High-precision estimation method for pointer offset of weak measurement system

Abstract

The invention provides a high-precision pointer offset estimation method for a weak measurement system, and the method comprises the steps: determining the centroid position of a light spot through a gray centroid method, extracting the energy feature of the light spot based on a gray co-occurrence matrix, and constructing a multi-modal pointer according to the fusion of the centroid position of the light spot and the energy feature; improving the U-Net network based on the residual structure and the multi-modal pointer to obtain a light spot image noise reduction model; inputting the actually measured light spot image into a light spot image noise reduction model for noise reduction processing; and calculating the pointer offset according to the denoised light spot image. According to the light spot image noise reduction model, gradient stable propagation is ensured through residual error mapping, local noise and global features are fused through hierarchical convolution, a loss function is constructed based on a multi-mode pointer to carry out back propagation to optimize a network architecture, and dynamic coupling of data driving and a physical mechanism is achieved. According to the method, the estimation precision of the pointer offset is high, the stability is good, and a high-robustness pointer offset estimation framework is provided for a weak measurement system.

Description

Technical Field

[0001] The present invention relates to the technical field of weak measurement, and particularly relates to a method for high-precision estimation of pointer offset in a weak measurement system. Background Art

[0002] Weak measurement technology can achieve high-sensitivity detection of tiny physical quantities through the quantum weak value amplification effect, and shows unique advantages in fields such as time delay, temperature detection, phase measurement, and frequency detection. In a weak measurement system, as the core characterization carrier of pointer offset, the spot image can encode the tiny changes of the measured physical quantity into the spatial intensity distribution characteristics of the spot image through optical modulation, and use these distribution characteristics as the physical mapping of the pointer offset, so that the tiny physical quantity changes that are difficult to directly observe are transformed into light intensity distribution characteristics that can be quantitatively analyzed, providing an effective means for weak measurement.

[0003] However, in the actual measurement process, various noise sources and interference factors will significantly reduce the image signal-to-noise ratio, directly affecting the final measurement accuracy; how to establish a high-precision and high-stability pointer offset estimation method has become a key issue in promoting the practical application of weak measurement technology. Summary of the Invention

[0004] Aiming at the deficiencies of the existing technology, the present invention proposes a method for high-precision estimation of pointer offset in a weak measurement system to solve the technical problems that the pointer offset estimation method in the existing technology is limited by various noise sources and interference factors, and the accuracy is not high enough and the stability is not good enough.

[0005] The technical solution adopted by the present invention is as follows:

[0006] In the first aspect, a method for high-precision estimation of pointer offset in a weak measurement system is provided, including the following steps: inputting the measured spot image into a spot image denoising model for denoising processing to obtain a denoised spot image;

[0007] Calculating the pointer offset according to the denoised spot image.

[0008] Further, the construction method of the spot image denoising model includes: constructing a multi-modal pointer according to the centroid position and energy characteristics of the spot;

[0009] Improving the traditional U-Net network based on the residual structure, embedding the multi-modal pointer into the loss function to optimize the U-Net neural network improved by the residual structure, and obtaining the spot image denoising model.

[0010] Further, constructing a multi-modal pointer according to the centroid position and energy characteristics of the spot includes:

[0011] Using the gray centroid method to determine the centroid position of the spot;

[0012] Extract the energy feature of the light spot based on the gray-level co-occurrence matrix;

[0013] Construct a multi-modal pointer according to the centroid position and energy feature of the light spot.

[0014] Furthermore, when using the gray-level centroid method to determine the centroid position of the light spot, the centroid position of the light spot is determined by solving the weighted average of the pixel gray values of the light spot image.

[0015] Furthermore, when extracting the energy feature of the light spot based on the gray-level co-occurrence matrix, the gray-level co-occurrence matrix records the joint probability distribution of the gray values of pixel pairs in the light spot image at a specific direction and distance. The texture energy parameter is based on the statistical characteristics of the gray-level co-occurrence matrix and is mathematically represented as the sum of the squares of the elements of the normalized co-occurrence matrix; the monotonicity interval of the centroid offset trajectory is half of the entire phase interval.

[0016] Furthermore, fuse the centroid position and energy feature of the light spot according to the following formula to construct a multi-modal pointer:

[0017] Pointer=sign(C x -c center )×(Energy-Energy min )

[0018]

[0019] In the above formula, Pointer represents the multi-modal pointer, C x represents the horizontal axis coordinate of the light spot centroid, c center represents the geometric center coordinate of the light spot image, Energy min represents the energy value when the centroid coordinate is at the geometric center of the light spot.

[0020] Furthermore, the light spot image denoising model uses U-Net as the backbone network, adopts a residual structure to reconstruct the downsampling module in the encoding path into a cross-layer connection unit, and establishes a stable path for gradient propagation through residual mapping; through multi-layer stacked hierarchical convolution operations, fuse the local noise distribution and global intensity feature of the light spot, and incorporate the multi-modal pointer into the loss function for backpropagation to optimize the network parameters.

[0021] Furthermore, the residual structure is the ResNet-34 structure. The input feature generates a residual feature through the residual mapping function and is fused with the original feature through the cross-layer connection mechanism; when the residual function approaches zero, the mapping relationship turns into an identity mapping; the gradient calculation formula during backpropagation is:

[0022]

[0023] In the above formula, H(x) represents the residual feature, x represents the input feature, and F(x) represents the residual mapping function.

[0024] Furthermore, during the training of the spot image denoising model, the training objective is to minimize the pointer calculation error, and the network parameters Θ are as follows:

[0025]

[0026] In the above formula, Θ is the network parameter, and f c is the pointer calculation function, represents the neural network, and I raw is the actual spot intensity, I0 represents the spot without noise, and the loss function L uses the 2-norm constraint:

[0027] L = ‖Pointer0 - Pointer raw ‖2

[0028] In the calculation formula of the loss function L, Pointer0 is the multi-modal pointer of the noise-free spot, and Pointer raw is the multi-modal pointer of the denoised spot.

[0029] In the second aspect, a weak measurement system is provided for the high-precision estimation method of the pointer offset of the weak measurement system described in the first aspect, including: a pre-selection module composed of polarization optical elements, a transverse shear differential optical path module, and a post-selection module; the physical quantity to be measured is manifested as an observable spot image through the coupling effect in the weak measurement system.

[0030] As can be seen from the above technical solutions, the beneficial technical effects of the present invention are as follows:

[0031] The spot image denoising model uses residual mapping to ensure the stable propagation of gradients, fuses local noise and global features through hierarchical convolution, and constructs a loss function based on the multi-modal pointer for backpropagation to optimize the network architecture, realizing the dynamic coupling of data-driven and physical mechanisms. It has high estimation accuracy and good stability for the pointer offset, provides a highly robust pointer offset estimation framework for the weak measurement system, and at the same time can lay a technical foundation for the engineering deployment of the multi-parameter collaborative measurement system. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the specific embodiments of the present invention or the technical solutions in the prior art, the following will briefly introduce the drawings required for the description of the specific embodiments or the prior art. In all the drawings, similar elements or parts are generally identified by similar reference numerals. In the drawings, the elements or parts are not necessarily drawn to scale.

[0033] Figure 1 is a schematic diagram of the architecture of the weak measurement system according to the embodiment of the present invention;

[0034] Figure 2 Schematic diagram of the relationship between pixel pairs of the gray-level co-occurrence matrix according to an embodiment of the present invention;

[0035] Figure 3 Schematic diagram of the index offset trajectory according to an embodiment of the present invention;

[0036] Figure 4 Neural network architecture diagram of the spot image noise reduction model according to an embodiment of the present invention;

[0037] Figure 5 Schematic diagram of the residual module for improving the U-Net network according to an embodiment of the present invention;

[0038] Figure 6 Comparison diagram of the measured spot and the spot after being processed by the spot image noise reduction model according to an embodiment of the present invention;

[0039] Figure 7 Schematic diagram of the influence curve of the spot image noise reduction model on the dynamic distribution of the spot center of multiple physical quantities according to an embodiment of the present invention;

[0040] Figure 8 Flowchart of the high-precision estimation method for the pointer offset of the weak measurement system according to an embodiment of the present invention. Detailed implementation manners

[0041] Hereinafter, embodiments of the technical solution of the present invention will be described in detail with reference to the accompanying drawings. The following embodiments are only used to illustrate the technical solution of the present invention more clearly, so they are only examples and cannot be used to limit the protection scope of the present invention.

[0042] It should be noted that unless otherwise specified, the technical terms or scientific terms used in this application should have the ordinary meanings understood by those skilled in the art to which the present invention belongs.

[0043] Embodiment

[0044] The weak measurement system described in this embodiment is as Figure 1 shown. This system mainly consists of a pre-selection module composed of polarization optical elements, a transverse shear differential optical path module, and a post-selection module. The physical quantity to be measured is manifested as an observable spot image through a series of coupling effects.

[0045] The high-precision estimation method for the pointer offset of the weak measurement system provided in this embodiment includes the following steps:

[0046] Input the measured spot image into the spot image noise reduction model for noise reduction processing to obtain the noise-reduced spot image;

[0047] Calculate the pointer offset according to the noise-reduced spot image.

[0048] In a weak measurement system, the spot image serves as the core representation carrier of the pointer offset. Its physical essence is the observable presentation after the physical quantity to be measured is coupled and converted by the optical system. Specifically, the minute changes in the physical quantity to be measured are converted into the spatial intensity distribution characteristics of the light through modulating the optical parameters. These distribution characteristics (such as centroid offset and texture change, etc.) are the physical mappings of the pointer offset. This conversion mechanism enables the conversion of the minute physical quantity changes that are originally difficult to directly observe into the light intensity distribution characteristics that can be quantitatively analyzed, providing an effective means for observing minute physical quantities. However, in the actual measurement process, interference factors such as noise and non-linearity will significantly reduce the signal-to-noise ratio of the image and affect the final measurement accuracy. Therefore, to improve the measurement accuracy of the pointer offset, the core is to improve the image quality (i.e., denoise and enhance the image), optimize the image, so as to serve the calculation of the pointer offset (parameters such as centroid, energy characteristics, etc., all of which characterize the distribution changes of the image). In a specific implementation manner, the pointer offset is calculated based on the denoised spot image, and its implementation form is not limited. The spot image is the projection of the pointer, and the change in its position or shape reflects the offset of the pointer.

[0049] The spot image denoising model of this embodiment is constructed in the following manner:

[0050] S1. Construct a multi-modal pointer based on the centroid position and energy characteristics of the spot

[0051] The inventors of this application found through experiments that when the spot undergoes large distortion or the physical quantity to be measured exceeds a certain range, the linear relationship and one-to-one mapping relationship between the centroid offset and the physical quantity are damaged, resulting in a limited measurement range. While the energy characteristics can maintain monotonicity within a larger physical quantity range, thus expanding the measurement range. This step is divided into the following sub-steps:

[0052] S11. Determine the centroid position of the spot through the gray centroid method

[0053] The gray centroid method determines the centroid position of the spot by solving the weighted average of the pixel gray values of the spot image. In a specific implementation manner, assume that the size of the spot image collected by the image acquisition device is M×N, the pixel coordinates are (u, v), and the gray value is I(u, v). Then the calculation formula for the centroid coordinates (x c , y c ) is:

[0054]

[0055] S12. Extract the energy characteristics of the spot based on the gray-level co-occurrence matrix

[0056] Quantify the texture characteristics of the spot image by constructing a gray-level co-occurrence matrix. The gray-level co-occurrence matrix records the joint probability distribution of the gray values of pixel pairs in the spot image at a specific direction and distance. The texture energy parameter is based on the statistical characteristics of the gray-level co-occurrence matrix and is mathematically represented as the sum of the squares of the elements of the normalized co-occurrence matrix, as shown in the following equation:

[0057] Energy=∑ i,j p θ,d (i,j) 2

[0058] In the above equation, Energy represents the energy feature, (i,j) represents the element position of the gray-level co-occurrence matrix, and p θ,d (i,j) 2 represents the square of the element at the (i,j) position of the gray-level co-occurrence matrix of the image obtained at the θ direction and the d-step distance.

[0059] In some embodiments, the specific direction described in this step is the θ direction, and the specific distance is the d-step distance, as follows:

[0060] If the grayscale image contains M gray levels, its gray-level co-occurrence matrix is a square matrix with M rows and M columns. The elements of the gray-level co-occurrence matrix describe the occurrence probability that a pair of pixels with gray levels i and j respectively are separated by d pixels (picture elements) in the θ direction (two-way) of the grayscale image, which can specifically reflect the texture characteristics of the image, where i and j satisfy the fixed position relationship d=(Δx,Δy), and are represented by p θ,d (i,j)(i,j = 0,1,…,T - 1), where T is the gray level. After specifying the position relationship d, it is also necessary to specify the generation direction θ of the gray-level co-occurrence matrix. Usually, θ takes 0°, 45°, 90°, and 135°, as Figure 2 shown:

[0061] The gray-level co-occurrence matrix p θ,d (i,j) in a certain direction has the following expression:

[0062] p 0°,d (i,j)=|{[(k,l),(m,n)]∈D:k - m=0,|l - n|=d,f(k,l)=i,f(m,n)

[0063] =j}|

[0064] p 45°,d (i,j)=|{[(k,l),(m,n)]

[0065] ∈D:(k - m=d,l - n= - d)or(k - m= - d,l - n=d),

[0066] f(k,l)=i,f(m,n)=j}|

[0067] p 90°,d (i,j)=|{[(k,l),(m,n)]∈D:km=d,|ln|=0,f(k,l)=i,f(m,n)

[0068] =j}|

[0069] p 135°,d (i,j)=|{[(k,l),(m,n)]

[0070] ∈D:(km=d,ln=-d)or(km=-d,ln=-d),

[0071] f(k,l)=i,f(m,n)=j}|

[0072] In the above formula, f(k,l) and f(m,n) represent a pair of pixels at the pixel positions (k,l) and (m,n) of the image, k and m are the pixel coordinates on the horizontal axis, and l and n are the pixel coordinates on the vertical axis; (i,j) represents the position element of the image grayscale co-occurrence matrix, d represents the distance between pixels, and D represents the set of all pixels that satisfy a specific position relationship.

[0073] When using energy features, the monotonicity interval of the centroid shift trajectory is half of the entire phase interval, and the monotonicity interval is nearly twice that of the centroid shift trajectory. Compared with the grayscale centroid method, the measurement range can be increased by nearly 1 times.

[0074] In a specific implementation manner, steps S11 and S12 are executed in any order and can be performed simultaneously.

[0075] S13. Construct a multi-modal pointer based on the centroid position and energy characteristics of the light spot

[0076] Considering that the light spot has symmetry with respect to the phase, the energy value of the light spot image is completely consistent under the phase parameter with the same absolute value. The center of mass position and energy characteristics of the light spot are fused according to the following formula to construct a multi-modal pointer:

[0077] Pointer = f c (I) = sign (C x -c center )×(Energy-Energy min )

[0078]

[0079] In the above formula, Pointer represents a multimodal pointer, f c For pointer calculation function, C x represents the horizontal axis coordinate of the center of mass of the light spot, ccenter represents the geometric center coordinates of the spot image, Energy min represents the energy value when the centroid coordinates are at the geometric center of the spot.

[0080] Through experimental data Figure 3 It shows that the multi-modal pointer that fuses the centroid position and energy characteristics of the spot exhibits strict monotonicity in a wide dynamic range, and its fitting linearity is close to the ideal linear response. The two work together to achieve the mapping relationship between the spot intensity distribution and the pointer parameters in a wide measurement range.

[0081] S2. Construct a loss function based on the multi-modal pointer, and optimize the improved U-Net neural network to obtain a spot image denoising model

[0082] During the measurement process, the actual spot intensity I raw is composed of the noise-free spot I0 and the noise n superimposed, as shown in the following formula:

[0083] I raw = I0 + n

[0084] Through the neural network denoise the noisy spot I raw as follows:

[0085]

[0086] can generate an approximately noise-free spot When using this spot to calculate the pointer offset, various noise interferences can be removed as much as possible, making the calculated pointer offset more accurate and stable.

[0087] The spot image denoising model of this embodiment is obtained by training a neural network. During training, its training objective is to minimize the pointer calculation error. The network parameters Θ are as follows:

[0088]

[0089] In the above formula, Θ is the network parameter, and f c is the pointer calculation function, represents the neural network, I raw is the actual spot intensity, I0 represents the noise-free spot, and the loss function L uses the 2-norm constraint:

[0090] L = ‖Pointer0 - Pointer raw ‖2

[0091] In the calculation formula of the loss function L, Pointer0 is the multi-modal pointer of the noise-free spot, and Pointer raw is the multi-modal pointer of the denoised spot.

[0092] The neural network selected for constructing the spot image denoising model in this embodiment has an architecture as follows Figure 4 shown. Taking the original U-Net as the core network, it is improved using residuals, and then optimized by embedding the multi-modal pointers constructed above into the loss function.

[0093] In the scenario of spot noise reduction in a weak measurement system, the limitations of the traditional U-Net gradually emerge. In the encoding path, each downsampling module extracts features only through a single-layer 3×3 convolution, making it difficult to fully capture the multi-scale distribution characteristics of spot noise, such as the coupling effect between high-frequency shot noise and low-frequency background interference. If the network depth is simply increased to enhance the feature extraction ability, the stacked convolutional layers will exacerbate the gradient attenuation phenomenon, resulting in slow update of shallow-layer parameters, and the deep network is prone to degenerate into an inefficient identity mapping, manifested as the coexistence of blurred spot edges and residual noise after denoising. To address the above problems, the present invention proposes a deep network architecture that combines a residual structure and physical constraints. A hierarchical expansion residual enhancement strategy is proposed for the poor gradient stability and feature extraction limitations of the traditional U-Net architecture. The model captures the light intensity distribution characteristics of different frequency bands through multi-scale convolutional kernels, and combines the physical equation-constrained spot propagation law to achieve the coordinated enhancement of high-frequency noise component suppression and low-frequency effective signals.

[0094] The residual module is as follows Figure 5 shown. The residual learning mechanism of the residual module fuses the input features with the features after non-linear transformation through the cross-layer feature reuse strategy, alleviating the training difficulties of deep networks. Its mathematical expression is:

[0095] H(x) = F(x) + x

[0096] where the input feature x generates the residual feature H(x) through the residual mapping function F(x), and finally fuses with the original feature through the cross-layer connection mechanism to achieve the coordinated optimization of shallow-layer details and deep-layer semantics. When the residual function F(x) approaches zero, the module degenerates into an identity mapping, ensuring that the network performance does not deteriorate. This design enables the deep model to be gradually optimized by stacking residual units, rather than directly fitting complex transformations. The gradient calculation formula during backpropagation is:

[0097]

[0098] In the above formula, 1 comes from the derivative contribution of the skip connection. Even if the gradient of the residual function F(x) approaches 0 due to weight decay, the gradient can still be stably transmitted through the identity term 1, ensuring that the deep-layer parameters can be effectively updated.

[0099] First, in view of the gradient stability and feature extraction limitations of the traditional U-Net architecture, the present invention proposes a hierarchical expansion residual enhancement strategy. Using the residual structure design of ResNet-34, the downsampling module in the encoding path is reconstructed into a cross-layer connection unit, and a stable path for gradient propagation is established through residual mapping, effectively suppressing the gradient attenuation phenomenon in the training of deep networks. Through 34 layers of stacked hierarchical convolution operations, the local noise distribution and global intensity features of the light spot are fused, and combined with the shallow feature reuse mechanism of cross-layer skip connections, significantly enhancing the multi-scale semantic expression ability and detail reconstruction efficiency; at the same time, the multi-modal pointer constructed in step S1 is incorporated into the loss function for backpropagation to optimize network parameters, realizing the deep integration of physical mechanism and data-driven methods to meet the high-precision requirements of light spot noise reduction.

[0100] When training the improved U-Net neural network, the training set is constructed in the following way:

[0101] 1. Generate ideal light spot images

[0102] Based on the measured light spot images with noise collected by the image acquisition device, the two-dimensional light spot distribution function is used for least squares fitting to determine the fitting parameter range, and ideal light spot images are generated according to the fitting parameters. In a specific embodiment, the expression of the two-dimensional light spot distribution function is as follows:

[0103]

[0104] Among them, I(x, y) represents the pixel intensity at the pixel position (x, y) of the light spot image, x is the pixel coordinate in the horizontal axis direction, and y is the pixel coordinate on the vertical axis; the fitting parameters g and σ are set according to prior knowledge, and the value range of the fitting parameter is selected between (-10, 10) in this embodiment, and e represents the natural constant.

[0105] 2. Inject noise into the ideal light spot images to obtain simulated light spot images simulating the measured light spot images. By different noise injection methods, the types of noise in the simulated light spot images are increased.

[0106] (1) Perform two-dimensional wavelet transform on the measured light spot image to obtain multi-scale subband coefficients. The maximum selection method is used to weight and fuse the subband coefficients to generate synthetic coefficients with both ideal structure and real noise characteristics, and then the simulated light spot image after injecting noise is generated through inverse wavelet transform.

[0107] (2) Adopt denoising residual modeling. Estimate the noise residual of the measured light spot through the non-local means denoising algorithm, and add the extracted noise to the ideal light spot to generate high-fidelity simulated light spot images.

[0108] (3) Generate noise samples using a generative adversarial network based on the simulated spot image, and superimpose the noise samples on the ideal spot to construct a training data pair.

[0109] Use the dataset constructed above to train the proposed spot image denoising model, and then serve for spot denoising processing, and finally calculate the spot pointer offset. To evaluate the noise suppression ability of the spot image denoising model for the system, Figure 6 The comparison effect before and after spot image processing is shown. The left one is the original morphological features of the measured spot. The gradient mutation caused by its edge sharpening, the spatial non-uniform distribution of discrete noise points, and the local contrast abnormality caused by texture disorder significantly affect the stability of centroid positioning (pointer calculation). After being processed by the spot image denoising model, the spot morphological features are as Figure 6 shown in the right one. The spot edge has a smooth transition and the noise base is uniform, which fully shows that the processed spot has a balance optimization mechanism between maintaining the integrity of geometric features and noise robustness.

[0110] To verify the noise suppression efficiency of the spot image denoising model of this embodiment in a complex multi-physical field coupling scenario, the performance improvement of the estimation method of this embodiment is evaluated through traditional centroid positioning. The following experiments are specifically carried out:

[0111] Through an image acquisition device, collect a 10-second time-series noise spot dataset for performance evaluation; Figure 7 The optimization process of the statistical characteristics of centroid positioning is shown: the standard deviation mean of the original centroid distribution (solid curve) is 0.557, and after being processed by the technical solution of this embodiment (dashed curve), the standard deviation is significantly reduced to 0.302, with a decrease of 45.8%. The experiment shows that the technical solution of this embodiment effectively suppresses cross-interference noise through the joint optimization of cross-scale feature decoupling and physical law constraints, improves the time-domain stability by 25.5%, verifies its decoupling ability for cross-interference noise, provides a reliable data source for the estimation of the pointer offset of a weak measurement system, and provides a highly robust solution for the engineering deployment of a multi-parameter weak measurement system.

[0112] 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 them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the various embodiments of the present invention, and they should all be covered by the scope of the claims and the description of the present invention.

Claims

1. A high-precision estimation method for the pointer offset of a weak measurement system, characterized in that It includes the following steps: Input the measured spot image into the spot image denoising model for denoising processing to obtain the denoised spot image; Calculate the pointer offset according to the denoised spot image.

2. The high-precision estimation method for the pointer offset of the weak measurement system according to claim 1, wherein The construction method of the spot image denoising model includes: Construct a multimodal pointer according to the centroid position and energy characteristics of the spot; Improve the traditional U-Net network based on the residual structure, embed the multimodal pointer into the loss function to optimize the U-Net neural network improved by the residual structure, and obtain the spot image denoising model.

3. The high-precision estimation method for the pointer offset of the weak measurement system according to claim 2, wherein Constructing a multimodal pointer according to the centroid position and energy characteristics of the spot includes: Use the gray centroid method to determine the centroid position of the spot; Extract the energy characteristics of the spot based on the gray-level co-occurrence matrix; Construct a multimodal pointer according to the centroid position and energy characteristics of the spot.

4. The high-precision estimation method for the pointer offset of the weak measurement system according to claim 3, characterized in that When using the gray centroid method to determine the centroid position of the spot, the centroid position of the spot is determined by solving the weighted average of the pixel gray values of the spot image.

5. The high-precision estimation method for the pointer offset of the weak measurement system according to claim 3, characterized in that When extracting the energy characteristics of the spot based on the gray-level co-occurrence matrix, the gray-level co-occurrence matrix records the joint probability distribution of pixel pairs in the spot image at a specific direction and distance. The texture energy parameter is based on the statistical characteristics of the gray-level co-occurrence matrix and is mathematically characterized as the sum of the squares of the elements of the normalized co-occurrence matrix; the monotonicity interval of the centroid offset trajectory is half of the entire phase interval.

6. The method for high-precision estimation of pointer offset in the weak measurement system according to claim 3, wherein Construct a multimodal pointer by fusing the centroid position and energy characteristics of the spot according to the following formula: Pointer=sign(C x -ccenter)×(Energy-Energy min ) In the above formula, Pointer represents the multimodal pointer, C x represents the horizontal axis coordinate of the centroid of the light spot, c center represents the geometric center coordinate of the light spot image, Energy min represents the energy value when the centroid coordinate is at the geometric center of the light spot.

7. The high-precision estimation method for the pointer offset of the weak measurement system according to claim 2, wherein The spot image denoising model uses U-Net as the backbone network, adopts the residual structure to reconstruct the downsampling module in the encoding path into a cross-layer connection unit, and establishes a stable path for gradient propagation through residual mapping; through multi-layer stacked hierarchical convolution operations, fuse the local noise distribution and global intensity characteristics of the spot; integrate the multimodal pointer into the loss function for backpropagation to optimize the network parameters.

8. The method for high-precision estimation of pointer offset in the weak measurement system according to claim 7, characterized in that The residual structure is the ResNet-34 structure. The input feature generates a residual feature through the residual mapping function and is fused with the original feature through the cross-layer connection mechanism; when the residual function approaches zero, the mapping relationship becomes an identity mapping; the gradient calculation formula during backpropagation is: In the above formula, H(x) represents the residual feature, x represents the input feature, and F(x) represents the residual mapping function.

9. The method for high-precision estimation of pointer offset in the weak measurement system according to claim 2, wherein During the training of the spot image denoising model, the training objective is to minimize the pointer calculation error, and the network parameters Θ are as follows: In the above formula, Θ is a network parameter, and f c is a pointer calculation function, represents a neural network, and I raw is the actual spot intensity, I0 represents the spot without noise, and the loss function L uses a 2-norm constraint: L = ‖Pointer0 - Pointer raw ‖2 In the calculation formula of the loss function L, Pointer0 is the multi-modal pointer of the noise-free light spot, and Pointer raw is the multi-modal pointer of the denoised light spot.

10. A weak measurement system, characterized in that, For the high-precision estimation method of the pointer offset of the weak measurement system described in any one of claims 1-9, it includes: a pre-selection module composed of polarization optical elements, a transverse shear differential optical path module, and a post-selection module; the physical quantity to be measured is manifested as an observable spot image in the weak measurement system through the coupling effect.

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