Pulse passing rate improving method based on stacked signal demodulation

Abstract

The invention provides a pulse passing rate improving method based on accumulation signal demodulation, and belongs to the technical field of nuclear electronics digital pulse processing. Comprising the following steps: performing baseline deduction and monopulse screening on a radiation field pulse signal; constructing a nuclear pulse signal model, fitting to obtain model parameters, and constructing a system response matrix; modeling a nuclear detection physical process into a mathematical model; solving a constraint optimization problem by using a non-negative least square method; and demodulating and calculating all the pulse signals including the stacked pulses which are discarded by stacking, so as to obtain delta pulses containing energy information. According to the invention, the accumulation signal which is abandoned by a traditional accumulation abandoning algorithm is demodulated, so that the technical problem of increasing the pulse passing rate is solved, and meanwhile, heavy peaks and high-energy trailing in an energy spectrum are inhibited. Compared with an existing accumulation discarding method, the pulse passing rate effect is remarkably improved on the premise that the energy spectrum accuracy is guaranteed.

Description

Technical Field

[0001] The present invention belongs to the technical field of digital pulse processing of nuclear electronics, and in particular relates to a method for improving pulse pass rate based on pile-up signal demodulation. Background Art

[0002] Energy-dispersive X-ray fluorescence (EDXRF) analysis is a nuclear analysis technique based on the principle of X-ray measurement. Currently, this technique is widely used in the measurement and analysis of environmental samples, the detection of lunar soil mineral composition, and the elemental analysis of alloy materials. Semiconductor detectors, such as silicon p-type intrinsic n-type (Si-PIN) detectors and silicon drift detectors (SDDs), are used in EDXRF measurements due to their superior energy resolution, fast response characteristics, and excellent detection sensitivity. In recent years, the FAST SDD has been developed based on the SDD, which has a smaller time constant and better energy resolution.

[0003] EDXRF analysis uses a multi-channel pulse amplitude analyzer to acquire X-ray energy spectra. The type and content of elements in a sample are determined by identifying and analyzing characteristic X-ray spectral peaks. Therefore, the acquisition process of X-ray energy spectra is fundamental to EDXRF analysis and directly impacts the accuracy of elemental analysis. In the past, X-ray spectra were acquired using analog circuits, which lacked flexibility. Notably, the continuous development of high-speed analog-to-digital converters (ADCs) and programmable logic devices has led to significant advancements in signal processing methods. Digital technology has gradually replaced traditional analog electronics as the dominant method.

[0004] Domestic academia has made significant progress in nuclear pulse signal processing technology. In X-ray spectroscopy electronics, Zhang et al. developed a high-speed analog multichannel system for SDD detectors. Through optimized low-noise front-end circuitry, they achieved an energy resolution of 178 eV at 5.9 keV, thereby reducing pulse pile-up at increased count rates. Simultaneously, Meng et al. implemented an FPGA-based digital acquisition architecture using a FAST SDD with a resistive feedback preamplifier, in which the shaped exponential signal undergoes programmable gain amplification and 14-bit ADC conversion before digital pulse processing. Jie Yu et al. proposed a method for calculating peak intensity and applied it to high-purity germanium, SDD, and sodium iodide detectors. The results showed good peak correction at low count rates, but the accuracy of the results decreased as the count rate increased. In other fields, researchers have attempted to improve pulse throughput or energy resolution through optimization methods, but the results have shown that pile-up rejection occurs in all cases.

[0005] To ensure pulse amplitude accuracy, a pile-up rejection method is often used to reject pile-up pulses that could affect the energy spectrum. This method maintains energy resolution, but also introduces dead time. At high count rates, pile-up rejection can significantly reduce the system's pulse throughput and extend measurement time. To address the issue of pulse pile-up in systems, a pulse processing method is needed to improve the system's pulse throughput. Summary of the Invention

[0006] (1) Purpose of the invention and technical problems

[0007] The purpose of the present invention is to propose a pulse pass rate improvement method based on pile-up signal demodulation, which achieves the technical problem of improving the pulse pass rate by demodulating the pile-up signal rejected by the traditional pile-up rejection algorithm, while suppressing the heavy peaks and high-energy tails in the energy spectrum.

[0008] (2) Technical solution

[0009] In order to solve the above technical problems, the present invention proposes a pulse pass rate improvement method based on pile-up signal demodulation, which includes the following steps:

[0010] S1. Use a high-speed digital acquisition card to collect detector output signals and obtain all detector output signals within a specified time;

[0011] S2. Preprocess the collected signal to obtain a nuclear pulse signal after subtracting the baseline.

[0012] S3. Filter out the single pulse signal from the collected signals, use the single pulse signal to fit the nuclear pulse signal model and obtain the model parameters, and use the model and parameters to construct the system response matrix. The nuclear pulse signal model is expressed as:

[0013]

[0014] Where H is the amplitude factor; σ is the standard deviation of the Gaussian kernel; τ1 and τ2 are the decay time constants of the fast and slow components, respectively; and erf is the error function.

[0015] S4. The physical process of nuclear detection can be represented by a mathematical model:

[0016] y=Ax+n,x≥0

[0017] Where x represents the energy deposition of the incident particle; A represents the response matrix of the system; y represents the anode output signal of the detector-coupled photomultiplier tube; and n represents the statistical fluctuation of the amount of de-excited particles in the detector and the electronic noise.

[0018] S5. Solving for x can be considered as an inverse problem under constraints. Use the non-negative least squares method to solve the constrained optimization problem in S4. The non-negative least squares algorithm is:

[0019]

[0020] subject to:x≥0

[0021] In the formula represents the l2 norm used to maintain the similarity between the measured value and its expected value; the constraint term x≥0 is used to constrain the solutions in the non-negative solution set.

[0022] S6. Using the above method, all signals including the pile-up signal rejected by the pile-up judgment can be demodulated into delta pulses with energy information, thereby improving the pulse pass rate.

[0023] Furthermore, the detector uses a detector whose output signal waveform changes little at different counting rates.

[0024] Furthermore, in step S2, the preprocessing method is:

[0025] S2-1. Calculate the pulse baseline using the arithmetic mean method for the pre-trigger baseline and deduct it;

[0026] Furthermore, in step S3, the method for screening the single pulse signal is:

[0027] S3-1. Set the threshold parameter to mark the trigger and end of the useful pulse signal;

[0028] S3-2. Record the number of sampling points from the trigger of each signal to the end and compare it with the set number of single pulse sampling points;

[0029] S3-3. A pulse smaller than the set single pulse sampling point number is a single pulse signal.

[0030] (3) Beneficial effects

[0031] In nuclear radiation energy spectrum measurements, accurate identification and processing of pile-up pulses is necessary to prevent interference between cascaded pulses and ensure accurate spectrum measurements. To address the issue of pulse pile-up in nuclear radiation measurements, the current mainstream nuclear pulse signal processing method is pile-up rejection. This method identifies and rejects pile-up signals based on trigger time and pulse width. For the remaining single pulse signals, the system calculates the pulse amplitudes using algorithms such as trapezoidal shaping and accumulates them into a spectrum. Because the pile-up signals are rejected and their amplitudes are no longer calculated, the impact of the pile-up effect on the energy spectrum measurement is reduced. While this pile-up rejection method mitigates the impact of pile-up signals on the final spectrum and maintains energy resolution, it does so at the expense of pulse throughput. In strong radiation fields, this method can introduce significant dead time into the system, severely impacting measurement efficiency and extending measurement time.

[0032] This invention abandons the traditional forward pulse processing model and, by abstracting the entire physical process of nuclear radiation measurement into a mathematical representation, implements a model-based constrained optimization problem to obtain the pulse signal amplitude. In the traditional "stacked rejection + trapezoidal shaping" signal processing method, the signal flow is always in a forward transmission state. Signals rejected during the signal flow are no longer included in the final energy spectrum, resulting in information loss. This invention mathematically models the physical entity and transforms the deconvolution process for obtaining the pulse amplitude into the inverse solution of an algebraic equation with certain constraints.

[0033] This paper constructs a nuclear pulse signal model applicable to a variety of detectors. Using a semiconductor detector (SDD) as an example, measured data and calculation results demonstrate that the nuclear pulse signal model matches the measured pulse data with a goodness-of-fit value exceeding 0.998, demonstrating the accuracy of the constructed model and laying the foundation for the next step of accurately constructing the system response matrix and inversely solving the demodulated pulse signal.

[0034] By incorporating the non-negativity of the incident particle's deposited energy into the inverse equation solution, coupled with a precisely constructed system response matrix, this method employs a non-negative least squares algorithm to constrain the solution process, yielding a highly sparse solution. This mathematical sparsity ensures the physical high temporal resolution between pulses, enabling demodulation of the full pulse signal stream, particularly the accumulated signal.

[0035] Compared with the existing pile-up rejection method, the present invention significantly improves the pulse pass rate while ensuring the energy resolution, and effectively suppresses the high-energy tailing and heavy peak effects on the energy spectrum. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a comparison chart of the fitting results of the SDD detector output waveform and the pulse signal model;

[0037] Figure 2 The output signal of the SDD detector and its inverse solution result diagram in the present invention;

[0038] Figure 3 This is a comparison chart of the energy resolution and pulse pass rate results of the trapezoidal shaping method and the UTB method;

[0039] (a) Comparison of energy resolution results between the trapezoidal shaping method and the UTB method;

[0040] (b) is a comparison of the pulse pass rate results of the trapezoidal shaping method and the UTB method;

[0041] Figure 4 Comparison of energy spectra between the trapezoidal shaping method and the UTB method under different input currents;

[0042] a is 0.04mA; b is 0.09mA; c is 0.15mA; d is 0.20mA; e is 0.27mA. DETAILED DESCRIPTION

[0043] In order to make the purpose, content and advantages of the present invention more clear, the specific implementation methods of the present invention are further described in detail below with reference to the accompanying drawings and examples.

[0044] The physical layer of nuclear radiation measurement mainly includes four parts: radiation source, detector part, high-speed digitizer and high-performance computer. After the particles interact with the detector, light pulse signals are generated, which are converted into electrical signals through photomultiplier tubes and input into the high-speed digitizer; the analog signal is sampled by the front-end conditioning circuit and high-speed ADC to obtain a digital signal, which is then transmitted to the high-performance computer for further processing. Corresponding to the physical entity, the modeling layer describes the abstract mathematical expression of the physical behavior of each entity in the measurement process. x·δ(t) represents incident particle events with different energies, that is, the initial nuclear radiation event information; the detector output signal model needs to be modeled according to its own characteristics; the input information convolution system response is digitized to become the collected digital pulse signal; the final result to be solved is This is the expected solution of x·δ(t). In the actual measurement process, the output signal is known. The system response matrix can be constructed through the pulse signal model, and the original input information can be finally demodulated through the inverse solution process. Based on this idea, the present invention proposes a pulse pass rate improvement method based on stacked signal demodulation, which specifically includes the following steps:

[0045] S1. To obtain the most complete information about the pulse signal, it is necessary to record all signals within the measurement time for subsequent analysis. Use a high-speed digitizer to collect the detector output signal and obtain the entire detector output signal within the measurement time.

[0046] S2. Because nuclear signals have a random distribution, their temporal distribution can cause baseline fluctuations. At high count rates, after the detector output signal is processed by the preamplifier and filter, the system's impulse response will have a tail, which can also cause baseline drift. Therefore, it is necessary to preprocess the collected pulse signal to obtain a nuclear pulse signal with the baseline subtracted. The preprocessing method is as follows:

[0047] S2-1. Since the pulse duration is very short, it can be assumed that the baseline changes little during this period. Therefore, the arithmetic mean method is used to calculate the average baseline of the pulse portion before the trigger and deduct it;

[0048] S2-2. If a pile-up signal is encountered, it is considered as a signal with a small baseline change. Repeat the baseline calculation method of S2-1 and subtract it.

[0049] S3. The detector output pulse response model will seriously affect the accuracy of the final demodulation result. Therefore, in order to achieve a certain statistical representativeness, it is necessary to screen out a certain number of single pulse signals from the collected signal, fit each single pulse signal with the detector output pulse response model and calculate the average value of the parameters. The calculated average model parameters will be used together with the model to construct the system response matrix for subsequent inverse solution calculations. Figure 1 shown.

[0050] By analyzing the primary physical processes underlying nuclear pulse signal formation, a relatively accurate pulse signal model can be derived. The original input particle can be mathematically represented as an impulse signal with a certain energy. After being captured by the detector, the particle generates a large number of electrons and holes, which migrate through the lattice until they excite activation centers. These are numerous independent and identically distributed low-probability events, which can be represented by Gaussian functions with a certain amplitude. The process of generating fluorescence at the excitation center and multiplying it in the photomultiplier tube can be represented by several exponential decay functions. Therefore, the nuclear pulse signal model for the nuclear radiation detection cascade can be represented as the convolution product of the above processes:

[0051]

[0052] Where H is the amplitude factor; σ is the standard deviation of the Gaussian kernel; τ1 and τ2 are the decay time constants of the fast and slow components, respectively; and erf is the error function.

[0053] The method for screening single pulse signals is:

[0054] S3-1. Set the threshold parameter to mark the trigger and end of the useful pulse signal to avoid interference from noise and other signals on the processing process;

[0055] S3-2. Record the number of sampling points from the triggering of each signal to the end and compare it with the set number of single pulse sampling points. Pulse signals exceeding the number of sampling points are piled up signals and are removed to ensure the accuracy of the fitting sample.

[0056] S3-3. Pulses that do not exceed the set number of single pulse sampling points are single pulse signals, which are recorded for subsequent analysis.

[0057] S4. If the detector and digital signal acquisition components are considered as a single system, the entire nuclear radiation detection process can be simplified to the convolution of the original input impulse signal with the detection system's response function. In this process, the statistical fluctuations caused by de-excitation photons in the detector and electronic noise are both classified as noise. The physical process of nuclear detection can then be expressed mathematically as:

[0058] y=Ax+n,x≥0

[0059] Where x represents the energy deposition of the incident particle; A represents the response matrix of the system; y represents the anode output signal of the detector-coupled photomultiplier tube; and n represents the statistical fluctuation of the amount of de-emitted particles in the detector and the electronic noise. Under the condition that y is known, A is constructed and the initial input information x is obtained by inverse solution. Figure 2 shown.

[0060] S5. Solve the mathematical equation in S4. The simplest way is to use the least squares method to minimize the objective function ‖y-Ax‖ 2 . Although this method converts the equation into a simple linear regression problem, direct solution is often restricted by some conditions and cannot obtain correct results. Since the column vectors of the response matrix A are highly correlated, the matrix is ​​close to singular and the condition number is too large, so a small measurement error will cause the solution to deviate seriously, and the incident signal obtained by direct deconvolution cannot reflect the real input signal. Combined with the non-negative characteristic of the deposited energy, the present invention imposes non-negative inequality constraints on the solution set and uses the non-negative least squares method to solve the constrained optimization problem in S4:

[0061]

[0062] subject to:x≥0

[0063] In the formula represents the l2 norm used to maintain the similarity between the measured value and its expected value; the constraint term x ≥ 0 is used to constrain the solutions in the non-negative solution set. Even for a pile-up signal, the present invention can calculate and demodulate it to obtain a delta pulse with energy information, that is, the original input value x.

[0064] S6. Since S2 has completed the baseline subtraction calculation, the amplitude of each δ pulse in the result x obtained by S5 demodulation calculation is the amplitude of the input pulse signal. Then, all the demodulated amplitudes are accumulated into a histogram to obtain the energy spectrum.

[0065] The results of pulse pass rate improvement were verified and compared through experiments:

[0066] The experimental equipment and parameters are set as follows: 64 The Cu elemental sample is used as the sample source, and the characteristic X-ray energy of the Cu element is K α =8.04keV, K β =8.91keV. This experiment uses the KYW2000A X-ray tube from Cowin, which is a low-energy multi-purpose side-window X-ray tube with an anode voltage of 50kV and a maximum anode current adjustable to 1mA. The detector part uses the XR-100SDD silicon drift detector from AMPTEK, which consists of a thermoelectrically cooled solid-state silicon drift detector and a preamplifier; the high-voltage power supply uses the MNX50P50 X-ray generator from Spellman, whose high-voltage output voltage matches the KYW2000A X-ray tube and the maximum current output value is 2mA, which meets the experimental requirements. 6 Li's CLYC scintillator detector, connected to a digitizer and high-performance computer, collected and calculated data for the pulse throughput improvement experiment. The digitizer, a DT-5730, has a sampling rate of 500 MS / s, a sampling depth of 14 bits, and a single pulse acquisition duration of 100 μs. The collected nuclear pulse signals were transferred to the high-performance computer for calculation using MATLAB software.

[0067] The following comparison uses the trapezoidal shaping method and the ultra-high pulse throughput boosting method (UTB). In subsequent experiments, the adjustable parameters of both methods were optimized. The results presented here represent the best discrimination performance achieved by both methods under these experimental conditions.

[0068] Figure 3 a~b are the energy spectrum parameters obtained by processing pulses at different counting rates using the above two methods, Figure 3 a is the energy resolution result, Figure 3 b is the pulse pass rate result. It can be seen that the two methods can maintain good energy resolution at low counting rates, but as the counting rate increases, the energy resolution of the two methods gradually deteriorates, but the energy resolution of the trapezoidal forming method is always better than the UTB method. However, the price of maintaining a good energy resolution is that the trapezoidal forming method discards a large number of accumulated pulses, resulting in a large amount of dead time. As the counting rate increases, the dead time of the trapezoidal forming method becomes longer, and even the following will occur: Figure 3As shown in Figure b, the system saturates after a count rate of 300 kcps, and the pulse pass rate decreases instead of increases as the count rate increases. In contrast, the UTB method, which can demodulate the pileup signal, effectively resolves the pulse pileup problem and achieves a higher pulse pass rate. At an input count rate of 620 kcps, the UTB method achieves a pulse pass rate of 566 kcps, significantly higher than the 143 kcps achieved by the trapezoidal shaping method.

[0069] In order to compare the details of the two methods, Figure 4 Demonstrates two methods for calculating SDD detector test 64 Energy spectrum results of the output signal of the Cu elemental sample. At high count rates, the pileup rejection logic rejected a large number of pileup signals, resulting in a significant difference in the energy spectrum counts after the two methods were generated. To compare the algorithm's suppression of the pileup effect, this section performs peak normalization on the two methods to demonstrate the proportional relationship between the full-energy peak and the sum peak. The results show that both methods exhibit a sum peak effect at high count rates, but the sum peak area after the UTB method is significantly smaller than the trapezoidal shape, demonstrating that the UTB method can suppress the pileup effect. However, the algorithm's recognition ability has an upper limit and cannot distinguish all pileup signals, resulting in the presence of a sum peak after the spectrum is generated. This shows that although the UTB method cannot completely eliminate the sum peak effect, it can, to a certain extent, demodulate the peak pileup signal and suppress the pileup effect.

[0070] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for improving pulse pass rate based on pile-up signal demodulation, characterized in that: The method for improving the pulse passing rate comprises the following steps: S1. Use a high-speed digital acquisition card to collect detector output signals and obtain all detector output signals within a specified time; S2. Preprocess the collected signal to obtain a nuclear pulse signal after subtracting the baseline. S3. Filter out the single pulse signal from the collected signals, use the single pulse signal to fit the nuclear pulse signal model and obtain the model parameters, and use the model and parameters to construct the system response matrix. The nuclear pulse signal model is expressed as: Where H is the amplitude factor; σ is the standard deviation of the Gaussian kernel; τ1 and τ2 are the decay time constants of the fast and slow components, respectively; and erf is the error function. S4. The physical process of nuclear detection can be represented by a mathematical model: y=Ax+n,x≥0 Where x represents the energy deposition of the incident particle; A represents the response matrix of the system; y represents the anode output signal of the detector-coupled photomultiplier tube; and n represents the statistical fluctuation of the amount of de-excited particles in the detector and the electronic noise. S5. Solving for x can be considered as an inverse problem under constraints. Use the non-negative least squares method to solve the constrained optimization problem in S4. The non-negative least squares algorithm is: subject to:x≥0 In the formula represents the l2 norm used to maintain the similarity between the measured value and its expected value; the constraint term x≥0 is used to constrain the solutions in the non-negative solution set. S6. Demodulate all signals including the pile-up signal rejected by the pile-up judgment into delta pulses with energy information to improve the pulse pass rate.

2. The method for improving pulse pass rate based on pile-up signal demodulation according to claim 1, wherein: The detector used is a detector whose output signal waveform changes little at different counting rates.

3. The method for improving pulse pass rate based on pile-up signal demodulation according to claim 1, wherein: In step S2, the preprocessing method is: S2-1. Calculate the pulse baseline using the arithmetic mean method for the baseline portion before triggering and deduct it.

4. The method for improving pulse pass rate based on pile-up signal demodulation according to claim 1, wherein: In step S3, the method for screening single pulse signals is: S3-1. Set the threshold parameter to mark the trigger and end of the useful pulse signal; S3-2. Record the number of sampling points from the trigger of each signal to the end and compare it with the set number of single pulse sampling points; S3-3. A pulse smaller than the set single pulse sampling point number is a single pulse signal.

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