A spot center positioning method for a weak measurement system

Abstract

The application designs a spot center positioning method for a weak measurement system, comprising: generating a spot intensity distribution physical model according to the imaging principle of the weak measurement system; fitting the spot intensity distribution physical model by using a least square method according to a measured spot image collected by a CCD to obtain parameters corresponding to the spot intensity distribution model; randomly generating N spot images as ideal spot images according to the parameters corresponding to the spot intensity distribution model; generating N simulated spot images by using a wavelet analysis technology according to the measured spot image collected by the CCD and the N ideal spot images; training a convolutional auto-encoding neural network by taking the N simulated spot images as a training set and taking the ideal spot image corresponding to each simulated spot image as a label; inputting a target measured spot image collected by the CCD into the trained convolutional auto-encoding neural network to generate a corresponding target ideal spot image and positioning the center of the target measured spot image.

Description

Technical Field

[0001] This invention belongs to the field of precision measurement, and in particular relates to a method for locating the center of a light spot in a weak measurement system. Background Technology

[0002] The core technical challenge in precision measurement lies in improving measurement accuracy. Weak measurement, on the other hand, can amplify the measurement of minute physical quantities, thereby achieving high-precision measurements. Therefore, weak measurement holds immense potential in the field of precision measurement. In weak measurement systems, minute physical quantities are primarily observed through pointer offset; however, the estimation of pointer offset is based on calculations performed at the center of the light spot image.

[0003] Noise and interference in the measurement system cause errors in the center of the spot image. For spot image localization, researchers in the field of weak measurement mainly use traditional methods such as gray-scale centroid method and fitting method. At present, traditional methods can achieve certain effects in noise reduction (Gaussian noise), but they are not effective in suppressing low-frequency noise and various interferences. However, in weak measurement systems, interference and low-frequency noise are the main reasons for the low accuracy of spot image center localization. Therefore, traditional methods often fail to achieve ideal results in practical applications.

[0004] Various noises and interferences exist in weak measurement systems. Noises mainly include Gaussian noise, shot noise, flicker noise, and background noise; interferences mainly include the instability of the light source itself and environmental changes.

[0005] Currently, the methods for locating the center of weak measurement spot images can only effectively suppress Gaussian noise, but cannot effectively suppress other noise interference. This results in low center positioning accuracy of the weak measurement system, ultimately preventing the weak measurement system from achieving high-precision measurements. Summary of the Invention

[0006] To address the problems existing in the background technology, the present invention provides a spot center localization method for weak measurement systems. By suppressing noise interference in the spot image, the method achieves high-precision center localization, thereby ultimately improving the measurement accuracy of weak measurement systems.

[0007] The specific technical solution is as follows: a method for locating the center of a light spot in a weak measurement system. The weak measurement system includes a He-Ne laser, an fiber collimator FC, a first birefringent crystal polarization beam splitter BD1, a polarizer P1, a 50 / 50 unpolarized beam splitter BS, a second birefringent crystal polarization beam splitter BD2, a cantilever beam deformable mirror SR, a quarter-wave plate QWP, a half-wave plate HWP, a 45° Glan Taylor polarization prism P2, and a CCD. The He-Ne laser is used to generate randomly polarized light and introduces it into the fiber collimator FC through a single-mode fiber to collimate the laser light in the single-mode fiber into Gaussian light. A Gaussian beam is sequentially incident on a first birefringent crystal polarizing beam splitter BD1, a polarizer P1, a 50 / 50 unpolarized beam splitter BS, a second birefringent crystal polarizing beam splitter BD2, and a cantilever beam deformable reflector SR; the incident surface of the unpolarized beam splitter BS forms a 45° angle with the Gaussian beam; SR is set to rotate around the z-axis by an angle θ, so that the reflected light forms a 2θ angle with the original beam in the xy plane; S reflects the Gaussian beam and sequentially incident it on a quarter-wave plate QWP, a half-wave plate HWP, a 45° GranTaylor polarizing prism P2, and a CCD; a measured spot image is acquired by the CCD, characterized by comprising:

[0008] S1: Generate a physical model of the light spot intensity distribution based on the imaging principle of the weak measurement system;

[0009] Preferably, the center of the light spot distribution map is taken as the origin of the coordinate system, and the physical model of the light spot intensity distribution includes:

[0010]

[0011] I(x,y)=A[f(x,y)sin(gx+b)] 2

[0012]

[0013]

[0014] x′=xs x cosθ-ys x sinθ+Δx

[0015] y′=ys y cosθ-xs y sinθ+Δy

[0016] I′(x, y)=I(x′, y′)

[0017] Where f(x, y) represents the original transverse amplitude distribution of the light spot corresponding to the coordinate point (x, y), Δ x，yLet represent the diameter of the Gaussian beam, sin(gx+b) represent the phase difference between the two polarization components of the beam, I(x,y) represent the light intensity at coordinate point (x,y), A represent the initial spot intensity of the system, I′(x,y) represent the spot intensity distribution acquired by the CCD, T(x,y) represent the affine transformation matrix, and s x and s y θ is the scaling factor along the x and y directions, θ is the rotation angle of the spot image, Δx represents the translation of the spot along the x-axis, Δy represents the translation of the spot along the y-axis, S represents the area of ​​the spot image, g represents the incident angle of the Gaussian beam, and b represents the extinction position of the spot image.

[0018] S2: Based on the measured spot image acquired by CCD, the least squares method is used to fit the physical model of spot intensity distribution to obtain the parameters corresponding to the spot intensity distribution model;

[0019] Preferably, the parameters corresponding to the light spot intensity distribution model include:

[0020] Due to parameters A, S, Δx, Δy, s x s y θ depends on the hardware of the weak measurement system. During the fitting process, A, S, Δx, Δy, and s x s y θ and θ are fixed, while parameter b changes dynamically during the measurement process. Parameter b changes with the physical quantity being measured. By transforming the weak physical quantity and acquiring multiple measured images of the physical quantity being measured, the minimum value of parameter b is obtained by fitting the parameter b. min and maximum value b max .

[0021] S3: Randomly generate N spot images as ideal spot images based on the parameters corresponding to the spot intensity distribution model;

[0022] Preferably, generating N light spot images includes:

[0023] At the minimum value of parameter b min and maximum value b max Randomly select parameter br, and generate an ideal light spot image using the physical model of light spot intensity distribution based on the selected parameter br. Repeat N times to obtain N ideal light spot images.

[0024] S4: Based on the measured spot image acquired by CCD and N ideal spot images, N simulated spot images are generated using wavelet decomposition technology;

[0025] Preferably, the step of generating N simulated light spot images using wavelet decomposition technology includes:

[0026] S41: Multiple measured light spot images under the same weak physical quantity are acquired by CCD. Let the light spot image at time t be I. t ;

[0027] S42: Select Haar as the wavelet basis for the light spot image I. t Perform two-level wavelet decomposition, first for I t Perform wavelet decomposition at the first level to obtain the first-level low-frequency part LL1 and the high-frequency parts HL1, LH1, and HH1; then perform wavelet decomposition on the first-level low-frequency part LL1 to obtain the second-level low-frequency part LL2 and the high-frequency parts HL2, LH2, and HH2.

[0028] S43: Transfer the light spot image I t The high-frequency components HL1, LH1, HH1, HL2, LH2 and HH2 after wavelet decomposition are fused with the ideal light spot image to obtain N simulated light spot images.

[0029] S5: Use N simulated light spot images as the training set, and use the ideal light spot image corresponding to each simulated light spot image as the label to train the convolutional autoencoder neural network;

[0030] Preferably, the convolutional autoencoder neural network includes: an encoding part, a hidden layer, and a decoding part connected in sequence; the hidden layer is composed of fully connected layers for denoising features of the input image; the decoding part is used for extracting features from the input image; and the decoding part is used for reconstructing the input image.

[0031] Preferably, training the convolutional autoencoder neural network includes: inputting a simulated light spot image into the convolutional autoencoder neural network to reconstruct the image and generate a corresponding predicted light spot image; constructing a loss function for the convolutional autoencoder neural network based on the center of the predicted light spot image and the center of the corresponding ideal light spot image; updating the parameters of the convolutional autoencoder neural network using the Adam optimizer based on the loss function until the loss function is less than a set threshold or a preset number of training rounds is reached to complete the training of the convolutional autoencoder neural network.

[0032] Preferably, the loss function of the convolutional autoencoder neural network includes:

[0033]

[0034] in, Let x represent the loss function of a convolutional autoencoder neural network. p y p (x) represents the center of the predicted spot image. o y o ) represents the center of the corresponding ideal light spot image.

[0035] Preferably, the center of the light spot image includes:

[0036]

[0037] Where, x i y i I represents the row and column positions of the pixel value in the image, respectively. i Represents the corresponding coordinate point (x i y i The grayscale value of ) x c y c These represent the coordinates of the center.

[0038] S6: Input the target measured spot image acquired by CCD into the trained convolutional autoencoder neural network to generate the corresponding target ideal spot image, and use the center of the target ideal spot image as the center of the target measured spot image for positioning.

[0039] The present invention has at least the following beneficial effects

[0040] To achieve high-precision positioning of the weak measurement center, this invention models the weak measurement system and uses the least squares method to fit the system parameters to generate an ideal light spot image. Based on the measured light spot image and the ideal light spot image, wavelet analysis is used to generate a training set. A convolutional autoencoder neural network incorporating physical information is designed, trained, and optimized, achieving excellent results on both the training and test sets. In actual measurements, high-precision positioning of the weak measurement system center is achieved, improving both the measurement accuracy and stability of the weak measurement system. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the weak measurement system in this invention;

[0042] Figure 2 This is a schematic diagram of the method flow framework of the present invention;

[0043] Figure 3 This is a schematic diagram of the structure of the convolutional autoencoder neural network of the present invention. Detailed Implementation

[0044] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0045] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures, and should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0046] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0047] In classical optical measurement systems, weak amplification can be achieved using asymmetric interference of polarized light. A two-level system is constructed using the polarization states of light, and a polarizer is used to create forward and backward selection. The measurement is converted into a difference component between the two polarization states. By setting appropriate system parameters, special asymmetric interference is achieved, thereby amplifying the pointer offset.

[0048] Please see Figure 1 and Figure 2This invention provides a method for locating the center of a light spot in a weak measurement system. The weak measurement system includes a He-Ne laser, an fiber collimator FC, a first birefringent crystal polarizing beam splitter BD1, a polarizer P1, a 50 / 50 unpolarized beam splitter BS, a second birefringent crystal polarizing beam splitter BD2, a cantilever beam deformable mirror SR, a quarter-wave plate QWP, a half-wave plate HWP, a 45° Glan Taylor polarizing prism P2, and a CCD. The He-Ne laser is used to generate randomly polarized light and introduces it into the fiber collimator FC through a single-mode fiber to collimate the laser light in the single-mode fiber into a Gaussian beam. A Gaussian beam is sequentially incident on a first birefringent crystal polarizing beam splitter BD1, a polarizer P1, a 50 / 50 unpolarized beam splitter BS, a second birefringent crystal polarizing beam splitter BD2, and a cantilever beam deformable reflector SR; the incident surface of the unpolarized beam splitter BS forms a 45° angle with the Gaussian beam; SR is set to rotate around the z-axis by an angle θ, such that the reflected light forms a 2θ angle with the original beam in the xy plane; after reflecting the Gaussian beam, SR sequentially incident on a quarter-wave plate QWP, a half-wave plate HWP, a 45° Glan Taylor polarizing prism P2, and a CCD; a measured beam spot image is acquired by the CCD, characterized by comprising:

[0049] S1: Generate a physical model of the light spot intensity distribution based on the imaging principle of the weak measurement system;

[0050] S2: Based on the measured spot image acquired by CCD, the least squares method is used to fit the physical model of spot intensity distribution to obtain the parameters corresponding to the spot intensity distribution model;

[0051] S3: Randomly generate N spot images as ideal spot images based on the parameters corresponding to the spot intensity distribution model;

[0052] S4: Based on the measured spot image acquired by CCD and N ideal spot images, N simulated spot images are generated using wavelet decomposition technology;

[0053] S5: Use N simulated light spot images as the training set, and use the ideal light spot image corresponding to each simulated light spot image as the label to train the convolutional autoencoder neural network;

[0054] S6: Input the target measured spot image acquired by CCD into the trained convolutional autoencoder neural network to generate the corresponding target ideal spot image, and use the center of the target ideal spot image as the center of the target measured spot image for positioning.

[0055] This invention's algorithm research on spot images mainly involves three key parts. First, the first part focuses on analyzing the error sources of the center displacement error in the spot image and conducting forward simulation evaluation for a single error source. Second, in the second part, through modeling and analyzing the spot center error, the effective extraction of noise interference features in the spot is achieved. Finally, the third part focuses on a machine learning-based spot image processing model. Utilizing the noise interference feature distribution and the physical prior distribution of the spot, a machine learning model is used for modeling, thereby achieving effective suppression of noise interference in the spot image.

[0056] Preferably, the physical model for the light spot intensity distribution includes:

[0057]

[0058] I(x,y)=A[f(x,y)sin(gx+b)] 2

[0059]

[0060]

[0061] x′=xs x cosθ-ys x sinθ+Δx

[0062] y′=ys y cosθ-xs y sinθ+Δy

[0063] I′(x, y)=I(x′, y′) where f(x, y) represents the original transverse amplitude distribution of the light spot corresponding to the coordinate point (x, y), Δ x，y Let represent the diameter of the Gaussian beam, sin(gx+b) represent the phase difference between the two polarization components of the beam, I(x,y) represent the light intensity at coordinate point (x,y), A represent the initial spot intensity of the system, I′(x′,y′) represent the spot intensity distribution acquired by the CCD, T(x,y) represent the affine transformation matrix, and s x and s y θ is the scaling factor along the x and y directions, θ is the rotation angle of the spot image, Δx represents the translation of the spot along the x-axis, Δy represents the translation of the spot along the y-axis, S represents the area of ​​the spot image, g represents the incident angle of the Gaussian beam, and b represents the extinction position of the spot image.

[0064] sin(gx+b) represents the phase difference between the two polarization components of the beam, which is related to the coordinates in the x-direction. The coupling strength g is determined by the incident angle of the beam, and b is determined by the physical quantity to be measured. In the optical measurement system constructed in this invention, without considering noise interference and affine transformation of the spot image, the spot intensity distribution follows I(x,y), where I(x,y) represents the light intensity corresponding to the coordinate point (x,y), and A represents the initial spot intensity of the system, determined by the laser power. Without considering noise interference, the spot intensity distribution acquired by the CCD follows I′(x,y), which is obtained by affine transformation of I(x,y). T(x,y) represents the affine transformation matrix, and s x and s y θ is the scaling factor along the x and x directions, and θ is the rotation angle of the spot image.

[0065] Preferably, the parameters corresponding to the light spot intensity distribution model include: due to parameters A, S, Δx, Δy, s x s y θ depends on the hardware of the weak measurement system. During the fitting process, A, S, Δx, Δy, and s x s y θ and θ are fixed, while parameter b changes dynamically during the measurement process. Parameter b changes with the physical quantity being measured. By transforming the weak physical quantity and acquiring multiple measured images of the physical quantity being measured, the minimum value of parameter b is obtained by fitting the parameter b. min and maximum value b max .

[0066] Preferably, generating N light spot images includes:

[0067] At the minimum value of parameter b min and maximum value b max Randomly select parameter br, and generate an ideal light spot image using the physical model of light spot intensity distribution based on the selected parameter br. Repeat N times to obtain N ideal light spot images.

[0068] Preferably, the step of generating N simulated light spot images using wavelet decomposition technology includes:

[0069] S41: Multiple measured light spot images under the same weak physical quantity are acquired by CCD. Let the light spot image at time t be I. t ;

[0070] S42: Select Haar as the wavelet basis for the light spot image I. t Perform two-level wavelet decomposition, first for I tPerform wavelet decomposition at the first level to obtain the first-level low-frequency part LL1 and the high-frequency parts HL1, LH1, and HH1; then perform wavelet decomposition on the first-level low-frequency part LL1 to obtain the second-level low-frequency part LL2 and the high-frequency parts HL2, LH2, and HH2.

[0071] S43: Transfer the light spot image I t The high-frequency components HL1, LH1, HH1, HL2, LH2 and HH2 after wavelet decomposition are fused with the ideal light spot image to obtain N simulated light spot images.

[0072] This invention employs Haar wavelets to decompose time-series light spot images, extracts features from high-frequency noise in the images, and fuses the high-frequency noise components with the ideal image to generate a training set for training subsequent prediction models. This enables the model to fully learn the interference and noise affecting the light spot images, thereby accurately suppressing the interference and noise.

[0073] Preferably, the convolutional autoencoder neural network includes: an encoding part, a hidden layer, and a decoding part connected in sequence; the hidden layer is composed of fully connected layers for denoising features of the input image; the decoding part is used for extracting features from the input image; and the decoding part is used for reconstructing the input image.

[0074] Please see Figure 3 A preferred implementation of a convolutional autoencoder neural network is described, in which the encoder consists of four convolutional layers and four pooling layers. The hidden layers in the middle are composed of fully connected layers. The decoder, symmetrical to the encoder but with the opposite function, consists of four deconvolutional layers and four unpooling layers. The processing flow of the convolutional autoencoder network (i.e., the encoding and decoding process in the figure) for the spot image is as follows: taking a 512×512 image as input, the first convolutional layer uses 64 3×3 convolutional kernels with a stride of 1 and padding = same, resulting in an output size of 512×512×64. The second layer is a pooling layer; the pooling layer in the experimental network structure uses max pooling, with a pooling region of 2×2 and a stride of 2. Subsequently, 32 3×3 convolutional kernels, 32 3×3 convolutional kernels, and 16 3×3 convolutional kernels are used alternately with pooling. The decoder is the inverse operation of the encoder. During decoding, the parameters of each layer remain consistent with the parameters of the corresponding convolutional and pooling layers in the encoding process, but the operations are reversed. The final output of the decoding layer is required to minimize the error with the input of the encoding layer. These steps are used to reconstruct the input samples and update the hidden layer parameters.

[0075] Preferably, training the convolutional autoencoder neural network includes:

[0076] The simulated light spot image is input into the convolutional autoencoder neural network for image reconstruction to generate the corresponding predicted light spot image. The loss function of the convolutional autoencoder neural network is constructed based on the center of the predicted light spot image and the center of the corresponding ideal light spot image. The parameters of the convolutional autoencoder neural network are updated using the Adam optimizer based on the loss function until the loss function is less than a set threshold or the preset number of training rounds is reached to complete the training of the convolutional autoencoder neural network.

[0077] Preferably, the loss function of the convolutional autoencoder neural network includes:

[0078]

[0079] in, Let x represent the loss function of a convolutional autoencoder neural network. p y p (x) represents the center of the predicted spot image. o y o ) represents the center of the corresponding ideal light spot image.

[0080] Preferably, the center of the light spot image includes:

[0081]

[0082] Where, x i y i I represents the row and column positions of the pixel value in the image, respectively. i Represents the corresponding coordinate point (x i y i The grayscale value of ) x c y c These represent the coordinates of the center.

[0083] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0084] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for locating the center of a light spot in a weak measurement system, the weak measurement system comprising a He-Ne laser, an optical fiber collimator FC, a first birefringent crystal polarization beam splitter BD1, a polarizer P1, a 50 / 50 unpolarized beam splitter BS, a second birefringent crystal polarization beam splitter BD2, a cantilever beam deformable mirror SR, a quarter-wave plate QWP, a half-wave plate HWP, a 45° Glan Taylor polarizing prism P2, and a CCD. The He-Ne laser is used to generate randomly polarized light and introduces it into the optical fiber collimator FC through a single-mode fiber to collimate the laser in the single-mode fiber into a Gaussian beam. The Gaussian beam is sequentially incident on the first birefringent crystal polarization beam splitter BD1, the polarizer P1, the 50 / 50 unpolarized beam splitter BS, the second birefringent crystal polarization beam splitter BD2, and the cantilever beam deformable mirror SR. The angle between the incident surface of the unpolarized beam splitter BS and the Gaussian beam is 45°. SR is configured to rotate around... The axis rotates through an angle This causes the reflected light to meet the original light beam at the same time. The included angle on the plane is The Gaussian beam is reflected by S and sequentially incident on a quarter-wave plate (QWP), a half-wave plate (HWP) at 45°, a GranTaylor polarizing prism (P2), and a CCD; the measured light spot image is acquired by the CCD. The characteristic feature is that... include: S1: Generate a physical model of the light spot intensity distribution based on the imaging principle of the weak measurement system; S2: Based on the measured spot image acquired by CCD, the least squares method is used to fit the physical model of spot intensity distribution to obtain the parameters corresponding to the spot intensity distribution model; S3: Randomly generate N spot images as ideal spot images based on the parameters corresponding to the spot intensity distribution model; The generation of N light spot images includes: At the minimum value of the parameter and maximum value Parameter br is randomly selected, and an ideal light spot image is generated using a physical model of light spot intensity distribution based on the selected parameter br. This process is repeated N times to obtain N ideal light spot images. b represents the extinction position of the light spot image. Parameter b changes dynamically during the measurement process, varying with the physical quantity being measured. The minimum value of parameter b is obtained by fitting multiple measured images of the physical quantity being measured by transforming a weak physical quantity. and maximum value ; S4: Based on the measured spot image acquired by CCD and N ideal spot images, N simulated spot images are generated using wavelet decomposition technology; The generation of N simulated light spot images using wavelet decomposition technology includes: S41: Multiple frames of measured light spot images under the same weak physical quantity are acquired by CCD. Let the light spot image at time t be... ; S42: Select Haar as the wavelet basis for the spot image. Perform two-level wavelet decomposition, first... Perform the first-level wavelet decomposition to obtain the first-level low-frequency component. and high-frequency components , , Then, for the first layer of low-frequency components... Wavelet decomposition is performed to obtain the low-frequency component of the second layer. and high-frequency components , , ; S43: Image of light spot High-frequency components after wavelet decomposition , , , , and Each image is fused with an ideal light spot image to obtain N simulated light spot images; S5: Use N simulated light spot images as the training set, and use the ideal light spot image corresponding to each simulated light spot image as the label to train the convolutional autoencoder neural network; S6: Input the target measured spot image acquired by CCD into the trained convolutional autoencoder neural network to generate the corresponding target ideal spot image, and use the center of the target ideal spot image as the center of the target measured spot image for positioning.

2. The method for locating the center of a light spot in a weak measurement system according to claim 1, characterized in that, Using the center of the light spot distribution map as the origin of the coordinate system, the physical model of the light spot intensity distribution includes: in, This represents the original transverse amplitude distribution of the light spot corresponding to the coordinate point (x, y). This represents the diameter of the Gaussian beam. Let I(x, y) represent the phase difference between the two polarization components of the beam, and let I(x, y) represent the light intensity at the coordinate point (x, y). This represents the initial spot intensity of the system. This represents the intensity distribution of the light spot acquired by the CCD. Denotes the affine transformation matrix. and It is along and Scaling factor of direction It is the rotation angle of the light spot image. This represents the amount of translation of the light spot along the x-axis. denoted by y, S represents the area of ​​the light spot image, g represents the incident angle of the Gaussian beam, and b represents the extinction position of the light spot image.

3. The method for locating the center of a light spot in a weak measurement system according to claim 2, characterized in that, The parameters corresponding to the light spot intensity distribution model include: Due to parameters A, S, , , , , Depending on the hardware of the weak measurement system, A, S, , , , , They are all fixed and unchanging.

4. The method for locating the center of a light spot in a weak measurement system according to claim 1, characterized in that, The convolutional autoencoder neural network includes: an encoding part, a hidden layer, and a decoding part connected in sequence; the hidden layer is composed of fully connected layers for denoising the features of the input image; the decoding part is used for extracting features from the input image; and the decoding part is used for reconstructing the input image.

5. The method for locating the center of a light spot in a weak measurement system according to claim 1, characterized in that, The training of the convolutional autoencoder neural network includes: The simulated light spot image is input into the convolutional autoencoder neural network for image reconstruction to generate the corresponding predicted light spot image. The loss function of the convolutional autoencoder neural network is constructed based on the center of the predicted light spot image and the center of the corresponding ideal light spot image. The parameters of the convolutional autoencoder neural network are updated using the Adam optimizer based on the loss function until the loss function is less than a set threshold or the preset number of training rounds is reached to complete the training of the convolutional autoencoder neural network.

6. The method for locating the center of a light spot in a weak measurement system according to claim 5, characterized in that, The loss function of the convolutional autoencoder neural network includes: in, Let x represent the loss function of a convolutional autoencoder neural network. p y p (x) represents the center of the predicted spot image. o y o ) represents the center of the corresponding ideal light spot image.

7. The method for locating the center of a light spot in a weak measurement system according to claim 6, characterized in that, The center of the light spot image includes: Where, x i y i These represent the row and column positions of the pixel value in the image, respectively. Represents the corresponding coordinate point grayscale value, , These represent the coordinates of the center.

Images