Method and system for evaluating siPM output discrimination threshold on lidar system detection performance

Abstract

The application provides a method and system for evaluating the influence of SiPM output discrimination threshold on the detection performance of a laser radar system, which can accurately and efficiently select the optimal discrimination threshold under different conditions and promote the device to exhibit the best detection performance. The method comprises the following steps: step 1, establishing a photon time domain distribution model of a single pixel of SiPM; step 2, introducing a dead time effect and a multi-pixel joint probability model to establish a SiPM photon event response model; step 3, considering the influence of the response pulse waveform and the discrimination threshold size on the number of output photon events in the actual output process, establishing an approximate time domain distribution model of the shielding effect D PB and the trigger effect D CF ; step 4, estimating the detection probability and false alarm probability of SiPM under different discrimination threshold conditions; and step 5, evaluating the denoising effect of the discrimination threshold based on the recall rate and the precision rate and the F1 coefficient index, and then determining the optimal discrimination threshold interval.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of laser radar detection, and particularly relates to a method and system for evaluating the influence of SiPM output discrimination threshold on the detection performance of a laser radar system. BACKGROUND

[0002] A silicon photomultiplier is a new type of semiconductor light detector developed in recent years. It is composed of hundreds of thousands of Geiger-mode avalanche photodiodes (Gm-APD) connected in series with quenching resistors in parallel, sharing a power supply terminal and an output terminal. The parallel connection of so many pixels together will cause large dark count and optical crosstalk, but due to the characteristics of independent operation of each pixel and linear superposition of response waveform, the SiPM has good photon counting ability, and in addition, it has high sensitivity, large dynamic range and is less affected by environmental temperature and magnetic field, so it has broad application prospects in multi-photon detection conditions, and has been applied in laser radar, medical imaging, astrophysics and other fields, and is widely considered as the best choice to replace traditional weak light detectors.

[0003] Due to the special pulse superposition threshold discrimination output mode of SiPM, the research on system detection probability and false alarm probability generally stays in the approximate case without considering the pulse stacking effect. Without considering the pulse stacking effect, the output terminal of threshold discrimination will have two problems: one is that the waveform of multiple photon event responses in adjacent time bins can only detect the first photon event; the other is that multiple photon events that do not reach the threshold in adjacent time bins may also be superimposed into a waveform exceeding the threshold and be discriminated and output. These problems will affect the estimation of detection probability and false alarm probability, and reduce the accuracy of performance evaluation method. SUMMARY

[0004] The application is carried out to solve the above problems, and aims to provide a method and system for evaluating the influence of SiPM output discrimination threshold on the detection performance of a laser radar system, which can select the SiPM output discrimination threshold with the best detection performance for the laser radar system, and promote the device to play the best detection performance.

[0005] In order to achieve the above purpose, the application adopts the following scheme:

[0006] <Method>

[0007] As shown in Figure 1 The application provides a method for evaluating the influence of SiPM output discrimination threshold on the detection performance of a laser radar system, which comprises the following steps:

[0008] Step 1, establishing a photon time domain distribution model of a single pixel of SiPM;

[0009] Step 2, introducing dead time effect and multi-pixel joint probability model, establishing SiPM photon event response model;

[0010] Step 3, considering the influence of response pulse waveform and discrimination threshold size on the number of output photon events in the actual output process, establishing shielding effect D PB and trigger effect D CF approximate time domain distribution model;

[0011] Let the amplitude of the output voltage pulse v ( t ) of a single pixel be V , the discrimination threshold be T , R = T / V , k = floor( R ), floor() represents the floor function, and the total number of photon events of all pixels responding in the time interval t i, t i + τ be n i ; the time domain distribution combination of the photon events that produce shielding effect is:

[0012] (3-1)

[0013] The time domain distribution combination of the photon events that produce trigger effect is:

[0014] (3-2)

[0015] In the formula, m , p respectively represent the combination vector of time interval position and the number of responding photon events in the corresponding time interval;

[0016] Step 4, estimating the detection probability and false alarm probability of SiPM under different discrimination threshold conditions;

[0017] Step 5, based on the recall rate and precision rate and F 1 coefficient index to evaluate the denoising effect of the discrimination threshold, and then determine the optimal discrimination threshold interval.

[0018] Preferably, the method for evaluating the influence of the discrimination threshold of SiPM output on the detection performance of the laser radar system provided by the application, in step 2, the single pixel of SiPM in the time interval t i , ti + τ number of photon events responded by a single pixel in a time interval ε satisfy Poisson distribution:

[0019] (2-1)

[0020] where, τ is the minimum time resolution of the timing device used by the photon counting lidar system, t i , t i + τ is the time interval, n s ( t i , t i + τ ) and n n ( t i , t i + τ ) are the numbers of signal and noise photons received in each time interval, N cell is the number of pixels of the SiPM,! denotes factorial; N single denotes the number of photons received by a single pixel in each time interval; K is the number of photon events responded by a single pixel of the SiPM in a time interval;

[0021] The probability of the photon event response of a single pixel is:

[0022] (2-2)

[0023] where, n td is the number of time intervals separated by the minimum resolution and contained in the dead time;

[0024] The probability that the whole SiPM responds n number of photon events in a time interval is:

[0025] (2-3)

[0026] where, C Nell n = N cell ![ n ( N cell- n ] is binomial coefficient.

[0027] Preferably, the method for evaluating the influence of SiPM output discrimination threshold on the detection performance of a laser radar system provided by the present application comprises the following sub-steps in step 4:

[0028] Step 4.1, estimate the detection probability of SiPM under different discrimination thresholds, and calculate the expected number of recorded signal photon events under the discrimination threshold;

[0029] The detection probability of SiPM under different discrimination thresholds in the time interval (t1, t2) is represented as: t i , t i + τ ) is represented as:

[0030] (4-1-1)

[0031] In the formula, P [ D PB ( V , T ; n , m , p )]、 P [ D CF ( V , T ; n , m , p )] respectively represent the probability of occurrence of a combination of time-domain distribution of photon events that produce shielding effect and triggering effect; by accumulating the detection probabilities of all time intervals in the signal pulse width range, the total detection probability under the discrimination threshold condition is obtained;

[0032] Step 4.2, estimate the false alarm probability of SiPM under different discrimination thresholds, and calculate the expected number of recorded noise photon events under the discrimination threshold;

[0033] The photon event response probability of a single pixel or a single Gm-APD of SiPM in the presence of only background noise needs to be rewritten as:

[0034] (4-2-1)

[0035] In the formula, f n represents the total noise rate of the system; by substituting the above formula into formula (2-3) and formula (4-1-1), the probability that a photon event can still be recorded under the discrimination threshold condition is calculated, which is the false alarm probability P f( V , T ):

[0036] (4-2-2)

[0037] wherein, ;

[0038] The expected number of noise photon events in the time interval of the time threshold range excluding the signal range is obtained by counting the false alarm probability:

[0039] (4-2-3)

[0040] wherein, range is the threshold duration, σ p is the root mean square pulse width of the received signal.

[0041] Preferably, the method for evaluating the influence of the SiPM output discrimination threshold on the detection performance of the lidar system provided by the present application, in step 4.1, when the pulse width of the voltage pulse v ( t ) is very narrow, there is a case where the detection probability is greater than 1, and in this case, the detection probability of all time intervals in the cumulative signal pulse width range is represented as the expected number of signal photon events:

[0042] (4-1-2)

[0043] wherein, t target is the corresponding moment of the target position.

[0044] Preferably, the method for evaluating the influence of the SiPM output discrimination threshold on the detection performance of the lidar system provided by the present application, in step 5, the recall R ec and the precision P re of the point cloud distribution for different discrimination thresholds are quantitatively evaluated, the recall R ec represents the proportion of successfully recorded signal photon events corresponding to the discrimination threshold to all received signal photons, and the precision P re represents the proportion of true received signal photon events in the successfully recorded photon events corresponding to the discrimination threshold.

[0045] The calculation formulas of the two metrics are as follows:

[0046] (5-1)

[0047] (5-2)

[0048] TP represents the number of signal photon events screened by the discrimination threshold, FN represents the number of signal photons that are not recorded as signal photon events, FP represents the number of noise photon events screened by the discrimination threshold;

[0049] In the photon point cloud data, the recall rate R ec The larger the value, the more photon events are screened by the discrimination threshold, and when R ec = 1, it means that the discrimination threshold successfully screens all the signal photons detected each time; the precision rate P re The larger the value, the smaller the proportion of noise photon events recorded by the discrimination threshold, and when P re = 1, it means that all the photon events screened by the discrimination threshold are signal photon events;

[0050] For the same discrimination threshold, the harmonic mean R ec of the recall rate P re and the precision rate F is used to quantitatively evaluate the denoising effect of the discrimination threshold, F The larger the coefficient, the better the screening result of the discrimination threshold on the signal photon events, and the formula is as follows:

[0051] (5-3)

[0052] β is a weight factor, and when β = 1, the recall rate R ec and the precision rate P re have the same weight, that is:

[0053] (5-4).

[0054] Preferably, the method for evaluating the discrimination threshold of SiPM output on the detection performance of a laser radar system provided by the present application comprises the following sub-steps in step 1:

[0055] Step 1.1, determining the signal and noise photon time domain distribution of the laser radar system:

[0056] (1-1)

[0057] σ p ​​​The root mean square pulse width of the received signal, t target The corresponding time of the target position, N s The number of signal photons received within the laser pulse range at the target arrival time;

[0058] The total noise of the system is represented as f n = f b · η PDE + f d Where, f n The total noise rate of the system is represented as f b The background light noise rate is represented as f d The dark count noise rate of the single photon detector is represented as η PDE The photon detection efficiency is represented as

[0059] Step 1.2, according to the time resolution, divide the time interval, establish the photon time domain distribution model of each pixel;

[0060] The number of photons received by a single pixel within each time interval t i , t i + τ is:

[0061] (1-2)

[0062] Where, n s ( t i , t i + τ ) and n n ( t i , t i + τ ) are the number of signal and noise photons received within each time interval, N cell N is the number of pixels of the SiPM.

[0063] [SYSTEM]

[0064] Further, the application also provides a system for evaluating the influence of SiPM output discrimination threshold on the detection performance of a laser radar system, which can automatically implement the above-mentioned method, comprising:

[0065] a single-pixel model construction unit for establishing a photon time-domain distribution model of a single pixel of the SiPM;

[0066] an event response model construction unit for introducing a dead time effect and a multi-pixel joint probability model to establish a SiPM photon event response model;

[0067] a time-domain distribution model construction unit for considering the influence of a response pulse waveform and a discrimination threshold size on the number of output photon events in an actual output process to establish an approximate time-domain distribution model of a shielding effect D PB and a trigger effect D CF ; assuming that the amplitude of an output voltage pulse v ( t ) of a single pixel is V , the discrimination threshold is T , R = T / V , k = floor( R ), floor() represents a floor function, and the total number of photon events of all pixels responding in a time interval t i, t i + τ is n i ; the time-domain distribution combination of a photon event causing a shielding effect is:

[0068] (3-1)

[0069] the time-domain distribution combination of a photon event causing a trigger effect is:

[0070] (3-2)

[0071] in the formulae, m , p respectively represent a combination vector of a time interval position and a corresponding number of responding photon events in the time interval;

[0072] a probability estimation unit for estimating the detection probability and false alarm probability of the SiPM under different discrimination threshold conditions;

[0073] an evaluation and determination unit for evaluating the denoising effect of the discrimination threshold based on the recall rate and precision rate and F 1 coefficient index, and further determining an optimal discrimination threshold interval;

[0074] The control unit is in communication with the single-pixel model construction unit, the event response model construction unit, the time-domain distribution model construction unit, the probability estimation unit and the evaluation determination unit, and controls the operation of them.

[0075] Preferably, the system for evaluating the influence of the SiPM output discrimination threshold on the detection performance of the lidar system provided by the application further comprises an input display unit in communication with the control unit, for allowing a user to input operation instructions and display accordingly.

[0076] Preferably, in the event response model construction unit, the number of photon events responded by the single pixel of the SiPM in the time interval (T1, T2) is t i , t i + τ τ satisfies the Poisson distribution:

[0077] (2-1)

[0078] wherein, τ is the minimum time resolution of the timing device used by the photon counting lidar system, t i , t i + τ n s t i , t i + τ n n t i , t i + τ N cell is the number of pixels of the SiPM, and n! represents the factorial; N single represents the number of photons received by the single pixel in each time interval; K is the number of photon events responded by the single pixel of the SiPM in the time interval;

[0079] The photon event response probability of the single pixel is:

[0080] (2-2) ​​​​​​

[0081] wherein, n td the number of time intervals separated by the minimum resolution and contained in the dead time;

[0082] the whole SiPM responds to a certain number of photon events in a time interval n The probability of a certain number of photon events is expressed as:

[0083] (2-3)

[0084] wherein, C Nell n = N cell [ n ( N cell - n )!] is the binomial coefficient.

[0085] Preferably, the system for evaluating the influence of the SiPM output discrimination threshold on the detection performance of a lidar system according to the present application estimates the detection probability and false alarm probability using the following steps 4.1-4.2:

[0086] Step 4.1, estimate the detection probability of the SiPM under different discrimination thresholds, calculate the expected number of recorded photon events under the discrimination threshold;

[0087] The detection probability of the SiPM under different discrimination thresholds in the time interval t i , t i + τ is expressed as:

[0088] (4-1-1)

[0089] wherein, P [ D PB ( V , T ; n , m , p )]、 P [ D CF ( V , T ; n , m , p) respectively represent the probability of the combination of the time domain distribution of the photon events that produce shielding effect and triggering effect; the total detection probability under the discrimination threshold condition is obtained by accumulating the detection probability of all time intervals in the signal pulse width range;

[0090] Step 4.2, estimate the false alarm probability of SiPM under different discrimination threshold conditions, and calculate the expected number of noise photon events recorded under the discrimination threshold;

[0091] The photon event response probability of SiPM single pixel or single Gm-APD under only background noise needs to be rewritten as:

[0092] (4-2-1)

[0093] In the formula, f n The total noise rate of the system is represented; the formula (2-3) and formula (4-1-1) are calculated by bringing the above formula into formula (2-3), and the probability that a photon event can still be recorded under the discrimination threshold condition is the false alarm probability P f ( V , T ) :

[0094] (4-1-2)

[0095] In the formula, ;

[0096] The expected number of noise photon events is obtained by counting the false alarm probability of the time interval in the time threshold range except the signal range:

[0097] (4-1-3)

[0098] In the formula, range is the threshold duration, σ p is the root mean square pulse width of the received signal.

[0099] Effects of the application

[0100] The method and system for evaluating the discrimination threshold of SiPM output on the detection performance of a laser radar system provided by the application first establish a single pixel receiving model, then construct a statistical model of the number of photon events responded by SiPM in a certain time interval based on the independence of SiPM pixels and the dead time effect, then approximately give the time domain distribution combination of photon events that produce shielding effect and triggering effect under different discrimination thresholds according to the stacking effect of SiPM output voltage waveform, then establish a semi-analytical detection probability and false alarm probability model of SiPM, calculate the detection probability and false alarm probability, and introduce the recall rate and precision rate, andF The denoising effect of the discrimination threshold is evaluated using a coefficient, yielding corresponding recall and precision performance indicators. Based on these indicators, the SiPM output discrimination threshold that optimizes the detection performance of the lidar system is finally selected. This method can evaluate the detection performance under different discrimination thresholds using only lidar system parameters and measurement environment parameters. It is fast, accurate, and fully considers the pulse stacking effect. When applied to photon-counting lidar systems equipped with SiPM detectors, it can effectively guide the selection of discrimination thresholds, significantly improving the detection efficiency of photon-counting lidar systems. It has great application value and potential in the field of multi-photon, low signal-to-noise ratio detection and provides important guidance for the design and theoretical analysis of SiPM-based photon-counting lidar systems. Attached Figure Description

[0101] Figure 1 is a flowchart of the method for evaluating the effect of SiPM output discrimination threshold on the detection performance of a lidar system, which is involved in this invention.

[0102] Figure 2 is a schematic diagram of the pulse stacking effect involved in the embodiment of the present invention, wherein (a) shielding effect and (b) triggering effect;

[0103] Figure 3 is a comparison of the theoretical and measured results of false alarm probability and detection probability based on different discrimination thresholds of SiPM detector in Embodiment 1 of the present invention, wherein, (a) N s = 0.35、 f n = 7MHz, (b) N s = 1.5、 f n = 7MHz, (c) N s =3、 f n = 5MHz, (d) N s =3、 f n = 15MHz;

[0104] Figure 4 shows the precision, recall, and accuracy of different discrimination thresholds based on the SiPM detector in Embodiment 1 of the present invention. F A comparison of theoretical and experimental results for coefficient 1, where (a) N s = 0.35、 f n = 7MHz, (b) N s = 1.5、 f n = 7MHz, (c)N s = 3, f n = 5 MHz, (d) N s = 3, f n = 15 MHz. DETAILED DESCRIPTION

[0105] The method and system for evaluating the influence of SiPM output discrimination threshold on the detection performance of a laser radar system will be described in detail below with reference to the accompanying drawings.

[0106] [Example One]

[0107] In this embodiment, a photon counting radar system based on SiPM detectors was built to verify the technical solutions of the present application. A semiconductor-pumped solid-state laser was excited by a function generator to emit laser pulses with a wavelength of 532 nm and a full width at half maximum of 1.8 ns. Part of the laser was reflected to a photodiode (PIN) to generate a Start signal, and the other part of the laser was attenuated to the energy level of several to tens of photons by a fixed attenuator and a continuous adjustable attenuator (NDC-100C-2), and was finally collected by a receiving telescope, transmitted to a SiPM (JOINBON JPC-1050-TEC) through an optical fiber. The output signal of the SiPM was used as a Stop signal, which was transmitted to a time-of-flight instrument (TCSPC-TDC Fast ComTec MCS6A4T2) together with the Start signal. A computer controlled the discrimination threshold of the time-of-flight instrument to collect and record the photon event data at different discrimination thresholds.

[0108] For the photon counting radar system based on SiPM detectors, the system hardware parameters are known values, and in the embodiment, these parameters take the following values: total number of pixels N cell = 324, single-pixel dead time t d = 45 ns, 532 nm quantum efficiency η PDE = 25%, dark count f d = 3.3 kHz, output signal amplitude V= 100 mV, output signal pulse width σ v= 50 ns, time resolution τ= 200 ps, time threshold range= 800 ns.

[0109] By adjusting the continuous adjustable attenuation sheet and the background light intensity, setting N s = 0.35、 f n = 7MHz, N s = 1.5、 f n =7MHz, N s =3、 f n = 5MHz, N s =3、 f n = 15MHz.

[0110] As Figure 1 shown, based on the SiPM output discrimination threshold detection performance evaluation model, the specific implementation process is:

[0111] Step S1. Establishing a photon time-domain distribution model of a single pixel of SiPM;

[0112] S1.1: Deriving the signal and noise photon time-domain distribution of the laser radar system;

[0113] The signal photons reflected by laser reaching the target object approximately satisfy Gaussian distribution in time domain, which can be expressed as:

[0114] (1)

[0115] In the formula, σ p is the root mean square pulse width of the received signal, t target is the corresponding moment of the target position, N s represents the number of signal photons received within the laser pulse range at the target arrival time, which is related to the peak power of the emitted laser pulse, the target distance, the atmospheric transmittance and the receiving system parameters, etc. It is usually estimated by the laser radar equation. In addition to the signal, the detection system will also receive noise photons. The noise in the laser radar system mainly comes from the sun background light noise in the field of view of the detector and the dark count noise of the internal circuit of the detector, which are independent of each other and subject to uniform distribution in time domain. Therefore, the total noise of the system can be expressed as f n = f b · η PDE + f d , in which, f ntotal noise rate of the system (in units of Hertz), f b background light noise rate, f d dark count noise rate of the single photon detector.

[0116] S1.2: Divide the time interval according to the time resolution, and establish the photon time domain distribution model of each pixel;

[0117] Let the minimum time resolution of the timing device used by the photon counting lidar system be τ , and the number of pixels of the SiPM be N cell . Then the number of photons received by a single pixel in each time interval t i , t i + τ ) is:

[0118] (2)

[0119] Step S2. Introduce the dead time effect and the multi-pixel joint probability model, and establish the SiPM photon event response model;

[0120] The number of photon events responded by a single pixel of the SiPM in the time interval t i , t i + τ ) satisfies the Poisson distribution: ε

[0121] (3)

[0122] Since each pixel of the SiPM responds independently, and there is a dead time effect, i.e. the same pixel cannot respond to other photon events within a fixed time after responding to a photon event, the photon event response probability of a single pixel is:

[0123] (4)

[0124] In the formula, n td is the number of time intervals included in the dead time, with the minimum resolution as the width. Since the width τ is small, and in addition, the number of echo signal photons that a single pixel can receive is very small, the probability that a single pixel responds to multiple photon events within a unified time interval can be ignored, i.e. P ( t i , t i +​τ ; K ≥2)≈0. Thus, the entire SiPM response within a certain time interval... n The probability of a number of photon events can be represented by a binomial distribution as follows:

[0125] (5)

[0126] in C Nell n = N cell ! / [ n !( N cell - n )!] represents the binomial coefficient.

[0127] Step S3. Discuss the influence of the response pulse waveform and the discrimination threshold on the number of output photon events during the actual output process, and establish the shielding effect. D PB With triggering effect D CF An approximate time-domain distribution model;

[0128] Since the number of photon events derived from S2 is not the final number of photon events output after threshold discrimination, the photon events still need to undergo the process of voltage waveform superposition in the analog circuit and threshold discrimination. Specifically, from the response to the recorded output, the photon event response is superimposed as a voltage pulse waveform in the analog circuit, producing a pulse stacking effect. Figure 2 As shown, the discrimination threshold may fail to distinguish multiple pulses during discrimination, recording them as a single photon event. This phenomenon is called the shielding effect. Alternatively, it may incorrectly record voltage waveforms that, while not reaching the threshold initially, exceed it after stacking as photon events. This phenomenon is called the triggering effect. Clearly, the occurrence of these two phenomena depends primarily on the waveform of the response pulse and the magnitude of the discrimination threshold. Since the response pulse is typically only related to the SiPM circuit design and generally cannot be changed, this discussion mainly focuses on the impact of different discrimination thresholds on the system's detection performance.

[0129] Assume the output voltage pulse of a single pixel v ( t The amplitude of ) V The identification threshold is T , R = T / V , k = floor( R ), where floor() represents the floor function, and the time interval is ( t i, ti + τ The total number of photon events in the response of all pixels within the range is n i It is possible to list within a time range ( t i, t i + τ There are two scenarios in which a photon event is successfully recorded within a given time interval: 1) The pulse amplitude generated in response to the photon event in the current time interval exceeds the threshold, while the pulse in the previous time interval does not exceed the threshold, i.e., no shielding effect occurs; 2) The pulse amplitude generated in response to the photon event in the current time interval and several previous time intervals does not exceed the threshold, but the waveform stacking causes the waveform in the current time interval to exceed the threshold while the waveform in the previous time interval does not exceed the threshold, i.e., a triggering effect occurs.

[0130] The combination of photon event temporal distributions that result in a shielding effect can be approximated as follows: n i > k The union of all distribution combinations:

[0131] (6)

[0132] In the formula, m , p These are combined vectors representing the time interval location and the number of photon events responding to the corresponding time interval. For example, if the discrimination threshold... T = 2.5 V If the current time interval responds to 3 photon events, a shielding effect will occur when responding to 3 photon events in the first 1-3 time intervals, but no shielding effect will occur when responding to 3 photon events in the first 4 time intervals. Therefore, it can be assumed that any combination of randomly responding to [3, +∞) photon events within the first 3 time intervals will produce a shielding effect. Similarly, a shielding effect will occur when responding to 4 photon events in the first 1-4 time intervals, but no shielding effect will occur when responding to 4 photon events in the first 5 time intervals. Therefore, it can be assumed that any combination of randomly responding to [4, +∞) photon events within the first 4 time intervals will produce a shielding effect. Simplified to:

[0133] (7)

[0134] Similarly, the temporal distribution combination of photon events that produce the triggering effect can be approximated as follows: n i ≤ k The union of all distribution combinations:

[0135] (8)

[0136] For example, if the discrimination threshold T = 2.5V, the trigger effect occurs when 1 or 2 photon events are responded in the first 1~2 time intervals, and the shielding effect occurs when 2 photon events are responded in the first 1~3 time intervals, which can be simplified as:

[0137] (9)

[0138] (10)

[0139] Step S4. Estimate the detection probability and false alarm probability of SiPM under different discrimination thresholds.

[0140] S4.1: Estimate the detection probability of SiPM under different discrimination thresholds, and calculate the expected number of recorded signal photon events under the discrimination threshold.

[0141] The detection probability of SiPM under different discrimination thresholds in the time interval (t1, t2) can be approximately expressed as: t i , t i + τ ) is:

[0142] (11)

[0143] In the formula, P [ D PB ( V , T ; n , m , p )]、 P [ D CF ( V , T ; n , m , p )] respectively represent the probability of the combination of photon event time domain distribution that produces shielding effect and trigger effect. In the specific calculation process, since the number of photons received by SiPM in each time interval is different within the signal pulse width range, the number of photon events responded in each time interval respectively obeys different probability binomial distribution, and at this time P [ D PB ( V, T ; n , m , p )]、 P [ D CF ( V , T ; n , m , p )] (i.e. the probability distribution of the photon events in the consecutive time intervals) is the joint probability of the multi-dimensional discrete variables, whose probability density is the discrete convolution of the binomial probability density of each time interval. By accumulating the detection probability of all time intervals in the signal pulse width range, the total detection probability under the discrimination threshold condition can be obtained. It should be noted that when the pulse width of the voltage pulse v ( t ) is very narrow, the detection probability is greater than 1, and its physical meaning is represented as the expected number of signal photon events:

[0144] (12)

[0145] S4.2: Estimate the false alarm probability of SiPM under different discrimination threshold conditions, and calculate the expected number of noise photon events recorded under the discrimination threshold;

[0146] The photon event response probability of a single pixel (or a single Gm-APD) of SiPM when there is only background noise needs to be rewritten as:

[0147] (13)

[0148] By substituting the above formula into formula (5) and formula (11), the probability that a photon event can still be recorded under the discrimination threshold condition can be calculated, which is the false alarm probability P f ( V , T ) :

[0149] (14)

[0150] In the formula, .

[0151] Since the background noise is uniformly distributed in the time domain, the number of responding photon events in each time interval follows the binomial distribution with the same probability, and P [ D PB ( V , T ; n , m , p )],P [ D CF ( V , T ; n , m , p )]can be calculated by using the additivity of binomial distribution. The expected number of noise photon events can be obtained by counting the false alarm probability of the time interval within the time threshold range (excluding the signal range):

[0152] (15)

[0153] wherein, range is the threshold duration.

[0154] Step S5. The noise removal effect of the discrimination threshold is evaluated based on the recall and precision and the coefficient indicator. F 1. The coefficient indicator is used to evaluate the noise removal effect of the discrimination threshold.

[0155] In order to quantitatively evaluate the point cloud distribution of different discrimination thresholds, two measurement values, recall (Recall) and precision (Precision), are introduced. The recall represents the proportion of successfully recorded signal photon events corresponding to the discrimination threshold in all received signal photons; the precision represents the proportion of true received signal photon events in the successfully recorded photon events corresponding to the discrimination threshold. The calculation formulas of the two measurement values are as follows: R ec P re

[0156] (16)

[0157] (17)

[0158] wherein, TP represents the number of signal photon events screened by the discrimination threshold, FN represents the number of received signal photons that are not recorded as signal photon events, FP represents the number of noise photon events screened by the discrimination threshold. In the photon point cloud data, the larger the recall value is, the more photon events are screened by the discrimination threshold. When R ec = 1, it indicates that the discrimination threshold successfully screens every detected signal photon; the larger the precision value is, the smaller the proportion of noise photon events recorded by the discrimination threshold is. When R ec = 1, it indicates that the discrimination threshold successfully screens every detected signal photon; the larger the precision value is, the smaller the proportion of noise photon events recorded by the discrimination threshold is. P re = 1, it indicates that the discrimination threshold successfully screens every detected signal photon; the larger the precision value is, the smaller the proportion of noise photon events recorded by the discrimination threshold is. P re ​​= 1, it means that all the photon events screened by the discrimination threshold are signal photon events. For the same discrimination threshold, the recall rate R ec and the precision rate P re are two factors that restrict each other, so the harmonic mean R ec coefficient of the recall rate P re and the precision rate F is used to quantitatively evaluate the denoising effect of the discrimination threshold, and the larger the coefficient is, the better the screening result of the discrimination threshold on the signal photon events is, and the formula is as follows: F

[0159] (18)

[0160] In the formula, β is a weight factor, and when β = 1, the recall rate R ec and the precision rate P re have the same weight, that is:

[0161] (19)

[0162] In this embodiment, based on the above method, the SiPM semi-analytical detection probability and false alarm probability model of the photon counting radar system using the built SiPM detector is established, and the recall rate and the precision rate and F 1 coefficient are introduced to evaluate the denoising effect of the discrimination threshold, and the optimal discrimination threshold interval is given. Figure 3 The theoretical and experimental results of the false alarm probability and the detection probability under different discrimination thresholds are given, in which the solid line is the theoretical calculation result and the asterisk “*” is the experimental result. It can be seen that the theoretical calculation results under different discrimination thresholds are in good agreement with the experimental results, and the average R 2 is greater than 0.95. Figure 4 The theoretical and experimental results of the precision rate, the recall rate and the F 1 coefficient of different discrimination thresholds in the embodiment are given, and it can be seen that the theoretical calculation results are in good agreement with the experimental results. By observing the F 1 coefficient under different average signal photon numbers and background noise rates, when the background noise rate and the average signal photon number level are small, the discrimination threshold R ​The optimal selection interval of the SiPM output discrimination threshold is 1.5-2. Therefore, the evaluation method proposed in the application is more in line with the actual working characteristics of the SiPM than the evaluation method of the existing SiPM-based photon counting laser radar system, which has important guiding significance for the optimization design of the hardware parameters of the SiPM-based photon counting laser radar system and the quantitative analysis of the detection performance.

[0163] <Embodiment Two>

[0164] Further, the embodiment also provides a system capable of automatically implementing the above method for evaluating the SiPM output discrimination threshold on the detection performance of the laser radar system, which comprises a single-pixel model construction part, an event response model construction part, a time-domain distribution model construction part, a probability estimation part, an evaluation determination part, an input display part and a control part.

[0165] The single-pixel model construction part is used to perform the content described in step 1 above, and establish the photon time-domain distribution model of the single pixel of the SiPM.

[0166] The event response model construction part is used to perform the content described in step 2 above, and introduce the dead time effect and the multi-pixel joint probability model to establish the SiPM photon event response model.

[0167] The time-domain distribution model construction part is used to perform the content described in step 3 above, and consider the influence of the response pulse waveform and the discrimination threshold size on the number of output photon events in the actual output process to establish the approximate time-domain distribution model of the shielding effect D PB and the trigger effect. D CF

[0168] The probability estimation part is used to perform the content described in step 4 above, and estimate the detection probability and the false alarm probability of the SiPM under different discrimination threshold conditions.

[0169] The evaluation determination part is used to perform the content described in step 5 above, and perform the noise removal effect evaluation of the discrimination threshold based on the recall rate and the precision rate and F 1 coefficient index, and then determine the optimal discrimination threshold interval.

[0170] The input display part is used to input the operation instruction of the user, and display the input, output and intermediate processing data of the corresponding part according to the operation instruction.

[0171] The control part is in communication connection with the single-pixel model construction part, the event response model construction part, the time-domain distribution model construction part, the probability estimation part and the evaluation determination part, and controls the operation of them.

[0172] ​The above examples are only illustrative of the technical solutions of the present application. The method and system for evaluating the influence of the SiPM output discrimination threshold on the detection performance of the laser radar system involved in the present application are not limited to the content described in the above examples, but are subject to the scope defined in the claims. Any modification or supplement or equivalent replacement made by the person skilled in the art on the basis of the examples is within the scope of the claims of the present application.

Claims

1. A method for evaluating the effect of SiPM output discrimination threshold on the detection performance of a lidar system, characterized in that, Includes the following steps: Step 1: Establish a photon temporal distribution model for a single pixel in the SiPM; Step 2: Introduce the dead-time effect and multi-pixel joint probability model to establish the SiPM photon event response model; Step 3: Consider the impact of the response pulse waveform and the discrimination threshold on the number of output photon events during the actual output process, and establish the shielding effect. D PB With triggering effect D CF An approximate time-domain distribution model; Assume the output voltage pulse of a single pixel v ( t The amplitude of ) V The identification threshold is T , R = T / V , k = floor( R ), floor() represents the floor function, which rounds down the time interval ( t i, t i + τ The total number of photon events in the response of all pixels within the range is n i The temporal distribution combination of photon events exhibiting a shielding effect is as follows: (3-1) The temporal distribution combination of photon events that produce the triggering effect is as follows: (3-2) In the formula, m , p These are combined vectors representing the time interval position and the number of photon events in the corresponding time interval, respectively. Step 4: Estimate the detection probability and false alarm probability of SiPM under different discrimination threshold conditions; Step 5, based on recall and precision, and F The denoising effect of the discrimination threshold is evaluated using a coefficient index, thereby determining the optimal discrimination threshold range.

2. The method for evaluating the effect of SiPM output discrimination threshold on the detection performance of a lidar system according to claim 1, characterized in that: in, In step 2, a single SiPM pixel is within a time interval ( t i , t i + τ Number of photon events in the internal response ε Satisfies a Poisson distribution: (2-1) In the formula, τ The minimum time resolution of the timing device used in a photon counting lidar system, t i , t i + τ () represents the time interval. n s ( t i , t i + τ )and n n ( t i , t i + τ The number of signal and noise photons received within each time interval. N cell Let be the number of pixels in SiPM, and ! denotes factorial; N single This represents the number of photons received by a single pixel within each time interval; K The number of photon events in the response of a single pixel in the SiPM within a time interval; The photon event response probability of a single pixel is: (2-2) In the formula, n td The number of time intervals, separated by the minimum resolution, contained within the dead time; The response of the entire SiPM within a certain time interval n The probability of a number of photon events is expressed as: (2-3) In the formula, C Nell n = N cell ! / [ n !( N cell - n )!] represents the binomial coefficient.

3. The method for evaluating the effect of SiPM output discrimination threshold on the detection performance of a lidar system according to claim 2, characterized in that: in, Step 4 includes the following sub-steps: Step 4.1: Estimate the detection probability of SiPM under different discrimination thresholds and calculate the expected number of recorded signal photon events under the discrimination threshold. SiPM under different discrimination thresholds in time intervals ( t i , t i + τ The detection probability of ) is expressed as: (4-1-1) In the formula, P [ D PB ( V , T ; n , m , p )]、 P [ D CF ( V , T ; n , m , p The numbers ) and ) represent the probabilities of the time-domain distribution combinations of photon events that produce shielding and triggering effects, respectively; the total detection probability under this discrimination threshold condition is obtained by accumulating the detection probabilities of all time intervals within the cumulative signal pulse width. Step 4.2: Estimate the false alarm probability of SiPM under different discrimination thresholds, and calculate the expected number of noisy photon events recorded under the discrimination threshold. The photon event response probability of a single SiPM pixel or a single Gm-APD in the presence of only background noise needs to be rewritten as follows: (4-2-1) In the formula, f n Let represent the total noise rate of the system; substituting the above equation into equations (2-3) and (4-1-1), the probability that a photon event can still be recorded under the discrimination threshold condition is the false alarm probability. P f ( V , T ): (4-2-2) In the formula, ; By statistically analyzing the false alarm probability within the time interval of the time threshold outside the signal range, the expected number of noisy photon events can be obtained: (4-2-3) In the formula, range For threshold duration, σ p This is the root mean square pulse width of the received signal.

4. The method for evaluating the effect of SiPM output discrimination threshold on the detection performance of a lidar system according to claim 3, characterized in that: in, In step 4.1, when the voltage pulse v ( t When the pulse width is very narrow, there are cases where the detection probability is greater than 1. In this case, the detection probability of all time intervals within the cumulative signal pulse width range is expressed as the expected number of signal photon events: (4-1-2) In the formula, t target This corresponds to the time at the target location.

5. The method for evaluating the effect of SiPM output discrimination threshold on the detection performance of a lidar system according to claim 1, characterized in that: in, In step 5, recall is used. R ec precision P re Quantitative evaluation of point cloud distributions with different discrimination thresholds, recall rate R ec Precision represents the proportion of successfully recorded signal photon events out of all received signal photons, corresponding to the discrimination threshold. P re This indicates the proportion of photon events that actually received signals among the successfully recorded photon events, corresponding to the identification threshold. The formulas for calculating the two measures are as follows: (5-1) (5-2) In the formula, TP This indicates the number of signal photon events filtered by the discrimination threshold. FN This indicates the number of events among the received signal photons that were not recorded as signal photon events. FP This indicates the number of noisy photon events filtered out by the discrimination threshold; In photon point cloud data, recall R ec The higher the value, the more photon events are filtered by the discrimination threshold. R ec When the precision is 1, it means that the discrimination threshold successfully filters out all the signal photons detected each time; P re The larger the value, the smaller the proportion of noisy photon events recorded by the discrimination threshold. P re When =1, it means that all photon events filtered by the discrimination threshold are signal photon events; For the same discrimination threshold, use recall. R ec precision P re Harmonic average F The coefficient is used to quantitatively evaluate the denoising effect of the discrimination threshold. F The larger the coefficient, the better the screening result of the discrimination threshold for signal photon events. The formula is as follows: (5-3) In the formula, β As a weighting factor, when β = Recall rate at time 1 R ec precision P re Both have the same weight, that is: (5-4)。 6. The method for evaluating the effect of SiPM output discrimination threshold on the detection performance of a lidar system according to claim 1, characterized in that: in, Step 1 includes the following sub-steps: Step 1.1: Determine the temporal distribution of signal and noise photons in the lidar system: (1-1) In the formula, σ p The root mean square pulse width of the received signal. t target The corresponding time for the target location. N s This indicates the number of signal photons received within the laser pulse range at the moment the target arrives; The total system noise is expressed as f n = f b · η PDE + f d ,in, f n This represents the total noise rate of the system. f b Indicates the background light noise rate. f d This represents the dark count noise rate of a single-photon detector. η PDE Indicates photon detection efficiency; Step 1.2: Divide the time interval according to the time resolution and establish a photon temporal distribution model for each pixel; Each time interval ( t i , t i + τ The number of photons received by a single pixel within the area is: (1-2) In the formula, n s ( t i , t i + τ )and n n ( t i , t i + τ The number of signal and noise photons received within each time interval. N cell denoted as the number of pixels in the SiPM.

7. A system for evaluating the effect of SiPM output discrimination threshold on the detection performance of a lidar system, characterized in that, include: The single-pixel model construction unit establishes a photon temporal distribution model for a single pixel in the SiPM. The event response model construction department introduces the dead-time effect and the multi-pixel joint probability model to establish the SiPM photon event response model; The temporal distribution model construction section considers the influence of the response pulse waveform and the discrimination threshold on the number of output photon events during the actual output process, and establishes a shielding effect. D PB With triggering effect D CF An approximate time-domain distribution model; assuming the output voltage pulse of a single pixel. v ( t The amplitude of ) V The identification threshold is T , R = T / V , k = floor( R ), floor() represents the floor function, which rounds down the time interval ( t i, t i + τ The total number of photon events in the response of all pixels within the range is n i The temporal distribution combination of photon events exhibiting a shielding effect is as follows: (3-1) The temporal distribution combination of photon events that produce the triggering effect is as follows: (3-2) In the formula, m , p These are combined vectors representing the time interval position and the number of photon events in the corresponding time interval, respectively. The probability estimation unit estimates the detection probability and false alarm probability of SiPM under different discrimination threshold conditions; The assessment and determination department, based on recall and precision, and F The denoising effect of the discrimination threshold is evaluated using a coefficient index, thereby determining the optimal discrimination threshold range; The control unit is communicatively connected to the single-pixel model construction unit, the event response model construction unit, the time-domain distribution model construction unit, the probability estimation unit, and the evaluation and determination unit, and controls their operation.

8. The system for evaluating the effect of SiPM output discrimination threshold on the detection performance of a lidar system according to claim 7, characterized in that, Also includes: The input display unit is connected in communication with the control unit and is used to allow users to input operation commands and display the corresponding commands.

9. The system for evaluating the effect of SiPM output discrimination threshold on the detection performance of a lidar system according to claim 7, characterized in that: in, In the event response model construction section, a single SiPM cell exists within a time interval ( t i , t i + τ Number of photon events in the internal response ε Satisfies a Poisson distribution: (2-1) In the formula, τ The minimum time resolution of the timing device used in a photon counting lidar system, t i , t i + τ () represents the time interval. n s ( t i , t i + τ )and n n ( t i , t i + τ The number of signal and noise photons received within each time interval. N cell Let be the number of pixels in SiPM, and ! denotes factorial; N single This represents the number of photons received by a single pixel within each time interval; K The number of photon events in the response of a single pixel in the SiPM within a time interval; The photon event response probability of a single pixel is: (2-2) In the formula, n td The number of time intervals, separated by the minimum resolution, contained within the dead time; The response of the entire SiPM within a certain time interval n The probability of a number of photon events is expressed as: (2-3) In the formula, C Nell n = N cell ! / [ n !( N cell - n )!] represents the binomial coefficient.

10. The system for evaluating the effect of SiPM output discrimination threshold on the detection performance of a lidar system according to claim 9, characterized in that: in, The probability estimation department estimates the detection probability and false alarm probability using the methods described in steps 4.1 to 4.2 below: Step 4.1: Estimate the detection probability of SiPM under different discrimination thresholds and calculate the expected number of recorded signal photon events under the discrimination threshold. SiPM under different discrimination thresholds in time intervals t i , t i + τ The detection probability of ) is expressed as: (4-1-1) In the formula, P [ D PB ( V , T ; n , m , p )]、 P [ D CF ( V , T ; n , m , p The numbers ) and ) represent the probabilities of the time-domain distribution combinations of photon events that produce shielding and triggering effects, respectively; the total detection probability under this discrimination threshold condition is obtained by accumulating the detection probabilities of all time intervals within the cumulative signal pulse width. Step 4.2: Estimate the false alarm probability of SiPM under different discrimination thresholds, and calculate the expected number of noisy photon events recorded under the discrimination threshold. The photon event response probability of a single SiPM pixel or a single Gm-APD in the presence of only background noise needs to be rewritten as follows: (4-2-1) In the formula, f n Let represent the total noise rate of the system; substituting the above equation into equations (2-3) and (4-1-1), the probability that a photon event can still be recorded under the discrimination threshold condition is the false alarm probability. P f ( V , T ): (4-1-2) In the formula, ; By statistically analyzing the false alarm probability within the time interval of the time threshold outside the signal range, the expected number of noisy photon events can be obtained: (4-1-3) In the formula, range For threshold duration, σ p This is the root mean square pulse width of the received signal.

Images