An analytical method for the full-energy peak function of a cadmium zinc telluride detector gamma energy spectrum

Abstract

The present invention discloses an analytical method based on a gamma energy spectrum full-energy peak function of a cadmium telluride detector, which can accurately fit a function model for the full-energy peak of a cadmium telluride detector to detect gamma energy spectrum and quickly and accurately find the initial values of parameters, so as to accurately and efficiently realize the analysis of the gamma energy spectrum detected by cadmium telluride. This analytical method based on a gamma energy spectrum full-energy peak function of a cadmium telluride detector uses an exponential function as a variable standard deviation to replace the constant standard deviation in the pure Gaussian function and calculates the initial values of the function by a peak search fitting method, and uses a nonlinear least squares fitting method to obtain the parameter values of the function, thereby calculating the net peak area of the full-energy peak and realizing the analysis of the gamma energy spectrum detected by cadmium telluride. Using this analytical method based on a gamma energy spectrum full-energy peak function of a cadmium telluride detector can increase the analysis accuracy of the gamma energy spectrum detected by cadmium telluride and improve the fitting speed and accuracy of energy spectrum analysis.

Description

Technical Field

[0001] The present invention relates to the field of gamma energy spectrum analysis, and particularly to an analysis method based on a gamma energy spectrum full-energy peak function of a cadmium zinc telluride detector. Background Art

[0002] As is well known, the detection principle of γ-rays is mainly the interaction between rays and matter. The measurement of the energy spectrum is achieved by recording the energy deposited by rays in the detector. By analyzing the energy spectrum measured by the detector, the types and radioactive activities of incident γ-particles can be known.

[0003] In recent years, cadmium zinc telluride detectors have been widely used due to their high energy resolution and small size, which is easy to carry. However, due to their small size, charges cannot be completely collected by the detector, resulting in serious tailing at the low energy end, making the full-energy peak no longer symmetrically distributed. The existence of this problem greatly increases the difficulty of energy spectrum analysis, especially for complex energy spectra. In the field of energy spectrum analysis, the most commonly used spectrum analysis method is to use the least squares method to fit the actually measured energy spectrum with a function to obtain a peak-shaped curve approximating the experimental spectrum for subsequent processing of spectrum data. Therefore, the function model used to fit the spectrum peak is crucial. Due to the asymmetric characteristics of the gamma energy spectrum peak of cadmium zinc telluride detectors, it is obviously inaccurate to still use the traditional Gaussian function as the analysis function approximating its peak shape. Therefore, it is particularly important to seek a function model that can perfectly fit the asymmetric peak shape for the analysis of the gamma energy spectrum of cadmium zinc telluride detectors. In addition, since the fitting effect of the function has a great relationship with the initial parameter values, incorrect initial values may lead to serious fitting errors. Traditional initial parameter values usually use empirical values, which usually makes the fitting results inaccurate. Although some researchers have proposed a method to find the initial values using genetic algorithms, this method is relatively cumbersome and time-consuming. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide an analysis method for a gamma energy spectrum full-energy peak function of a cadmium zinc telluride detector that can accurately fit the full-energy peak of the gamma energy spectrum of a cadmium zinc telluride detector and quickly and accurately find the initial parameter values, so as to accurately and efficiently realize the analysis of the gamma energy spectrum of a cadmium zinc telluride detector.

[0005] The technical solution adopted by the present invention to solve its technical problems is: an analysis method based on a gamma energy spectrum full-energy peak function of a cadmium zinc telluride detector, including the following steps:

[0006] S1. Obtain a γ energy spectrum through a cadmium zinc telluride detector; use the mean shift method to smooth the γ energy spectrum data. Take the coordinates of the point to be smoothed as x0 = i, take m points on each side, a total of 2m + 1 points, and use the arithmetic mean of these 2m + 1 points as the corrected value of this point to obtain the smoothed spectrum data:

[0007]

[0008] S2. For the spectral data obtained in step S1 subtract the energy spectrum background; obtain the net count spectrum data n(i);

[0009] S3. Determine the peak position of the net count spectrum data n(i) obtained in step S2 through a simple comparison method;

[0010] S4. Perform curve fitting on the full-energy peak of the energy spectrum after background subtraction obtained in step S3, including the following process:

[0011] Adopt the ERSD response function:

[0012]

[0013] where H represents the peak height, the peak position u is a position parameter, and σ x is the variable standard deviation of the Gaussian function, and the specific expression is as follows:

[0014] σ x = w[b + exp(-a(x - u)]

[0015] where a is the coefficient of the independent variable (x - u); w is the coefficient of the entire exponential function. When a < 0, the peak shape shows a front tail; when a > 0, the peak shape shows a back tail. The change of the entire peak shape mainly gathers in the interval a ∈ (-1, 1). When a is outside this interval, the influence on the peak shape is very small; the value of w affects the peak width. For peaks with similar energies, the closer the value of w is to 0, the wider the peak width. The influence of the value of w on both sides of 0 on the peak shape is the same, and the value of w cannot be 0;

[0016] b is the tailing correction coefficient, and whether this coefficient is added is considered according to the specific peak shape. When the asymmetry of the peak shape is very low, this item does not need to be added;

[0017] Then use the non-linear least squares fitting method to fit the peak shape;

[0018] S5. Calculate the net peak area of the full-energy peak through the key parameter values of the response function obtained in step 4, so as to realize the quantitative analysis of the energy spectrum.

[0019] Specifically, in step S2, the improved Simpson SNIP algorithm is used to subtract the energy spectrum background; it includes the following steps:

[0020] First, it is necessary to transform the count value of each channel with the LLS operator

[0021] Then perform iteration on Y(i), and the iteration formula is:

[0022]

[0023] Among them, n represents the nth iteration, whose value starts from 1 and is incremented by 1 after each iteration until its value is equal to the given m value, where m represents the peak width parameter; and then the background spectrum data is obtained through the inverse LLS transform:

[0024]

[0025] Finally, the net count spectrum after background subtraction is obtained by subtracting the background spectrum data obtained through the inverse LLS transform from the spectrum data obtained in step 1

[0026] Specifically, determining the peak position through the simple comparison method in step S3 includes the following steps:

[0027] Taking x0 = i as the coordinates of the peak search point, m points are taken on both the left and right sides,

[0028] When the condition: is satisfied, the existence of the peak is determined, where the k value is usually taken from 1 to 1.5;

[0029] By finding the maximum value in n i-m and n i+m the corresponding channel address is the peak position found;

[0030] For a single peak, the energy corresponding to the peak position is directly obtained through energy calibration based on the peak search result to achieve qualitative analysis of the nuclide;

[0031] For complex multiple peaks, the nonlinear least squares fitting method is used for deconvolution to obtain the peak position parameter u, and then qualitative analysis of the nuclide is achieved through energy calibration;

[0032] Using the above simple comparison method to determine the boundary of the full-energy peak, when a certain point in the energy spectrum satisfies the conditions and the left and right boundaries i - l and i + r of the full-energy peak can be obtained.

[0033] Specifically, the nonlinear least squares fitting method reaches the best fitting state by minimizing the difference between the objective function and the experimental data, and its expression is:

[0034]

[0035] Among them, l and r are the left and right channel addresses of the region of interest of the energy spectrum, f i is the peak shape fitting value of the ith channel, n i is the net count value of the energy spectrum of the ith channel after background subtraction, and Q 2 represents the difference between the fitting data and the experimental data.

[0036] Specifically, the initial value of the nonlinear least squares fitting method is found by the following method:

[0037] The peak position u and peak height H of the total energy peak are obtained by a simple peak finding method. The known values of peak position u and peak height H are substituted into the objective function as constants. The three unknown parameters w, a and b are fitted by the least squares method to obtain the initial values of the parameters.

[0038] The beneficial effects of the present invention are as follows: the present invention discloses an analytical method based on a gamma energy spectrum full energy peak function of a cadmium zinc telluride detector, constructs a gamma energy spectrum full energy peak response function measured by a CZT detector, fits the gamma energy spectrum full energy peak measured by the CZT detector through the response function, and proposes a new method to quickly obtain the initial value of the least squares fitting parameters, thereby improving the fitting speed and accuracy of energy spectrum analysis; the invention has the following advantages:

[0039] 1) A function model that can accurately describe the asymmetric peak is constructed, which makes up for the defect that the traditional Gaussian fitting cannot correctly fit the asymmetric peak, provides convenience for the subsequent gamma energy spectrum analysis, and increases the analytical accuracy of the gamma energy spectrum of the CdZnTe detector;

[0040] 2) The method for calculating the initial value of the parameter in the analytical method based on the full energy peak function of the gamma energy spectrum of a cadmium zinc telluride detector described in the present invention is not only convenient and fast, but also highly accurate, thereby improving the analytical speed of the gamma energy spectrum of the cadmium zinc telluride detector. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 It is a flow chart of the analytical method of the gamma energy spectrum full energy peak function model of the cadmium zinc telluride detector in the present invention;

[0042] Figure 2 This is a graph showing the result of fitting the Cs-137γ spectrum using a Gaussian function model according to an embodiment of the present invention;

[0043] In the figure, the calculation formula of the residual w is as follows:

[0044]

[0045] In the formula, f i is the fitted data, y i is experimental data;

[0046] Figure 3 This is a diagram showing the result of fitting the Cs-137γ energy spectrum with the ERSD function model in an embodiment of the present invention. DETAILED DESCRIPTION

[0047] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0048] As attached Figure 1As shown in the figure, the analytical method for the full-energy peak function of the gamma energy spectrum based on a cadmium telluride detector in the present invention uses an exponential function as a variable standard deviation to replace the constant standard deviation in the pure Gaussian function and the peak-seeking fitting method to calculate the initial value of the function, and uses the nonlinear least squares fitting method to obtain the parameter values of the function, thereby calculating the net peak area of the full-energy peak and realizing the analysis of the gamma energy spectrum of the cadmium telluride detector, including the following steps:

[0049] S1. Obtain the γ energy spectrum through a cadmium telluride detector; use the average shift method to smooth the γ energy spectrum data. Taking x0 = i as the coordinate of the point to be smoothed, m points are taken on each side, with a total of 2m + 1 points. Use the arithmetic mean of these 2m + 1 points as the corrected value of this point, so as to obtain the smoothed spectrum data:

[0050]

[0051] S2. For the spectrum data obtained in step 1 Use the improved Simpson SNIP (the statistics sensitive nonlinear iterative peak-clipping) algorithm to subtract the energy spectrum background. First, it is necessary to transform the count value of each channel with the LLS operator

[0052] Then iterate Y(i), and the iteration formula is:

[0053]

[0054] where n represents the nth iteration, its value starts from 1, and is incremented by 1 after each iteration until its value is equal to the given m value, and m represents the peak width parameter; then obtain the background spectrum data through the inverse LLS (Square root and Ln operator twice) transformation Finally, subtract the background spectrum data obtained by the inverse LLS transformation from the spectrum data obtained in step 1 to obtain the net count spectrum after background subtraction

[0055] S3. Determine the peak position of the net count spectrum data n(i) obtained in step 2 through the simple comparison method; taking x0 = i as the coordinate of the point to be peak-seeking, m points are taken on each side. When the condition: is satisfied, it can be considered that there is a peak. Among them, the k value is usually taken as 1 to 1.5. The larger the m value, the lower the peak-seeking sensitivity, resulting in some weak peaks that may be ignored. By finding the maximum value in n i-m and n i+m the corresponding channel address is the peak position found; then use the energy scale to obtain the energy corresponding to the peak position, thereby realizing the qualitative analysis of the nuclide.

[0056] For a single peak, the energy corresponding to the peak position is directly obtained by energy calibration through the result of peak searching, and qualitative analysis of nuclides is realized;

[0057] For a complex multiple peak, deconvolution is performed using the non - linear least - squares fitting method to obtain the peak position parameter u, and then qualitative analysis of nuclides is realized through energy calibration;

[0058] This method is also used to determine the boundaries of the full - energy peak. When a certain point in the energy spectrum satisfies the conditions and the left and right boundaries i - l and i + r of the full - energy peak can be obtained;

[0059] S4. Curve fitting is performed on the full - energy peak of the energy spectrum after background subtraction in step 3, including the following process:

[0060] For a general γ - spectrum, after background subtraction, its full - energy peak response function is usually a Gaussian function. However, due to the small volume of the cadmium zinc telluride detector and the incomplete charge collection characteristics, serious tailing appears at the low - energy end of the full - energy peak. Using the traditional Gaussian function to fit the full - energy peak will have a large error. To solve this problem and improve the accuracy of energy spectrum analysis, the present invention proposes a new full - energy peak function model. As is well known, the Gaussian function is a symmetric function, and the standard deviation parameter in it is the peak - shape parameter, which affects and determines the peak shape. When the standard deviation is a constant, the peak shape is symmetrically distributed, that is, the abscissa distance between the same height position on both sides of the peak position and the peak position is equal. When the standard deviation is variable, the peak shape will be determined by this variable standard deviation. Therefore, as long as a suitable function is found to replace the constant standard deviation in the Gaussian function, any peak shape can be described. However, this function must have the following two properties: First, the function must depend on the peak position; Second, the function must have a high degree of flexibility and will not over - correct the peak shape. Considering the above two factors, the present invention selects an exponential function as a method to modify the Gaussian function for the variable standard deviation of the Gaussian function to adapt to the situation where the peak shape is asymmetric due to tailing at the low - energy end. This new response function is called the ERSD function (Exponential Replacement Standard Deviation Function):

[0061]

[0062] where H represents the peak height, the peak position u is the position parameter, and σ x is the variable standard deviation of the Gaussian function, and the specific expression is as follows:

[0063] σ x = w[b + exp(-a(x - u)]

[0064] Among them, a and w are parameters that determine the peak shape. The natural exponential function is a very flexible function. It is reasonable and effective to use this function as the basis function of the variable standard deviation function. To better control the influence of this function on the peak tailing, the present invention adds the coefficient a to the independent variable (x - u) that depends on the peak position. To prevent this function from over-correcting the peak shape, w is added as the coefficient of the entire natural exponential function to adapt to the correction of any peak shape. When a < 0, the peak shape shows front-end tailing; when a > 0, the peak shape shows back-end tailing. The change of the entire peak shape mainly concentrates in the interval a ∈ (-1, 1). When a is outside this interval, the influence on the peak shape is very small. The value of w affects the peak width. For peaks with similar energies, the closer the value of w is to 0, the wider the peak width. The influence of w values at both ends of 0 on the peak shape is the same, and the value of w cannot be 0. b is the tailing correction term, and whether this term needs to be added can be considered according to the specific peak shape. When the asymmetry of the peak shape is very low, this term does not need to be added.

[0065] After constructing the response function model, it is necessary to use the non-linear least squares fitting method to fit the peak shape. This method reaches the best fitting state by minimizing the difference between the objective function and the experimental data, and its expression is where l and r are the left and right channel addresses of the region of interest of the energy spectrum, f i is the peak shape fitting value of the i-th channel, n i is the net count value of the energy spectrum at the i-th channel after background subtraction, and Q 2 represents the difference between the fitting data and the experimental data. The smaller its value, the better the fitting effect.

[0066] In non-linear least squares fitting, the selection of the initial value has a great influence on the fitting effect. To ensure that the fitting function can correctly fit and improve the speed and accuracy of energy spectrum analysis, the present invention proposes a new method to find the initial value, that is, the peak position u and peak height H of the full-energy peak are obtained through the simple peak search method, and the known values of the peak position u and peak height H are substituted into the objective function as constants, and the three unknown parameters w, a, and b are obtained through least squares fitting, so that the initial values of the parameters are found. According to the above operations, relatively accurate initial values of the parameters can be obtained, and then through the non-linear least squares fitting method, the unknown parameters H, u, w, a, and b in the function model can be obtained.

[0067] S5. Calculate the net peak area of the full-energy peak through the key parameter values of the response function obtained in step 4, and realize the quantitative analysis of the energy spectrum.

[0068] Embodiment

[0069] The above analytical method of the gamma energy spectrum full-energy peak function model of the cadmium telluride detector described in the present invention is used for γ energy spectrum testing; specifically as follows:

[0070] In this embodiment, the energy spectrum test is performed using an antimony-zinc-cadmium energy spectrometer μSPEC 1500 (the energy resolution at 662 keV of γ-rays is 3.5%), and the test source is Cs-137. To better evaluate the goodness of fit of the function model, uncertainty and standardized chi-square are introduced for comparison. The specific fitting parameter values, uncertainty, and standardized chi-square are shown in Table 2, and the expression of the standardized chi-square Reχ 2 is as follows:

[0071]

[0072] where v is the degree of freedom, v = r - l - m, m is the number of parameters, r and l are the left and right boundary channel addresses respectively, f i and n i are the peak shape fitting value and the net count value of the energy spectrum at the i-th channel respectively. The closer the value of the standardized chi-square Reχ 2 is to 1, the better the fitting effect.

[0073] The γ energy spectrum collected by the antimony-zinc-cadmium energy spectrometer μSPEC 1500 is analyzed through the following steps:

[0074] S1. For the smoothing of the spectral data, the moving average method is adopted. Taking x0 = i as the coordinate of the point to be smoothed, m points are taken on each side, with a total of 2m + 1 points. The arithmetic average of these 2m + 1 points is used as the corrected value of this point to obtain the smoothed spectral data:

[0075]

[0076] S2. The spectral data obtained in step S1 is used to subtract the energy spectrum background by adopting the improved Simpson SNIP algorithm to obtain the net count spectral data n(i);

[0077] S3. The net count spectral data n(i) obtained in step S2 is used to determine the peak position through the simple comparison method. Taking x0 = i as the coordinate of the peak searching point, m points are taken on each side,

[0078] When the condition: is satisfied, the existence of the peak is determined, where the k value is usually taken as 1 to 1.5. By finding the maximum value in n i-m and n i+m , the corresponding channel address is the peak position found. For a single peak, the energy corresponding to the peak position is directly obtained through energy calibration based on the result of peak searching to realize the qualitative analysis of the nuclide. For a complex multiple peak, the nonlinear least squares fitting method is used for deconvolution to obtain the peak position parameter u, and then the qualitative analysis of the nuclide is realized through energy calibration;

[0079] The boundary of the full energy peak is determined by adopting the above simple comparison method. When a certain point in the energy spectrum satisfies the condition and When it is, the left and right boundaries i-l and i+r of the full-energy peak can be obtained;

[0080] S4. Perform curve fitting on the full-energy peak of the background-subtracted energy spectrum obtained in step S3, including the following process:

[0081] Adopt the ERSD response function:

[0082]

[0083] Among them, H represents the peak height, the peak position u is the position parameter, and σ x is the variable standard deviation of the Gaussian function, and the specific expression is as follows:

[0084] σ x = w[b + exp(-a(x - u)]

[0085] Among them, a is the coefficient of the independent variable (x - u); w is the coefficient of the entire natural exponential function. When a < 0, the peak shape shows a front tail; when a > 0, the peak shape has a back tail. The change of the entire peak shape mainly concentrates in the interval a ∈ (-1, 1). When a is outside this interval, the influence on the peak shape is very small; the value of w affects the peak width. For peaks with similar energies, the closer the value of w is to 0, the wider the peak width. The influence of the value of w at both ends of 0 on the peak shape is the same, and the value of w cannot be 0;

[0086] b is the tailing correction coefficient, and whether this coefficient is added is considered according to the specific peak shape. When the asymmetry of the peak shape is very low, this item does not need to be added;

[0087] Then use the non-linear least squares fitting method to fit the peak shape;

[0088] The non-linear least squares fitting method reaches the best fitting state by minimizing the difference between the objective function and the experimental data, and its expression is:

[0089]

[0090] Among them, l and r are the left and right channel addresses of the region of interest of the energy spectrum, and f i is the peak shape fitting value of the i-th channel, and n i is the net count value of the energy spectrum of the i-th channel after background subtraction, and Q 2 represents the difference between the fitting data and the experimental data. The initial value of the non-linear least squares fitting method is found through the following method:

[0091] Obtain the peak position u and peak height H of the full-energy peak through the simple peak search method, substitute the known values of the peak position u and peak height H as constants into the objective function, and obtain the three unknown parameters w, a, and b through the least squares fitting to obtain the initial values of the parameters.

[0092] S5. Obtain the respective key parameter values of the response function obtained in step 4, thereby calculating the net peak area of the full-energy peak and realizing the quantitative analysis of the energy spectrum; obtain Table 1, Figure 2 and Figure 3 the fitting results of

[0093] Table 1 Initial parameter fitting result table:

[0094]

[0095] As can be seen from Table 1, the fitting results obtained by calculating the initial values using the analytical method of the full-energy peak function model of the cadmium telluride detector described in the present invention are basically consistent with the actual energy spectrum data, while the fitting results obtained by the random number method have serious errors, indicating that the fitting initial values have a very important influence on the fitting results, and the method for calculating the initial values proposed by the present invention is effective and accurate.

[0096] Table 2 Parameter values, uncertainties, and Reχ 2 value results of the ERSD model and the Gaussian model for fitting Cs-137:

[0097]

[0098] As can be seen from Table 2, whether viewed from the uncertainty or from the Reχ 2 viewpoint, the superiority of the fitting result with the Gaussian function as the peak shape function model is far inferior to that of the ERSD function model. The Reχ 2 value of the ERSD model for fitting Cs137 is 1.15, which is very close to 1, while the Reχ 2 value of the Gaussian function model is 8.93, indicating that the model has a very good effect in fitting the asymmetric peaks of the cadmium telluride detector gamma energy spectrum.

[0099] Such as Figure 2 and Figure 3From the fitting results, it can be seen that the Gaussian function model has a very poor fitting effect on the Cs-137 energy spectrum, especially at the low-energy end tail, where the experimental data points in this part are not fitted at all. However, the fitting curve of the ERSD function model can almost perfectly approach the experimental spectral peak. This indicates that the peak shape function model proposed in this paper is not only feasible but also extremely excellent in fitting the asymmetric peaks of the gamma energy spectrum of cadmium zinc telluride detectors. A good fitting effect plays a crucial role in calculating the net peak area of the full-energy peak. Only a curve that can perfectly approximate the experimental data of the gamma energy spectrum can accurately calculate the area of the full-energy peak, thereby accurately analyzing the activity of radionuclides and achieving accurate quantitative analysis of the gamma energy spectrum. This also strongly proves that the analytical method of the full-energy peak function model of the gamma energy spectrum of the cadmium zinc telluride detector described in the present invention is extremely excellent, greatly increasing the analytical accuracy of the gamma energy spectrum of the cadmium zinc telluride detector.

Claims

1. An analytical method based on a gamma energy spectrum full-energy peak function of a cadmium zinc telluride detector, characterized in that, It includes the following steps: S1. Obtain the γ energy spectrum through an antimony-zinc-cadmium detector; smooth the γ energy spectrum data using the moving average method. Taking \(x_0 = i\) as the coordinate of the point to be smoothed, \(m\) points are taken on each side, with a total of \(2m + 1\) points. Use the arithmetic mean of these \(2m + 1\) points as the corrected value of this point to obtain the spectrum data after smoothing: S2. For the spectral data obtained in step S1 subtract the energy spectrum background to obtain the net count spectral data n(i); S3. Determine the peak position of the net count spectrum data \(n(i)\) obtained in step S2 through a simple comparison method; S4. Perform curve fitting on the full-energy peak of the spectrum after background subtraction obtained in step S3, including the following process: Adopt the ERSD response function: where H represents the peak height, the peak position u is the position parameter, and σ x is the variable standard deviation of the Gaussian function, and the specific expression is as follows: σ x = w[b + exp(-a(x - u))] Among them, \(a\) is the coefficient of the independent variable \((x - u)\); \(w\) is the coefficient of the entire natural exponential function. When \(a \lt 0\), the peak shape shows a front tail; when \(a \gt 0\), the peak shape has a back tail. The change of the entire peak shape mainly gathers in the interval \(a\in(-1,1)\). When \(a\) is outside this interval, the influence on the peak shape is very small; the value of \(w\) affects the peak width. For peaks with similar energies, the closer the value of \(w\) is to 0, the wider the peak width. The influence of the value of \(w\) on both sides of 0 on the peak shape is the same, and the value of \(w\) cannot be 0; \(b\) is the tailing correction coefficient, and whether this coefficient is added is considered according to the specific peak shape. When the asymmetry of the peak shape is very low, this item does not need to be added; Then use the non-linear least squares fitting method to fit the peak shape; S5. Calculate the net peak area of the full-energy peak through the key parameter values of the response function obtained in step 4, so as to realize the quantitative analysis of the energy spectrum.

2. The analytical method for the full-energy peak function of gamma energy spectrum based on a cadmium zinc telluride detector according to claim 1, wherein: In step S2, the improved Simpson SNIP algorithm is used to subtract the spectrum background; it includes the following steps: First, the spectral data need to be processed The LLS operator is used to transform the count value of each channel Then perform iteration on \(Y(i)\), and the iteration formula is: Among them, \(n\) represents the \(n\)th iteration, and its value starts from 1 and is incremented by 1 after each iteration until its value is equal to the given \(m\) value, where \(m\) represents the peak width parameter; then obtain the background spectrum data through the inverse LLS transform: Finally, subtract the background spectral data obtained by the inverse LLS transform from the spectral data obtained in step 1 to obtain the net count spectrum after background subtraction 3. The analytical method for the full-energy peak function of gamma energy spectrum based on a cadmium telluride detector according to claim 2, wherein In step S3, determining the peak position through the simple comparison method includes the following steps: Taking \(x_0 = i\) as the coordinate of the peak-seeking point, \(m\) points are taken on each side, When the condition: is satisfied, the presence of a peak is determined, where the value of k is typically taken as 1 to 1.5; By finding the maximum value among n i-m and n i+m the corresponding track address is the peak position found; For a single peak, directly perform energy calibration through the peak-seeking result to obtain the energy corresponding to the peak position, and realize the qualitative analysis of the nuclide; For a complex multiple peak, use the non-linear least squares fitting method to deconvolute to obtain the peak position parameter \(u\), and then realize the qualitative analysis of the nuclide through energy calibration; Using the above simple comparison method to determine the boundaries of the full-energy peak, when a certain point in the energy spectrum satisfies the conditions and , the left and right boundaries i-l and i+r of the full-energy peak can be obtained.

4. The analytical method for the full-energy peak function of a gamma energy spectrum based on a cadmium zinc telluride detector as described in claim 3, characterized in that: The non-linear least squares fitting method reaches the best fitting state by minimizing the difference between the objective function and the experimental data, and its expression is: where l and r are the left and right channel addresses of the energy spectrum region of interest, f i is the peak shape fitting value of the i-th channel, n i is the net count value of the energy spectrum at the i-th channel after background subtraction, Q 2 represents the difference between the fitted data and the experimental data.

5. The analytical method for the full-energy peak function of the gamma energy spectrum based on a cadmium zinc telluride detector as described in claim 4, wherein: The initial value of the non-linear least squares fitting method is found through the following method: Obtain the peak position \(u\) and peak height \(H\) of the full-energy peak through the simple peak-seeking method, substitute the known values of the peak position \(u\) and peak height \(H\) as constants into the objective function, and obtain the three unknown parameters \(w\), \(a\), and \(b\) through the least squares fitting to obtain the initial values of the parameters.

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