Automatic fitting method for decay time constant of exponential decay pulse

Abstract

The invention belongs to the technical field of photon counting imaging, and particularly relates to an automatic fitting method for decay time constants of exponential decay pulses. The method comprises the following steps: S1, acquiring a pulse signal output by a charge sensitive amplifier, and carrying out baseline return-to-zero and pole-zero cancellation preprocessing on each pulse event sample contained in the pulse signal to obtain a pole-zero cancellation signal corresponding to each pulse event sample; s2, based on the characteristics of the polar zero cancellation signal, screening a pulse event sample to be fitted; and S3, setting fitting parameters, fitting the pulse event sample to be fitted by using a least square method, and screening and processing a fitting result to obtain an exponential decay time constant. According to the method, individual sample differences caused by measurement conditions are fully considered, the samples can be flexibly screened, and the fitting condition of the samples can be visually evaluated.

Description

Technical Field

[0001] The present invention belongs to the technical field of photon counting imaging, and in particular relates to an automatic fitting method for a decay time constant of an exponential decay pulse. Background Art

[0002] Photon counting imaging is a technology for single-photon imaging of weak light intensity targets. The imaging system primarily consists of a microchannel plate (MCP), a position-sensitive anode, a charge-sensitive amplifier, a pulse shaper, a pulse peak identification module, and an image inversion module. The principle is as follows: a single photon is amplified by the MCP, generating a photoelectron cluster that lands on the photodetector of the position-sensitive anode. The detector then outputs an exponentially decaying pulse signal with an amplitude that corresponds to the centroid of the photoelectron cluster falling on the position of the photodetector of the position-sensitive anode. After preprocessing the signal using methods such as a charge-sensitive amplifier and pulse shaping filtering, a low-noise, precise-amplitude pulse signal is generated. Pulse identification and amplitude extraction methods are then used to accurately extract the pulse signal. Finally, a specific method is used to calculate the position where the single photon landed on the photodetector, achieving single-photon imaging.

[0003] The closest existing implementation to the present invention uses the circuit structure of a photodetector to calculate the exponential decay time constant. When a photodetector receives a single photon, it generates a corresponding electrical pulse signal, and the decay time constant of the electrical pulse signal is assumed to be constant.

[0004] Disadvantages of existing technologies: A full understanding of the circuit structure inside the photodetector is required, but parasitic circuits and environmental noise can cause the actual decay time constant to change, making it impossible to find an accurate decay time constant. If a fixed decay time constant model is used, it is not conducive to accurate extraction of pulse features. Summary of the Invention

[0005] In view of this, the present invention aims to provide an automatic fitting method for the decay time constant of an exponentially decaying pulse to solve the problem that the existing method for obtaining the exponential decay time constant is easily affected by the internal circuit structure of the photodetector, which is not conducive to engineering implementation. The present invention can also obtain the exponential decay time constant without prior knowledge of the performance parameters of the photodetector.

[0006] To achieve the above object, the technical solution created by the present invention is implemented as follows:

[0007] An automatic fitting method for the decay time constant of an exponentially decaying pulse comprises the following steps:

[0008] S1: Acquire the pulse signal output by the charge-sensitive amplifier, and perform baseline zeroing and pole-zero cancellation preprocessing on each pulse event sample contained in the pulse signal to obtain the pole-zero cancellation signal corresponding to each pulse event sample;

[0009] S2: Screening the pulse event samples to be fitted based on the characteristics of each pole-zero cancellation signal;

[0010] S3: Set fitting parameters, use the least squares method to fit the pulse event samples to be fitted, and screen and process the fitting results to obtain the decay time constant.

[0011] Furthermore, step S1 specifically includes the following steps:

[0012] S11: intercept the pulse-free signal output by the charge-sensitive amplifier and average the signal to obtain the reference signal V base , each pulse event sample V CSA With the reference signal V base Perform the difference in sequence to obtain the signal to be processed V corresponding to each pulse event sample after the baseline is zeroed. CSA1 ;

[0013] S12: Perform pole-zero cancellation processing on each signal to be processed using the following formula to obtain a pole-zero cancellation signal corresponding to each pulse event sample:

[0014]

[0015]

[0016]

[0017]

[0018]

[0019] Among them, V pz [n] and V pz [n-1] are all pole-zero cancellation signals, V CSA1 [n] and V CSA1 [n-1] are all signals to be processed, a, b, c and d are intermediate parameters for obtaining the pole-zero cancellation signal and have no physical meaning. s is the sampling period, τ1 is the first time constant, τ2 is the second time constant, and n is the index of the discrete signal, which is a positive integer.

[0020] Furthermore, step S2 specifically includes the following steps:

[0021] S201: Perform differential processing on each signal to be processed in sequence using the following formula to obtain a differential signal corresponding to each pulse event sample:

[0022] V CSA1 [n]=V CSS1 [n+1]-V CSA1 [n];

[0023] S202: Calculate the standard deviation of the differential signal without a pulse event, use 10 times the standard deviation as a threshold, and construct a rising edge height sequence using the differential signal exceeding the threshold, and construct a pulse starting point sequence using the time series of the differential signal exceeding the threshold;

[0024] S203: Determine whether the absolute difference between adjacent items of each sample point included in the rising edge height sequence corresponding to the pulse starting point sequence is greater than 2τ1. If so, retain the currently determined sample; otherwise, delete the currently determined sample.

[0025] S204: After the processing of step S203, the sequence lengths of the rising edge height sequence and the corresponding pulse starting point sequence are both L0;

[0026] S205: Arrange the rising edge height sequence and the corresponding pulse starting point sequence in step S204 in descending order according to the rising edge height to obtain a descending rising edge height sequence and a corresponding descending pulse starting point sequence;

[0027] S206: Retrieve the sampling point of the pole-zero cancellation signal corresponding to the first differential signal of the descending pulse starting point sequence. If all sampling points within the second time constant range of the current pole-zero cancellation signal are greater than 0, execute step S207; otherwise, remove the first differential signal, update the descending pulse starting point sequence, and execute step S211.

[0028] S207: Retrieve the sampling point of the first differential signal in the descending pulse starting point sequence. If the amplitude of the differential signal corresponding to the next sampling point of the first differential signal is less than 1 / 10 of the amplitude of the differential signal corresponding to the previous sampling point, remove the first differential signal, update the descending pulse starting point sequence, and execute step S211. Otherwise, execute step S208.

[0029] S208: Retrieve each sampling point of the first differential signal of the descending pulse starting point sequence. If the sampling values ​​corresponding to two adjacent sampling points of the first differential signal are 0, remove the first differential signal, update the descending pulse starting point sequence, and execute step S211; otherwise, execute step S209.

[0030] S209: Retrieve the sampling point of the pole-zero cancellation signal corresponding to the first differential signal of the descending pulse starting point sequence. If the sampling values ​​corresponding to ten consecutive sampling points are less than 0 within the first time constant range of the current pole-zero cancellation signal, then take the first sampling point with a sampling value less than 0 among the ten consecutive sampling points as the second zero point, record the position of the second zero point, and execute step S210. Otherwise, execute step S211.

[0031] S210: searching for a sampling point of the pole-zero cancellation signal corresponding to the first differential signal of the descending pulse starting point sequence, taking the first sampling point of the current pole-zero cancellation signal as the first zero point, and if a sampling value greater than 0 exists in the search position within the range from the second zero point to four times the first time constant of the current pole-zero cancellation signal, taking the sampling point corresponding to the first sampling value greater than 0 as the third zero point and executing step S211; otherwise, removing the first differential signal, updating the descending pulse starting point sequence, and executing step S211;

[0032] S211: intercept the signal within the range from the first zero point to the third zero point in the first pole-zero cancellation signal as the pulse event sample to be fitted, the first pole-zero cancellation signal corresponds to the first differential signal of the current descending pulse starting point sequence, and replace the first differential signal of the current descending pulse starting point sequence with the second differential signal of the current descending pulse starting point sequence, repeat steps S206 to S211 until the number of pulse event samples to be fitted reaches 80, stop the search, and obtain all the pulse event samples to be fitted.

[0033] Furthermore, in step S3, a double exponential fitting method or a triple exponential fitting method is used to fit each pulse event sample.

[0034] Furthermore, the specific process of fitting each pulse event sample using the double exponential fitting method is as follows:

[0035] Clipping each pulse event sample to be fitted, retaining a signal within a range from a first zero point to a second zero point of each pulse event sample to be fitted, and updating each pulse event sample to be fitted;

[0036] The updated pulse event samples are fitted using a double exponential model to obtain the first decay time constant and the second decay time constant of the double exponential model:

[0037]

[0038] Where A is the pulse amplitude parameter, t1 and t2 are the first and second decay time constants of the double exponential model, t1>t2>0, B is the baseline parameter used to correct deviations in the data, such as deviations caused by instrument drift or background noise, x is the time variable of the double exponential model, is the independent variable, y 2exp (x) is the amplitude strength of the double exponential model and is the dependent variable.

[0039] The least squares method is used in combination with the double exponential model to iterate each pulse event sample to be fitted to minimize the sum of squared errors SSR:

[0040]

[0041]

[0042] Where n is the length of the pulse event sample to be fitted, (x i ,y i ) is the data point of the pulse event sample;

[0043] Taking the first decay time constant and the second decay time constant of the double exponential model corresponding to each pulse event sample to be fitted when the sum of squares of the errors between the predicted value of the double exponential model and each pulse event sample to be fitted is minimized;

[0044] The first decay time constant mean and the second decay time constant mean are respectively averaged to obtain the first decay time constant mean and the second decay time constant mean, and the first decay time constant mean and the second decay time constant mean are used as the fitting results of the double exponential model.

[0045] Furthermore, the specific process of fitting each pulse event sample using the three-exponential fitting method is as follows:

[0046] The three-exponential model is used to fit each pulse event sample to obtain the fitting parameters of the three-exponential model:

[0047]

[0048] Where D and E are both pulse amplitude parameters, T1 is the first decay time constant of the three-exponential model, T2 is the second decay time constant of the three-exponential model, T3 is the third decay time constant of the three-exponential model, T1>T2>T3>0, F is the baseline parameter, x is the time variable of the three-exponential model, is the independent variable, y 3exp (x) is the amplitude strength of the three-exponential model and is the dependent variable;

[0049] The least squares method is used in combination with the three-exponential model to iterate the parameters D, E, F, T1, T2, and T3 of each pulse event sample to be fitted to minimize the sum of squared errors SSR:

[0050]

[0051]

[0052] Where n is the length of the pulse event sample to be fitted, (x i ,y i ) is the data point of the pulse event sample;

[0053] The fitting parameters of the pulse event samples that meet the preset indicators are averaged. The fitting parameters include the first decay time constant T1, the second decay time constant T2, the third decay time constant t3, the pulse amplitude parameter D, the pulse amplitude parameter E and the baseline parameter F of the three-exponential model, and the mean of the fitting parameters is used as the fitting result of the three-exponential model.

[0054] Furthermore, the preset index setting method is: calculate the determination coefficient R of each pulse event sample after each fitting 2 value, and filter out R 2 The pulse event samples with the smallest value are filtered out, and the number of pulse event samples that are filtered out accounts for 20% of the total number of pulse event samples. The remaining pulse event samples are pulse event samples that meet the preset indicators.

[0055] Furthermore, the deconvolution recursive formula of the double exponential model is:

[0056] V impulse [n]=(V pz [n+1]-(M 11 +M 12 )V pz [n]

[0057] +M 11 M 12 V pz [n-1]) / (M 11 -M 12 );

[0058]

[0059]

[0060] Among them, M 11 and M 12 These are parameters used to express the deconvolution recursive formula of the double exponential model and have no physical meaning.

[0061] Furthermore, the deconvolution recursive formula of the three-exponential model is:

[0062]

[0063]

[0064]

[0065]

[0066] a0=0;

[0067] a1=-DM 22 -DM 23 -EM 21 -EM 23 +(D+E)M 21 +(D+E)M 22 ;

[0068] a2=DM 22 M 23 +EM 21 M 23 -(D+E)M 21 M 22 ;

[0069] b0=1;

[0070] b1=-M 21 -M 22 -M 23 ;

[0071] b2=M 21 M 22 +M 22 M 23 +M 21 M 23 ;

[0072] b3=-M 21 M 22 M 23 ;

[0073] Among them, M 21 、M 22 、M 23 , a0, a1, a2, b0, b1, b2 and b3 are coefficients of the deconvolution system transfer function expressing the three-exponential model and have no physical meaning.

[0074] Furthermore, the deconvolution signal V is of length N. impulse [n] The formula for polarity evaluation is:

[0075]

[0076] Where σ0 is the standard deviation of the deconvolution signal in the event-free state, I(·) is the indicator function, P is the polarity, and α and β are parameters indicating polarity and have no actual physical meaning.

[0077] Compared with the prior art, the present invention can achieve the following beneficial effects:

[0078] (1) The present invention creates an automatic fitting method for the decay time constant of the exponential decay pulse. The parameters involved in baseline zeroing and pole-zero cancellation can be estimated only by the signal of the charge-sensitive amplifier itself, and do not rely on the prior knowledge of the electronics of the charge-sensitive amplifier, thereby simplifying the operating cost.

[0079] (2) The present invention creates an automatic fitting method for the decay time constant of the exponential decay pulse, and sets a screening and adjustment method for the samples to be fitted, thereby filtering out some samples with common abnormal characteristics, improving the consistency of the fitting samples, and improving the stability of the fitting results.

[0080] (3) The present invention provides an automatic fitting method for the decay time constant of an exponentially decaying pulse. The method first performs a separate fitting on each sample, and then synthesizes the fitting results based on the goodness of fit. This method fully accounts for individual sample differences caused by measurement conditions, enables flexible sample screening, and intuitively evaluates the sample fit. BRIEF DESCRIPTION OF THE DRAWINGS

[0081] The accompanying drawings, which constitute part of the present invention, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings:

[0082] Figure 1 A schematic flow chart of a method for automatically fitting the decay time constant of an exponentially decaying pulse according to an embodiment of the present invention;

[0083] Figure 2 A schematic diagram of an output signal of a charge sensitive amplifier according to an embodiment of the present invention;

[0084] Figure 3 A schematic diagram of an output signal of baseline zeroing according to an embodiment of the present invention;

[0085] Figure 4 A schematic diagram of estimating a first time constant according to an embodiment of the present invention;

[0086] Figure 5 A schematic diagram of a curve of a pole-zero cancellation signal according to an embodiment of the present invention;

[0087] Figure 6A schematic diagram of a curve of a differential signal according to an embodiment of the present invention;

[0088] Figure 7 A schematic diagram of a curve of a pulse event sample to be fitted according to an embodiment of the present invention;

[0089] Figure 8 A schematic diagram of a curve of a differential signal that meets the screening conditions according to an embodiment of the present invention;

[0090] Figure 9 Schematic diagram of the deconvolution results of the three-exponential model described in the embodiment of the present invention;

[0091] Figure 10 A schematic diagram of a curve of a three-exponential fitting curve and a pole-zero cancellation signal according to an embodiment of the present invention;

[0092] Figure 11 Schematic diagram of the deconvolution results of the double exponential model described in the embodiment of the present invention;

[0093] Figure 12 This is a schematic diagram of the fitting results of the three-exponential time decay constants described in the embodiment of the present invention;

[0094] Figure 13 This is a schematic diagram of the fitting results of the three-exponential pulse amplitude parameters described in the embodiment of the present invention;

[0095] Figure 14 This is a schematic diagram of the fitting results of the double exponential time decay constant described in the embodiment of the present invention;

[0096] Figure 15 This is a schematic diagram of the fitting results of the double-exponential pulse amplitude parameters described in the embodiment of the present invention. DETAILED DESCRIPTION

[0097] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not constitute a limitation of the present invention.

[0098] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0099] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second" and the like are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, features defined as "first", "second" and the like may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0100] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; they can refer to mechanical connections or electrical connections; they can refer to direct connections or indirect connections through an intermediate medium; and they can refer to internal connections between two components. Those skilled in the art can understand the specific meanings of the above terms in the present invention based on specific circumstances.

[0101] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0102] like Figure 1 As shown, the present invention proposes an automatic fitting method for the decay time constant of an exponentially decaying pulse, which specifically includes the following steps: S1: obtaining a pulse signal (exponentially decaying pulse) output by a charge-sensitive amplifier, and performing baseline zeroing and pole-zero cancellation preprocessing on each pulse event sample contained in the pulse signal to obtain a pole-zero cancellation signal corresponding to each pulse event sample; S2: screening the pulse event samples to be fitted based on the characteristics of each pole-zero cancellation signal;

[0103] S3: Set fitting parameters, use the least squares method to fit the pulse event samples to be fitted, and screen and process the fitting results to obtain the decay time constant.

[0104] This invention proposes a method for calculating the exponential decay time constant for fitting a target signal. This method preprocesses pulse signals with undershoot characteristics through pole-to-zero cancellation, performs feature screening on the pulse event samples to be fitted, and analyzes the distribution of the fitted pulse event samples. This method then determines an ideal exponential decay time constant and verifies the rationality of this exponential decay time constant using the polarity of the deconvolution signal. This method is suitable for applications where deconvolution results in an ambiguous and fluctuating exponential decay time constant.

[0105] It should be noted that the present invention is a method for calculating the exponential decay time constant designed for the output signal of a specific position-sensitive anode detector. The method preprocesses the pulse signal by performing baseline zeroing and pole-zero cancellation to achieve pulse compression and remove or suppress undershoot. The method also screens pulse event samples to be fitted based on the characteristics of each pole-zero cancellation signal, primarily eliminating unique objects and improving the stability of the fitting results. Fitting parameters are set, and the least squares method is used to fit the pulse event samples to be fitted. Finally, the fitting results are sorted by distribution, and the optimal exponential decay time constant is obtained based on different methods.

[0106] In some embodiments, step S1 specifically includes the following steps:

[0107] S11: intercept the pulse-free signal output by the charge-sensitive amplifier and average the signal to obtain the reference signal V base , each pulse event sample V CSA With the reference signal V base Perform the difference in sequence to obtain the signal to be processed V corresponding to each pulse event sample after the baseline is zeroed. CSA1 ;

[0108] S12: Perform pole-zero cancellation processing on each signal to be processed using the following formula to obtain a pole-zero cancellation signal corresponding to each pulse event sample:

[0109]

[0110]

[0111]

[0112]

[0113]

[0114] Among them, V pz [n] and V pz [n-1] are all pole-zero cancellation signals, V CSA1 [n] and V CSA1[n-1] are all signals to be processed, a, b, c and d are intermediate parameters for obtaining the pole-zero cancellation signal and have no physical meaning. s is the sampling period, τ1 is the first time constant, τ2 is the second time constant, and n is the index of the discrete signal, which is a positive integer.

[0115] It should be noted that when the detector is illuminated, the photon count rate is typically less than 300 kcps, and the resulting signal is a time series of multiple pulse events. Due to the detector's circuit characteristics, the output pulse signal is often accompanied by significant undershoot and pulse pileup. Furthermore, the decay rates of the pulses due to environmental interference are not completely consistent. Therefore, these pulse signals can be processed accordingly through pole-zero cancellation.

[0116] Furthermore, the input of the pole-zero cancellation processing is the signal to be processed after baseline zeroing, and the output is the pole-zero cancellation signal. Built-in parameters include a first time constant, τ1, and a second time constant, τ2. The first time constant is set to the detector's own time constant. If there is no prior knowledge of the detector or the detector time constant is uncertain, several independent and non-overlapping pulse signals are intercepted under low-light conditions. The time length for each signal to decay to 1 / e of the height of its rising edge is calculated, and the maximum of these time lengths is selected as the detector's first time constant, τ1. The second time constant is set between 0.5 and 0.05 of the detector time constant. The smaller the setting, the narrower the pulse width of the pole-zero cancellation signal.

[0117] In some embodiments, step S2 specifically includes the following steps:

[0118] S201: Perform differential processing on each signal to be processed in sequence using the following formula to obtain a differential signal corresponding to each pulse event sample:

[0119] V CSA1 [n]=V CSS1 [n+1]-V CSA1 [n];

[0120] S202: Calculate the standard deviation of the differential signal without a pulse event, use 10 times the standard deviation as a threshold, and construct a rising edge height sequence using the differential signal exceeding the threshold, and construct a pulse starting point sequence using the time series of the differential signal exceeding the threshold;

[0121] S203: Determine whether the absolute difference between adjacent items of each sample point included in the rising edge height sequence corresponding to the pulse starting point sequence is greater than 2τ1. If so, retain the currently determined sample; otherwise, delete the currently determined sample.

[0122] S204: After the processing of step S203, the sequence lengths of the rising edge height sequence and the corresponding pulse starting point sequence are both L0;

[0123] The sequence length refers to the number of samples participating in the subsequent pulse selection. The number of samples is determined to be greater than 1000 to ensure that the number of samples is sufficient. If the number of samples is insufficient, the length of time for intercepting the signal can be increased until the number of samples is sufficient.

[0124] S205: Arrange the rising edge height sequence and the corresponding pulse starting point sequence in step S204 in descending order according to the rising edge height to obtain a descending rising edge height sequence and a corresponding descending pulse starting point sequence;

[0125] S206: Retrieve the sampling point of the pole-zero cancellation signal corresponding to the first differential signal of the descending pulse starting point sequence. If all sampling points within the second time constant range of the current pole-zero cancellation signal are greater than 0, execute step S207; otherwise, remove the first differential signal, update the descending pulse starting point sequence, and execute step S211.

[0126] This step is to ensure that the samples involved in the exponential fitting have a certain pulse width and eliminate the fitting object errors caused by some noise.

[0127] S207: Retrieve the sampling point of the first differential signal in the descending pulse starting point sequence. If the amplitude of the differential signal corresponding to the next sampling point of the first differential signal is less than 1 / 10 of the amplitude of the differential signal corresponding to the previous sampling point, remove the first differential signal, update the descending pulse starting point sequence, and execute step S211. Otherwise, execute step S208.

[0128] This step is to ensure that the samples involved in the exponential fitting do not have abnormal falling edges caused by electronic noise.

[0129] S208: Retrieve each sampling point of the first differential signal of the descending pulse starting point sequence. If the sampling values ​​corresponding to two adjacent sampling points of the first differential signal are 0, remove the first differential signal, update the descending pulse starting point sequence, and execute step S211; otherwise, execute step S209.

[0130] This step is to ensure that the samples involved in the exponential fitting are not saturated and distorted due to excessive amplitude.

[0131] S209: Retrieve the sampling point of the pole-zero cancellation signal corresponding to the first differential signal of the descending pulse starting point sequence. If the sampling values ​​corresponding to ten consecutive sampling points are less than 0 within the first time constant range of the current pole-zero cancellation signal, then take the first sampling point with a sampling value less than 0 among the ten consecutive sampling points as the second zero point, record the position of the second zero point, and execute step S210. Otherwise, execute step S211.

[0132] This step is to ensure that the samples involved in the exponential fitting have similar pulse undershoot levels, which is conducive to the consistency of the fitting object.

[0133] S210: searching for a sampling point of the pole-zero cancellation signal corresponding to the first differential signal of the descending pulse starting point sequence, taking the first sampling point of the current pole-zero cancellation signal as the first zero point, and if a sampling value greater than 0 exists in the search position within the range from the second zero point to four times the first time constant of the current pole-zero cancellation signal, taking the sampling point corresponding to the first sampling value greater than 0 as the third zero point and executing step S211; otherwise, removing the first differential signal, updating the descending pulse starting point sequence, and executing step S211;

[0134] This step is to ensure that the samples involved in the exponential fitting have complete first, second, and third zero points, and to prevent the fitting sample data from being too long, resulting in fitting errors.

[0135] S211: intercept the signal within the range from the first zero point to the third zero point in the first pole-zero cancellation signal as the pulse event sample to be fitted, the first pole-zero cancellation signal corresponds to the first differential signal of the current descending pulse starting point sequence, and replace the first differential signal of the current descending pulse starting point sequence with the second differential signal of the current descending pulse starting point sequence, repeat steps S206 to S211 until the number of pulse event samples to be fitted reaches 80, stop the search, and obtain all the pulse event samples to be fitted.

[0136] It should be noted that the absolute difference of adjacent items is: Assume that the pulse starting point sequence in the previous step is [100, 200, 250, 300], and assume that 2τ1=60;

[0137] Then, for the first sample, the absolute difference between the adjacent items of the pulse starting point sequence is 200-100, which is greater than 60, indicating a non-pile-up pulse.

[0138] Judging the second sample, the absolute difference of adjacent items in the pulse starting point sequence is 250-200=50<60 and 200-100=100>60, which is a pile-up pulse.

[0139] Similarly, for the third pulse, 300-250=50<60 and 250-200=50<60, it is a pile-up pulse.

[0140] It should be noted that the principles for selecting specific fitting objects include: 1. Prioritize high-amplitude pulse signals. 2. The number of fitted pulse signals must be at least 80. 3. Non-pile-up pulse signals. 4. The intercepted segment must meet the exponential decay signal characteristics after ideal pole-zero cancellation, namely, the first zero point at the time of signal occurrence, a rapid rising edge, a first pole with a width of one sampling point, a slow falling edge without a sudden change, a second zero point that drops to the baseline, an undershoot that drops below the baseline, and a third zero point that returns to the baseline.

[0141] In some embodiments, in step S3, a double exponential fitting method or a triple exponential fitting method is used to fit each pulse event sample.

[0142] In some embodiments, the specific process of fitting each pulse event sample to be fitted using the double exponential fitting method is as follows:

[0143] Clipping each pulse event sample to be fitted, retaining a signal within a range from a first zero point to a second zero point of each pulse event sample to be fitted, and updating each pulse event sample to be fitted;

[0144] The updated pulse event samples are fitted using a double exponential model to obtain the first decay time constant and the second decay time constant of the double exponential model:

[0145]

[0146] Where A is the pulse amplitude parameter, t1 and t2 are the first and second decay time constants of the double exponential model, t1>t2>0, B is the baseline parameter used to correct deviations in the data, such as deviations caused by instrument drift or background noise, x is the time variable of the double exponential model, is the independent variable, y 2exp (x) is the amplitude strength of the double exponential model and is the dependent variable.

[0147] The least squares method is used in combination with the double exponential model to iterate each pulse event sample to be fitted to minimize the sum of squared errors SSR:

[0148]

[0149]

[0150] Where n is the length of the pulse event sample to be fitted, (x i ,y i ) is the data point of the pulse event sample;

[0151] Taking the first decay time constant and the second decay time constant of the double exponential model corresponding to each pulse event sample to be fitted when the sum of squares of the errors between the predicted value of the double exponential model and each pulse event sample to be fitted is minimized;

[0152] The first decay time constant mean and the second decay time constant mean are respectively averaged to obtain the first decay time constant mean and the second decay time constant mean, and the first decay time constant mean and the second decay time constant mean are used as the fitting results of the double exponential model.

[0153] It should be noted that the "trust-region-reflective algorithm" in the Matlab algorithm library is used to implement fitting and iteration. It is a trust region method that is often used to deal with small and medium-sized nonlinear least squares problems. The maximum number of function evaluations that can be performed before the algorithm stops is set to 5000 times, and the maximum number of iterations that can be performed before the algorithm stops is set to 5000 times. The initial fitting parameters [A, t1, t2, B] of the double exponential model are set to [1, τ2, τ2, 0], and the R after sample fitting of each pulse event sample to be fitted is calculated. 2 Coefficient of determination.

[0154] Each pulse event sample to be fitted can get a fitting result, which includes fitting parameters and SSR. Finally, the fitting parameters t1 and t2 of all pulse event samples to be fitted are averaged, and the average value is calculated. and mean As the fitting result of the bi-exponential model.

[0155] In some embodiments, the specific process of fitting each pulse event sample to be fitted using the three-exponential fitting method is as follows:

[0156] The three-exponential model is used to fit each pulse event sample to obtain the fitting parameters of the three-exponential model:

[0157]

[0158] Where D and E are both pulse amplitude parameters, T1 is the first decay time constant of the three-exponential model, T2 is the second decay time constant of the three-exponential model, T3 is the third decay time constant of the three-exponential model, T1>T2>T3>0, F is the baseline parameter, x is the time variable of the three-exponential model, is the independent variable, y 3exp (x) is the amplitude strength of the three-exponential model and is the dependent variable;

[0159] The least squares method is used in combination with the three-exponential model to iterate the parameters D, E, F, T1, T2, and T3 of each pulse event sample to be fitted to minimize the sum of squared errors SSR:

[0160]

[0161]

[0162] Where n is the length of the pulse event sample to be fitted, (x i ,y i ) is the data point of the pulse event sample;

[0163] The fitting parameters of the pulse event samples that meet the preset indicators are averaged. The fitting parameters include the first decay time constant T1, the second decay time constant T2, the third decay time constant T3, the pulse amplitude parameter D, the pulse amplitude parameter E and the baseline parameter F of the three-exponential model, and the mean of the fitting parameters is used as the fitting result of the three-exponential model.

[0164] In some implementations, the preset index is set by calculating the coefficient of determination R of each pulse event sample after each fitting. 2 value, and filter out R 2 The pulse event samples with the smallest value are filtered out, and the number of pulse event samples that are filtered out accounts for 20% of the total number of pulse event samples. The remaining pulse event samples are pulse event samples that meet the preset indicators.

[0165] It should be noted that the pulse event samples fitted by the three-exponential fitting method include the first zero point to the third zero point, and the three-exponential model is used for fitting. Similarly, the least squares method is used to make Minimum, set the maximum number of function evaluations that can be performed before the algorithm stops to 5000, and set the initial parameters [D, T1, E, T2, T3, F] to Set the fitting parameter lower limit lb = [0, 0, -10M, 0, 0, -0.2M], and the fitting parameter upper limit ub = [20M, ∞, 20M, ∞, ∞, 0.2M], where M is the upper limit of the signal amplitude that the acquisition device can collect.

[0166] Record the fitting results of each evolution, including the fitting parameters T1, T2, T3, D, E, F and R 2 . Analyze the R of each pulse event sample 2 value, filter out 2R 2 The pulse event sample with the smallest value (accounting for 20% of the total number of samples) is used to calculate the mean of the fitting parameters T1, T2, etc. of the remaining pulse event samples. mean mean mean mean mean As the fitting result of the three-exponential model.

[0167] In some embodiments, the deconvolution recursion formula of the double exponential model is:

[0168] V impulse [n]=(V pz [n+1]-(M 11 +M 12 )V pz [n]

[0169] +M 11 M 12 V pz [n-1]) / (M 11 -M 12 );

[0170]

[0171]

[0172] Among them, M 11 and M 12 These are parameters used to express the deconvolution recursive formula of the double exponential model and have no physical meaning.

[0173] In some embodiments, the deconvolution recursion formula of the three-exponential model is:

[0174]

[0175]

[0176]

[0177]

[0178] a0=0;

[0179] a1=-DM 22 -DM 23 -EM 21 -EM 23 +(D+E)M 21 +(D+E)M 22 ;

[0180] a2=DM 22 M 23 +EM 21 M 23 -(D+E)M 21 M 22 ;

[0181] b0=1;

[0182] b1=-M 21 -M 22-M 23 ;

[0183] b2=M 21 M 22 +M 22 M 23 +M 21 M 23 ;

[0184] b3=-M 21 M 22 M 23 ;

[0185] Among them, M 21 、M 22 、M 23 , a0, a1, a2, b0, b1, b2 and b3 are coefficients of the deconvolution system transfer function expressing the three-exponential model and have no physical meaning.

[0186] In some embodiments, the deconvolved signal V of length N is impulse [n] The formula for polarity evaluation is:

[0187]

[0188]

[0189]

[0190] Where σ0 is the standard deviation of the deconvolution signal in the event-free state, I(·) is the indicator function, P is the polarity, and α and β are parameters indicating polarity and have no actual physical meaning.

[0191] It should be noted that in the evaluation process of the fitting results: the deconvolution formula is used to perform deconvolution operations on the pole-zero cancellation signal respectively, and a polarity degree algorithm is used to evaluate the fitting results. The standard deviation of the deconvolution signal in the event-free state is denoted as σ0, where I(·) is the indicator function. When the value in the brackets meets the conditions, its value is 1, and when it does not meet the conditions, it is 0. The range of the polarity evaluation P is -1 to 1. When it is a negative value, it means that the deconvolution signal has a negative polarity. This is caused by overfitting the pulse signal with undershoot. The length of each pulse time sample to be fitted can be appropriately reduced, and only the part from the first zero point to the second zero point of the pulse time sample to be fitted is retained. When the P value is greater than zero and the closer P is to 1, the better the deconvolution result is and the less significant the undershoot effect of the pulse signal.

[0192] Example 1

[0193] Build a photon counting imaging system. The working process of the photon counting imaging system is as follows: the light source emits a weak single photon that hits the microchannel plate, and after photomultiplication, a photoelectron group is output. The photoelectron group falls on the anode of the two-dimensional position-sensitive detector. The detector generates an electrical signal with the position information of the photoelectron group. The pulsed electrical signal passes through the charge-sensitive amplifier and is output to the acquisition card. The collected data is transmitted to the computer for processing. The event-free segment signal can be obtained by turning off the light source. Some of the collected signals are as follows Figure 2 As shown, where the sampling frequency F S =5×10 7 Hz, sampling period T s =0.02μs.

[0194] Step 1: First intercept a signal without events, Figure 2 The pulse signal V of the charge sensitive amplifier in CSA With 1.5×10 4 to 2.5×10 4 The sampling points are calculated and their mean is obtained. base =-1.277756083687114V, where V is the voltage unit. The output signal of the charge sensitive amplifier is V CSA First subtract V base , get the baseline zero output signal V CSA1 ,like Figure 3 shown.

[0195] Intercept several single pulse signals and estimate the time constant, such as Figure 4 As shown, the rising edge height is 0.996V, 1 / e times the rising edge is 0.3664V, find the coordinates of the sampling point where the falling edge drops to about 0.3664, and get the first time constant τ1=2787160T s -2786990T s =170T s =3.4μs. Similarly, the first time constant τ1 values ​​of several similar single pulse signals are intercepted, and the maximum value selected from these time lengths is used as the time constant τ1 of the detector. In the present invention, the final τ1=220T s =4.4μs, the second time constant τ2 is set to 0.5-0.05 of the first time constant τ1 of the detector. The smaller the second time constant τ2 is set, the narrower the pulse width of the pole-zero cancellation signal. In the present invention, the second time constant τ2 is set to 10T s =0.2μs. The pulse signal output by the charge sensitive amplifier is processed by pole-zero cancellation using the formula to obtain a pole-zero cancellation signal, such as Figure 5 shown.

[0196] Step 2: Perform differential processing on the pole-zero cancellation signal to obtain the differential signal, such as Figure 6 As shown, the standard deviation σ of the event-free segment of the differential signal is calculated V =0.0140V, then the threshold Va=0.140V. Record the sampling value and timing corresponding to the differential amplitude of the differential signal greater than the threshold Va. Figure 6 In the example, the differential amplitude is 0.663974V, and the timing is the 1606830th sampling cycle. If the timing interval between adjacent sampling points is less than 2τ1, it is considered as a pile-up sample and the pile-up sample is discarded. Record more than 1000 sample data to ensure that the sample is rich. If it is less than 1000, increase the exposure time to collect more signals. Arrange these pulse event samples in reverse order according to the size of the differential amplitude. Then, perform subsequent screening and judgment on these samples. The samples suitable for fitting have the following characteristics: Figure 7 The feature is that the first zero point is the retrieval position of the pulse signal. The complete pulse signal includes the first zero point, the first extreme point, the second zero point, the undershoot area, and the third zero point where the undershoot area ends, and the judgment results are matched one by one.

[0197] like Figure 7 As shown, whether the sampling signals within the range of the second time constant τ2 after the current search position are all greater than 0, Figure 7 In the range from the 1st sampling point to the 10th sampling point, the value is greater than 0.

[0198] like Figure 8 As shown, the current peak value of the differential signal is 0.686937V, and the amplitude of the subsequent sampling point is -0.0460148V, which is greater than -0.0686937V, meeting the screening condition. In addition, the subsequent sampling points of the differential signal peak value are not equal to 0, meeting the screening condition.

[0199] like Figure 7 As shown, the first time constant after the current search position is τ1=220τ s In the range of , there are 10 consecutive sampling points below 0. Figure 7 If the position in the equation is from the 38th to the 48th sampling point, the 38th sampling point is recorded as the second zero point, and is within the range of 4 times the first time constant τ1, that is, 880T s Within the range, a third zero point greater than 0 is found, which is located at the 355th sampling point. At this time, the pulse event sample can be regarded as complete and is used as the pulse event sample to be fitted.

[0200] The sampling points in the range from the first zero point to the third zero point of the pulse event sample to be fitted are intercepted, and the next pulse event sample is determined. The search is stopped when the number of pulse event samples to be fitted reaches 80.

[0201] Step 3: Perform a three-exponential fitting or a two-exponential fitting on the pulse event samples selected in step 2. The three-exponential fitting requires setting the initial parameters [D, T1, E, T2, T3, F] to [1V, 220T s ,0V,22T s ,2.2T s ,0V], in this embodiment, the upper limit of the signal of the acquisition card M=10, so the lower limit of the fitting parameter is set [0V,0T s ,-100V,0T s ,0T s ,-2V], the upper limit of the fitting parameter is set as ub=[200V,∞,200V,∞,∞,2V], and the fitting results are shown in the attached Figure 12 、 Figure 13 , the sampling points and amplitude curves of the three exponential curves are as follows Figure 10 As shown, retain R 2 The mean is calculated for the first 80% of the samples.

[0202] The obtained three-exponential fitting results

[0203] Then the double exponential fitting is performed, and the initial parameters [A, t1, t2, B] are set to [1V, 220T s ,22T s ,0V], set M=10, set the lower limit of fitting parameters lb=[0V,0T s ,0T s ,-2V], set the upper limit of fitting parameters ub=[10V,∞,∞,2V].

[0204] The fitting results are shown in the attached Figure 14 , attached Figure 15 . Keep R 2 The mean is calculated for the first 80% of the samples.

[0205] Obtained double exponential fitting results

[0206] Finally, the deconvolution formula is used to perform deconvolution of the double exponential model and the triple exponential model on the extreme-zero cancellation signal, and the results are as follows: Figure 9 and Figure 11 As shown in Figure 2, the standard deviation of the deconvolution signal is calculated using the event-free signal segment. The standard deviation of the deconvolution signal for the double exponential model is 0.0396 V, and the standard deviation of the deconvolution signal for the triple exponential model is 0.0093 V. The corresponding polarity evaluation value of the deconvolution signal for the double exponential model is P = 0.989, and the polarity evaluation value of the deconvolution signal for the triple exponential model is P = 1.

[0207] The present invention is designed for the output signals of specific detectors and charge-sensitive amplifiers to realize the calculation of fitting and deconvolution parameters. For the output signals of standard charge-sensitive amplifiers without undershoot, a double exponential model with fewer parameters can be used to prevent the inability to collect parameters due to too many parameters, and the integrity condition of the fitting sample of the double exponential model must also be changed to: having a first zero point, a first pole, and a second zero point.

[0208] It should be understood that the various forms of the processes shown above can be used to reorder, add, or delete steps. For example, the steps described in the present disclosure can be performed in parallel, sequentially, or in a different order, as long as the desired results of the technical solutions disclosed in the present disclosure can be achieved. This is not limited herein.

[0209] The above specific embodiments do not limit the scope of protection of the present invention. Those skilled in the art will appreciate that various modifications, combinations, sub-combinations, and substitutions may be made based on design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention are intended to be included within the scope of protection of the present invention.

Claims

1. A method for automatically fitting the decay time constant of an exponentially decaying pulse, characterized by: The specific steps include: S1: Acquire the pulse signal output by the charge-sensitive amplifier, and perform baseline zeroing and pole-zero cancellation preprocessing on each pulse event sample contained in the pulse signal to obtain the pole-zero cancellation signal corresponding to each pulse event sample; S2: Screening the pulse event samples to be fitted based on the characteristics of each pole-zero cancellation signal; S3: Set fitting parameters, use the least squares method to fit the pulse event samples to be fitted, and screen and process the fitting results to obtain the decay time constant.

2. The automatic fitting method for the decay time constant of an exponentially decaying pulse according to claim 1, characterized in that: Step S1 specifically includes the following steps: S11: intercept the pulse-free signal output by the charge-sensitive amplifier and average the signal to obtain the reference signal V base , each pulse event sample V CSA With the reference signal V base Perform the difference in sequence to obtain the signal to be processed V corresponding to each pulse event sample after the baseline is zeroed. CSA1 ; S12: Perform pole-zero cancellation processing on each signal to be processed using the following formula to obtain a pole-zero cancellation signal corresponding to each pulse event sample: Among them, V pz [n] and V pz [n-1] are all pole-zero cancellation signals, V CSA1 [n] and V CSA1 [n-1] are all signals to be processed, a, b, c and d are intermediate parameters for obtaining the pole-zero cancellation signal and have no physical meaning. s is the sampling period, τ1 is the first time constant, τ2 is the second time constant, and n is the index of the discrete signal, which is a positive integer.

3. The automatic fitting method for the decay time constant of an exponentially decaying pulse according to claim 2, characterized in that: Step S2 specifically includes the following steps: S201: Perform differential processing on each signal to be processed in sequence using the following formula to obtain a differential signal corresponding to each pulse event sample: V CSA1 [n]=V CSA1 [n+1]-V CSA1 [n]; S202: Calculate the standard deviation of the differential signal without a pulse event, use 10 times the standard deviation as a threshold, and construct a rising edge height sequence using the differential signal exceeding the threshold, and construct a pulse starting point sequence using the time series of the differential signal exceeding the threshold; S203: Determine whether the absolute difference between adjacent items of each sample point included in the rising edge height sequence corresponding to the pulse starting point sequence is greater than 2τ1. If so, retain the currently determined sample; otherwise, delete the currently determined sample. S204: After the processing of step S203, the sequence lengths of the rising edge height sequence and the corresponding pulse starting point sequence are both L0; S205: Arrange the rising edge height sequence and the corresponding pulse starting point sequence in step S204 in descending order according to the rising edge height to obtain a descending rising edge height sequence and a corresponding descending pulse starting point sequence; S206: Retrieve the sampling point of the pole-zero cancellation signal corresponding to the first differential signal of the descending pulse starting point sequence. If all sampling points within the second time constant range of the current pole-zero cancellation signal are greater than 0, execute step S207; otherwise, remove the first differential signal, update the descending pulse starting point sequence, and execute step S211. S207: Retrieve the sampling point of the first differential signal in the descending pulse starting point sequence. If the amplitude of the differential signal corresponding to the next sampling point of the first differential signal is less than 1 / 10 of the amplitude of the differential signal corresponding to the previous sampling point, remove the first differential signal, update the descending pulse starting point sequence, and execute step S211. Otherwise, execute step S208. S208: Retrieve each sampling point of the first differential signal of the descending pulse starting point sequence. If the sampling values ​​corresponding to two adjacent sampling points of the first differential signal are 0, remove the first differential signal, update the descending pulse starting point sequence, and execute step S211; otherwise, execute step S209. S209: Retrieve the sampling point of the pole-zero cancellation signal corresponding to the first differential signal of the descending pulse starting point sequence. If the sampling values ​​corresponding to ten consecutive sampling points are less than 0 within the first time constant range of the current pole-zero cancellation signal, then take the first sampling point with a sampling value less than 0 among the ten consecutive sampling points as the second zero point, record the position of the second zero point, and execute step S210. Otherwise, execute step S211. S210: searching for a sampling point of the pole-zero cancellation signal corresponding to the first differential signal of the descending pulse starting point sequence, taking the first sampling point of the current pole-zero cancellation signal as the first zero point, and if a sampling value greater than 0 exists in the search position within the range from the second zero point to four times the first time constant of the current pole-zero cancellation signal, taking the sampling point corresponding to the first sampling value greater than 0 as the third zero point and executing step S211; otherwise, removing the first differential signal, updating the descending pulse starting point sequence, and executing step S211; S211: intercept the signal within the range from the first zero point to the third zero point in the first pole-zero cancellation signal as the pulse event sample to be fitted, the first pole-zero cancellation signal corresponds to the first differential signal of the current descending pulse starting point sequence, and replace the first differential signal of the current descending pulse starting point sequence with the second differential signal of the current descending pulse starting point sequence, repeat steps S206 to S211 until the number of pulse event samples to be fitted reaches 80, stop the search, and obtain all the pulse event samples to be fitted.

4. The automatic fitting method for the decay time constant of an exponentially decaying pulse according to claim 3, characterized in that: In step S3, a double exponential fitting method or a triple exponential fitting method is used to fit each pulse event sample.

5. The automatic fitting method for the decay time constant of an exponential decay pulse according to claim 4, characterized in that: The specific process of fitting each pulse event sample using the double exponential fitting method is as follows: Clipping each pulse event sample to be fitted, retaining a signal within a range from a first zero point to a second zero point of each pulse event sample to be fitted, and updating each pulse event sample to be fitted; The updated pulse event samples are fitted using a double exponential model to obtain the first decay time constant and the second decay time constant of the double exponential model: Where A is the pulse amplitude parameter, t1 and t2 are the first and second decay time constants of the double exponential model, t1>t2>0, B is the baseline parameter, x is the time variable of the double exponential model, is the independent variable, y 2exp (x) is the amplitude strength of the double exponential model and is the dependent variable. The least squares method is used in combination with the double exponential model to iterate each pulse event sample to be fitted to minimize the sum of squared errors SSR: Where n is the length of the pulse event sample to be fitted, (x i ,y i ) is the data point of the pulse event sample; Taking the first decay time constant and the second decay time constant of the double exponential model corresponding to each pulse event sample to be fitted when the sum of squares of the errors between the predicted value of the double exponential model and each pulse event sample to be fitted is minimized; The first decay time constant mean and the second decay time constant mean are respectively averaged to obtain the first decay time constant mean and the second decay time constant mean, and the first decay time constant mean and the second decay time constant mean are used as the fitting results of the double exponential model.

6. The automatic fitting method for the decay time constant of an exponential decay pulse according to claim 4, characterized in that: The specific process of fitting each pulse event sample using the three-exponential fitting method is as follows: The three-exponential model is used to fit each pulse event sample to obtain the fitting parameters of the three-exponential model: Where D and E are both pulse amplitude parameters, T1 is the first decay time constant of the three-exponential model, T2 is the second decay time constant of the three-exponential model, T3 is the third decay time constant of the three-exponential model, T1>T2>T3>0, F is the baseline parameter, x is the time variable of the three-exponential model, is the independent variable, y 3exp (x) is the amplitude strength of the three-exponential model and is the dependent variable; The least squares method is used in combination with the three-exponential model to iterate the parameters D, E, F, T1, T2, and T3 of each pulse event sample to be fitted to minimize the sum of squared errors SSR: Where n is the length of the pulse event sample to be fitted, (x i ,y i ) is the data point of the pulse event sample; The fitting parameters of the pulse event samples that meet the preset indicators are averaged. The fitting parameters include the first decay time constant T1, the second decay time constant T2, the third decay time constant T3, the pulse amplitude parameter D, the pulse amplitude parameter E and the baseline parameter F of the three-exponential model, and the mean of the fitting parameters is used as the fitting result of the three-exponential model.

7. The automatic fitting method for the decay time constant of an exponential decay pulse according to claim 6, characterized in that: The method for setting the preset indicators is to calculate the determination coefficient R of each pulse event sample after each fitting. 2 value, and filter out R 2 The pulse event samples with the smallest value are filtered out, and the number of pulse event samples that are filtered out accounts for 20% of the total number of pulse event samples. The remaining pulse event samples are pulse event samples that meet the preset indicators.

8. The automatic fitting method for the decay time constant of an exponential decay pulse according to claim 5, characterized in that: The deconvolution recursive formula of the double exponential model is: V impulse [n]=(V pz [n+1]-(M 11 +M 12 )V pz [n]+M 11 M 12 V pz [n-1]) / (M 11 -M 12 ); Among them, M 11 and M 12 These are parameters used to express the deconvolution recursive formula of the double exponential model and have no physical meaning.

9. The automatic fitting method for the decay time constant of an exponential decay pulse according to claim 6, characterized in that: The deconvolution recursive formula of the three-exponential model is: a0＝0； a1=-DM 22 -DM 23 -EM 21 -EM 23 +(D+E)M 21 +(D+E)M 22 ; a2=DM 22 M 23 +EM 21 M 23 -(D+E)M 21 M 22 ; b0＝1； b1=-M 21 -M 22 -M 23 ; b2=M 21 M 22 +M 22 M 23 +M 21 M 23 ; b3=-M 21 M 22 M 23 ; Among them, M 21 、M 22 、M 23 , a0, a1, a2, b0, b1, b2 and b3 are coefficients of the deconvolution system transfer function expressing the three-exponential model and have no physical meaning.

10. The automatic fitting method for the decay time constant of an exponential decay pulse according to claim 8 or 9, characterized in that: Deconvolve the signal V of length N impulse [n] The formula for polarity evaluation is: Where σ0 is the standard deviation of the deconvolution signal in the event-free state, I(·) is the indicator function, P is the polarity, and α and β are parameters indicating polarity and have no actual physical meaning.

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