Three-dimensional laser positioning and accuracy calculation method and system based on noisy CCD detection

Abstract

The present invention discloses a three-dimensional laser positioning and precision calculation method and system based on noisy CCD detection. This method uses a lens, CCD and a displacement stage as measuring devices at a distance from the light source, first statistically models the dark count of the CCD; then calibrates the relationship between the incident light power and the photocurrent count; then, based on the parameter estimation theory, gives the probability distribution of the CCD pixel count with respect to the light source position parameter; then uses the measuring device to measure and process the data to obtain the three-dimensional coordinates of the light source; finally, further precision calculations can be performed to give the optimal position for three-dimensional positioning with noisy CCD intensity detection and three theoretical limit measurement accuracies. Compared with the prior art, the present invention can simultaneously measure the horizontal and vertical positions of the laser; in addition, through the precision calculation method of the present invention, the optimal position of the CCD horizontal and vertical positioning along the light propagation direction can be given, and the limit accuracy of positioning in the presence of noise can be achieved.

Description

Technical Field

[0001] The present invention belongs to the field of laser positioning, and relates to estimating the position of a light source based on detection of a CCD (Charge-coupled Device), and in particular to a method and system for three-dimensionally positioning a laser using a noisy CCD and calculating the ultimate measurement accuracy that can be achieved. Background Art

[0002] Laser positioning has a wide range of applications in military reconnaissance, astronomical detection, engineering exploration, etc. Three-dimensional positioning refers to the simultaneous measurement of the position of a light source along its propagation direction (longitudinal) and in its orthogonal plane (lateral).

[0003] At present, vertical positioning, such as laser ranging technology and laser radar technology, is obtained by the information of reflected light from the laser hitting the surface of an object. This method is generally used in long-distance scenarios and requires the receiving end and the transmitting end to be in the same position. The application scenarios are limited, and there is no analysis of the optimal measurement accuracy.

[0004] For lateral positioning, the current commercial beam quality analyzers can give the lateral position and width of the spot. For example, Dataray's WinCamD-LCM-1"CMOS beam quality analyzer uses a Gaussian fitting algorithm to give measurement results. However, this can only give the average value of the lateral position or width, and cannot quantitatively analyze the measurement accuracy, nor can it directly obtain the data of the longitudinal position. Summary of the invention

[0005] Purpose of the invention: In order to solve the problems existing in the prior art, the present invention provides a three-dimensional laser positioning method and system based on noisy CCD intensity detection, which can simultaneously measure the lateral and longitudinal positions of the laser. In addition, the present invention also provides an accuracy calculation method, which can obtain the theoretical optimal accuracy limit and the optimal measurement accuracy that can be achieved, calculate the optimal position of CCD measurement, and compare the gap between the measurement result and the accuracy limit.

[0006] Technical solution: To achieve the above-mentioned purpose of the invention, the present invention provides a three-dimensional laser positioning method based on noisy CCD detection, which does not require reflection from an object, and only requires placing a measuring device consisting of a lens, a CCD and a displacement stage along the propagation direction of the light source; the specific steps include:

[0007] Step 1: calibrate the dark count detected by the CCD to obtain the dark count d of the pixel at the i-th row and j-th column. i,j The probability P(d i,j );

[0008] Step 2, calibrating the relationship between the total photocurrent count and the incident light power to determine the photoelectric conversion efficiency;

[0009] Step 3, establish a theoretical model of the relationship between the three-dimensional position coordinates (x0, y0, z0) of the light source to be estimated and the reading of each pixel point of the CCD; the three-dimensional position coordinates (x0, y0, z0) of the light source include the average count of the photocurrent at each pixel point inside:

[0010]

[0011] Where N is the total photocurrent count calculated according to the relationship calibrated in step 2, S(i,j) represents the spatial position of the pixel in the i-th row and j-th column; the information of the longitudinal position z0 of the light source is contained in the width of the light beam:

[0012]

[0013]

[0014] z w ′=m 2 (z0-f)+f

[0015]

[0016] where w w 、w w ′ is the beam waist radius of the Gaussian light before and after passing through the lens, z′ is the distance between the CCD detection plane and the lens, f is the focal length of the lens, λ is the wavelength, and m is the lens transformation coefficient; the actual count of the photocurrent l i,j Satisfy is a Poisson distribution with mean:

[0017]

[0018] The actual CCD pixel count k in row i and column j i,j The probability P(k i,j ) is the convolution of the dark count and photocurrent count probability:

[0019]

[0020] Step 4: Place the measuring device consisting of the lens, CCD and translation stage at a suitable position before or after the convergence point of the light source along the propagation direction of the light source, move the translation stage along the direction of light propagation, change and record the distance between the CCD detection plane and the lens, take multiple photos with the CCD at each position, use these photos as the measurement results, and extract the three-dimensional position coordinates (x0, y0, z0) information of the light source from the probability distribution obtained in step 3.

[0021] Preferably, in step 1, the statistical law of the count of each pixel of the CCD when there is no light incident is calibrated. In the case of no light incident, the CCD is allowed to take multiple photos, and the distribution law of the reading of each pixel is counted, and the mean value μ of the dark count reading is obtained by fitting. d With variance σ d ; Dark count d of the pixel at row i and column j i,j Satisfies normal distribution:

[0022]

[0023] Preferably, in step 2, for a measurement with a photoelectric conversion efficiency of α, a power of P, and an exposure time of t, the total photocurrent count satisfies the relationship:

[0024]

[0025] Where λ is the wavelength, h is Planck's constant, and c is the speed of light; set multiple groups of different powers as independent variables, change the power and measure the corresponding total number of photocurrent counts, fit a linear curve, and determine the photoelectric conversion efficiency α based on the slope obtained by the fitting and the above formula; after calibration, measure the incident light power and directly calculate the total photocurrent count N from the above formula.

[0026] Preferably, in step 4, maximum likelihood estimation is used as the parameter estimation method for laser three-dimensional positioning, and a CCD photo is used as a measurement result, and its likelihood function is:

[0027]

[0028] Where θ is the parameter to be estimated, and the estimated value is the point where the likelihood function takes the maximum value; an estimated value is obtained for each photo, and the mean of multiple photos is taken as the final estimated value.

[0029] Furthermore, the three-dimensional laser positioning accuracy calculation method based on noisy CCD detection uses quantum Fisher information to characterize the measurement accuracy, specifically:

[0030] For a single photon with a Gaussian wave function, its quantum state |ψ> is written as:

[0031]

[0032] Where |·> is the Dirac state vector symbol, i is the imaginary unit, k is the wave vector, R(z0) is the radius of curvature of the Gaussian wavefront at that position, and ζ(z0) is the Gouy phase; the quantum Fisher information of this quantum state is:

[0033]

[0034] where <·|·> represents the inner product of the quantum state, and the quantum Fisher information gives the optimal accuracy of all measurement methods.

[0035] Furthermore, based on the three-dimensional laser positioning accuracy calculation method of noisy CCD detection, the classical Fisher information of ideal intensity detection is used to characterize the measurement accuracy. The detected intensity and the ideal classical Fisher information are calculated by the following formulas:

[0036] I(x,y,z′|θ)=|<x,y|ψ> | 2

[0037]

[0038] Where I(x,y,z′|θ) refers to the intensity probability of the CCD detection surface with the lateral coordinate (x,y) and the distance from the lens z′ under the condition of parameter θ, |<x,y|ψ> | 2 It is the square of the modulus of the inner product of the quantum state, representing the probability of projecting the quantum state |ψ> onto the transverse coordinate state |x,y>; the theoretical optimal accuracy can only be achieved when the classical Fisher information is equal to the quantum Fisher information.

[0039] Furthermore, the 3D laser positioning accuracy calculation method based on noisy CCD detection uses the Fisher information of noisy CCD intensity detection to characterize the measurement accuracy. The Fisher information is written as the accumulation of information provided by all pixels and all possible counts of each pixel, and the Fisher information estimated for the light source position information (x0, y0, z0) is obtained:

[0040]

[0041] Based on the same inventive concept, the present invention provides a three-dimensional laser positioning system based on noisy CCD detection, comprising:

[0042] The dark count calibration module is used to calibrate the dark count detected by the CCD to obtain the dark count d of the pixel at the i-th row and j-th column. i,j The probability P(d i,j );

[0043] The photoelectric conversion efficiency calibration module is used to calibrate the relationship between the total photocurrent count and the incident light power to determine the photoelectric conversion efficiency;

[0044] Theoretical model building module, used to establish a theoretical model of the relationship between the three-dimensional position coordinates (x0, y0, z0) of the light source to be estimated and the reading of each pixel point of the CCD;

[0045] And, a measurement and data processing module is used to place a measuring device consisting of a lens, a CCD and a displacement stage at a suitable position before and after the convergence point of the light source along the propagation direction of the light source, move the displacement stage along the direction of light propagation, change and record the distance between the CCD detection plane and the lens, take multiple photos with the CCD at each position, use these photos as measurement results, and extract the three-dimensional position coordinate (x0, y0, z0) information of the light source from the probability distribution obtained by the theoretical model construction module.

[0046] Furthermore, it also includes a measurement accuracy calculation module for using quantum Fisher information QFI θ , Classical Fisher Information CFI for ideal intensity detection θ , or the Fisher information F for noisy CCD intensity detection θ To characterize the measurement accuracy; the calculated Fisher information is used to guide the optimal measurement position of three-dimensional positioning.

[0047] Based on the same inventive concept, the present invention provides a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, the three-dimensional laser positioning method and accuracy calculation method based on noisy CCD detection are implemented.

[0048] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0049] 1. Able to simultaneously measure the horizontal and vertical three-dimensional coordinate positions of the laser;

[0050] 2. The measurement method is based on CCD intensity detection, and the measuring instrument does not need to be in the same position as the light source;

[0051] 3. A method for calculating the measurement accuracy is given, which can provide the optimal position of the CCD horizontally and vertically along the direction of light propagation;

[0052] 4. The accuracy calculation method of the noisy CCD intensity detection provided by the present invention can be used as a yardstick for the accuracy of actual measurement data;

[0053] 5. The accuracy calculation of the present invention directly demonstrates the influence of noise and pixel discretization on the optimal measurement position and measurement accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 is a diagram of a device for three-dimensional laser positioning in an embodiment of the present invention;

[0055] Figure 2 It is a method flow chart of an embodiment of the present invention.

[0056] Figure 3is a diagram of the accuracy analysis result of lateral positioning in an embodiment of the present invention;

[0057] Figure 4 It is a diagram of the accuracy analysis result of longitudinal positioning in an embodiment of the present invention. DETAILED DESCRIPTION

[0058] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0059] like Figure 1 As shown, at a distance away from the light source, a lens, CCD and a translation stage are used as measuring devices to simultaneously measure the horizontal and vertical positions of the laser. In the three-dimensional laser positioning method based on noisy CCD detection disclosed in the embodiment of the present invention, a right-handed coordinate system is established with the horizontal line of the CCD detection surface as the x-axis and the plumb line as the y-axis, so that the z-axis points to the light source. The main process of the method is as follows Figure 2 As shown, firstly, the dark count detected by CCD is calibrated, and the relationship between the total photocurrent count and the incident light power is calibrated to determine the photoelectric conversion efficiency; then a theoretical model of the relationship between the estimated parameter and the reading of each pixel of CCD is established; finally, the translation stage is moved to perform CCD photo measurement to estimate the horizontal and vertical positions of the light source. Furthermore, the measurement accuracy is calculated to guide the selection of the measurement position. The detailed steps are as follows:

[0060] Step 1: calibrate the dark count detected by the CCD. This step requires calibrating the statistical law of the count of each pixel of the CCD when there is no light incident. Generally speaking, the difference between CCD pixels is negligible, so the dark count d of the pixel at the i-th row and j-th column is i,j Should satisfy the normal distribution:

[0061]

[0062] where μ d With σ d In the absence of light, let the CCD take enough photos, count the distribution of each pixel reading, and fit the mean value of the dark count reading μ d With variance σ d .

[0063] Step 2: calibrate the change relationship between the total photocurrent count and the incident light power to determine the photoelectric conversion efficiency α. For a measurement with a photoelectric conversion efficiency of α, a power of P, and an exposure time of t, the total photocurrent count satisfies the relationship:

[0064]

[0065] Where λ is the wavelength, h is Planck's constant, and c is the speed of light. Set multiple groups of different powers as independent variables, change the power and measure the corresponding total number of photocurrent counts (total counts minus total number of dark noise counts), fit to obtain a linear curve, and determine the photoelectric conversion efficiency α based on the slope obtained by the fit and the above formula. After the calibration is completed, the total photocurrent count N can be directly calculated from the above formula by measuring the incident light power.

[0066] Step 3, using the results of the previous two steps, establish a theoretical model of the relationship between the parameter to be estimated and the reading of each pixel of the CCD. In the present invention, the parameter to be estimated is the three-dimensional position coordinates (x0, y0, z0) of the light source, and the parameter information is the average count of the photocurrent at each pixel. For a Gaussian beam, the average photocurrent count of each pixel is proportional to the integral of the Gaussian probability density at the spatial position of the pixel:

[0067]

[0068] Where S(i,j) represents the spatial position of the pixel in the i-th row and j-th column; the information of the longitudinal position z0 of the light source is contained in the width of the light beam, and its relationship is determined by the following equation:

[0069]

[0070]

[0071] z w ′=m 2 (z0-f)+f

[0072]

[0073] where w w 、w w ′ is the beam waist radius of the Gaussian light before and after passing through the lens, z′ is the distance between the CCD detection plane and the lens, f is the focal length of the lens, λ is the wavelength, and m is the lens transformation coefficient. The actual count of the photocurrent l i,j Satisfy The Poisson distribution with a mean value is used. The count fluctuations caused by this distribution are called shot noise. Its statistical rules are as follows:

[0074]

[0075] The actual CCD pixel count k in row i and column j i,j is the photocurrent count plus the dark count k i,j = l i,j +d i,j , so the count is k i,j The probability P(k i,j) is the convolution of the dark count and photocurrent count probability:

[0076]

[0077] The summation requires that for all possible d i,j Sum, d i,j The summation range can be set from [μ d -9σ d ] to [μ d +9σ d ], where [·] indicates rounding, 9σ d The probability of dark counts other than is very small and has no effect on the result, so it can be ignored. The other independent variable of convolution is l i,j The corresponding i,j =k i,j -d i,j So far, we have given the conditional probability distribution P(k i,j |x0,y0,z0).

[0078] Step 4, measurement and data processing. Place the measuring device consisting of the lens, CCD and displacement stage at a suitable position before or after the convergence point of the light source along the propagation direction of the light source. Move the displacement stage along the direction of light propagation, change and record the distance z′ between the CCD detection plane and the lens, take enough photos with the CCD at each position, use these photos as measurement results, and extract parameter information from the probability distribution obtained in step 3. Here, maximum likelihood estimation is used as the parameter estimation method for laser three-dimensional positioning. One CCD photo is used as a measurement result, and its likelihood function is:

[0079]

[0080] Where θ is the parameter to be estimated (in this problem, θ is x0, y0, z0 respectively). The estimated value is the point where the likelihood function takes the maximum value. You can write code to use the dichotomy method to determine the zero point of the derivative of the likelihood function under the condition of setting appropriate initial values, which is the estimated value of the parameter. For each photo, an estimated value can be obtained. Generally, the mean of a sufficient number of photos is used as the final estimated value, and the variance of these estimated values ​​is used as a measure of whether the estimate is accurate. As for where the CCD is placed to estimate the most accurately, and whether the variance of the estimated value can reach the theoretical limit of accuracy, it is necessary to calculate and analyze according to the next step 5.

[0081] Step 5, calculate the measurement accuracy. The present invention uses Fisher information to characterize the measurement accuracy. Fisher information is the information of extracting parameters from probability distribution. If the Fisher information of a single experiment is F, and N experiments are performed, then the variance of the estimated measurement parameter θ will not be less than the inverse of the total Fisher information, that is,

[0082]

[0083] Three types of Fisher information are calculated below to demonstrate the theoretical limit accuracy achieved by the solution provided by the present invention. The first type is to calculate quantum Fisher information based on the quantum parameter estimation theory. Quantum Fisher information gives the best accuracy that can be achieved by all measurement methods, which is the quantum limit accuracy. For a single photon with a Gaussian wave function, its quantum state is written as:

[0084]

[0085] Where |·> is the Dirac state vector symbol, i is the imaginary unit, k is the wave vector, R(z0) is the radius of curvature of the Gaussian wavefront at that position, and ζ(z0) is the Gouy phase. Then the quantum Fisher information of this quantum state is:

[0086]

[0087] Where θ is the parameter to be estimated (in this problem, θ is x0, y0, z0 respectively), and <·|·> represents the inner product of the quantum state. Quantum Fisher information gives the optimal accuracy of all measurement methods. The second method is to select different measurement methods, corresponding to different classical Fisher information. Here, ideal intensity detection is selected as the measurement method to calculate the classical Fisher information. The detected intensity distribution and the ideal classical Fisher information are calculated by the following formulas:

[0088] I(x,y,z′|θ)=|<x,y|ψ> | 2

[0089]

[0090] Where I(x,y,z′|θ) refers to the intensity probability density at the lateral coordinate (x,y) on the CCD detection surface and at a distance of z′ from the lens under the condition of parameter θ, |<x,y|ψ> | 2It is the square of the modulus of the inner product of the quantum state, representing the probability of the quantum state |ψ> being projected onto the transverse coordinate state |x,y>. The theoretical optimal accuracy can only be achieved when the classical Fisher information is equal to the quantum Fisher information. By analyzing and calculating the classical Fisher information, it is found that in order to achieve the optimal accuracy, the CCD needs to be moved to a specific position using a translation stage: the optimal lateral measurement position is at the waist of the light beam; the optimal longitudinal measurement position is at two positions before and after the waist of the light beam. The third type is the actual classical Fisher information considering the CCD pixel noise given by the present invention. The Fisher information can be written as the accumulation of information provided by all pixels and all possible counts of each pixel, and the Fisher information estimated for the light source position information (x0, y0, z0) under the experimental setup is obtained:

[0091]

[0092] where θ is the parameter to be estimated (in this problem, θ is x0, y0, z0 respectively), P(k i,j ) is the parameter probability distribution of the detector noise model obtained in step 3. This formula directly and quantitatively gives the actual optimal accuracy that can be achieved in measuring the three-dimensional coordinates of the laser under a given experimental device, taking into account the influence of CCD dark noise and the influence of pixel discretization on the estimation accuracy during the actual detection process. According to the method of the present invention, F is calculated. θ After that, there are two direct benefits. (1) It can directly guide the optimal measurement position of three-dimensional positioning using CCD in actual detection: for lateral positioning, the optimal measurement position is at the waist of the beam; for longitudinal positioning, the optimal measurement position is at two positions before and after the waist of the beam, and is closer to the waist than the optimal measurement position given by intensity detection under ideal conditions. (2) It directly gives the optimal accuracy that can be achieved under the detection conditions, and can also be compared and analyzed with the theoretically unbreakable quantum limit accuracy.

[0093] To verify the effect of the present invention, this embodiment uses a CCD of model iStar 05577H of Andor Company as a data acquisition tool to perform three-dimensional positioning on a point light source of a He-Ne laser with a wavelength λ of 633nm after being converged by a lens.

[0094] Step 1: According to the dark count calibration method, the average value μ of CCD dark count is obtained. d =514, standard deviation σ d =7.14;

[0095] Step 2: calibrate the change relationship between the total photocurrent count and the incident light power to determine the photoelectric conversion efficiency α. In this embodiment, the exposure time t is 1ms, and the total photocurrent count satisfies the relationship:

[0096]

[0097] Where λ is the wavelength, h is the Planck constant, and c is the speed of light. Set multiple groups of different powers P as independent variables, change the power and measure the corresponding total number of photocurrent counts (total counts minus total number of dark noise counts), fit to obtain a linear curve, and determine the photoelectric conversion efficiency α to be 0.11 based on the slope obtained by fitting and the above formula. After calibration, the incident light power P of the embodiment is measured to be 0.57nW, and the total photocurrent count N is directly calculated from the above formula to be 2.0×10 5 ;

[0098] Step 3, according to the method of the present invention, obtain P(k i,j |x0, y0, z0). In this embodiment, the focal length of the lens is 100 mm, and the waist radius of the light source passing through the lens is w w ' is 15.4μm;

[0099] Step 4, measurement and data processing. Place the measuring device consisting of the lens, CCD and translation stage at appropriate positions before and after the light source convergence point along the propagation direction of the light source. Move the translation stage along the light propagation direction, change and record the distance z′ between the CCD detection plane and the lens, take enough photos with the CCD at each position, use these photos as the measurement results, and extract parameter information from the probability distribution obtained in step 3. Use maximum likelihood estimation to process the data. For a measurement of a CCD photo, the likelihood function is:

[0100]

[0101] Where θ is the parameter to be estimated (in this problem, θ is x0, y0, z0 respectively). The point where the estimated parameter makes the likelihood function take the maximum value is the estimated value. Write the code, set the appropriate initial value conditions, and use the dichotomy method to determine the zero point of the derivative of the likelihood function, which is the estimated value of the parameter. For each photo, you can get an estimated value, and take the average of 10,000 photos as the final estimated value;

[0102] Step 5, according to the accuracy calculation method of the present invention, the quantum Fisher information of the lateral estimation (parameter θ is x0, y0) is calculated respectively Classical Fisher information for ideal intensity detection and Fisher information of noisy CCD intensity detection The results are as follows Figure 3 As shown; then calculate the quantum Fisher information of the longitudinal estimation (parameter θ is z0) Classical Fisher information for ideal intensity detection and Fisher information of noisy CCD intensity detection The results are as follows Figure 4 shown.

[0103] Based on the same inventive concept, the three-dimensional laser positioning system based on noisy CCD detection provided by the embodiment of the present invention mainly includes: a dark count calibration module, which is used to calibrate the dark count detected by the CCD to obtain a normal distribution model of the dark count; a photoelectric conversion efficiency calibration module, which is used to calibrate the change relationship between the total photocurrent count and the incident light power to determine the photoelectric conversion efficiency; a theoretical model construction module, which is used to establish a theoretical model of the relationship between the three-dimensional position coordinates (x0, y0, z0) of the light source to be estimated and the reading of each pixel point of the CCD; a measurement and data processing module, which is used to place the measuring device composed of a lens, a CCD and a displacement stage at a suitable position before and after the light source convergence point along the propagation direction of the light source, move the displacement stage along the light propagation direction, change and record the distance between the CCD detection plane and the lens, take enough photos with the CCD at each position, use these photos as the measurement results, and extract the three-dimensional position coordinates (x0, y0, z0) information of the light source from the probability distribution obtained by the theoretical model construction module. It further includes a measurement accuracy calculation module, which is used to use quantum Fisher information QFI θ , Classical Fisher Information CFI for ideal intensity detection θ , or the Fisher information F for noisy CCD intensity detection θ To characterize the measurement accuracy, the calculated Fisher information is used to guide the optimal measurement position of the three-dimensional positioning. The specific implementation of each module refers to the above method embodiment, which will not be repeated here.

[0104] Based on the same inventive concept, an embodiment of the present invention also provides a computer system, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the computer program is loaded into the processor, the three-dimensional laser positioning method based on noisy CCD detection and its accuracy calculation method are implemented.

[0105] The above disclosure is only the preferred embodiment of the present invention, which cannot be used to limit the scope of the present invention. Therefore, equivalent changes made according to the claims of the present invention are still within the scope of the present invention.

Claims

1. A three-dimensional laser positioning method based on noisy CCD detection, characterized in that: The following steps are involved: Step 1: calibrate the dark count detected by the CCD to obtain the dark count d of the pixel at the i-th row and j-th column. i，j The probability P(d i，j ); Step 2, calibrating the relationship between the total photocurrent count and the incident light power to determine the photoelectric conversion efficiency; Step 3, establish a theoretical model of the relationship between the three-dimensional position coordinates (x0, y0, z0) of the light source to be estimated and the reading of each pixel point of the CCD; The three-dimensional position coordinates of the light source (x0, y0, z0), including the average count of the photocurrent at each pixel inside: Where N is the total photocurrent count calculated according to the relationship calibrated in step 2, S(i, j) represents the spatial position of the pixel in the i-th row and j-th column; the information of the longitudinal position z0 of the light source is contained in the width of the light beam: z w m 2 (z0-f)+f where w w 、w w ′ is the beam waist radius of the Gaussian light before and after passing through the lens, z′ is the distance between the CCD detection plane and the lens, f is the focal length of the lens, λ is the wavelength, and m is the lens transformation coefficient; the actual count of the photocurrent l i，j Satisfy is a Poisson distribution with mean: The actual CCD pixel count k in row i and column j i，j The probability P(k i，j ) is the convolution of the dark count and photocurrent count probability: Step 4: Place the measuring device consisting of the lens, CCD and translation stage at a suitable position before or after the convergence point of the light source along the propagation direction of the light source, move the translation stage along the direction of light propagation, change and record the distance between the CCD detection plane and the lens, take multiple photos with the CCD at each position, use these photos as the measurement results, and extract the three-dimensional position coordinates (x0, y0, z0) information of the light source from the probability distribution obtained in step 3.

2. The three-dimensional laser positioning method based on noisy CCD detection according to claim 1 is characterized in that: In step 1, the statistical law of the count of each pixel of the CCD is calibrated when there is no light incident. In the case of no light incident, the CCD is allowed to take multiple photos, and the distribution law of the reading of each pixel is statistically analyzed, and the mean value μ of the dark count reading is obtained by fitting. d With variance σ d ; Dark count d of the pixel at row i and column j i，j Satisfies normal distribution:

3. The three-dimensional laser positioning method based on noisy CCD detection according to claim 1, characterized in that: In step 2, for a measurement with a photoelectric conversion efficiency of α, a power of P, and an exposure time of t, the total photocurrent count satisfies the relationship: Where λ is the wavelength, h is Planck's constant, and c is the speed of light; set multiple groups of different powers as independent variables, change the power and measure the corresponding total number of photocurrent counts, fit a linear curve, and determine the photoelectric conversion efficiency α based on the slope obtained by the fitting and the above formula; after calibration, measure the incident light power and directly calculate the total photocurrent count N from the above formula.

4. The three-dimensional laser positioning method based on noisy CCD detection according to claim 1, characterized in that: In step 4, maximum likelihood estimation is used as the parameter estimation method for laser 3D positioning, and a CCD photo is used as a measurement result. Its likelihood function is: Where θ is the parameter to be estimated, and the estimated value is the point where the likelihood function takes the maximum value; an estimated value is obtained for each photo, and the mean of multiple photos is taken as the final estimated value.

5. The accuracy calculation method of the three-dimensional laser positioning method based on noisy CCD detection according to claim 1 is characterized in that: Quantum Fisher information is used to characterize the measurement accuracy, specifically: For a single photon with a Gaussian wave function, its quantum state |Ψ> is written as: Where |·> is the Dirac state vector symbol, i is the imaginary unit, k is the wave vector, R(z0) is the radius of curvature of the Gaussian wavefront at that position, and ξ(z0) is the Gouy phase; the quantum Fisher information of this quantum state is: Where θ is the parameter to be estimated, <·|·> represents the inner product of the quantum state, and the quantum Fisher information gives the optimal accuracy of all measurement methods.

6. The accuracy calculation method of the three-dimensional laser positioning method based on noisy CCD detection according to claim 5 is characterized in that: The classical Fisher information of ideal intensity detection is used to characterize the measurement accuracy. The detected intensity and the ideal classical Fisher information are calculated by the following formulas: I(x,y,z′|θ)=|<x,y|ψ>| 2 Where I(x, y, z′|θ) refers to the intensity probability at the lateral coordinate (x, y) on the CCD detection surface and at a distance of z′ from the lens under the condition of parameter θ, |<x,y|ψ> | 2 It is the square of the modulus of the inner product of the quantum state, representing the probability of projecting the quantum state |ψ> onto the transverse coordinate state |x, y>; the theoretical optimal accuracy can only be achieved when the classical Fisher information is equal to the quantum Fisher information.

7. The accuracy calculation method of the three-dimensional laser positioning method based on noisy CCD detection according to claim 1 is characterized in that: The Fisher information of noisy CCD intensity detection is used to characterize the measurement accuracy. The Fisher information is written as the accumulation of information provided by all pixels and all possible counts of each pixel, and the Fisher information estimated for the light source position information (x0, y0, z0) is obtained: Where θ is the parameter to be estimated.

8. A three-dimensional laser positioning system based on noisy CCD detection, characterized in that: include: The dark count calibration module is used to calibrate the dark count detected by the CCD to obtain the dark count d of the pixel at the i-th row and j-th column. i，j The probability P(d i，j ); The photoelectric conversion efficiency calibration module is used to calibrate the relationship between the total photocurrent count and the incident light power to determine the photoelectric conversion efficiency; Theoretical model building module is used to establish a theoretical model of the relationship between the three-dimensional position coordinates (x0, y0, z0) of the light source to be estimated and the reading of each pixel point of the CCD; The three-dimensional position coordinates of the light source (x0, y0, z0), including the average count of the photocurrent at each pixel inside: Where N is the total photocurrent count calculated according to the relationship calibrated by the photoelectric conversion efficiency calibration module, S(i, j) represents the spatial position of the pixel in the i-th row and j-th column; the information of the longitudinal position z0 of the light source is contained in the width of the light beam: z w m 2 (z0-f)+f where w w 、w w ′ is the beam waist radius of the Gaussian light before and after passing through the lens, z′ is the distance between the CCD detection plane and the lens, f is the focal length of the lens, λ is the wavelength, and m is the lens transformation coefficient; The actual photocurrent count l i，j Satisfy is a Poisson distribution with mean: The actual CCD pixel count k in row i and column j i，j The probability P(k i，j ) is the convolution of the dark count and photocurrent count probability: And, a measurement and data processing module is used to place a measuring device consisting of a lens, a CCD and a displacement stage at a suitable position before and after the convergence point of the light source along the propagation direction of the light source, move the displacement stage along the direction of light propagation, change and record the distance between the CCD detection plane and the lens, take multiple photos with the CCD at each position, use these photos as measurement results, and extract the three-dimensional position coordinates (x0, y0, z0) information of the light source from the probability distribution obtained by the theoretical model construction module.

9. The three-dimensional laser positioning system based on noisy CCD detection according to claim 8, characterized in that: Also includes a measurement accuracy calculation module for using quantum Fisher information QFI θ , Classical Fisher Information CFI for ideal intensity detection θ , or the Fisher information F for noisy CCD intensity detection θ To characterize the measurement accuracy; Where θ is the parameter to be estimated; the calculated Fisher information is used to guide the optimal measurement position of three-dimensional positioning.

10. A computer system comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the computer program is loaded into the processor, it implements the three-dimensional laser positioning method based on noisy CCD detection according to any one of claims 1-4, or implements the accuracy calculation method of the three-dimensional laser positioning method based on noisy CCD detection according to any one of claims 5-7.

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