Gamma ray energy spectrum and polarization degree integrated measurement method
By obtaining the spatial distribution measurement results and response functions of scattered γ rays, a system of equations is constructed, and the integrated measurement problem of MeV-level γ ray energy spectrum and polarization degree is solved, achieving a fast and accurate measurement effect.
Patent Information
- Application Number
- CN202510745723.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-06-05
- Publication Date
- 2025-08-26
AI Technical Summary
Existing measurement methods cannot accurately measure the energy spectrum and polarization degree of pulsed gamma rays at the MeV level.
By obtaining the spatial distribution measurement results of the scattered γ rays generated by Compton scattering, the energy spectrum of the γ ray and the response function between the polarization degree and the spatial distribution of the scattered γ rays are determined, and the system of equations is constructed and solved to achieve integrated measurement of the energy spectrum and polarization degree.
It realizes rapid and accurate measurement of the energy spectrum and polarization degree of MeV-level gamma rays, reduces costs, and meets the high-efficiency and low-cost testing and diagnosis requirements of pulsed gamma rays and X-rays.
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Figure CN120539780A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of gamma ray measurement, and in particular to a method for integrated measurement of the energy spectrum and polarization degree of gamma rays. Background Art
[0002] Currently, common methods for measuring pulsed gamma-ray (γ-ray) energy spectra include attenuation, Bragg diffraction, and magnetic spectrometry. Bragg diffraction can be used for energy spectrum measurements when the gamma-ray energy is in the keV range. For example, existing methods use HOPG to measure the Kα-ray energy spectrum of Cu plasma. However, this method cannot measure pulsed gamma-rays above 100 keV, or even at the MeV level.
[0003] When gamma-ray energies reach the MeV level, the pulsed gamma-ray spectrum can be measured using attenuation methods and magnetic spectrometers. For example, the Compton magnetic spectrometer uses recoil electrons generated by Compton scattering to measure the energy spectrum. However, neither the attenuation method nor the magnetic spectrometer can measure the polarization degree of pulsed gamma-rays.
[0004] For gamma-ray polarization measurements, the photoelectric effect can be used to measure the polarization of low-energy X-rays. However, this method can only measure energies up to a few hundred keV, making it unsuitable for MeV-level gamma-ray diagnostics. For MeV-level gamma-rays, some research has developed detectors using single-photon counting approaches, achieving high measurement accuracy. However, when used for pulsed gamma-ray measurements, this approach can produce pulse pile-up, preventing accurate results.
[0005] In summary, existing measurement methods are unable to accurately integrate the energy spectrum and polarization degree of pulsed gamma rays. Summary of the Invention
[0006] Based on this, it is necessary to provide an integrated measurement method for the energy spectrum and polarization degree of gamma rays to address the above technical problems.
[0007] The present invention adopts the following technical solutions: The present invention provides an integrated measurement method for the energy spectrum and polarization degree of gamma rays. The method first obtains the spatial distribution measurement results of scattered gamma rays generated by Compton scattering of the gamma rays to be measured, and then determines the response function between the energy spectrum and polarization degree of the gamma rays and the spatial distribution of the scattered gamma rays. Based on the spatial distribution measurement results and the response function, a set of equations between the energy spectrum and polarization degree of the gamma rays to be measured and the spatial distribution measurement results is constructed and solved to obtain the energy spectrum and polarization degree of the gamma rays to be measured.
[0008] At least one of the above technical solutions adopted by the present invention can achieve the following beneficial effects: The present invention only needs to obtain the spatial distribution measurement results of scattered gamma rays generated by Compton scattering of the gamma rays to be measured. Based on the Compton scattering principle, the energy spectrum and polarization degree of the gamma rays to be measured can be quickly and accurately measured indirectly and simultaneously through inverse calculation. BRIEF DESCRIPTION OF THE DRAWINGS
[0009] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:
[0010] Figure 1 A schematic flow chart of a method for integrated measurement of gamma-ray energy spectrum and polarization degree provided by the present invention; Figure 2 A schematic diagram of Compton scattering and scattered gamma-ray spatial distribution detection provided by the present invention; Figure 3 A schematic diagram of the response of a 100keV gamma ray with a linear polarization degree of 1 provided by the present invention; Figure 4 A schematic diagram of a 100keV unpolarized gamma-ray response provided by the present invention; Figure 5 A schematic diagram of the response of a 1MeV gamma ray with a linear polarization degree of 1 provided by the present invention; Figure 6 A schematic diagram of the response of a 1MeV unpolarized gamma ray provided by the present invention; Figure 7 A schematic diagram of the energy spectrum and polarization degree of a pulsed gamma ray to be measured provided by the present invention. DETAILED DESCRIPTION
[0011] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with specific embodiments of the present invention and corresponding drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.
[0012] The technical solutions provided by various embodiments of the present invention are described in detail below with reference to the accompanying drawings.
[0013] Figure 1 The present invention is a flow chart of a method for integrated measurement of the energy spectrum and polarization degree of gamma rays, which specifically includes the following steps: S101: Obtaining a measurement result of the spatial distribution of scattered gamma rays generated by Compton scattering of the gamma rays to be measured.
[0014] S102: Determine a response function between the energy spectrum and polarization degree of the gamma rays and the spatial distribution of the scattered gamma rays.
[0015] S103: Based on the spatial distribution measurement results and the response function, a set of equations between the energy spectrum and polarization degree of the gamma ray to be measured and the spatial distribution measurement results is constructed and solved to obtain the energy spectrum and polarization degree of the gamma ray to be measured.
[0016] The present invention converts incident pulsed gamma rays into scattered gamma rays using a Compton scattering target, and measures the spatial distribution of the scattered gamma rays using a gamma ray spatial distribution detector, thereby inferring the energy and polarization degree of the incident pulsed gamma rays.
[0017] The Compton effect is one of three effects of gamma-ray interactions with matter. It generally refers to the process by which incident gamma-rays are scattered by inelastic collisions with electrons in atoms. The gamma-ray transfers some of its energy to the electrons, causing them to break free from the atoms and become recoil electrons. This changes the energy and direction of the gamma-rays. The differential cross section of the scattered gamma-rays is related to the energy and polarization of the incident gamma-rays and can be determined using the Klein-Nishina equation: .
[0018] Where, is the classical electron radius, is the azimuth of the scattered γ-ray (the angle between the electric field direction of the scattered γ-ray and the incident γ-ray), is the scattering angle of the scattered γ-ray (the angle between the scattered γ-ray and the incident γ-ray), is the incident γ-ray energy, is the energy of scattered gamma rays.
[0019] and .
[0020] When the incident γ-ray is linearly polarized, the spatial distribution of the scattered γ-ray is related to the azimuth angle. The probability of scattered gamma rays perpendicular to the electric field (polarization) direction of the incident gamma ray is the highest, and the probability of scattered gamma rays parallel to the electric field direction is the lowest. When the incident gamma ray is circularly polarized or unpolarized, it is equivalent to the superposition of two linearly polarized gamma rays with perpendicular polarization directions and the same other parameters. is no longer relevant, and the differential cross section is now: .
[0021] When the incident gamma ray energy is high, the scattered gamma rays have a strong tendency to scatter forward. When the incident gamma ray energy is low, the probability of forward and backward scattering is equal.
[0022] In summary, the scattering angle The intensity of the scattered gamma rays on the surface is determined by the energy of the incident gamma rays and the azimuth angle The intensity of scattered gamma rays is determined by the polarization of the incident gamma rays. By measuring the spatial distribution of scattered gamma rays, its distribution pattern in scattering angle and azimuth can be obtained, and further deduced to obtain the energy and polarization degree of the incident gamma rays.
[0023] Based on this, the present invention proposes a method for measuring the energy and polarization degree of gamma rays based on the Compton scattering effect. A pulsed gamma ray energy spectrum and polarization degree measurement system is constructed by using a Compton scattering target, a scattered gamma ray spatial distribution detector and a reconstruction algorithm. The function of the Compton scattering target is to convert the incident gamma rays into scattered gamma rays. The spatial distribution detector of scattered gamma rays is used to measure the distribution of scattered gamma rays in space, including the scattering angle and azimuth angle. The choice of detector is based on the energy of the scattered gamma rays: for energies at the hundred keV level, an IP imaging plate can be used; for energies at the MeV level, a scintillator or a semiconductor detector can be used. The detailed schematic diagram is as follows Figure 2 As shown, Figure 2 This is a schematic diagram of Compton scattering and scattered gamma ray spatial distribution detection in the present invention.
[0024] The principle of the above measurement process can be expressed as: .
[0025] Where g is the spatial distribution measurement of scattered gamma rays output by the scattered gamma ray spatial distribution detector, f is the energy spectrum and polarization of the incident pulsed gamma ray, h is the response function between the energy spectrum and polarization of the incident gamma ray and the spatial distribution of the scattered gamma ray, and Ƞ is the noise signal. The energy spectrum and polarization measurement process is essentially an inverse matrix problem: given the response function h between the energy spectrum and polarization of the gamma ray and the spatial distribution of the scattered gamma ray and the spatial distribution measurement g, the energy spectrum and polarization f of the incident gamma ray are calculated.
[0026] The integral form of the above formula can be expressed as: .
[0027] Where, is the measurement result of the spatial distribution of scattered γ-rays, ( x , y ) are spatial distribution coordinates. is the energy and polarization distribution of the incident pulsed gamma ray, with the polarization degree p. The incident pulsed gamma ray can be equivalently decomposed into two parts: a completely linearly polarized pulsed gamma ray P = 1 (with an intensity ratio of p) and an unpolarized pulsed gamma ray P = 0 (with an intensity ratio of 1-p). At each energy point E, it can be equivalently decomposed into two parts and ,get and The energy spectrum and polarization degree of the pulsed gamma ray can be obtained. It is the response function between the energy spectrum and polarization degree of gamma rays and the spatial distribution of scattered gamma rays, indicating that the signal generated on the scattered gamma ray spatial distribution detector after the pulsed gamma ray with energy E and linear polarization degree p passes through the Compton scattering system , ( u , v ) is the spatial distribution coordinate. For a pulsed gamma ray with energy E and polarization degree p, the response function between its energy spectrum and polarization degree and the spatial distribution of the scattered gamma ray is , which can be obtained from the response function between the spatial distribution of linearly polarized γ-rays and scattered γ-rays at the current energy E and the response function between the spatial distribution of unpolarized γ-rays and scattered γ-rays composition:
[0028] .
[0029] The discrete form of the above integral form can be expressed as: .
[0030] Where, Describe the source intensity of gamma rays at energy m and polarization degree 1, represents the source intensity of gamma rays at energy m and polarization degree 0, Indicates the measured image n The intensity of pixel units, coefficient Represents Source intensity versus pixel The contribution of Represents Source intensity versus pixel The contribution of the discrete form n-th coefficient matrix , by the response function Rearranged as a vector.
[0031] The above discrete form can be expressed by matrix multiplication as: ; Right now, .
[0032] Based on this, after obtaining the spatial distribution measurement result g and response function h of the scattered gamma rays formed by Compton scattering of the pulsed gamma rays, the above matrix can be solved to determine the energy spectrum of the incident pulsed gamma rays. and polarization .
[0033] Therefore, in one or more embodiments of the present invention, the spatial distribution measurement results of the scattered gamma rays generated by the Compton scattering of the gamma rays to be measured can be measured first. , 、 are two-dimensional distribution coordinates. The spatial distribution measurement results of scattered gamma rays may include a two-dimensional distribution of at least one parameter of the scattered gamma ray flux density, count rate, and dose rate. The spatial distribution measurement results may be obtained by measuring any one of the gamma detection systems, including scintillators, semiconductor detectors, and imaging panels.
[0034] Then, the response function between the energy spectrum and polarization degree of the gamma rays and the spatial distribution of the scattered gamma rays is determined. Specifically, it can be constructed by calculating the Compton scattering process of sampled gamma rays of different energies and different polarization degrees through Monte Carlo simulation; or it can be constructed through experimental calibration measurement or numerical analysis.
[0035] Afterwards, the following equations can be constructed based on the spatial distribution measurement results and the response function to establish the relationship between the energy spectrum and polarization degree of the gamma ray to be measured and the spatial distribution measurement results: ; Where, For the i Two-dimensional distribution of unpolarized γ-ray pairs at energies The response function of a point, For the i The flux density corresponding to the unpolarized gamma ray at the energy is, For the i Two-dimensional distribution of linearly polarized γ-ray pairs at energies The response function of a point, For the i The flux density corresponding to linearly polarized gamma rays at each energy.
[0036] Thus 、 and To constrain the error, the conditional expectation of the error function (such as the Kullback-Leibler information divergence) between the spatial distribution results of the corresponding scattered γ-rays and the spatial distribution measurement results is determined according to the flux density corresponding to the unpolarized γ-rays and the flux density corresponding to the linearly polarized γ-rays at each energy corresponding to each round of iteration.
[0037] The equations are iteratively solved with the optimization goal of minimizing the conditional expectation of the error function (Kullback-Leibler information divergence) to obtain the final flux density corresponding to the unpolarized gamma ray and the flux density corresponding to the linearly polarized gamma ray at each energy: ; The energy spectrum and polarization degree of the gamma ray to be measured are determined by the following formula based on the flux density corresponding to the unpolarized gamma ray and the flux density corresponding to the linearly polarized gamma ray at each energy: ; ; Where, For the k The flux density corresponding to the unpolarized gamma ray and the flux density corresponding to the linearly polarized gamma ray at each energy corresponding to the iteration, n is the total number of different energies, is the polarization degree of the γ-ray to be measured, is the energy spectrum of the gamma ray to be measured.
[0038] In addition, the above equations can also be solved by using algorithms such as the least squares method, the expectation-maximization algorithm (EM), the regularization algorithm, the genetic algorithm, and the neural network.
[0039] For example, simulations can be performed for 100keV pulsed gamma rays with a linear polarization degree of 1 and unpolarized pulsed gamma rays to determine their corresponding responses. Comparisons show that for different degrees of polarization of pulsed gamma rays, the Compton scattering system response distribution is consistent in the x-direction, but significantly different in the y-direction, providing physical information for polarization diagnosis. Compton scattering results can also be obtained for polarized and unpolarized pulsed gamma rays when the incident gamma ray energy is 1MeV. Comparisons show that the central bright spot position is offset, a feature that can provide physical information for energy spectrum reconstruction.
[0040] Figure 3 This is a schematic diagram of the response of a 100keV gamma ray with a linear polarization degree of 1 in the present invention. Figure 4 This is a schematic diagram of a 100keV unpolarized gamma-ray response in the present invention. Figure 5 This is a schematic diagram of the response of a 1MeV gamma ray with a linear polarization degree of 1 in the present invention. Figure 6 Schematic diagram of the response of a 1MeV unpolarized gamma ray in the present invention.
[0041] After constructing the response function between the energy and polarization of the pulsed gamma ray and the spatial distribution of the scattered gamma rays formed after Compton scattering in the gamma energy spectrum-polarization measurement system, the following types of reconstruction algorithms can be used to solve the matrix problem mentioned above. The first type of reconstruction algorithm solves the equation by minimizing a certain error function, such as the least squares method, the EM algorithm, and the RL algorithm. The second type of algorithm constrains the solution space by introducing a regularization function. Representative algorithms include Tikhonov regularization and total variation regularization. The third type of algorithm uses deep learning to solve the problem, such as genetic algorithms and BP neural networks.
[0042] Taking the EM algorithm as an example, the spatial distribution measurement result g measured by the scattered γ-ray spatial distribution detector is compared with the response function h( ), solve to get the matrix f( ) value, thereby obtaining the energy spectrum of the pulsed γ-ray and polarization degree , and its iterative process is: First choose Kullback-Leibler information divergence as the error function: ; or the associated negative Poisson log-likelihood function: .
[0043] Pick , as well as , that is, normalize the energy spectrum and polarization distribution f of the pulsed gamma ray, the response function h, and the spatial distribution measurement result g obtained by detection. , minimizing the KL information divergence is equivalent to minimizing the negative Poisson log-likelihood function. The EM algorithm seeks the minimum value of the KL information divergence or the negative Poisson log-likelihood function through iteration. Taking the negative Poisson log-likelihood function as an example, the following formula is used in the iteration according to the result of the k-th step: Compute the conditional expectation of the negative Poisson log-likelihood function: .
[0044] Under the constraints and In the case of , find f when the conditional expectation Q is the maximum value, and use it as the maximum likelihood estimation result in the next iteration. The iteration format is: .
[0045] After reconstruction, the energy spectrum of the pulse gamma ray to be measured, the probability of linear polarization / unpolarization of the pulse gamma ray to be measured, and then the energy spectrum and polarization degree of the pulse gamma ray to be measured are obtained. Figure 7 As shown, Figure 7 Schematic diagram of the energy spectrum and polarization degree of a pulsed gamma ray to be measured in the present invention.
[0046] based on Figure 1 The illustrated integrated gamma-ray energy spectrum and polarization degree measurement method first obtains the spatial distribution measurement results of scattered gamma-rays generated by Compton scattering of the gamma-ray to be measured. Then, a response function between the energy spectrum and polarization degree of the gamma-ray and the spatial distribution of the scattered gamma-rays is determined. Based on the spatial distribution measurement results and the response function, a system of equations is constructed and solved to obtain the energy spectrum and polarization degree of the gamma-ray to be measured. The present invention only requires obtaining the spatial distribution measurement results of scattered gamma-rays generated by Compton scattering of the gamma-ray to be measured. Based on the Compton scattering principle, the inverse solution can quickly and accurately indirectly and simultaneously measure the energy spectrum and polarization degree of the pulsed gamma-ray to be measured.
[0047] The method of the present invention reduces costs and can meet the high-efficiency, low-cost testing and diagnosis requirements for the polarization and energy spectrum of pulsed gamma rays and X-rays generated by inverse Compton scattering sources, laser plasma Betatron radiation sources, etc.
[0048] When applying the integrated measurement method of gamma ray energy spectrum and polarization degree provided by the present invention, it is not necessary to Figure 1 The steps are executed in the order shown. The specific execution order of the steps can be determined according to needs, and the present invention does not limit this.
[0049] The technical features of the above embodiments can be combined arbitrarily. In order to make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of the present invention.
Claims
1. A method for integrated measurement of gamma-ray energy spectrum and polarization degree, characterized in that: include: Obtaining a measurement result of the spatial distribution of scattered gamma rays generated by Compton scattering of the gamma rays to be measured; Determine the response function between the energy spectrum and polarization degree of gamma rays and the spatial distribution of scattered gamma rays; According to the spatial distribution measurement results and the response function, a set of equations between the energy spectrum and polarization degree of the gamma ray to be measured and the spatial distribution measurement results are constructed and solved to obtain the energy spectrum and polarization degree of the gamma ray to be measured.
2. The method for integrated measurement of energy spectrum and polarization degree of gamma rays according to claim 1, wherein: The method of constructing a set of equations between the energy spectrum and polarization degree of the gamma ray to be measured and the spatial distribution measurement results based on the spatial distribution measurement results and the response function specifically includes: The following equations are constructed based on the spatial distribution measurement results and the response function to establish the relationship between the energy spectrum and polarization degree of the gamma ray to be measured and the spatial distribution measurement results: ； in, is the spatial distribution measurement result, 、 is the two-dimensional distribution coordinate, For the i Two-dimensional distribution of unpolarized γ-ray pairs at energies The response function of a point, For the i The flux density corresponding to the unpolarized gamma ray at the energy is, For the i Two-dimensional distribution of linearly polarized γ-ray pairs at energies The response function of a point, For the i The flux density corresponding to linearly polarized gamma rays at each energy.
3. The method for integrated measurement of energy spectrum and polarization degree of gamma rays according to claim 2, wherein: Solve the equations between the energy spectrum and polarization degree of the gamma ray to be measured and the spatial distribution measurement results to obtain the energy spectrum and polarization degree of the gamma ray to be measured, specifically including: by 、 and To constrain the error, the conditional expectation of the error function between the spatial distribution results of the scattered γ-rays and the spatial distribution measurement results is determined according to the flux density corresponding to the unpolarized γ-rays and the flux density corresponding to the linearly polarized γ-rays at each energy corresponding to each round of iteration. The system of equations is iteratively solved with the optimization goal of minimizing the conditional expectation of the error function to obtain the final flux density corresponding to the unpolarized gamma ray and the flux density corresponding to the linearly polarized gamma ray at each energy: ； The energy spectrum and polarization degree of the gamma ray to be measured are determined by the following formula based on the flux density corresponding to the unpolarized gamma ray and the flux density corresponding to the linearly polarized gamma ray at each energy: ； ； Where, For the k The flux density corresponding to the unpolarized gamma ray and the flux density corresponding to the linearly polarized gamma ray at each energy corresponding to the iteration, n is the total number of different energies, is the polarization degree of the γ-ray to be measured, is the energy spectrum of the gamma ray to be measured.
4. The method for integrated measurement of energy spectrum and polarization degree of gamma rays according to claim 1, wherein: The spatial distribution measurement result of the scattered gamma rays includes a two-dimensional distribution of at least one parameter of the flux density, count rate and dose rate of the scattered gamma rays.
5. The method for integrated measurement of energy spectrum and polarization degree of gamma rays according to claim 1, wherein: The spatial distribution measurement result of the scattered gamma rays is obtained by measuring any one of the gamma detection systems including a scintillator, a semiconductor detector and an imaging plate.
6. The method for integrated measurement of energy spectrum and polarization degree of gamma rays according to claim 1, wherein: The response function is constructed by Monte Carlo simulation of the Compton scattering process of sampled gamma rays with different energies and different polarization degrees; or the response function is constructed by experimental calibration measurement or numerical analysis.
7. The method for integrated measurement of gamma-ray energy spectrum and polarization degree according to claim 1, wherein: The equations between the energy spectrum and polarization degree of the gamma ray to be measured and the spatial distribution measurement results are solved by any one of the least square method, maximum expectation algorithm, regularization algorithm, genetic algorithm and neural network.