a geometric occupancy map. S22. Use a pre-trained deep learning model to perform instance segmentation and material category recognition on visual image data to obtain pixel-level material category labels; S23. Based on the geometric occupancy map, the visual image data is registered with the 3D point cloud data, the mapping relationship between image pixels and voxels is established, and the material category label is mapped to the corresponding occupancy voxel to form a multi-material voxel map. S24. For each known occupying voxel of the material, calculate the equivalent linear thickness of the voxel in the preset direction based on the spatial distribution of its internal point cloud or a predefined material density table, and obtain the equivalent thickness of the voxel. S25. For each material category in the multi-material voxel map, establish a physical parameter mapping table related to radiative transfer calculation. The physical parameter mapping table should include at least the mass attenuation coefficient or linear attenuation coefficient at different energies, so that the radiative forward transfer model can dynamically determine its attenuation capability according to the material category of the voxel and the energy spectrum of the radiation source during calculation.

[0011] Furthermore: In S3, the voxel-space-based forward radiative transport model includes: (1) Model parameter input layer, used to receive the activity, energy spectrum, location and multi-material voxel map of the radioactive source; (2) Ray path resolution layer, used to perform ray projection algorithm in voxel space to determine the sequence of voxels through which the line from the radiation source to the detector passes; (3) Material property mapping layer, used to query the linear decay coefficient at the corresponding energy from the preset material physical parameter database according to the material category label of each voxel on the path; (4) Thickness acquisition layer, used to obtain the equivalent travel distance of each voxel along the ray direction; (5) Response calculation layer, used to accumulate distance attenuation factor and material attenuation factor along the path and combine them with detector energy response to calculate theoretical response value.

[0012] Further: In S3, for gamma rays, the detector predicted dose rate of the ray reaching the detector after material attenuation is calculated as the theoretical response value, where the detector predicted dose rate... The specific expression is: In the formula, The number of radioactive sources, For the first The activity of a radioactive source, Its dose rate constant, This represents the straight-line distance between the radiation source and the detector. For the ray path, the first Linear decay coefficient of individual units, For the ray in the first The distance traveled within an individual element. The energy response efficiency of the detector. For radiation energy, This represents the set of all voxels along the path from the radiation source to the detector.

[0013] Furthermore: In S4, the objective function is constructed. The specific expression is: In the formula, The total number of measurement points. For the first Measured radiation response values ​​at each measurement point Based on current radioactive source parameters The calculated values ​​of the forward radiation transfer model, The regularization coefficient is . For regularization, the radioactive source parameters This includes the location coordinates and activity of the radioactive source.

[0014] A three-dimensional radiation field reconstruction system includes a data acquisition module for acquiring three-dimensional point cloud data and visual image data of the target environment; a multi-material voxel map construction module for voxelizing the three-dimensional point cloud data and constructing a multi-material voxel map containing geometric structure, material category, and equivalent thickness by combining semantic segmentation and material recognition results of the visual image data; a radiation forward transmission modeling module for establishing a radiation forward transmission model based on voxel space and calculating the theoretical response value of the detector based on the radiation source parameters and the multi-material voxel map; and a source term inversion and radiation field reconstruction module for acquiring the measured radiation response value of the detector, constructing an objective function based on the theoretical and measured radiation response values, solving for the optimal radiation source parameters through an optimization algorithm, and then reconstructing the three-dimensional radiation field distribution of the entire space.

[0015] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of a three-dimensional reconstruction method for a radiation field.

[0016] A computer-readable storage medium storing a computer program, wherein executing the computer program implements the steps of a method for three-dimensional reconstruction of a radiation field.

[0017] The beneficial effects of this invention are as follows: (1) This invention deeply integrates environmental geometry and material properties into a unified three-dimensional voxel mesh, realizing the accurate correspondence between radiation propagation path and real physical environment, and solving the problem of separation between physical model and environmental model in traditional methods.

[0018] (2) By establishing a forward radiation transmission model based on voxel space, this invention directly couples the acquisition of attenuation coefficient and travel distance to the material labels and geometric information of multi-material voxel maps, so that radiation transmission calculation can truly reflect the local shielding effect of different materials and thicknesses of blocking bodies on radiation, while still maintaining high-precision dose prediction, which supports the accuracy of subsequent source term inversion and full-space radiation field reconstruction.

[0019] (3) This invention provides a highly integrated multimodal information fusion framework that organically combines lidar geometric data, visual semantic data and radiation physics model, so that the radiation field reconstruction results have higher physical interpretability and spatial consistency. Attached Figure Description

[0020] Figure 1 This is a flowchart of a three-dimensional reconstruction method for a radiation field according to the present invention.

[0021] Figure 2 This is a visualization of the three-dimensional radiation field reconstruction results.

[0022] Figure 3 This is a schematic diagram of a three-dimensional radiation field reconstruction system according to the present invention. Detailed Implementation

[0023] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0024] like Figure 1 As shown, in one embodiment of the present invention, a method for three-dimensional reconstruction of a radiation field includes the following steps: S1. Acquire 3D point cloud data and visual image data of the target environment; S2. Perform voxelization on the 3D point cloud data to generate a 3D voxel mesh, and perform semantic segmentation and material identification on the visual image data. Map the identified material category information to the corresponding voxels to form a multi-material voxel map. Combine the geometric information of the point cloud within the voxel to calculate the equivalent thickness of each voxel along a specific direction. S3. Establish a forward radiation transfer model based on voxel space. The forward radiation transfer model uses the activity, energy spectrum and position of the radiation source as parameters. Based on the material type and equivalent thickness of each voxel through which the line connecting the radiation source and the detector passes in the multi-material voxel map, calculate the theoretical response value of the radiation particles after material attenuation to reach the detector. S4. Obtain the measured radiation response value of at least one detector, construct an objective function based on the measured radiation response value and the theoretical response value, solve the optimal radiation source parameters through optimization algorithm iteration, and reconstruct the three-dimensional radiation field distribution of the whole space based on the optimal radiation source parameters and multi-material voxel map.

[0025] This invention achieves high-precision, interpretable 3D radiation field reconstruction and visualization in complex occlusion environments by deeply integrating radiation physics, spatial geometry, and material properties into a unified voxel framework.

[0026] S1 specifically refers to: First, a mobile measurement platform, integrating a LiDAR (Light Detection and Ranging) sensor, an RGB camera, and a gamma detector, is deployed or handheld in the target environment. The platform's real-time pose in space is acquired using SLAM (Simultaneous Localization and Mapping) technology or external positioning devices. The LiDAR sensor then acquires 3D point cloud data of the environment. Each point Includes three-dimensional coordinates The visual camera acquires RGB image data of the environment. This data is used for subsequent semantic recognition. The radiation detector acquires measured radiation response values ​​at multiple measurement points. And record the pose of the corresponding measurement point.

[0027] S2 includes the following steps: S21. Transfer 3D point cloud data Transform to the world coordinate system, based on the preset voxel resolution. (For example, 5cm) Divide the space into a three-dimensional voxel grid and count the values ​​of each voxel. The number of point clouds within the cloud is determined, and it is determined whether the number of point clouds exceeds a preset point cloud number threshold. If so, the voxel state is marked as occupied. In this embodiment, the state is set as follows: If not, the voxel state is marked as idle or unknown. In this embodiment, the state is set to... This forms a geometrically occupied map; S22. Use a pre-trained deep learning model to perform instance segmentation and material category recognition on visual image data to obtain pixel-level material category labels; In this embodiment, a pre-trained deep learning model (such as Mask R-CNN or DeepLabV3+) is used to process RGB image data. The model, after training, is capable of recognizing and segmenting different objects in a scene and outputting pixel-level material category labels. Examples include "concrete wall", "lead shielding", and "iron pipe".

[0028] S23. Based on the geometric occupancy map, the visual image data is registered with the 3D point cloud data, the mapping relationship between image pixels and voxels is established, and the material category label is mapped to the corresponding occupancy voxel to form a multi-material voxel map. In this embodiment, the extrinsic parameter calibration matrix between the camera and LiDAR is used to calibrate the pixels on the image. Projecting into 3D space, finding the corresponding voxel For voxels labeled "occupied," they are compared with the material category labels in the image recognition results. Associativity is performed. When a voxel corresponds to the recognition results of multiple image frames, a voting mechanism or Bayesian update method can be used to determine the final material category. Thus, this invention yields a multi-material voxel map. S24. For each known occupying voxel of the material, calculate the equivalent linear thickness of the voxel in the preset direction based on the spatial distribution of its internal point cloud or a predefined material density table, and obtain the equivalent thickness of the voxel. S25. For each material category in the multi-material voxel map, establish a physical parameter mapping table related to radiative transfer calculation. The physical parameter mapping table should include at least the mass attenuation coefficient or linear attenuation coefficient at different energies, so that the radiative forward transfer model can dynamically determine its attenuation capability according to the material category of the voxel and the energy spectrum of the radiation source during calculation.

[0029] For each voxel with a known material, its equivalent thickness in the ray propagation direction needs to be calculated. Since a voxel is a cube, the path length of a ray passing through it depends on the intersection of the ray and the voxel. In forward calculations, this can be calculated precisely based on the voxel geometry. Furthermore, for simplification, for voxels with uniform material, their equivalent thickness in the three principal axes can be pre-calculated, or the voxel side length can be used directly as an approximation of the travel distance. For voxels with non-uniform filling (such as partially occupied voxels), the equivalent areal density can be estimated based on the point cloud density.

[0030] In S3, the forward radiative transport model based on voxel space includes: (1) Model parameter input layer, used to receive the activity, energy spectrum, location and multi-material voxel map of the radioactive source; (2) Ray path resolution layer, used to perform ray projection algorithm in voxel space to determine the sequence of voxels through which the line from the radiation source to the detector passes; (3) Material property mapping layer, used to query the linear decay coefficient at the corresponding energy from the preset material physical parameter database according to the material category label of each voxel on the path; (4) Thickness acquisition layer, used to obtain the equivalent travel distance of each voxel along the ray direction; (5) Response calculation layer, used to accumulate distance attenuation factor and material attenuation factor along the path and combine them with detector energy response to calculate theoretical response value.

[0031] In S3, for gamma rays, the detector predicted dose rate is calculated after the ray is attenuated by the material and reaches the detector, serving as the theoretical response value. The detector predicted dose rate is... The specific expression is: In the formula, The number of radioactive sources, For the first The activity of a radioactive source, Its dose rate constant, This represents the straight-line distance between the radiation source and the detector. For the ray path, the first Linear decay coefficient of individual units, For the ray in the first The distance traveled within an individual element. The energy response efficiency of the detector. For radiation energy, This represents the set of all voxels along the path from the radiation source to the detector.

[0032] After establishing a multi-material voxel map containing material information, this embodiment needs to establish the radiative transfer equation from the radiation source to the detector. Assume there are one or more radiation sources in space, and the radiation source parameters... , Indicates activity. Indicates the location. For a given detector location... Detector predicted dose rate This can be obtained by integrating attenuation along the path. For gamma rays, the detector predicts the dose rate. It can also be calculated using the following formula: In the formula, Indicates based on physical qualities and radiation energy The linear attenuation coefficient is obtained by looking up a table. For the ray in the first The distance traveled within an individual element. This represents the total number of voxels traversed by the ray path. This step is implemented using ray casting algorithms in computer graphics: from the... The source point of each radioactive source To the detector position A ray is emitted, and the attenuation factor of each voxel is accumulated, traversing all voxels along the path of the ray. ,in This is the linear decay coefficient of the voxel. The distance the ray travels within the voxel is denoted as .

[0033] In S4, after obtaining the measured radiation response values ​​of detectors at multiple measurement points, an inversion problem is constructed to solve for the radiation source parameters. To prevent overfitting and incorporate prior information, a regularization term is added, such as a spatial sparsity constraint on the location of the radiation source. The objective function is constructed using the norm, or the nonnegativity constraint of the radioactive source activity. The specific expression is: In the formula, The total number of measurement points. For the first Measured radiation response values ​​at each measurement point Based on current radioactive source parameters The calculated values ​​of the forward radiation transfer model, The regularization coefficient is . For regularization, the radioactive source parameters This includes the location coordinates and activity of the radioactive source. A numerical optimization algorithm (particle swarm optimization algorithm with dynamic state clustering) is used to solve for the minimum value of the objective function, obtaining the optimal radioactive source location and predicted radioactive source parameters. .

[0034] Finally, the solved radioactive source parameters are used to predict... and the constructed multi-material voxel map Again, using the forward radiation model, for any point in space... Calculate dose rate This allows for the reconstruction of the radiation field distribution across the entire three-dimensional space. The reconstruction results can be shown as follows: Figure 2 The visualization is shown, where different colors represent different dose rate intensities, and translucent voxels represent environmental structures.

[0035] like Figure 3 As shown, a three-dimensional radiation field reconstruction system includes a data acquisition module for acquiring three-dimensional point cloud data and visual image data of the target environment; a multi-material voxel map construction module for voxelizing the three-dimensional point cloud data and constructing a multi-material voxel map containing geometric structure, material category, and equivalent thickness by combining semantic segmentation and material recognition results of the visual image data; a radiation forward transmission modeling module for establishing a radiation forward transmission model based on voxel space and calculating the theoretical response value of the detector based on the radiation source parameters and the multi-material voxel map; and a source term inversion and radiation field reconstruction module for acquiring the measured radiation response value of the detector, constructing an objective function based on the theoretical response value and the measured radiation response value, solving for the optimal radiation source parameters through an optimization algorithm, and then reconstructing the three-dimensional radiation field distribution of the entire space.

[0036] An electronic device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of a three-dimensional reconstruction method for a radiation field.

[0037] A computer-readable storage medium storing a computer program, wherein executing the computer program implements the steps of a method for three-dimensional reconstruction of a radiation field.

[0038] In the description of this invention, the above are merely preferred embodiments and are not intended to limit the scope of protection of this invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for three-dimensional reconstruction of a radiation field, characterized in that, Includes the following steps: S1. Acquire 3D point cloud data and visual image data of the target environment; S2. Perform voxelization on the 3D point cloud data to generate a 3D voxel mesh, and perform semantic segmentation and material identification on the visual image data. Map the identified material category information to the corresponding voxels to form a multi-material voxel map. Combine the geometric information of the point cloud within the voxel to calculate the equivalent thickness of each voxel along a specific direction. S3. Establish a forward radiation transfer model based on voxel space. The forward radiation transfer model uses the activity, energy spectrum and position of the radiation source as parameters. Based on the material type and equivalent thickness of each voxel through which the line connecting the radiation source and the detector passes in the multi-material voxel map, calculate the theoretical response value of the radiation particles after material attenuation to reach the detector. S4. Obtain the measured radiation response value of at least one detector, construct an objective function based on the measured radiation response value and the theoretical response value, solve the optimal radiation source parameters through optimization algorithm iteration, and reconstruct the three-dimensional radiation field distribution of the whole space based on the optimal radiation source parameters and multi-material voxel map.

2. The three-dimensional reconstruction method for radiation fields according to claim 1, characterized in that, S2 includes the following steps: S21. Transform the 3D point cloud data to the world coordinate system, divide the space into a 3D voxel grid according to the preset voxel resolution, count the number of points in each voxel, and determine whether the number of points is greater than the preset point cloud number threshold. If yes, mark the voxel as occupied; otherwise, mark the voxel as idle or unknown, thus forming a geometric occupancy map. S22. Use a pre-trained deep learning model to perform instance segmentation and material category recognition on visual image data to obtain pixel-level material category labels; S23. Based on the geometric occupancy map, the visual image data is registered with the 3D point cloud data, the mapping relationship between image pixels and voxels is established, and the material category label is mapped to the corresponding occupancy voxel to form a multi-material voxel map. S24. For each known occupying voxel of the material, calculate the equivalent linear thickness of the voxel in the preset direction based on the spatial distribution of its internal point cloud or a predefined material density table, and obtain the equivalent thickness of the voxel. S25. For each material category in the multi-material voxel map, establish a physical parameter mapping table related to radiative transfer calculation. The physical parameter mapping table should include at least the mass attenuation coefficient or linear attenuation coefficient at different energies, so that the radiative forward transfer model can dynamically determine its attenuation capability according to the material category of the voxel and the energy spectrum of the radiation source during calculation.

3. The three-dimensional reconstruction method for radiation field according to claim 1, characterized in that, In S3, the forward radiative transport model based on voxel space includes: (1) Model parameter input layer, used to receive the activity, energy spectrum, location and multi-material voxel map of the radioactive source; (2) Ray path resolution layer, used to perform ray projection algorithm in voxel space to determine the sequence of voxels through which the line from the radiation source to the detector passes; (3) Material property mapping layer, used to query the linear decay coefficient at the corresponding energy from the preset material physical parameter database according to the material category label of each voxel on the path; (4) Thickness acquisition layer, used to obtain the equivalent travel distance of each voxel along the ray direction; (5) Response calculation layer, used to accumulate distance attenuation factor and material attenuation factor along the path and combine them with detector energy response to calculate theoretical response value.

4. The three-dimensional reconstruction method for radiation field according to claim 3, characterized in that, In S3, for gamma rays, the detector predicted dose rate is calculated after the ray is attenuated by the material and reaches the detector, serving as the theoretical response value. The detector predicted dose rate is... The specific expression is: In the formula, The number of radioactive sources, For the first The activity of a radioactive source, Its dose rate constant, This represents the straight-line distance between the radiation source and the detector. For the ray path, the first Linear decay coefficient of individual units, For the ray in the first The distance traveled within an individual element. The energy response efficiency of the detector. For radiation energy, This represents the set of all voxels along the path from the radiation source to the detector.

5. The three-dimensional reconstruction method for radiation field according to claim 4, characterized in that, In S4, the objective function is constructed. The specific expression is: In the formula, The total number of measurement points. For the first Measured radiation response values ​​at each measurement point Based on current radioactive source parameters The calculated values ​​of the forward radiation transfer model, The regularization coefficient is . For regularization, the radioactive source parameters This includes the location coordinates and activity of the radioactive source.

6. A three-dimensional radiation field reconstruction system, applied to the three-dimensional radiation field reconstruction method as described in any one of claims 1 to 5, characterized in that, It includes a data acquisition module for acquiring 3D point cloud data and visual image data of the target environment; and a multi-material voxel map construction module for performing voxelization processing on the 3D point cloud data and combining the semantic segmentation and material recognition results of the visual image data to construct a multi-material voxel map containing geometric structure, material category and equivalent thickness. The radiation forward transport modeling module is used to establish a radiation forward transport model based on voxel space and calculate the theoretical response value of the detector based on the radiation source parameters and multi-material voxel maps. The source term inversion and radiation field reconstruction module is used to obtain the measured radiation response value of the detector, and construct an objective function based on the theoretical response value and the measured radiation response value. The optimal radiation source parameters are solved through optimization algorithms, and then the three-dimensional radiation field distribution of the entire space is reconstructed.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes a computer program, it implements the steps of the three-dimensional reconstruction method of the radiation field as described in any one of claims 1 to 5.

8. A computer-readable storage medium storing a computer program, characterized in that, The computer program executes the steps of the three-dimensional reconstruction method of the radiation field as described in any one of claims 1 to 5.

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