Distortion recovery method for output signal of silicon photomultiplier laser receiver

Abstract

The invention provides a distortion recovery method for an output signal of a silicon photomultiplier laser receiver, and belongs to the technical field of silicon photomultiplier laser detection. The method comprises the following steps: determining an output voltage signal of a silicon photomultiplier laser receiver; deconvolving an output voltage signal of the silicon photomultiplier laser receiver into a photon statistical distribution waveform; based on an inverse inference method, carrying out preliminary restoration on the photon statistical distribution waveform after noise reduction; based on an L-M method, performing depth restoration on the photon statistical distribution waveform after preliminary restoration; and convolution is carried out on the photon statistical distribution waveform after depth restoration, and a voltage signal output by the silicon photomultiplier laser receiver after distortion restoration is obtained. The method combines the advantages of the inverse method and the L-M method, has recovery efficiency and recovery precision, is suitable for scenes with different parameter conditions, and can quickly and effectively recover the distorted signal output by the silicon photomultiplier laser receiver, and the obtained recovery result is close to a real signal.

Description

Technical Field

[0001] The present invention belongs to the technical field of laser detection, and particularly relates to a method for restoring the distortion of the output signal of a silicon photomultiplier tube laser receiver. Background Art

[0002] As a remote sensing technology, lidar can monitor information such as the distance and position of objects in the environment in real time by emitting and receiving laser beams. However, since the energy of the laser pulse echo signal decays with the square of the detection distance, ranging of weak optical signals at long distances is a difficult problem in current lidar detection. Therefore, the development of lidar receivers capable of detecting weak optical signals has become a hot topic in recent years. On this basis, with the development of semiconductor material technology, the silicon photomultiplier tube has been proposed as a new type of single-photon detector. It has photon counting sensitivity and linear response characteristics at low fluxes, can quantitatively measure weak optical signals, and is very suitable for being designed into a lidar receiver.

[0003] A silicon photomultiplier tube is a pixel array composed of multiple Geiger-mode avalanche photodiodes and quenching resistors connected in parallel. Compared with Geiger-mode avalanche photodiodes, it has higher photon detection efficiency, stronger anti-interference ability and lower production cost, and also has advantages such as high gain, high sensitivity, high resolution, low operating voltage and compact structure. In addition, since the silicon photomultiplier tube has both photon counting sensitivity and can respond to single photons, and also has the ability to sense the intensity of optical signals and can linearly respond to incident optical signals under low-flux conditions. Therefore, the silicon photomultiplier tube solves the problem that Geiger-mode avalanche photodiodes are difficult to respond to multi-photon events, has a larger dynamic range, and can complete the detection and reception of signals for single photons to thousands of photons, and is applicable to multiple application fields such as astrophysics, biophotonics, fluorescence spectroscopy, high-energy physics, medical imaging and lidar ranging. However, due to the limitation of the dead time, as the number of incident photons further increases, that is, in the case of high fluxes, the silicon photomultiplier tube laser receiver can no longer linearly respond to incident photons, and its output signal will be distorted, resulting in deviation in the extraction of target information, affecting the detection accuracy of the silicon photomultiplier tube laser receiver, and making the detectable dynamic range and application scenarios still have great limitations.

[0004] Therefore, the development of a method for restoring the distortion of the output signal of a silicon photomultiplier tube laser receiver under high-flux conditions can expand the dynamic range of detectable signals, improve the measurement accuracy of the silicon photomultiplier tube laser receiver, and make the silicon photomultiplier tube laser receiver have more extensive application value. Summary of the Invention

[0005] In order to solve the distortion problem of the output signal of a silicon photomultiplier tube laser receiver under high fluxes, the present invention proposes a method for restoring the distortion of the output signal of a silicon photomultiplier tube laser receiver.

[0006] The technical solution for achieving the object of the present invention is as follows: A method for restoring the distortion of the output signal of a silicon photomultiplier laser receiver, comprising the following steps:

[0007] Step 1: Collect the output voltage signal of the silicon photomultiplier laser receiver;

[0008] Step 2: Collect the single-photon response voltage pulse signal when the incident light intensity is lower than the set threshold;

[0009] Step 3: Based on Fourier transform, deconvolve the output voltage signal of the silicon photomultiplier laser receiver into a photon statistical distribution waveform;

[0010] Step 4: Perform noise reduction processing on the photon statistical distribution waveform;

[0011] Step 5: Substitute the noise-reduced photon statistical distribution waveform into the inverse inference method model for preliminary restoration;

[0012] Step 6: Substitute the preliminarily restored photon statistical distribution waveform into the L-M method model for in-depth restoration;

[0013] Step 7: Convolve the in-depth restored photon statistical distribution waveform to obtain the output voltage signal of the silicon photomultiplier laser receiver after distortion restoration.

[0014] Preferably, the specific steps for deconvolving the output voltage signal of the silicon photomultiplier laser receiver based on Fourier transform in Step 3 are as follows:

[0015] Convert the output voltage signal and the single-photon response voltage pulse signal of the silicon photomultiplier laser receiver into frequency-domain signals through Fourier transform, divide the frequency-domain signal of the output voltage signal of the silicon photomultiplier laser receiver by the frequency-domain signal of the single-photon response voltage pulse signal to obtain the frequency-domain signal of the photon statistical distribution, and finally restore the frequency-domain signal of the photon statistical distribution to the time-domain signal through inverse Fourier transform to obtain the photon statistical distribution waveform.

[0016] Preferably, the specific method for performing noise reduction on the photon statistical distribution waveform using the average filtering method in Step 4 is as follows: Determine that the fixed length of the window is M, slide the window on the horizontal axis time t of the photon statistical distribution waveform, and calculate the average value of the data in the window, and output the average value corresponding to each time slot, which is the signal after noise reduction.

[0017] Preferably, the signal after noise reduction in the nth time slot is specifically:

[0018]

[0019] where N smooth (t n) represents the signal after noise reduction in the nth time slot, N out (t i ) represents the photon count in the ith time slot, τ represents the pulse width, t r represents the time slot width.

[0020] Preferably, the specific method of substituting the waveform of the photon statistical distribution after noise reduction into the inverse inference method model for preliminary restoration is as follows:

[0021] Step 5.1: Substitute the waveform N smooth (t n ) into the inverse inference method model, and combine with the probability P d (t n ) that the pixel is in the dead time, to obtain the theoretical detection probability P0(t n ):

[0022]

[0023] where, N f represents the number of pixels of the silicon photomultiplier laser receiver, P(t n ) represents the probability that the pixel responds to photons in the nth time slot under the influence of the dead time, P d (t n ) represents the probability that a single pixel is in the dead time in the nth time slot;

[0024] Step 5.2: Based on the Poisson distribution, obtain the waveform N n ) of the photon statistical distribution after preliminary restoration from the theoretical detection probability P0(t in (t n ):

[0025] N in (t n ) = -N f ·ln[1 - P0(t n )].

[0026] Preferably, the probability that a single pixel is in the dead time in the nth time slot is specifically:

[0027]

[0028] where, n d is the dead time.

[0029] Preferably, the specific method of substituting the waveform of the photon statistical distribution after preliminary restoration into the L - M method model for deep restoration is as follows:

[0030] Step 6.1: Extract the waveform N in (t nThe initial parameter values, which include the mean signal strength S0, the noise strength B0, and the target distance L0:

[0031] Step 6.2: Define the distortion restoration of the photon statistical distribution waveform as a least squares problem to be solved:

[0032]

[0033] where y(x,t i ) represents the waveform after target restoration, represents the true waveform;

[0034] Set the initial matrix x k =(S0, B0, L0), and initially k = 0;

[0035] Step 6.3: Calculate the Jacobian matrix J, the Hessian matrix H, and the gradient vector G corresponding to the matrix x k , and calculate the step size Δx:

[0036] Δx = -(H + λD T D) -1 G

[0037] where D is the coefficient matrix:

[0038]

[0039] Step 6.4: Calculate the restored matrix, and the specific formula is:

[0040] x k+1 = x k + Δx;

[0041] Calculate whether f(x k+1 ) is less than the set threshold ε. If f(x k+1 ) is less than the threshold ε, then output the photon statistical distribution waveform y(x k + Δx, t i ), otherwise take x k+1 as the new initial matrix, calculate the approximation factor ρ and update the damping coefficient according to the approximation factor ρ, and return to Step 6.3.

[0042] Compared with the prior art, the significant advantages of the present invention are as follows: 1) The present invention designs a reasonable method for restoring the distortion of the output signal of a silicon photomultiplier laser receiver under high-throughput conditions; 2) The present invention combines the inverse deduction method with the L-M method, having both restoration efficiency and restoration accuracy. By using the inverse deduction method, the distorted photon statistical distribution waveform quickly approaches the theoretical waveform, thereby reducing the number of iterative steps required by the L-M method, and being able to quickly and accurately restore the output signal to a restored signal approaching the true signal.

[0043] Other features and advantages of the present invention will be set forth in the following description, and in part will be obvious from the description, or may be learned by practice of the present invention. The objectives and other advantages of the present invention may be realized and attained by the structure particularly pointed out in the written description, claims, as well as the drawings. Description of the Drawings

[0044] The drawings are only for the purpose of illustrating specific embodiments and are not considered as limitations of the present invention. Throughout the drawings, the same reference numerals represent the same components.

[0045] Figure 1 It is a flowchart of the method of the present invention.

[0046] Figure 2 It is a schematic diagram of the result of restoring the distortion of the output voltage signal of the silicon photomultiplier laser receiver.

[0047] Figure 3 It is a schematic diagram of the result of restoring the distortion of the photon statistical distribution waveform. Detailed Embodiments

[0048] It is easily understood that according to the technical solution of the present invention, without changing the essence of the present invention, those of ordinary skill in the art can imagine various embodiments of the present invention. Therefore, the following detailed embodiments and drawings are only exemplary descriptions of the technical solution of the present invention and should not be regarded as all of the present invention or as limitations or restrictions on the technical solution of the present invention. On the contrary, the purpose of providing these embodiments is to enable those skilled in the art to understand the present invention more thoroughly. The preferred embodiments of the present invention will be specifically described below in conjunction with the drawings, where the drawings form a part of this application and are used together with the embodiments of the present invention to explain the innovative concept of the present invention.

[0049] The concept of the present invention is, as Figure 1 shown, a method for restoring the distortion of the output signal of a silicon photomultiplier laser receiver, the method comprising the following steps:

[0050] Step 1: Collect the output voltage signal of the silicon photomultiplier laser receiver, and the waveform of the output voltage signal presents a Gaussian type;

[0051] Step 2: Set the incident light under extremely weak conditions, and collect the single-photon response voltage pulse signal. The rising edge of the single-photon response voltage pulse signal is extremely short, and the falling edge has an obvious tail;

[0052] Step 3: Perform deconvolution on the output voltage signal of the silicon photomultiplier laser receiver based on Fourier transform. The specific steps of deconvolution are as follows: Convert the output voltage signal of the silicon photomultiplier laser receiver and the single-photon response voltage pulse signal into frequency-domain signals through Fourier transform. Divide the frequency-domain signal of the output voltage signal of the silicon photomultiplier laser receiver by the frequency-domain signal of the single-photon response voltage pulse signal to obtain the frequency-domain signal of the photon statistical distribution. Finally, restore the frequency-domain signal of the photon statistical distribution to the time-domain signal through inverse Fourier transform to obtain the photon statistical distribution waveform.

[0053] The expression of Fourier transform is:

[0054]

[0055] where X(ω) represents the frequency-domain signal and x(t) represents the time-domain signal.

[0056] Step 4: Denoise the photon statistical distribution waveform using the average filtering method. The specific method is as follows: Determine that the fixed length of the window is M. Slide the window on the time series and calculate the average value of the data in the window. Output the average value corresponding to each time slot, which is the denoised signal. The denoised signal at the nth time slot is specifically:

[0057]

[0058] where N smooth (t n ) represents the denoised signal at the nth time slot, N out (t i ) represents the photon count at the ith time slot, τ represents the pulse width, and t r represents the time slot width.

[0059] Step 5: Substitute the denoised photon statistical distribution waveform into the inverse inference method model for preliminary restoration, as Figure 2 shown. The specific steps are as follows:

[0060] Step 5.1: Substitute the denoised signal N smooth (t n ) into the inverse inference method model, and combine with the probability P d (t n ) that the pixel is in the dead time to obtain the theoretical detection probability P0(t n ) of a single pixel:

[0061]

[0062] where N f represents the number of pixels of the silicon photomultiplier laser receiver, and P(t n) represents the probability that a pixel responds to photons in the nth time slot under the influence of the dead time, P d (t n ) represents the probability that a single pixel is in the dead time in the nth time slot:

[0063]

[0064] Step 5.2: Based on the Poisson distribution, the preliminary restored photon statistical distribution waveform N n ) can be obtained from the theoretical detection probability P0(t in (t n ):

[0065] N in (t n ) = -N f ·ln[1 - P0(t n )]

[0066] Step 6: Substitute the preliminary restored photon statistical distribution waveform into the L - M method model for depth restoration. As Figure 3 shown, the specific process of the L - M method:

[0067] Step 6.1: Extract the initial parameter values of the photon statistical distribution waveform N in (t n ) obtained by the inverse - deduction method preliminary restoration. The initial parameter values include the signal intensity mean S0, the noise intensity B0, and the target distance L0.

[0068] The target distance L0 can be extracted by the centroid method:

[0069]

[0070] where c represents the speed of light, t r represents the time slot width, and N(n) represents the photon count in the nth time slot within the full pulse width range.

[0071] The noise intensity B0 can be represented by the photon count N b outside the full pulse width range:

[0072]

[0073] where τ represents the pulse width, t g represents the gate width, and N f represents the number of pixels of the silicon photomultiplier laser receiver.

[0074] And the photon count N s within the full pulse width range is generated by both the signal and the noise. Therefore, the signal intensity mean S0 can be expressed as:

[0075]

[0076] Step 6.2: Define the restoration of the distortion of the photon statistical distribution waveform as a least-squares problem to be solved:

[0077]

[0078] where y(x, t i ) represents the waveform after the target restoration, represents the true waveform.

[0079] Set the initial matrix x k =(S0, B0, L0), and initially k = 0.

[0080] Step 6.3: After calculating the corresponding Jacobi matrix J, Hessian matrix H, and gradient vector G of the matrix x k , then calculate the step size Δx:

[0081] Δx = -(H + λD T D) -1 G

[0082] where D is the coefficient matrix:

[0083]

[0084] Step 6.4: Obtain the restored matrix x k+1 = x k + Δx, calculate whether f(x k+1 ) is less than the set threshold ε. If it is greater than the threshold ε, take x k+1 as the new initial matrix, calculate the approximation factor ρ and update the damping coefficient according to the approximation factor ρ, and return to Step 6.3. The specific calculation method of the approximation factor ρ is:

[0085]

[0086] ρ can be used to judge the approximation degree of the waveform. When ρ is less than 0.25, it means that the step size is too large, and the value of the damping coefficient λ should be reduced. At this time, let When ρ is greater than 0.75, it means that the step size is too short. At this time, the value of the damping coefficient λ needs to be increased. Let λ k+1 = 2λ k ; In other cases, the value of the damping coefficient λ remains unchanged.

[0087] If f(x k+1 ) is less than the threshold ε, then output the photon statistical distribution waveform y(x k + Δx, t i ).

[0088] Step 7: Convert the photon statistical distribution waveform after depth restoration and the single-photon response voltage pulse signal into frequency-domain signals. Multiply the frequency-domain signal of the photon statistical distribution waveform after depth restoration by the frequency-domain signal of the single-photon response voltage pulse signal to obtain the frequency-domain signal of the output voltage of the silicon photomultiplier laser receiver. Finally, perform an inverse Fourier transform on the frequency-domain signal to restore it to the time domain signal, and the output voltage signal of the silicon photomultiplier laser receiver after depth restoration can be obtained.

[0089] As described above, only the preferred specific embodiments of the present invention are provided, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered by the protection scope of the present invention.

[0090] It should be understood that, in order to streamline the present invention and help those skilled in the art understand various aspects of the present invention, in the above description of the 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 meaning that the features included in the exemplary embodiments are all essential technical features of the claims of this patent.

[0091] It should be understood that the modules, units, components, etc. included in the device of an embodiment of the present invention can be adaptively changed to be arranged in a device different from that of this embodiment. Different modules, units, or components included in the device of the embodiment can be combined into one module, unit, or component, or they can be divided into multiple sub-modules, sub-units, or sub-components.

Claims

1. A method for restoring the distortion of the output signal of a silicon photomultiplier tube laser receiver, characterized in that: The following steps are involved: Step 1: Collect the output voltage signal of the silicon photomultiplier tube laser receiver; Step 2: Collecting a single-photon response voltage pulse signal when the incident light intensity is lower than a set threshold; Step 3: Deconvolute the output voltage signal of the silicon photomultiplier tube laser receiver into a photon statistical distribution waveform based on Fourier transform; Step 4: De-noise the photon statistical distribution waveform; Step 5: Substitute the photon statistical distribution waveform after noise reduction into the inverse method model for preliminary restoration; Step 6: Substitute the initially restored photon statistical distribution waveform into the LM method model for deep restoration; Step 7: Convolve the photon statistical distribution waveform after depth restoration to obtain the output voltage signal of the silicon photomultiplier tube laser receiver after distortion restoration.

2. The method for restoring the distortion of the output signal of the silicon photomultiplier tube laser receiver according to claim 1, characterized in that: The specific steps of deconvolving the output voltage signal of the silicon photomultiplier tube laser receiver based on Fourier transform in step 3 are: The output voltage signal of the silicon photomultiplier tube laser receiver and the single-photon response voltage pulse signal are converted into frequency domain signals through Fourier transform, and the frequency domain signal of the output voltage signal of the silicon photomultiplier tube laser receiver is divided by the frequency domain signal of the single-photon response voltage pulse signal to obtain the frequency domain signal of the photon statistical distribution. Finally, the frequency domain signal of the photon statistical distribution is restored to the time domain signal through inverse Fourier transform to obtain the photon statistical distribution waveform.

3. The method for restoring the distortion of the output signal of the silicon photomultiplier tube laser receiver according to claim 1, characterized in that: The specific method of using the average filtering method to reduce the noise of the photon statistical distribution waveform in step 4 is: determine the fixed length of the window as M, slide the window on the horizontal axis time t of the photon statistical distribution waveform, and calculate the average value of the data in the window, and output the average value corresponding to each time slot, which is the signal after noise reduction.

4. The method for restoring the distortion of the output signal of the silicon photomultiplier tube laser receiver according to claim 3, characterized in that: The signal after noise reduction in the nth time slot is specifically: Among them, N smooth (t n ) represents the signal after noise reduction in the nth time slot, N out (t i ) represents the photon count of the i-th time slot, τ represents the pulse width, and t r Indicates the time slot width.

5. The method for restoring the distortion of the output signal of the silicon photomultiplier tube laser receiver according to claim 1, characterized in that: The specific method of substituting the noise-reduced photon statistical distribution waveform into the inverse method model for preliminary restoration is: Step 5.1: Convert the noise-reduced waveform N smooth (t n ) is substituted into the inverse method model, combined with the probability P of the pixel being in the dead zone time d (t n ), and the theoretical detection probability of a single pixel P0(t n ): Among them, N f represents the number of pixels of the silicon photomultiplier tube laser receiver, P(t n ) represents the probability of a pixel responding to a photon in the nth time slot under the influence of the dead time, P d (t n ) represents the probability that a single pixel is in the dead time in the nth time slot; Step 5.2: The theoretical detection probability P0(t n ) to obtain the initial restored photon statistical distribution waveform N in (t n ): N in (t n )=-N f ·ln[1-P0(t n )]。 6. The method for restoring the distortion of the output signal of the silicon photomultiplier tube laser receiver according to claim 1, characterized in that: The probability of a single pixel being in the dead time in the nth time slot is specifically: Where n d is the dead time.

7. The method for restoring the distortion of the output signal of a silicon photomultiplier tube laser receiver according to claim 1, characterized in that: The specific method of substituting the initially restored photon statistical distribution waveform into the LM method model for deep restoration is: Step 6.1: Extract the photon statistical distribution waveform N obtained after the initial restoration by the inverse method in (t n ), wherein the initial parameter values ​​include the signal strength mean S0, the noise intensity B0, and the target distance L0: Step 6.2: Define the distortion restoration of the photon statistical distribution waveform as a least squares problem to be solved: Among them, y(x,t i ) represents the waveform after the target is restored. Represents the real waveform; Set the initial matrix x k =(S0, B0, L0), initially k = 0; Step 6.3: Calculate the matrix x k The corresponding Jacobian matrix J, Hessian matrix H and gradient vector G, calculate the step size Δx: Δx=-(H+λD T D) -1 G Where D is the coefficient matrix: Step 6.4: Calculate the restored matrix. The specific formula is: x k+1 =x k +Δx; Calculate f(x k+1 ) is less than the set threshold ε, if f(x k+1 ) is less than the threshold ε, then the output photon statistical distribution waveform y(x k +Δx,t i ), otherwise x k+1 As the new initial matrix, calculate the approximation factor ρ and update the damping coefficient according to the approximation factor ρ, and return to step 6.

3.

8. The method for restoring the distortion of the output signal of the silicon photomultiplier tube laser receiver according to claim 7, characterized in that: The calculation formula of target distance L0 is: Where c is the speed of light, t r represents the time slot width, N(n) represents the photon count of the nth time slot within the full pulse width; The noise intensity B0 is composed of the photon counts N outside the full pulse width range. b The specific calculation formula is: Where τ represents the pulse width, t g Indicates the door width, N f Indicates the number of pixels of the silicon photomultiplier tube; Photon counts N in the full pulse width range s The specific calculation formula of the signal strength mean S0 generated by the signal and noise is:

9. The method for restoring the distortion of the output signal of the silicon photomultiplier tube laser receiver according to claim 7, characterized in that: The specific calculation method of the approximate factor ρ is: In the formula, J(x k ) is the matrix x k The corresponding Jacobian matrix.

10. The method for restoring the distortion of the output signal of the silicon photomultiplier tube laser receiver according to claim 7, characterized in that: The specific method of updating the damping coefficient according to the approximate factor ρ is: When ρ is less than the first threshold, let When ρ is greater than the second threshold, let λ k+1 =2λ k .

Images