A method for processing energy spectrum of quasi-hemispherical CdZnTe detector
By employing dynamic energy threshold selection, rise time discrimination, and energy spectrum post-processing algorithms in a quasi-hemispherical CdZnTe detector, the problem of parameter failure caused by individual system differences and hardware replacement was solved, achieving a stable improvement in energy resolution and meeting the needs of high-end nuclear radiation detection.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHAANXI PHOTON NUCLEAR INSTR RADIATION DETECTION TECH CO LTD
- Filing Date
- 2025-10-24
- Publication Date
- 2026-06-30
AI Technical Summary
The existing quasi-hemispherical CdZnTe detectors have difficulty consistently achieving an energy resolution exceeding 1% at the 662 keV energy point. This is mainly due to individual system differences and the failure of discrimination parameters caused by hardware system replacements, which makes it impossible to accurately filter out induced signals with fast rise times and action positions close to the cathode region.
The algorithm employs dynamic selection of energy thresholds, rise time discrimination, and energy spectrum post-processing, including normalization, filtering and smoothing, and background subtraction. By dynamically selecting multiple energy thresholds and rise time ranges, signals with high charge collection efficiency are screened out, and the energy spectrum is optimized through Gaussian filtering and the SNIP algorithm to achieve adaptive parameter matching.
The energy resolution of the quasi-hemispherical CdZnTe detector has been significantly improved from 2%~3% to less than 1%, meeting the stringent requirements of high-end nuclear radiation detection applications and flexibly addressing the differences between different detectors and hardware systems.
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Figure CN121165147B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of nuclear radiation detection technology, and in particular to an energy spectrum processing method for a quasi-hemispherical CdZnTe detector. Background Technology
[0002] Cadmium zinc telluride (CdZnTe) semiconductor materials have become one of the most outstanding detection materials in the field of nuclear radiation detection due to their high atomic number, wide bandgap, high resistivity, and excellent electron mobility. Since the port mobility-lifetime product of CdZnTe materials is about two orders of magnitude lower than that of electrons, these detectors are usually designed as unipolar devices to optimize their charge collection performance. Among them, the quasi-hemispherical electrode structure can effectively improve the energy resolution of the detector by achieving a "small pixel effect." Gamma-ray spectroscopy detectors based on this structure not only have high energy resolution, small size, and ease of use, but can also operate stably at room temperature, thus finding wide application in nuclear safety inspection, radiation dose monitoring, and high-energy physics experiments.
[0003] Currently, in high-precision applications such as deep-earth trace element detection, novel radiopharmaceutical development, and nuclear safety monitoring, stringent requirements are placed on the energy resolution of detectors at the 662 keV energy point, demanding a resolution better than 1%. To improve energy resolution, rise time discrimination of the detector's output signal has become an important method. Rise time discrimination technology uses the rising edge waveform of the charge-sensitive preamplifier output signal to filter out event signals with shorter rise times and physical locations close to the detector's cathode region. Since the weighting potential corresponding to such signals is close to the ideal range of 0 to 1, theoretically, higher energy resolution can be achieved for complete energy deposition events. However, the energy resolution of current quasi-hemispherical CdZnTe detectors remains at the level of 2% to 3%, struggling to consistently break through the 1% bottleneck. The main reason for this is that the actual performance of this technology heavily relies on discrimination parameters, such as energy threshold and rise time threshold. However, these parameters face universality challenges in practical applications. On the one hand, different quasi-hemispherical CdZnTe detectors exhibit individual inconsistencies in key parameters such as electron and hole collection efficiency due to inherent differences in material growth and fabrication processes. This necessitates precise matching of different discrimination parameters, leading to the system algorithm's inability to effectively filter out induced signals with faster rise times and closer interaction locations to the cathode region under the same testing environment. On the other hand, after hardware system replacement, individual performance differences in electronic components (such as the feedback capacitor in the charge-sensitive preamplifier, whose tolerance is typically ±10%) directly alter the rise time characteristics of the output signal. This renders the fixed discrimination parameters in the original algorithm ineffective, failing to accurately adapt to new signal waveforms.
[0004] Therefore, proposing an energy spectrum processing method that can overcome individual differences in the system and achieve adaptive parameter matching is crucial for promoting the stable and reliable high energy resolution of quasi-hemispherical CdZnTe detectors. Summary of the Invention
[0005] To address the problems existing in the prior art, this invention provides an energy spectrum processing method for quasi-hemispherical CdZnTe detectors, which solves the problem that fixed-time discrimination parameters cannot be compatible with different detectors and hardware systems, and achieves the goal of significantly and stably improving the resolution of quasi-hemispherical CdZnTe detectors.
[0006] To achieve the above objectives, the present invention provides the following technical solution:
[0007] This invention proposes an energy spectrum processing method for a quasi-hemispherical CdZnTe detector, comprising the following steps:
[0008] Step 1: Acquire the raw signal collected by the quasi-hemispherical CdZnTe detector;
[0009] Step 2: After normalizing the amplitude of the original signal from the baseline to the highest point during the rising phase, dynamically select multiple energy thresholds and perform rise time discrimination on the normalized signal within each energy threshold; filter out signals with rise time greater than RTflag and determine the rise time range corresponding to the energy threshold.
[0010] Step 3: Construct the intermediate energy spectrum corresponding to each energy threshold based on the signal with a rise time greater than RTflag and the rise time range;
[0011] Step 4: Post-process the intermediate energy spectrum to obtain the target energy spectrum corresponding to each energy threshold.
[0012] Furthermore, the energy thresholds include: 5%-95%, 10%-95%, 5%-90%, and 10%-90%.
[0013] Further, in step 2, the method for determining RTflag is as follows: the sampling time is divided into groups of m sampling intervals, where 6≤m≤15. The integral count of the pulse amplitude corresponding to all normalized signals within each rise time interval is counted in the full spectrum. A graph showing the relationship between the rise time interval and the integral count of the signal within that interval in the full spectrum is plotted. Based on the graph, the rise time critical value RTflag within the energy threshold is determined. The rise time range corresponding to the energy threshold is (RTflag + 1ns) ~ (RTflag + effective interval width), where the effective interval is a continuous rise time interval in which the contribution of the integral count is ≥70%.
[0014] Further, in step 3, the method for constructing the intermediate energy spectrum includes: accumulating signals with rise times greater than RTflag within each energy threshold to obtain the total original energy spectrum corresponding to that energy threshold; filtering out signals corresponding to the rise time range from the total original energy spectrum; accumulating the signals corresponding to the rise time range to obtain the intermediate energy spectrum corresponding to that energy threshold.
[0015] Furthermore, in step 4, the post-processing of the intermediate energy spectrum includes: sequentially performing filtering and smoothing processing and background subtraction processing on the intermediate energy spectrum.
[0016] Furthermore, the filtering and smoothing process employs a Gaussian filtering function and is calculated according to the following formula:
[0017]
[0018] In the formula S i The energy spectrum after filtering and smoothing is at the 1st i The counting of the Tao; O i+j For the intermediate energy spectrum at the 1st i + j The counting of the Tao; C j For Gaussian filtering functions with a window width of - k arrive k The coefficient within.
[0019] Furthermore, the background subtraction process employs the SNIP algorithm.
[0020] Furthermore, the background subtraction process includes first performing digital filtering on the smoothed energy spectrum to obtain a numerically transformed energy spectrum, determining the background spectrum to be stripped based on the numerically transformed energy spectrum, and performing an inverse numerical transformation on the background spectrum to be stripped to obtain the target energy spectrum.
[0021] Furthermore, the smoothed energy spectrum is first digitally filtered using the following formula:
[0022]
[0023] In the formula, G i The energy spectrum after numerical transformation is at the th i The counting of the Tao.
[0024] Furthermore, the following formula is used to perform a numerical inverse transform on the background spectrum to be stripped:
[0025]
[0026] In the formula, b i In order to treat the stripping of the background spectrum in the first iThe counting of the Tao B i To determine the target energy spectrum in the first... i The counting of the Tao.
[0027] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0028] (1) By combining energy threshold discrimination, rise time discrimination and energy spectrum post-processing algorithm, this invention steadily improves the energy resolution of the quasi-hemispherical CdZnTe detector for 662 keV gamma rays from the conventional 2%~3% to less than 1%, which meets the stringent requirements of high-end nuclear radiation detection applications for high-performance detectors.
[0029] (2) After normalizing the amplitude of the original signal from the baseline to the highest point during the rising phase, this invention selects four energy thresholds of 5%-95%, 10%-95%, 5%-90%, and 10%-90% for dynamic changes. The energy contribution of the effective signal of the quasi-hemispherical CdZnTe detector is mainly concentrated in the middle to late stages of the rising phase. This invention can cover the core energy contribution range by normalization and the combination of wide and narrow thresholds. Different quasi-hemispherical CdZnTe detectors can capture effective signals with high charge collection efficiency by dynamically selecting matching energy thresholds. This invention can flexibly respond to individual differences in carrier collection efficiency of different CdZnTe detectors and changes in signal characteristics caused by different hardware systems (such as the tolerance of the preamplifier feedback capacitor), thereby steadily improving the energy resolution of the quasi-hemispherical CdZnTe detector.
[0030] (3) By matching a specific rise time range to each energy threshold, the present invention can accurately screen out “superior” signals with high charge collection efficiency and originating from the region near the detector cathode, while effectively eliminating noise signals and signals caused by long hole drift time and severe charge loss. This significantly reduces the background count and tailing effect of the energy spectrum from the source, further improving the energy resolution of the quasi-hemispherical CdZnTe detector.
[0031] (4) This invention integrates signal discrimination with subsequent energy spectrum post-processing (including filtering and smoothing and background subtraction). Filtering and smoothing suppresses statistical fluctuations in the energy spectrum, while background subtraction can subtract the Compton plateau and radiation background to the greatest extent. This combined processing further extracts a pure net energy spectrum, which together ensures the realization of the energy resolution index of the final quasi-hemispherical CdZnTe detector. Attached Figure Description
[0032] Figure 1 This is a flowchart of a method for achieving high energy resolution in a quasi-hemispherical CdZnTe detector according to an embodiment of the present invention.
[0033] Figure 2 This is a schematic diagram of the energy spectrum for different rise time ranges when the energy threshold is 5%-95% in Example 1;
[0034] Figure 3 This is a schematic diagram of the energy spectrum for different rise time ranges when the energy threshold is 10%-95% in Example 1;
[0035] Figure 4 This is a schematic diagram of the energy spectrum for different rise time ranges when the energy threshold is 5%-90% in Example 1;
[0036] Figure 5 This is a schematic diagram of the energy spectrum for different rise time ranges when the energy threshold is 10%-90% in Example 1;
[0037] Figure 6 This is a graph showing the relationship between the number of iterations for background subtraction and the target energy spectrum when the energy threshold is 10%-90% in Example 1.
[0038] Figure 7 The graphs shown in Example 1 are: iteration number-peak efficiency relationship (A) and iteration number-energy resolution relationship (B).
[0039] Figure 8 The diagram shows the total original energy spectrum (A) and the target energy spectrum (B) corresponding to different energy thresholds obtained in Example 1.
[0040] Figure 9 This is a schematic diagram of the energy spectrum for different rise time ranges when the energy threshold is 10%-90% in Example 2;
[0041] Figure 10 The diagram shows the energy spectrum (A) after rise time discrimination, the energy spectrum (B) after filtering and smoothing, and the target energy spectrum (C) corresponding to the energy threshold of 10%-90% obtained in Example 2.
[0042] Figure 11 This is the resolution spectrum obtained from the target energy spectrum in Example 2;
[0043] Figure 12 This is a schematic diagram of the energy spectrum for different rise time ranges when the energy threshold is 5%-95% in Example 3;
[0044] Figure 13 The diagram shows the energy spectrum (A) after rise time discrimination, the energy spectrum (B) after filtering and smoothing, and the target energy spectrum (C) corresponding to the energy threshold of 10%-90% obtained in Example 3.
[0045] Figure 14 This is the resolution spectrum obtained from the target energy spectrum in Example 3; Detailed Implementation
[0046] The present invention will now be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are merely some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the protection scope of the present invention.
[0047] Example 1
[0048] This embodiment proposes an energy spectrum processing method for a quasi-hemispherical CdZnTe detector, including the following steps:
[0049] Step 1: Use 137 A Cs radiation source produces gamma rays that are incident on the cathode surface of a quasi-hemispherical CdZnTe detector A. The charge signal output by the quasi-hemispherical CdZnTe detector A is converted into a voltage signal by a charge-sensitive preamplifier A, and then sampled and digitized by an analog-to-digital converter to obtain the original signal.
[0050] Step 2: After normalizing the amplitude of the original signal from the baseline to the highest point during the rising phase, dynamically select four energy thresholds: 5%-95%, 10%-95%, 5%-90%, and 10%-90%. For the normalized signal within each energy threshold, perform rise time discrimination; filter out signals with rise time greater than RTflag (rise time threshold) and determine the rise time range that matches the energy threshold.
[0051] The specific rise time discrimination process is as follows: Sampling time is divided into groups of m sampling intervals (m is 10 in this embodiment). The integral count of the pulse amplitude corresponding to all normalized signals within each rise time interval is calculated across the entire spectrum. A graph showing the relationship between the rise time interval and the integral count of the signal within that interval against the entire spectrum is plotted. Based on this graph, the rise time threshold value RTflag within the energy threshold is determined. Figures 2-5 These are schematic diagrams of the energy spectrum for different rise time ranges within the four energy thresholds of this embodiment; see reference. Figures 2-5 It can be observed that in the region with a short rise time, the integral count is low and stable, mainly due to noise. There exists a critical rise time point (RTflag). Beyond this point, the integral count begins to show a significant and sustained increase, indicating that the effective event signal begins to dominate. That is, RTflag can be determined by finding the inflection point where the energy spectrum diagram transitions from a "flat plateau" to a "rapidly growing slope." (Reference) Figure 2 It can be seen that the RTflag corresponding to the energy threshold of 5%-95% is 170ns; (Reference) Figure 3 It can be seen that the RTflag corresponding to the energy threshold of 10%-95% is 160ns; (Reference) Figure 4It can be seen that the RTflag corresponding to the energy threshold of 5%-90% is 150ns; (Reference) Figure 5 It can be seen that the RTflag corresponding to the energy threshold of 10%-90% is 140ns. The rise time range of the signals that mainly contribute to the energy spectrum and full-energy peak count is concentrated within the effective interval greater than RTflag. The effective interval is the continuous rise time interval where the contribution of the integral count is ≥70%. Based on this, (RTflag+1) to (RTflag + effective interval width) is taken as the rise time range matching this energy threshold. Typically, the effective interval width is approximately 20ns. Figures 2-5 As can be seen, in this embodiment, the rise time discrimination range corresponding to 5%-95% is 171~190ns, the rise time discrimination range corresponding to 10%-95% is 161~180ns, the rise time discrimination range corresponding to 5%-90% is 151~170ns, and the rise time discrimination range corresponding to 10%-90% is 141~160ns.
[0052] Step 3: For each energy threshold, accumulate signals with rise times greater than RTflag by energy channel address to obtain the total raw energy spectrum corresponding to that energy threshold. Filter signals from the total raw energy spectrum that correspond to the rise time range, and then accumulate these signals by energy channel address to obtain the intermediate energy spectrum corresponding to that energy threshold. For example, filter signals with rise times greater than 140ns within the energy threshold range of 5%-95%, accumulate these signals by energy channel address to obtain the total raw energy spectrum corresponding to the energy threshold range of 5%-95%, then filter all signals with rise times in the range of 171-190ns from the total raw energy spectrum corresponding to the energy threshold range of 5%-95%, and accumulate these signals by energy channel address to obtain the intermediate energy spectrum corresponding to the energy threshold range of 5%-95%. Similarly, obtain the intermediate energy spectra corresponding to energy thresholds of 10%-95%, 5%-90%, and 10%-90%, respectively.
[0053] Step 4: Perform point-by-point filtering and smoothing and background subtraction on each intermediate energy spectrum to obtain the target energy spectrum corresponding to each energy threshold.
[0054] The filtering and smoothing process uses a Gaussian filtering function and is calculated according to the following formula:
[0055]
[0056] In the formula S i The energy spectrum after filtering and smoothing is at the 1st i The counting of the Tao; O i+j For the intermediate energy spectrum at the 1st i +j The counting of the Tao; C j For Gaussian filtering functions with a window width of - k arrive k The coefficients within, in this embodiment, k It is 20.
[0057] After smoothing, the background is subtracted by a statistically sensitive nonlinear iterative peak stripping algorithm (SNIP) for each energy spectrum.
[0058] First, perform digital filtering according to the following formula:
[0059]
[0060] In the formula, G i The energy spectrum after numerical transformation is at the th i The counting of channels, where logarithmic and square root operations can reduce the difference between the maximum and minimum counts at different channel addresses, enhancing sensitivity to peaks. Then, the background spectrum to be stripped is determined, and the count at the current channel address is... G i The smaller value is used as the background count compared to the mean count at both edges of the window width. b i To minimize the impact on peak count while maximizing background subtraction, the final step is to... b i The background spectrum is obtained by performing the inverse numerical transformation according to the following formula. B i :
[0061]
[0062] Since the SNIP background subtraction algorithm can significantly affect the Compton plateau and the low-energy side of the full-energy peak, it is the main post-processing step affecting the full-energy peak efficiency. Choosing an appropriate number of iterations can reduce the impact of incomplete charge collection on the full-energy peak counting, while simultaneously improving the peak shape quality and energy resolution of the spectrum. Furthermore, the effect of the number of iterations on peak efficiency follows an exponential decay law, which facilitates quantitative energy spectrum analysis while achieving high energy resolution.
[0063] In this embodiment, the method for selecting the number of iterations is as follows: First, plot the relationship between the number of iterations and the target energy spectrum. Then, based on the plot of the number of iterations versus the target energy spectrum, plot the relationship between the number of iterations versus the peak efficiency and the energy resolution. Next, select the point of maximum peak efficiency from the points of overlap between the plot of the number of iterations versus the peak efficiency and the plot of the number of iterations versus the energy resolution. The number of iterations corresponding to this point is the optimal number of iterations. Figure 6This is a graph showing the relationship between the number of iterations for background subtraction and the target energy spectrum when the energy threshold is 10%-90% in this embodiment. Figure 7 This is a graph showing the relationship between the number of iterations, peak efficiency, and energy resolution when the energy threshold is 10%-90% in this embodiment; where A represents the relationship between the number of iterations and peak efficiency, and B represents the relationship between the number of iterations and energy resolution. Figure 7 It can be seen that in this embodiment, the optimal number of iterations for the SNIP algorithm corresponding to an energy threshold of 10%-90% is 20.
[0064] Figure 8 In this context, ET represents the energy threshold, RT represents the rise time, and the reference is... Figure 8 As can be seen, this embodiment improves the energy resolution of the total original energy spectrum to 662 keV from 1.56% to 0.78% through energy threshold selection, rise time discrimination, energy spectrum smoothing, and background subtraction.
[0065] Example 2
[0066] The difference between this embodiment and Embodiment 1 is that in this embodiment, the quasi-hemispherical CdZnTe detector A is replaced with the quasi-hemispherical CdZnTe detector B.
[0067] refer to Figures 9 to 11 As can be seen, in this embodiment, the quasi-hemispherical CdZnTe detector B, with an energy threshold of 10%-90% and a rise time range of 141-160 ns, achieves an energy resolution of 0.77% for the target energy spectrum at 662 keV. Figure 9 The energy spectrum (A) after rise time discrimination is the energy spectrum formed by signals with rise time greater than RTflag.
[0068] Example 3
[0069] The difference between this embodiment and Embodiment 1 is that in this embodiment, the charge-sensitive preamplifier A is replaced with the charge-sensitive preamplifier B.
[0070] refer to Figures 12-14 As can be seen, in this embodiment, the quasi-hemispherical CdZnTe detector A, with an energy threshold of 5%-95% and a rise time range of 171-190 ns, achieves an energy resolution of 0.97% for the target energy spectrum at 662 keV. Figure 12 In the above, the energy spectrum (A) after rise time discrimination is the energy spectrum formed by the signal with a rise time greater than RTflag.
[0071] As can be seen from the energy resolution results of the above embodiments, the energy spectrum processing method proposed in this invention, by combining energy threshold discrimination, rise time discrimination and energy spectrum post-processing algorithm, can overcome individual differences in the system and achieve adaptive parameter matching, and stably improve the energy resolution of the quasi-hemispherical CdZnTe detector for 662 keV gamma rays to less than 1%, meeting the stringent requirements of high-end nuclear radiation detection applications for high-performance detectors.
[0072] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention.
[0073] It should be understood that the present invention is not limited to the content already described above, and modifications and changes can be made without departing from its scope. The scope of the present invention is limited only by the appended claims.
Claims
1. A method for energy spectrum processing of a quasi-hemispherical CdZnTe detector, characterized in that, Includes the following steps: Step 1: Acquire the raw signal collected by the quasi-hemispherical CdZnTe detector; Step 2: After normalizing the amplitude of the original signal from the baseline to the highest point during the rising phase, dynamically select multiple energy thresholds and perform rise time discrimination on the normalized signal within each energy threshold. Signals with rise times greater than the rise time threshold RTflag are selected and the rise time range corresponding to this energy threshold is determined; multiple energy thresholds include: 5%-95%, 10%-95%, 5%-90%, and 10%-90%; Step 3: Construct the intermediate energy spectrum corresponding to each energy threshold based on the signals with a rise time greater than RTflag and the rise time range; the method for constructing the intermediate energy spectrum includes: accumulating the signals with a rise time greater than RTflag within each energy threshold to obtain the total original energy spectrum corresponding to that energy threshold, filtering out the signals corresponding to the rise time range from the total original energy spectrum, accumulating the signals corresponding to the rise time range to obtain the intermediate energy spectrum corresponding to that energy threshold. Step 4: Post-process the intermediate energy spectrum to obtain the target energy spectrum corresponding to each energy threshold.
2. The energy spectrum processing method for the quasi-hemispherical CdZnTe detector according to claim 1, characterized in that, In step 2, the method for determining RTflag is as follows: the sampling time is divided into groups of m sampling intervals, where 6≤m≤15. The integral count of the pulse amplitude corresponding to all normalized signals within each rise time interval is counted in the full spectrum. A graph showing the relationship between the rise time interval and the integral count of the signal within that interval in the full spectrum is plotted. Based on the graph, the rise time critical value RTflag within the energy threshold is determined. The rise time range corresponding to the energy threshold is (RTflag + 1ns) ~ (RTflag + effective interval width), where the effective interval is a continuous rise time interval in which the contribution of the integral count is ≥70%.
3. The energy spectrum processing method for a quasi-hemispherical CdZnTe detector according to claim 1, characterized in that, In step 4, the post-processing of the intermediate energy spectrum includes: sequentially performing filtering and smoothing processing and background subtraction processing on the intermediate energy spectrum.
4. The energy spectrum processing method for a quasi-hemispherical CdZnTe detector according to claim 3, characterized in that, The filtering and smoothing process uses a Gaussian filtering function and is calculated according to the following formula: In the formula The energy spectrum after filtering and smoothing is at the 1st The counting of the Tao; For the intermediate energy spectrum at the 1st The counting of the Tao; The coefficients of the Gaussian filter function are within the window width from -k to k.
5. The energy spectrum processing method for a quasi-hemispherical CdZnTe detector according to claim 3, characterized in that, The background subtraction process uses the SNIP algorithm.
6. The energy spectrum processing method for a quasi-hemispherical CdZnTe detector according to claim 5, characterized in that, The background subtraction process includes first performing digital filtering on the smoothed energy spectrum to obtain a numerically transformed energy spectrum, determining the background spectrum to be stripped based on the numerically transformed energy spectrum, and then performing an inverse numerical transformation on the background spectrum to be stripped to obtain the target energy spectrum.
7. The energy spectrum processing method for a quasi-hemispherical CdZnTe detector according to claim 6, characterized in that, The smoothed energy spectrum is first digitally filtered using the following formula: In the formula, The energy spectrum after numerical transformation is at the th The counting of the Tao.
8. The energy spectrum processing method for a quasi-hemispherical CdZnTe detector according to claim 6, characterized in that, The following formula is used to perform a numerical inverse transform on the background spectrum to be stripped: In the formula, In order to treat the stripping of the background spectrum in the first The counting of the Tao To determine the target energy spectrum in the first... The counting of the Tao.