A method for reconstructing waveform distortion of a photon counting lidar output signal

Abstract

The application provides a kind of photon counting laser radar output signal waveform distortion reconstruction method, belong to the field of photon counting laser radar echo signal analysis.The method comprises the following steps: determining the time-dependent photon counting statistical histogram of photon counting laser radar;Determine the theoretical model of the echo signal of the photon counting laser radar;Convert the time-dependent photon counting statistical histogram into a photon detection probability waveform diagram;Waveform denoising processing;Calculate the initial parameter value of the photon counting laser radar;The initial parameter value and the time-photon detection probability curve are substituted into the optimization algorithm to calculate the optimal solution of the joint theoretical model;The optimal solution is substituted into the detection model without dead time to obtain the reconstructed waveform.The application selects to make full use of the correctness of the theoretical model, reduces the error generated in the iteration process, compared with the prior art, the application principle is clear, the use range is wide, and the process is simple, the reconstruction result approaches the real waveform, and the information extracted therefrom is more accurate.

Description

Technical Field

[0001] This invention pertains to photon-counting lidar technology, specifically a method for reconstructing the waveform distortion of the output signal from a photon-counting lidar. Background Technology

[0002] With the increasing maturity of lidar technology, it has broad application prospects in deep space exploration, aerospace, and nighttime target recognition. Among the various lidar technologies, time-correlated photon-counting lidar, which uses Geiger-mode APD detectors for signal detection, has higher detection sensitivity and requires lower laser pulse energy compared to other lidar technologies. It ensures that the emitted laser energy remains within the safe range for the human eye and is considered a major development direction for next-generation lidar. Photon-counting lidar, with its single-photon detection sensitivity and range-gating technology, has shown significant advantages in long-range detection and extremely weak signal detection, and it has important potential applications in 3D imaging, Earth remote sensing, and non-line-of-sight imaging.

[0003] Avalanche photodiodes (APDs) are the core components of lidar systems. Due to the unique nature of their circuitry, these devices have a dead time for protection circuitry. This dead time causes a shielding effect on the detection of subsequent photons during the detection of the first photon, leading to distortion in the time-correlated photon count histogram, deviating from the theoretical time distribution of the echo signal. This phenomenon becomes more pronounced with increasing incident light flux. To address this, the manufacturer of the time-correlated single-photon counter (TCSPC), the core component of photon-counting lidar, proposed the classic low-flux criterion—the 5% criterion—as the basis for distortion-free detection applications. Currently, it is generally accepted that when the total number of photons counted in the system is less than 5% of the total number of periodic laser pulses, count loss and signal distortion can be ignored; in this case, the incident light flux is considered low flux. Conversely, it is considered high flux. Under high flux conditions, the echo signal will exhibit significant distortion. Using distorted echo signals directly for lidar measurements will lead to inaccuracies in calculating target distance, reflectivity, and target surface characteristics. This severely limits the measurement accuracy and application range of photon-counting lidar under high-throughput conditions.

[0004] Therefore, developing a method for reconstructing the waveform distortion of the output signal of photon-counting lidar is of great significance for expanding the application environment of photon-counting lidar and improving measurement accuracy. Summary of the Invention

[0005] To address the aforementioned technical deficiencies in the prior art, this invention proposes a method for reconstructing the waveform distortion of the output signal of a photon-counting lidar.

[0006] The technical solution to achieve the objective of this invention is: a method for reconstructing the waveform distortion of the output signal of a photon-counting lidar, comprising the following steps:

[0007] Step 1: Determine the time-correlated photon count statistical histogram for the photon counting lidar;

[0008] Step 2: Determine the theoretical model for the echo signal of the photon counting lidar;

[0009] Step 3: Convert the time-correlated photon count statistical histogram into a photon detection probability waveform;

[0010] Step 4: Denoising the waveform;

[0011] Step 5: Calculate the initial parameter values ​​for the photon counting lidar;

[0012] Step 6: Substitute the initial parameter values ​​and the time-photon detection probability curve into the optimization algorithm and the theoretical model to calculate the optimal solution;

[0013] Step 7: Substitute the optimal solution into the detection model without dead time to obtain the reconstructed waveform.

[0014] Preferably, the theoretical model expression for the photon-counting lidar echo signal in step 2 is as follows:

[0015] P(k;S,B,L)=P0(k;S,B,L)·P non (k;S,B,L)

[0016] Where P(k; S, B, L) represents the detection probability of the k-th photon outside the dead time range, and P0(k; S, B, L) is the probability that the photon counting lidar generates at least one primary photoelectron at time slot k, specifically expressed as:

[0017] P0(k;S,B,L)=1-exp[-N(k;S,B,L)]

[0018] N(k;S,B,L) represents the number of primary photoelectrons contained in time slot k;

[0019] P non (k;S,B,L) represents the probability that time slot k is not within the dead time range, and the specific expression is:

[0020]

[0021] Where, k CWSSFor the last time slot in which the system achieves continuous wave steady state, and the k-th time slot... CWSS The range of the signal echo entering the +1 time slot, where d is the number of time slots occupied by the dead time, is expressed as:

[0022]

[0023] T d P represents the dead time size. CWSS (k;S,B,L) represents the probability within the time slot when achieving noise steady state, expressed as:

[0024]

[0025] N b This represents a constant noise photon rate.

[0026] Preferably, the specific method for time-photon detection probability noise reduction processing is as follows:

[0027] Take any point on the waveform data chain as the center, calculate the average value of the center point and its neighborhood, and use the calculated average value as the center-smoothed value. Perform center smoothing on every point on the waveform data chain, and always select the same neighborhood size.

[0028] Preferably, the specific method for calculating the initial parameter values ​​of the photon counting lidar is as follows:

[0029] Extract the initial value of distance L from the noise-reduced waveform:

[0030]

[0031] c is the speed of light, s is the range of the signal, N(k) represents the number of photons contained in the k-th time slot starting from the first time slot of the signal s, and τ is the time resolution.

[0032] Extract the initial value of noise B from the denoised waveform:

[0033]

[0034] l1 and l2 are the lengths of the non-signal regions before and after the signal region, respectively. T1 represents the distance from the first time slot inside the gate. m For the last time slot within l1, T n For the first time slot within l2, T end This is the last time slot within l2, where M is the total number of probes and N is the number of probes. b (k) is the number of noise photons in the k-th time slot;

[0035] Extract the initial value of signal S from the noise-reduced waveform:

[0036]

[0037] In the formula, B is the extracted noise parameter.

[0038] Preferably, the specific method for obtaining the optimal solution through an optimization algorithm combined with a theoretical model using initial parameter values ​​and the time-photon detection probability curve is as follows:

[0039] Step 6.1: Use the extracted parameters as initial values ​​and substitute them into the theoretical model of the photon counting lidar echo signal to obtain a new time-correlated photon counting waveform f1;

[0040] Step 6.2: Substitute f1 into the residual sum of squares SSR (i) In the formula, the relative error err for calculating the sum of squared residuals is:

[0041]

[0042]

[0043] In the formula, f0 is the data chain obtained after denoising the time-correlated photon count statistical histogram of the photon counting lidar determined in step 6.1, and f0(k) is the k-th data in this data chain; i To make the parameter (S) i B i ,L i The data link obtained by substituting the theoretical model of the photon-counting lidar echo signal, f i (k;S i B i ,L i ) represents the k-th data item in this data chain; SSR (i) SSR is the sum of squared residuals calculated in the i-th iteration. (i-1) This is the sum of squared residuals calculated in the (i-1)th iteration;

[0044] Calculate the parameter iteration increment:

[0045]

[0046] dx is a three-dimensional matrix composed of dS, dB and dL, where dS, dB and dL are the increments of S, B and L respectively, J is the Jacobian matrix and J' is the transpose of J.

[0047] Step 6.3: Compare the relative error with the error threshold. If the absolute value of the relative error is greater than the error threshold ξ, calculate the parameter values ​​after iteration. The parameter values ​​after iteration are expressed as:

[0048] x i+1 =x i +dx

[0049] In the formula, xi and x i+1 These are the parameter matrices after the (i-1)th and i-th iterations, respectively.

[0050] Substituting the iterated parameters into the theoretical model of the photon-counting lidar echo signal, a new intercorrelation photon counting waveform f is obtained. i+1 ;

[0051] The iteration stops when the relative error is less than the error threshold, and the distance, signal strength, and noise parameters corresponding to the TCSPC waveform at this point are output.

[0052] Preferably, the detection model expression in step 7 that does not include dead time is:

[0053] P(t)=1-exp{-[F(t)+B·ct·τ]}

[0054] ct is the laser repetition frequency, and F(t) is the expression for the laser pulse waveform, which is:

[0055]

[0056]

[0057] Among them, P W Let A be the pulse width, and t be a function of the signal S. d This represents the time from the emission of the pulsed laser to its reception.

[0058] 7. The method for reconstructing the waveform distortion of the output signal of a photon-counting lidar according to claim 6, characterized in that the expression of the function containing signal S is:

[0059]

[0060] The specific time from pulsed laser emission to reception is as follows:

[0061]

[0062] c is the speed of light.

[0063] Compared with the prior art, the significant advantages of this invention are: 1) This invention designs a reasonable reconstruction method for the distorted output signal of photon counting lidar under high throughput conditions; 2) This invention makes full use of the theoretical model of photon counting lidar, reduces the error caused by model iteration during reconstruction, and the reconstruction process is simple and clear; 3) The reconstructed waveform is closer to the real waveform, and the information extracted is more accurate.

[0064] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description

[0065] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0066] Figure 1 This is a flowchart of the method of the present invention.

[0067] Figure 2 This is a schematic diagram showing the initial parameter values ​​for a photon counting lidar. Detailed Implementation

[0068] It is readily understood that, based on the technical solution of this invention, various embodiments of the invention can be conceived by those skilled in the art without altering the essential spirit of the invention. Therefore, the following detailed embodiments and accompanying drawings are merely illustrative examples of the technical solution of this invention and should not be considered as the entirety of the invention or as limitations or restrictions on the technical solution of this invention. Rather, these embodiments are provided to enable those skilled in the art to gain a more thorough understanding of the invention. Preferred embodiments of the invention are described below in conjunction with the accompanying drawings, which form part of this application and, together with the embodiments of the invention, serve to illustrate the innovative concept of the invention.

[0069] The present invention is conceived as follows: Figure 1 As shown, a method for reconstructing the waveform distortion of the output signal of a photon-counting lidar includes the following steps:

[0070] Step 1: Determine the time-correlated photon count statistical histogram for the photon counting lidar;

[0071] Step 2: Determine the theoretical model of the photon-counting lidar echo signal, its expression:

[0072] P(k;S,B,L)=P0(k;S,B,L)·P non (k;S,B,L)

[0073] Where P(k; S, B, L) represents the detection probability of the k-th photon outside the dead time range, and P0(k; S, B, L) is the probability that the photon-counting lidar generates at least one primary photoelectron at time slot k, and its expression is:

[0074] P(k;S,B,L)=P0(k;S,B,L)·P non(k;S,B,L)

[0075] N(k;S,B,L) represents the number of primary photoelectrons contained in time slot k.

[0076]

[0077] Where, k CWSS For the last time slot in which the system achieves continuous wave steady state, and the k-th time slot... CWSS The range of the signal echo entering the +1 time slot, where d is the number of time slots occupied by the dead time, is expressed as:

[0078]

[0079] T d P represents the dead time size. CWSS (k;S,B,L) represents the probability within the time slot when achieving noise steady state, expressed as:

[0080]

[0081] N b This represents a constant noise photon rate.

[0082] Step 3: Convert the time-correlated photon count statistical histogram into a photon detection probability waveform;

[0083] Step 4: Perform waveform noise reduction processing, the specific method is as follows:

[0084] Take any point on the waveform data chain as the center, calculate the average value of the center point and its neighborhood, and use the calculated average value as the center-smoothed value. Perform center smoothing on every point on the waveform data chain, and always select the same neighborhood size.

[0085] Step 5: As Figure 2 The diagram shown illustrates the calculation of initial parameter values ​​for a photon-counting lidar. The specific method is as follows:

[0086] Extract the initial value of distance L from the noise-reduced waveform:

[0087]

[0088] c is the speed of light, and s is the signal range, typically taken as the full pulse width (2P). W ), and take the time slot corresponding to the peak as the center point, N(k) represents the number of photons contained in the k-th time slot starting from the first time slot of signal s, and τ is the time resolution.

[0089] Extract the initial value of noise B from the denoised waveform:

[0090]

[0091] l1 and l2 are the lengths of the non-signal regions before and after the signal region, respectively. T1 represents the distance from the first time slot inside the gate. m For the last time slot within l1, T n For the first time slot within l2, T end This is the last time slot within l2, where M is the total number of probes and N is the number of probes. b (k) The number of noise photons in the i-th time slot;

[0092] Extract the initial value of signal S from the noise-reduced waveform:

[0093]

[0094] In the formula, B is the initial value of the extracted noise.

[0095] Step 6: Substitute the initial parameter values ​​and the time-photon detection probability curve into the optimization algorithm and the theoretical model to calculate the optimal solution. The specific method is as follows:

[0096] Step 6.1: Use the extracted parameters as initial values ​​and substitute them into the theoretical model of the photon counting lidar echo signal to obtain a new time-correlated photon counting waveform f1;

[0097] Step 6.2: Substitute f1 into the residual sum of squares SSR (i) In the formula, the relative error err for calculating the sum of squared residuals is:

[0098]

[0099]

[0100] In the formula, f0 is the data chain obtained after denoising the time-correlated photon count statistical histogram of the photon counting lidar determined in step 1, and f0(k) is the k-th data in this data chain; f i To make the parameter (S) i B i ,L i The data link obtained by substituting the theoretical model of the photon-counting lidar echo signal, f i (k;S i B i ,L i ) represents the k-th data item in this data chain; SSR (i) SSR is the sum of squared residuals calculated in the i-th iteration. (i-1) This is the sum of squared residuals calculated in the (i-1)th iteration.

[0101] Calculate the parameter iteration increment:

[0102]

[0103] dx is a three-dimensional matrix composed of dS, dB and dL, where dS, dB and dL are the increments of S, B and L respectively, J is the Jacobian matrix and J' is the transpose of J.

[0104] Step 6.3: Compare the relative error with the error threshold. If the absolute value of the relative error is greater than the error threshold ξ, calculate the parameter values ​​after iteration. The parameter values ​​after iteration are expressed as:

[0105] x i+1 =x i +dx

[0106] In the formula, x i and x i+1 These are the parameter matrices after the (i-1)th and i-th iterations, respectively.

[0107] Substituting the iterated parameters into the theoretical model of the photon-counting lidar echo signal, a new intercorrelation photon counting waveform f is obtained. i+1 ;

[0108] The iteration stops when the relative error is less than the error threshold, and the distance, signal strength, and noise parameters corresponding to the TCSPC waveform at this point are output.

[0109] Step 7: Substitute the optimal solution into the detection model without dead time to obtain the reconstructed waveform. Its expression is:

[0110] P(t)=1-exp{-[F(t)+B·ct·τ]}

[0111] ct is the laser repetition frequency, and F(t) is the expression for the laser pulse waveform, which is:

[0112]

[0113]

[0114] Among them, P W Let A be the pulse width, and t be a function of the signal S. d Let be the time from emission to reception of a pulsed laser, and its expression is:

[0115]

[0116]

[0117] c is the speed of light, taken as 3 × 10⁻⁶. 8 m / s.

[0118] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto.

[0119] Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this invention should be included within the protection scope of this invention.

[0120] It should be understood that, in order to simplify the present invention and help those skilled in the art understand its various aspects, in the above description of exemplary embodiments of the present invention, various features of the present invention are sometimes described in a single embodiment or with reference to a single figure. However, the present invention should not be construed as including all features in the exemplary embodiments as essential technical features of the claims of this patent.

[0121] It should be understood that the modules, units, components, etc., included in the device of one embodiment of the present invention can be adaptively changed to be placed in a device different from that embodiment. Different modules, units, or components included in the device of the embodiment can be combined into a single module, unit, or component, or they can be divided into multiple sub-modules, sub-units, or sub-components.

Claims

1. A method of reconstruction of waveform distortions of a photon counting lidar output signal, characterized in that, The method comprises the following steps: Step 1: determining a time-dependent photon counting statistical histogram of the photon counting lidar; Step 2: determining a theoretical model of a photon counting lidar echo signal; Step 3: converting the time-dependent photon counting statistical histogram into a photon detection probability waveform graph; Step 4: performing noise reduction processing on the waveform; Step 5: calculating initial parameter values of the photon counting lidar; Step 6: inputting the initial parameter values and the time-photon detection probability curve into an optimization algorithm to calculate optimal solutions in combination with the theoretical model; Step 7: inputting the optimal solutions into a detection model without dead time to obtain a reconstructed waveform.

2. The method of photon counting lidar output signal waveform distortion reconstruction of claim 1, wherein, The expression of the theoretical model of the photon counting lidar echo signal in step 2 is as follows: P(k; S, B, L) = P0(k; S, B, L) - P non (k; S, B, L) wherein P(k; S, B, L) represents the detection probability of the kth photon not in the range of dead time, B is an initial value of noise, S is an initial value of a signal, and P0(k; S, B, L) is a probability that the photon counting lidar generates at least one primary photoelectron at the kth time slot, and the specific expression is as follows: P0(k; S, B, L) = 1 - exp[-N(k; S, B, L)] N(k; S, B, L) is the number of primary photoelectrons contained in the kth time slot. P non (k; S, B, L) is the probability that time slot k is not in the dead time range, and the specific expression is: where k CWSS is the last time slot for the system to achieve the continuous wave steady state, and the k CWSS + 1 time slot enters the range of the signal echo, and d is the number of time slots occupied by the dead time, and the expression is: T d is the dead time size, τ is the time resolution; P CWSS (k; S, B, L) denotes the probability of being in a slot when the noise is stationary, expressed as: N b represents a constant noise photon rate.

3. The method of photon counting lidar output signal waveform distortion reconstruction of claim 1, wherein, The specific method for noise reduction processing of the time-photon detection probability is as follows: Taking any point on the waveform data chain as a center, the average value of the center point and the neighborhood of the center point is calculated, and the calculated average value is taken as the smoothed value of the center. The center smoothing processing is performed on each point on the waveform data chain, and the neighborhood size is selected to be the same each time.

4. The method of photon counting lidar output signal waveform distortion reconstruction of claim 1, wherein, The specific method for calculating the initial parameter values of the photon counting lidar is as follows: Extracting the initial value of distance L from the noise-reduced waveform: c is the speed of light, s is the range of the signal, N(k) represents the number of photons contained in the kth time slot with the first time slot of the signal s as the starting point, and τ is the time resolution; Extracting the initial value of noise B from the noise-reduced waveform: l1 and l2 are the length of the non-signal region before and after the signal region, respectively, T1 represents the first time slot from the gate, T m is the last time slot in l1, T n is the first time slot in l2, T end is the last time slot in l2, M is the total number of detections, N b (k) is the number of noise photons in the kth time slot. Extracting the initial value of signal S from the noise-reduced waveform: In the formula, B is the initial value of noise.

5. The method of photon counting lidar output signal waveform distortion reconstruction of claim 1, wherein, The specific method for calculating the optimal solutions in combination with the theoretical model through the optimization algorithm and the time-photon detection probability curve and the initial parameter values is as follows: Step 6.1: inputting the extracted parameters as initial values into the theoretical model of the photon counting lidar echo signal to obtain a new time-dependent photon counting waveform f1; Step 6.2: Substitute f1 into the residual sum of squares SSR (i) In the formula, the relative error err of the residual sum of squares is calculated: where f0 is the data chain obtained by denoising the photon counting lidar time-dependent photon counting statistical histogram determined in step 6.1, f0(k) is the kth data on the data chain; f i To substitute the parameters (S i , B i , L i ) into the data chain obtained from the theoretical model of the photon counting lidar echo signal, f i (k; S i , B i , L i ) is the kth data on the data chain; SSR (i) is the residual sum of squares of the i-th calculation, SSR (i-1) is the residual sum of squares of the i-1-th calculation; Calculating the parameter iteration increment: dx is a three-dimensional matrix composed of dS, dB and dL, dS, dB and dL are increments of S, B and L respectively, J is a Jacobian matrix, J' is the transpose of J, S is the initial value of the signal, B is the initial value of the noise, and L is the initial value of the distance; Step 6.3: comparing the size of the relative error and the error threshold value, if the absolute value of the relative error is greater than the error threshold value ξ, calculating the parameter values after iteration, and the parameter values after iteration are represented as: x i+1 = x i + dx where x i and x i+1 are the parameter matrices after the (i-1)th and ith iterations, respectively. Substituting the iterated parameters into the theoretical model of the photon counting lidar return signal, a new time-dependent photon count waveform f i+1 is obtained. Until the relative error is less than the error threshold value, the iteration is stopped, and the parameter values corresponding to the distance, the signal strength and the noise of the time-dependent photon counting waveform at this time are output.

6. The method of photon counting lidar output signal waveform distortion reconstruction according to claim 1, wherein, The expression of the detection model without dead time in step 7 is as follows: P(t) = 1 - exp{-[F(t) + B·ct·τ]} ct is the laser repetition rate, τ is the time resolution, F(t) is the laser pulse shape expression, the expression of which is: Among them, P W Let A be the pulse width, and t be a function of the signal S. d This represents the time from the emission of the pulsed laser to its reception.

7. The method of photon counting lidar output signal waveform distortion reconstruction according to claim 6, wherein, The expression of the function containing the signal S is: The time from emission to reception of the pulsed laser is specifically: c is the speed of light, and L is the distance from the initial value.

Images