Wide-field magnetic field imaging method based on sparse sampling and Bayesian estimation

Abstract

The invention provides a wide-field magnetic field imaging method based on sparse sampling and Bayesian estimation, and belongs to the field of magnetic field imaging. The method comprises the following steps: constructing an NV color center system, measuring and recording information of a magnetic field to be measured; selecting a small number of discrete sampling points to measure magnetic field intensity data in an imaging field of view of a measured area; the method comprises the following steps of: constructing an error correlation function among pixel points in a measured area, establishing a Bayesian estimation model, and predicting the magnetic field intensity of unmeasured pixel points in a full field of view by taking magnetic field intensity data of a small number of discrete sampling points as observed quantity to obtain a preliminarily reconstructed magnetic field distribution image; selecting a plurality of reference points in the measured area, acquiring nominal magnetic field values and actually measured magnetic field values of the reference points, and calibrating the preliminarily reconstructed magnetic field distribution image by adopting a mean value proportion correction mode; on the premise that the number of sampling points is greatly reduced, magnetic field distribution reconstruction with high spatial resolution and high structural similarity is achieved, and therefore imaging efficiency and reliability are improved.

Description

Technical Field

[0001] This application relates to the fields of quantum precision measurement and magnetic field imaging technology, and in particular to a wide-field magnetic field imaging method based on sparse sampling and Bayesian estimation. Background Technology

[0002] Nitrogen-vacancy (NV) color centers are point defect structures in the diamond lattice, possessing a triplet ground state with spin S=1 and a zero-field split of approximately D=2π×2.88GHz. Through optical pumping and microwave control, the initialization, coherent manipulation, and optical readout of the NV spin state can be achieved, enabling highly sensitive detection of external physical quantities such as magnetic fields, electric fields, temperature, and strain.

[0003] In magnetic field measurement, magnetometers based on NV color centers have been widely used in nanoscale condensed matter system research, geological and mineral sample imaging, biomagnetic signal detection, and integrated circuit current and defect diagnosis. Existing spatially resolved magnetic imaging mainly falls into two categories: one is scanning imaging based on a single NV probe, which achieves nanoscale resolution by maintaining an extremely small detection distance, but requires point-by-point scanning, resulting in a long imaging time; the other is wide-field imaging based on NV assemblies, which achieves rapid imaging through parallel camera readout, but its spatial resolution is limited by the optical diffraction limit and the distance between the NV layer and the sample.

[0004] In many application scenarios that require both high resolution and high speed, traditional point scanning and full-sampling wide-field imaging still have significant contradictions in terms of acquisition time, data volume and subsequent processing complexity. Therefore, there is an urgent need to develop a new imaging strategy that can still achieve high-quality reconstruction with a limited number of sampling points. Summary of the Invention

[0005] To address the aforementioned technical issues, this application proposes a wide-field magnetic field imaging method based on sparse sampling and Bayesian estimation. This method achieves high spatial resolution and high structural similarity in magnetic field distribution reconstruction while significantly reducing the number of sampling points. Furthermore, it can further reduce systematic errors through reference point correction, thereby improving imaging efficiency and reliability.

[0006] The technical solution adopted in this application is: a wide-field magnetic field imaging method based on sparse sampling and Bayesian estimation, comprising the following steps:

[0007] Step S1: Construct a diamond magnetic field detection system containing NV color centers, optically excite the area to be measured, and apply a dynamic decoupling sequence that matches the AC magnetic field signal to be measured, so that the spins of the NV color centers record the magnetic field information to be measured during the evolution process;

[0008] Step S2: Within the imaging field of view of the area under test, select a small number of discrete sampling points, measure the NV fluorescence signal or population of each sampling point, and convert the measurement results into magnetic field strength data based on the phase accumulation model.

[0009] Step S3: Construct the error correlation function between each pixel in the measured area, establish a Bayesian estimation model, use the magnetic field strength data of a small number of discrete sampling points as the observation, predict the magnetic field strength of the unmeasured pixels in the entire field of view, and obtain a preliminary reconstructed magnetic field distribution image.

[0010] Step S4: Select several reference points in the measured area, obtain their nominal magnetic field values ​​and measured magnetic field values, and use the mean ratio correction method to calibrate the initially reconstructed magnetic field distribution image to obtain the corrected magnetic field imaging result.

[0011] Furthermore, the diamond magnetic field detection system containing NV color centers constructed in step S1 is a two-level model. The total Hamiltonian H(t) of the two-level subspace of the NV color centers under the interaction representation is expressed as:

[0012] ;

[0013] in, For Pauli matrices, This represents the detuning between the microwave frequency and the energy difference between the two energy levels. The term represents the interaction between the measured alternating magnetic field and the spin. For microwave control pulse Hamiltonian;

[0014] Interaction term between the measured alternating magnetic field and spin Represented as:

[0015] ;

[0016] in, The coupling strength of the alternating magnetic field. The angular frequency of the alternating magnetic field;

[0017] Under ideal conditions, when performing Ramsey measurements on NV spins using a dynamically decoupled sequence, the NV spin phase accumulation... Approximately:

[0018] ;

[0019] in, For measuring time.

[0020] Furthermore, in step S2, the population at each sampling point is measured, and the measurement results are converted into magnetic field strength data based on the phase accumulation model:

[0021] ;

[0022] in, The gyromagnetic ratio of NV electron spin enables the conversion from frequency to magnetic field amplitude.

[0023] Furthermore, Static non-uniform broadened noise With time-varying dynamic noise Together they constitute:

[0024] ;

[0025] Static non-uniform broadening noise Follows a mean of 0 and a standard deviation of The probability density function follows a Gaussian distribution. for:

[0026] ;

[0027] Dynamic noise Satisfying the Ornstein-Uhlenbeck process:

[0028] ;

[0029] in, For time infinitesimal elements, For the relevant time constant, Let be the noise diffusion constant. To obey A random variable.

[0030] Furthermore, the Bayesian estimation model in step S3 constructs the optimal linear unbiased prediction operator by defining the error correlation between the sampling points and the points to be predicted, which predicts the magnetic field strength. Represented as:

[0031] ;

[0032] in, Let be the two-dimensional coordinates of the pixel to be predicted. For the set of sampling points The measured magnetic field strength vector on the surface, The correlation matrix is ​​of dimension n×n, and its elements are composed of... Give, This is a correlation vector of dimension n×1. It is a column vector whose components are all 1. This is the overall mean obtained from the maximum likelihood estimation.

[0033] Furthermore, the correlation matrix By distance function The distance function is defined as follows:

[0034] ;

[0035] in, For the i-th sampling point, For the j-th sampling point, Let i be the value of the i-th sampling point in the k-th coordinate component. , All are weighting coefficients. The value range is [1, 2].

[0036] Furthermore, and The likelihood function L is determined by maximizing the sample likelihood function, and is expressed as:

[0037] ;

[0038] in, For the overall variance, The determinant of the correlation matrix is ​​given by the likelihood function, and the optimal correlation parameters are obtained by optimizing the likelihood function.

[0039] Furthermore, the mean correction in step S4 adopts a proportional correction method, and the specific implementation steps are as follows:

[0040] Select several reference points within the area to be measured. Obtain the nominal magnetic field at each reference point. Compared with the average value obtained by measurement Then any coordinate The corrected magnetic field strength Represented as:

[0041] ;

[0042] in, The uncorrected magnetic field strength is obtained from the Bayesian estimate.

[0043] Furthermore, the method can be used in wide-field magnetic field imaging platforms based on NV color centers, scanning NV magnetometers, superconducting quantum interference devices, and magnetic field sensing platforms.

[0044] The advantages of this application over the prior art are as follows: This application extracts the phase accumulation information of the AC magnetic field by applying a dynamic decoupling sequence to the NV ensemble system; it measures only a few sampling points within the imaging field of view and constructs a Bayesian estimation model based on the correlation function to predict the magnetic field strength of the unmeasured pixels; and it uses the proportional relationship between the nominal values ​​and measured values ​​of several reference points to make overall corrections to the prediction results, thereby obtaining magnetic field imaging results with high accuracy and high similarity under the condition of a small number of sampling points. Attached Figure Description

[0045] The following description, in conjunction with the accompanying drawings, further illustrates this application:

[0046] Figure 1 This is a flowchart illustrating the wide-field magnetic field imaging method based on sparse sampling and Bayesian estimation provided in the embodiments of this application.

[0047] Figure 2 This is a schematic diagram of the spatial distribution of sampling points within the imaging field of view in an embodiment of this application.

[0048] Figure 3 This is a schematic diagram comparing magnetic field images reconstructed by different methods in the embodiments of this application. In the figure, MABE stands for Mean-adjusted Bayesian estimation.

[0049] Figure 4 This is a schematic diagram illustrating the change in error distribution before and after the reference point ratio correction in the embodiments of this application.

[0050] Figure 5 This is a schematic diagram illustrating the impact of sparse sampling quantity on reconstruction quality in an embodiment of this application. Detailed Implementation

[0051] like Figures 1 to 5 As shown, this application provides a wide-field magnetic field imaging method based on sparse sampling and Bayesian estimation, including the following steps:

[0052] Step S1: Construct a diamond magnetic field detection system containing nitrogen-vacancy (NV) color centers, optically excite the region to be measured, and apply a dynamic decoupling sequence that matches the AC magnetic field signal to be measured, so that the spins of the NV color centers record the magnetic field information to be measured during the evolution process;

[0053] Step S2: Within the imaging field of view of the area under test, select only a small number of discrete sampling points, measure the NV fluorescence signal or population of each sampling point, and convert the measurement results into magnetic field strength data based on the phase accumulation model;

[0054] Step S3: Construct the error correlation function between each pixel in the measured area, establish a Bayesian estimation model, use the magnetic field strength data of a small number of discrete sampling points as the observation, predict the magnetic field strength of the unmeasured pixels in the entire field of view, and obtain a preliminary reconstructed magnetic field distribution image.

[0055] Step S4: Select several reference points in the measured area, obtain their nominal magnetic field values ​​and measured magnetic field values, and use the mean ratio correction method to calibrate the initially reconstructed magnetic field distribution image to obtain the corrected magnetic field imaging result.

[0056] The diamond magnetic field detection system containing nitrogen-vacancy (NV) color centers constructed in step S1 is an NV color center two-level model. The total Hamiltonian H(t) of the NV color center two-level system under the interaction representation is expressed as:

[0057] ;

[0058] in, For Pauli matrices, For microwave frequency and , The detuning between the two energy levels The term represents the interaction between the measured alternating magnetic field and the spin. For microwave control pulse Hamiltonian;

[0059] Interaction term between the measured alternating magnetic field and spin Represented as:

[0060] ;

[0061] in, The coupling strength of the alternating magnetic field. ω is the angular frequency of the alternating magnetic field.

[0062] Under ideal conditions, when performing Ramsey measurements on NV spins using a dynamically decoupled sequence, the NV spin phase accumulation... Approximately:

[0063] ;

[0064] in, For measuring time.

[0065] After the system is read out via the final π / 2 pulse, the change in the ground-state population over time satisfies:

[0066] ;

[0067] pass Angular frequency is obtained by frequency fitting of the time evolution curve. Then, the amplitude B of the AC magnetic field to be measured can be expressed as:

[0068] ;

[0069] in, The gyromagnetic ratio of NV electron spin enables the conversion from frequency to magnetic field amplitude.

[0070] Detuning of the NV color center system Static non-uniform broadened noise With time-varying dynamic noise Together they constitute:

[0071] ;

[0072] Static non-uniform broadening noise Follows a mean of 0 and a standard deviation of The probability density function follows a Gaussian distribution. for:

[0073] .

[0074] Dynamic noise Satisfying the Ornstein-Uhlenbeck process:

[0075] ;

[0076] in, For time infinitesimal elements, For the relevant time constant, Let be the noise diffusion constant. To obey A random variable.

[0077] Under the aforementioned noise conditions, by employing an optimized dynamic decoupling sequence to control the NV spin, the effective population contrast can be improved, thereby enhancing the sensitivity of magnetic field measurements.

[0078] The Bayesian estimation model in step S3 constructs the optimal linear unbiased prediction operator by defining the error correlation between the sampling points and the points to be predicted, which predicts the magnetic field strength. Represented as:

[0079] ;

[0080] in, Let be the two-dimensional coordinates of the pixel to be predicted. For the set of sampling points The measured magnetic field strength vector on the surface, The correlation matrix is ​​of dimension n×n, and its elements are composed of... Give, This is a correlation vector of dimension n×1. It is a column vector whose components are all 1. This is the overall mean obtained from the maximum likelihood estimation.

[0081] Correlation matrix By distance function The distance function is defined as follows:

[0082] ;

[0083] in, For the i-th sampling point, For the j-th sampling point, Let i be the value of the i-th sampling point in the k-th coordinate component. , These are the weighting coefficients. Take non-negative values. The value range is [1, 2]; and The likelihood function L is determined by maximizing the sample likelihood function, and is expressed as:

[0084] ;

[0085] in, For the overall variance, The determinant of the correlation matrix is ​​given by the likelihood function, and the optimal correlation parameters are obtained by optimizing the likelihood function.

[0086] In step S4, the mean correction uses a proportional correction method, specifically as follows:

[0087] Select several reference points within the area to be measured. Obtain the nominal magnetic field at each reference point. Compared with the average value obtained by measurement Then any coordinate The corrected magnetic field strength Represented as:

[0088] ;

[0089] in, The uncorrected magnetic field strength is obtained from Bayesian estimation; the proportional correction method can reduce systematic bias and improve the overall accuracy and structural similarity of the full-field imaging results.

[0090] The present application will be further described below with reference to different embodiments.

[0091] Example 1: AC magnetic field measurement based on NV set.

[0092] In this embodiment, the two-level subspace of the NV color center is considered. and Under the interaction representation, its total Hamiltonian H(t) can be expressed as:

[0093] .

[0094] in, This is the detuning amount between the microwave frequency and the energy difference between energy levels; This represents the interaction term between the AC magnetic field to be measured and the spin. This refers to the Hamiltonian of the microwave control pulse.

[0095] In an ideal scenario, when the dynamic decoupling pulse acts precisely near the zero point of the AC magnetic field, its equivalent modulation function can be approximated as: The phase accumulation of NV spins within one evolution cycle approximately satisfies:

[0096] .

[0097] The system was polarized to [specific value] using Ramsey measurements. The state undergoes coherent evolution, and the readout ground state population is obtained. satisfy:

[0098] .

[0099] In practical data processing, by... The oscillation angular frequency can be obtained by fitting the time series. Thus, the amplitude of the alternating magnetic field B is obtained:

[0100] ,

[0101] in denoted as NV electron spin gyromagnetic ratio.

[0102] When considering the effects of noise, detuning Static non-uniform broadened noise With dynamic noise Composed of multiple layers:

[0103] .

[0104] Among them, static noise Follows a Gaussian distribution:

[0105] ;

[0106] Dynamic noise Follows the Ornstein-Uhlenbeck process:

[0107] ;

[0108] in For the relevant time, It is the diffusion constant. The input is a zero-mean, unit-variance Gaussian random variable. By optimizing the pulse shape and phase of the dynamically decoupled sequence, the fidelity of the π pulse over a wide detuning range can be improved, thereby enhancing population contrast and magnetic field measurement sensitivity.

[0109] Example 2: Magnetic field image reconstruction based on sparse sampling and Bayesian estimation.

[0110] In wide-field imaging mode, the area to be measured is discretized into several pixels, with the pixel position represented by a two-dimensional coordinate x, and y(x) representing the magnetic field strength at that position. In actual measurement, only n sampling points s = {s1, s2, …, s} are used. n Measurements are taken on the field of view to obtain the observation vector y(s). To predict the magnetic field across the entire field of view, this application employs a Bayesian estimation model based on the correlation function.

[0111] Define any two points and The correlation of the prediction error is:

[0112] ,

[0113] in, Let be the distance function. Then, under the optimal linear unbiased estimation framework, for any unsampled point... Its predicted magnetic field strength It can be represented as:

[0114] ;

[0115] in, Let be the two-dimensional coordinates of the pixel to be predicted. For the set of sampling points The measured magnetic field strength vector on the surface, The correlation matrix is ​​of dimension n×n, and its elements are composed of... Give, This is a correlation vector of dimension n×1. It is a column vector whose components are all 1. This is the overall mean obtained from the maximum likelihood estimation.

[0116] To flexibly characterize spatial correlation, this application adopts a distance function in the following form:

[0117] ;

[0118] in, Let i be the value of the i-th sampling point in the k-th coordinate component. These are non-negative weighting coefficients. The value range is [1, 2]. The optimal value can be obtained by maximizing the likelihood function of the observed samples. and :

[0119] .

[0120] Example 3: Mean correction based on reference point.

[0121] Due to sampling errors and model approximation, predictions obtained directly from Bayesian estimation may contain systematic biases. To further improve imaging accuracy, this embodiment selects several reference points within the field of view. Its nominal magnetic field value is Under the same measurement conditions, the corresponding average measured value was obtained. .

[0122] Under the scaling correction strategy, for any pixel Predicted value The following corrections are made:

[0123] ;

[0124] in and These are the averages of the nominal and measured values ​​on the reference point set, respectively.

[0125] Simulation results show that after scaling correction, the error distribution of sampling points is more concentrated near zero, and the overall average absolute error and root mean square error are significantly reduced.

[0126] In summary, the method proposed in this application can reconstruct a dataset containing 10 data points with only a small number of sampling points. 4 High-resolution magnetic field images with pixel counts. Under typical smooth field distributions, the structure similarity index (SSIM) can exceed 0.999, while the mean absolute error and root mean square error remain within 10. -4 The magnitude of the sampling points increases as the number of sampling points increases, and the imaging edge contour and peak position further approximate the true distribution, with the error index continuously decreasing. This indicates that the method in this application can flexibly compromise between sampling cost and imaging quality.

[0127] The wide-field magnetic field imaging framework proposed in this application, based on sparse sampling and Bayesian estimation, does not rely on a large-scale training dataset and can be directly used for the rapid reconstruction of actual measurement data. It can also be extended to other magnetic field sensing platforms, providing a general approach for achieving fast, compact, and high-resolution quantum magnetic imaging.

[0128] This application is applicable to wide-field magnetic field imaging platforms based on NV color centers, and can also be extended to magnetic field sensing platforms such as scanning NV magnetometers, superconducting quantum interference devices (SQUIDs), Hall sensors, and magnetic tunnel junctions, to achieve fast, compact magnetic field imaging with high spatial resolution.

[0129] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A wide-field magnetic field imaging method based on sparse sampling and Bayesian estimation, characterized in that: Includes the following steps: Step S1: Construct a diamond magnetic field detection system containing NV color centers, optically excite the area to be measured, and apply a dynamic decoupling sequence that matches the AC magnetic field signal to be measured, so that the spins of the NV color centers record the magnetic field information to be measured during the evolution process; Step S2: Within the imaging field of view of the area under test, select a small number of discrete sampling points, measure the NV fluorescence signal or population of each sampling point, and convert the measurement results into magnetic field strength data based on the phase accumulation model. Step S3: Construct the error correlation function between each pixel in the measured area, establish a Bayesian estimation model, use the magnetic field strength data of a small number of discrete sampling points as the observation, predict the magnetic field strength of the unmeasured pixels in the entire field of view, and obtain a preliminary reconstructed magnetic field distribution image. Step S4: Select several reference points in the measured area, obtain their nominal magnetic field values ​​and measured magnetic field values, and use the mean ratio correction method to calibrate the initially reconstructed magnetic field distribution image to obtain the corrected magnetic field imaging result.

2. The wide-field magnetic field imaging method based on sparse sampling and Bayesian estimation according to claim 1, characterized in that: The diamond magnetic field detection system containing NV color centers constructed in step S1 is a two-level model. The total Hamiltonian H(t) of the two-level subspace of the NV color centers under the interaction representation is expressed as: ； in, For Pauli matrices, This represents the detuning between the microwave frequency and the energy difference between the two energy levels. The term represents the interaction between the measured alternating magnetic field and the spin. For microwave control pulse Hamiltonian; Interaction term between the measured AC magnetic field and spin Represented as: ； in, The coupling strength of the alternating magnetic field. The angular frequency of the alternating magnetic field; Under ideal conditions, when performing Ramsey measurements on NV spins using a dynamically decoupled sequence, the NV spin phase accumulation... Approximately: ； in, For measuring time.

3. The wide-field magnetic field imaging method based on sparse sampling and Bayesian estimation according to claim 2, characterized in that: In step S2, the population at each sampling point is measured, and the measurement results are converted into magnetic field strength data based on the phase accumulation model. ； in, The gyromagnetic ratio of NV electron spin enables the conversion from frequency to magnetic field amplitude.

4. The wide-field magnetic field imaging method based on sparse sampling and Bayesian estimation according to claim 2, characterized in that: Static non-uniform broadened noise With time-varying dynamic noise Together they constitute: ； Static non-uniform broadening noise Follows a mean of 0 and a standard deviation of The probability density function follows a Gaussian distribution. for: ； Dynamic noise Satisfying the Ornstein-Uhlenbeck process: ； in, For time infinitesimal elements, For the relevant time constant, Let be the noise diffusion constant. To obey A random variable.

5. The wide-field magnetic field imaging method based on sparse sampling and Bayesian estimation according to claim 1, characterized in that: The Bayesian estimation model in step S3 constructs the optimal linear unbiased prediction operator by defining the error correlation between the sampling points and the points to be predicted, which predicts the magnetic field strength. Represented as: ； in, Let be the two-dimensional coordinates of the pixel to be predicted. For the set of sampling points The measured magnetic field strength vector on the surface, Let be an n×n correlation matrix, whose elements are formed by... Give, This is a correlation vector of dimension n×1. It is a column vector whose components are all 1. This is the overall mean obtained from the maximum likelihood estimation.

6. The wide-field magnetic field imaging method based on sparse sampling and Bayesian estimation according to claim 5, characterized in that: Correlation matrix By distance function The distance function is defined as follows: ； in, For the i-th sampling point, For the j-th sampling point, Let i be the value of the i-th sampling point in the k-th coordinate component. , All are weighting coefficients. The value range is [1, 2].

7. A wide-field magnetic field imaging method based on sparse sampling and Bayesian estimation according to claim 6, characterized in that: and The likelihood function L is determined by maximizing the sample likelihood function, and is expressed as: ； in, For the overall variance, The determinant of the correlation matrix is ​​given by the likelihood function, and the optimal correlation parameters are obtained by optimizing the likelihood function.

8. A wide-field magnetic field imaging method based on sparse sampling and Bayesian estimation according to claim 7, characterized in that: In step S4, the mean correction adopts a proportional correction method, and the specific implementation steps are as follows: Select several reference points within the area to be measured. Obtain the nominal magnetic field at each reference point. Compared with the average value obtained by measurement Then any coordinate The corrected magnetic field strength Represented as: ； in, The uncorrected magnetic field strength is obtained from the Bayesian estimate.

9. A wide-field magnetic field imaging method based on sparse sampling and Bayesian estimation according to any one of claims 1-8, characterized in that: The method can be used in wide-field magnetic field imaging platforms based on NV color centers, scanning NV magnetometers, superconducting quantum interference devices, and magnetic field sensing platforms.

Images