Self-shielding shimming coil system in chip atom magnetometer and design method

Abstract

The invention discloses a self-shielding shimming coil system in a chip atom magnetometer and a design method, provides a shimming coil which is composed of two pairs of biplanar coils and has a self-shielding effect, and belongs to the technical field of magnetic field control. The design of the double-plane coil is convenient to install, and is beneficial to being integrated in a chip atom magnetometer. On the basis of a weighting algorithm and SVD decomposition, the coil design gives consideration to the magnetic field uniformity of a high shimming area and the magnetic field attenuation of a self-shielding area at the same time, meanwhile, the problem that the solution of a stream function coefficient matrix is unstable due to the morbidity of an intermediate coefficient matrix is solved, the coil design precision is improved, and the design cost is reduced. The problem of signal crosstalk between chip atom magnetometer array probes is solved, and the chip atom magnetometer array probe array can adapt to the fields of chip atom magnetometers, array type heart and brain magnetic measurement, miniaturized biological magnetic imaging devices and the like.

Description

Self-shielded shimming coil system and design method in chip-based atomic magnetometer Technical Field

[0001] This invention relates to a self-shielded shimming coil system and its design method in a chip-based atomic magnetometer, belonging to the field of magnetic field manipulation technology. It meets the high requirements for magnetic field uniformity in the shimming region and magnetic field attenuation performance in the self-shielded region, and is applicable to chip-based atomic magnetometers, array-type cardiac and cerebrovascular magnetic measurement, and miniaturized biomagnetic imaging devices. Background Technology

[0002] Precision measurements in engineering fields such as chip-based atomic magnetometers, array-type magnetic field measurement of the heart and brain, and miniaturized biomagnetic imaging devices rely on magnetic fields with high uniformity and high stability.

[0003] In practical applications, array-type magnetic field sensing probes are prone to signal crosstalk, which can reduce the uniformity of the magnetic field generated by the coil and affect its performance. Self-shielded shimming coils are used to further overcome this signal interference. The uniformity of the magnetic field in the shimming region and the attenuation of the magnetic field in the self-shielded region are important performance indicators of self-shielded shimming coils and are key to achieving high-precision magnetic field control.

[0004] Existing self-shielded shimming coil designs are generally based on the inverse solution of the stream function. However, due to the ill-conditioned intermediate coefficient matrix, the solution of the stream function coefficient matrix is ​​unstable, affecting the non-uniformity of the magnetic field in the shimming region and the attenuation of the magnetic field in the self-shielded region, thus reducing the coil's performance. This invention addresses these problems by employing a combination of weighted algorithms and singular value decomposition to solve the instability problem in the solution of the stream function coefficient matrix caused by the ill-conditioned intermediate coefficient matrix. This approach balances the uniformity of the magnetic field in the shimming region and the attenuation of the magnetic field in the self-shielded region, improving the coil's performance. Furthermore, this invention uses the inverse solution method for the coil, taking the atomic magnetometer's gas chamber as the target shimming region. Considering the design complexity and the influence of current proximity effect on the magnetic field, an appropriate stream function design order is selected. The fabrication and usability of the miniature self-shielded shimming coil are fully considered, allowing it to be fabricated into a flexible PCB coil that can be integrated into a chip-based atomic magnetometer. This invention employs a planar coil structure, solving the problems of complex structure and inconvenient installation of existing self-shielded shimming coils. Summary of the Invention

[0005] This invention addresses the shortcomings of existing technologies by proposing a self-shielded shimming coil system and its design method for chip-based atomic magnetometers. By combining a weighted algorithm and singular value decomposition, the ill-conditioned intermediate coefficient matrix problem in the inverse stream function solution is solved, improving the stability of the stream function coefficient matrix solution. This approach balances the uniformity of the magnetic field in the shimming region and the attenuation of the magnetic field in the self-shielding region, enhancing the coil's performance and enabling its application in chip-based atomic magnetometers. The self-shielded shimming coil system designed by this invention consists of two pairs of biplane coils, reducing coil size and facilitating installation compared to Helmholtz coils, even allowing for integration into chip-based devices.

[0006] The technical solution of the present invention is as follows:

[0007] A self-shielding shimming coil system and design method in a chip-based atomic magnetometer, characterized by comprising: simplifying the chip-based atomic magnetometer chamber into a cube model with side length D, and establishing a coordinate system XYZ with the center point of the chip-based atomic magnetometer chamber as the origin. Using the chip-based atomic magnetometer chamber as the target shimming region, a cubic shimming target region is constructed with the origin as the center point, the half-side length of the cube being D. A cylindrical self-shielding region is constructed with the y-axis as the central axis, the radius of the cylinder being R, and the half-height of the cylinder being H. The cube is placed within an inner dual-plane coil, and the inner dual-plane coil is placed within an outer dual-plane coil. The inner dual-plane coil is a square with side length L1, and includes an inner negative direction plane coil and an inner positive direction plane coil. The inner negative direction plane coil is located in the z=-a1 plane, and the inner positive direction plane coil is located in the z=a1 plane, where a1 is the distance between the inner negative direction plane coil and the outer positive direction plane coil. The inner positive direction plane coil has a half-spacing. The outer double-plane coil is a square with a side length of L2. The outer double-plane coil includes an outer negative direction plane coil and an outer positive direction plane coil. The outer negative direction plane coil is located in the z=-a2 plane, and the outer positive direction plane coil is located in the z=a2 plane, where a2 is the half-spacing between the outer negative direction plane coil and the outer positive direction plane coil. A uniform field target point distribution is set in the cube, and a self-shielding target point distribution is set on the cylindrical surface. The weighted intermediate calculation matrix WA is obtained by multiplying the weighted diagonal matrix W and the intermediate function coefficient matrix A. The stream function coefficient matrix P is obtained by performing SVD decomposition and truncation on WA. mn Using P mn The flow function curve of the dual-plane coil is obtained, and the surface current is discretized into multiple wire segments to obtain the design result of the dual-plane coil.

[0008] Includes the following steps:

[0009] Step 1: Uniformly select target field points for uniform field selection within the cube, and preset the target magnetic field of each target field point to B_target; uniformly select shielding target field points on the cylindrical surface, and preset the target magnetic field of each shielding target field point to 0.01. B_target;

[0010] Step 2: Obtain the current density function based on the stream function and its symmetry, and calculate the magnetic field magnitude using the Biot-Savart law. The calculation formula is as follows:

[0011]

[0012]

[0013]

[0014]

[0015]

[0016]

[0017]

[0018]

[0019] in M is the magnitude of the magnetic field generated by the inner positive-direction planar coil in the X direction, where M is the mode order in the X direction, m is the index, N is the mode order in the Y direction, n is the index, and A is the magnetic field. mn1 P is the magnetic field response parameter of the inner positive direction planar coil. mn1 These are the current function coefficients of the inner dual-plane coils. The inner positive-direction plane coil and the inner negative-direction plane coil have the same current function coefficients. A is the magnitude of the magnetic field generated by the inner negative direction planar coil in the X direction. mn2 These are the magnetic field response parameters of the inner negative direction planar coil. B is the magnitude of the magnetic field generated by the outer positive-direction planar coil in the X direction. mn1 P is the magnetic field response parameter of the outer positive direction planar coil. mn2 These are the current function coefficients of the inner dual-plane coils. The inner positive-direction plane coil and the inner negative-direction plane coil have the same current function coefficients. B is the magnitude of the magnetic field generated by the outer negative-direction planar coil in the X direction. mn2 B is the magnetic field response parameter of the outer negative direction planar coil. x Let A be the total magnetic field magnitude of a target point in the X direction. mn B is the magnetic field response parameter of the inner double-plane coil. mn These are the magnetic field response parameters of the outer double-plane coil;

[0020] Step 3, Design the error function , Is with To minimize the error, the corresponding preset total magnetic field magnitude is determined by solving the equation. Let b be the target magnetic field matrix. The weighted stream function coefficient matrix is ​​obtained by solving the equation: By adding different weights based on the distance from the target field point to the origin, the coil performance can better balance the magnetic field uniformity in the uniform field region and the magnetic field attenuation in the self-shielding region.

[0021] Step 4, perform SVD decomposition on WA: U w It is a left singular vector matrix, S w It is a singular value matrix. It is the transpose of the right singular vector matrix. Let k be the truncation coefficient. Then, the SVD decomposition of WA is truncated to obtain... WA k It is a truncated weighted intermediate computation matrix, obtained from WA through truncated singular value decomposition, U w_k It is a truncated left singular vector matrix, S w_k It is a truncated singular value matrix. It is the transpose of the truncated right singular vector matrix, from which we obtain the new P. mn Solve the equation: ;

[0022] Step 5, the final matrix P is obtained. mnSubstituting into the stream function, the stream function curve is obtained. The surface current is discretized into multiple conductor segments, the shape of which represents the final design result of the coil, i.e., the conductor winding shape. The inner and outer double-plane coils have different winding methods. Their respective winding data are processed on a flexible PCB to obtain an inner negative-direction plane coil, an inner positive-direction plane coil, an outer negative-direction plane coil, and an outer positive-direction plane coil. The distance between the inner and outer negative-direction plane coils is a2-a1, and they are placed in the negative direction of the target area. The distance from the origin to the inner negative-direction plane coil is a1. The distance between the inner and outer positive-direction plane coils is a2-a1, and they are placed in the positive direction of the target area. The distance from the origin to the origin to the inner negative-direction plane coil is a1. The inner negative-direction plane coil, the inner positive-direction plane coil, the outer negative-direction plane coil, and the outer positive-direction plane coil constitute a self-shielded shimming coil system. Calculate the magnetic field magnitudes in the shimming region and the self-shimming region under this self-shimming coil system, calculate the relative error of magnetic field non-uniformity in the shimming region and the magnetic field attenuation in the self-shimming region, and evaluate the coil design effect.

[0023] The selection method for the 216 uniform field target points in step 1 is as follows: Divide the target into 6 overlapping squares with a vertical spacing of 0.4D. In each square, divide the rows and columns into 6 parts to obtain 36 points. The 6 squares yield 216 uniformly distributed uniform field target points. The selection method for the 1116 shielding target points is as follows: Cut out 31 circles radially and take 36 points evenly on each circle to obtain 1116 uniformly distributed shielding target points in the self-shielding area.

[0024] Step 3 includes the following expression:

[0025]

[0026] Where d is the distance from the target field point to the source point, and x t The x-axis coordinate of the target field point, y t It is the y-axis coordinate of the target field point, z t It is the z-axis coordinate of the target field point.

[0027] The weighted matrix design method in step 3 is as follows: W is a diagonal matrix, and different weights are assigned according to the target field point position. A distance threshold is set, and d is compared with the threshold to determine the weight magnitude. In the uniform field region, when d ≤ λ in When d > λ, the weight w1 = w1_1; when d > λ in At that time, the weight w1 = w1_2. In the self-shielding region, when d ≤ λ out When d > λ, the weight w2 = w2_1; when d > λ out At that time, the weight w1 = w2_2.

[0028] Where w1 is the weight of the target field point in the shimming region, w2 is the weight of the target field point in the shielding region, w1_1 is the weight value of the near point in the shimming region, w1_2 is the weight value of the far point in the shimming region, w2_1 is the weight value of the near point in the self-shimming region, w2_2 is the weight value of the far point in the self-shimming region, and λ in λ is the distance threshold of the target field point in the uniform field region. out The distance threshold for the target field point in the self-shielded area is taken.

[0029] Step 5 includes the following expression:

[0030]

[0031]

[0032] Where ε1 is the relative error of inhomogeneity in the uniform field region, used to evaluate the uniformity of the target magnetic field, and ε2 is the magnetic field attenuation in the self-shielding region. The magnitude of the source magnetic field. The magnitude of the magnetic field at the target point in the uniform field region. x represents the magnitude of the magnetic field in the self-shielding region. t The x-axis coordinate of the target field point, y t It is the y-axis coordinate of the target field point, z t ε1 is the z-axis coordinate of the target field point; the smaller ε1 is, the better the uniformity of the magnetic field in the shimming region generated by the self-shimming coil; the smaller ε2 is, the better the attenuation of the magnetic field in the self-shimming region generated by the self-shimming coil.

[0033] The technical effects of this invention are as follows: The self-shielded shimming coil system and design method in the chip-based atomic magnetometer of this invention, by combining a weighted algorithm and SVD decomposition, solves the problem of ill-conditioned intermediate coefficient matrix during inverse solution, improves the stability of stream function solution, and can balance the magnetic field uniformity in the shimming region and the magnetic field attenuation in the self-shielding region, thus improving coil performance. Considering the fabrication and usability of the self-shielded shimming coil system, this invention selects an appropriate stream function design order, solves the signal crosstalk problem between array probes of the chip-based atomic magnetometer, and is compatible with chip-based atomic magnetometers. Furthermore, the dual-plane coil structure facilitates installation.

[0034] This invention discloses a self-shielded shimming coil system and design method for a chip-based atomic magnetometer. It proposes a shimming coil with self-shielding effect, composed of two pairs of biplane coils, belonging to the field of magnetic field manipulation technology. The biplane coil design facilitates installation and integration into portable instruments. Based on weighted algorithms and SVD decomposition, this invention enables the coil design to simultaneously consider the magnetic field uniformity in the high-shimming region and the magnetic field attenuation in the self-shielding region. Furthermore, it solves the problem of unstable solution of the stream function coefficient matrix caused by the ill-conditioned intermediate coefficient matrix, improving the coil design accuracy. It also solves the signal crosstalk problem between array probes in chip-based atomic magnetometers, making it compatible with chip-based atomic magnetometers, array-type magnetic resonance imaging of the heart and brain, and miniaturized biomagnetic imaging devices. Attached Figure Description

[0035] Figure 1 is a schematic diagram of the self-shielded shimming coil system and design method involved in the chip-based atomic magnetometer of the present invention. SVD stands for Singular Value Decomposition. The chip-based atomic magnetometer chamber is represented as a cube, where D is half the side length of the cube. In Figure 1, the origin O is the center point of the chip-based atomic magnetometer chamber, and a coordinate system XYZ is established with O as the origin. The chip-based atomic magnetometer chamber is taken as the target shimming region. The inner dual-plane coil consists of an inner negative direction plane coil and an inner positive direction plane coil. Each coil is a square with a side length of L1. The inner negative direction plane coil is located in the z=-a1 plane, and the inner positive direction plane coil is located in the z=a1 plane, where a1 is the half-distance between the inner negative direction plane coil and the inner positive direction plane coil, and D < a1. The inner negative direction plane coil and the inner positive direction plane coil have the same winding method and the same current direction. The outer dual-plane coil consists of an outer negative-direction plane coil and an outer positive-direction plane coil. Each coil is square with a side length of L2. The outer negative-direction plane coil is located in the z=-a2 plane, and the outer positive-direction plane coil is located in the z=a2 plane, where a2 is half the distance between the outer negative-direction plane coil and the outer positive-direction plane coil, and a1 < a2. The outer negative-direction plane coil and the outer positive-direction plane coil have the same winding method and the same current direction.

[0036] Figure 2 is a schematic diagram of the selection scheme for the target field points in the cube of the target field region in Figure 1. Figure 2 includes dividing the cube into 6 overlapping squares along the z-axis with a spacing of 0.4D. In each square, the rows and columns are divided into 6 parts, resulting in 36 points. In this way, 216 uniformly distributed target field points are obtained in the field region.

[0037] Figure 3 is a schematic diagram of the self-shielded target field point selection scheme involved in the self-shielded shimming coil system and design method in the chip-based atomic magnetometer of the present invention. A cylindrical self-shielded region is set with the y-axis as the central axis, where H is the half-height of the self-shielded region and R is the radius of the cylindrical surface of the self-shielded region. In the self-shielded region, 31 circles are cut out along the y-axis of the cylindrical surface, and 36 points are evenly selected on each circle, thus obtaining 1116 evenly distributed shielded target field points in the self-shielded region.

[0038] Figure 4 is a schematic diagram of the winding method and current direction of the inner negative direction planar coil and the inner positive direction planar coil involved in the self-shielded shimming coil system and design method of the chip-based atomic magnetometer of the present invention. The inner negative direction planar coil and the inner positive direction planar coil are located in the z=-a1 and z=a1 planes respectively, and are both wound with wires of opposite current. The winding method and the current direction are the same for both. Therefore, the coil shape in Figure 4 is given as the design scheme for the two coils. The coil shape shown in Figure 4 is the winding method. The arrow direction indicates the current flow direction. Positive current flows in a clockwise direction, and negative current flows in a counterclockwise direction.

[0039] Figure 5 is a schematic diagram of the winding method and current direction of the outer negative direction planar coil and the outer positive direction planar coil involved in the self-shielded shimming coil system and design method of the chip-based atomic magnetometer of the present invention. The outer negative direction planar coil and the outer positive direction planar coil are located in the z=-a2 and z=a2 planes respectively, and are both wound with wires of opposite current. The winding method and the current direction are the same for both. Therefore, the coil shape shown in Figure 5 is given as the design scheme for the two coils. The coil shape shown in Figure 5 is the winding method, and the arrow direction is the current flow direction. Positive current flows in the clockwise direction, and negative current flows in the counterclockwise direction. Detailed Implementation

[0040] The present invention will now be described in conjunction with the accompanying drawings (Figures 1-5) and embodiments.

[0041] Figure 1 is a schematic diagram of the self-shielded shimming coil system structure involved in the design method of the chip-based atomic magnetometer of the present invention. Figure 2 is a schematic diagram of the selection scheme of the shimming target field point in the cube of the cubic shimming target region in Figure 1. Figure 3 is a schematic diagram of the selection scheme of the self-shielded target field point involved in the self-shielded shimming coil system and design method of the chip-based atomic magnetometer of the present invention. Figure 4 is a schematic diagram of the winding method and current direction of the inner negative direction planar coil and the inner positive direction planar coil involved in the self-shielded shimming coil system and design method of the chip-based atomic magnetometer of the present invention. Figure 5 is a schematic diagram of the winding method and current direction of the outer negative direction planar coil and the outer positive direction planar coil involved in the self-shielded shimming coil system and design method of the chip-based atomic magnetometer of the present invention. Referring to Figures 1 to 5, the self-shielded shimming coil system and design method of the chip-based atomic magnetometer includes: simplifying the gas chamber of the chip-based atomic magnetometer into a cube model with a side length of D, and establishing a coordinate system XYZ with the center point of the gas chamber of the chip-based atomic magnetometer as the origin. Using the chip-based atomic magnetometer chamber as the target shimming region, a cubic shimming target region is constructed with the origin as the center point. The half-side length of the cube is D. A cylindrical self-shielding region is constructed with the y-axis as the center axis. The radius of the cylindrical surface is R, and the half-height of the cylindrical surface is H. The cube is placed inside the inner dual-plane coil, which is placed inside the outer dual-plane coil. The inner dual-plane coil is a square with a side length L1. The inner dual-plane coil includes an inner negative direction plane coil and an inner positive direction plane coil. The inner negative direction plane coil is located in the z=-a1 plane, and the inner positive direction plane coil is located in the z=a1 plane, where a1 is the distance between the inner negative direction plane coil and the outer positive direction plane coil. The inner positive direction plane coil has a half-spacing. The outer double-plane coil is a square with a side length of L2. The outer double-plane coil includes an outer negative direction plane coil and an outer positive direction plane coil. The outer negative direction plane coil is located in the z=-a2 plane, and the outer positive direction plane coil is located in the z=a2 plane, where a2 is the half-spacing between the outer negative direction plane coil and the outer positive direction plane coil. A uniform field target point distribution is set in the cube, and a self-shielding target point distribution is set on the cylindrical surface. The weighted intermediate calculation matrix WA is obtained by multiplying the weighted diagonal matrix W and the intermediate function coefficient matrix A. The stream function coefficient matrix P is obtained by performing SVD decomposition and truncation on WA. mn Using P mn The flow function curve of the dual-plane coil is obtained, and the surface current is discretized into multiple wire segments to obtain the design result of the dual-plane coil.

[0042] The process includes the following steps: Step 1, uniformly selecting target field points for uniform field selection within the cube, and presetting the target magnetic field of each target field point to B_target; uniformly selecting shielding target field points on the cylindrical surface, and presetting the target magnetic field of each shielding target field point to 0.01. B_target; Step 2, obtain the current density function based on the stream function and its symmetry, and calculate the magnetic field magnitude according to the Biot-Savart law, as shown in the following formula:

[0043]

[0044]

[0045]

[0046]

[0047]

[0048]

[0049]

[0050]

[0051] in M is the magnitude of the magnetic field generated by the inner positive-direction planar coil in the X direction, where M is the mode order in the X direction, m is the index, N is the mode order in the Y direction, n is the index, and A is the magnetic field. mn1 P is the magnetic field response parameter of the inner positive direction planar coil. mn1 These are the current function coefficients of the inner dual-plane coils. The inner positive-direction plane coil and the inner negative-direction plane coil have the same current function coefficients. A is the magnitude of the magnetic field generated by the inner negative direction planar coil in the X direction. mn2 These are the magnetic field response parameters of the inner negative direction planar coil. B is the magnitude of the magnetic field generated by the outer positive-direction planar coil in the X direction. mn1 P is the magnetic field response parameter of the outer positive direction planar coil. mn2 These are the current function coefficients of the inner dual-plane coils. The inner positive-direction plane coil and the inner negative-direction plane coil have the same current function coefficients. B is the magnitude of the magnetic field generated by the outer negative-direction planar coil in the X direction. mn2 B is the magnetic field response parameter of the outer negative direction planar coil. x Let A be the total magnetic field magnitude of a target point in the X direction. mn B is the magnetic field response parameter of the inner double-plane coil.mn These are the magnetic field response parameters of the outer double-plane coil;

[0052] Step 3, Design the error function , Is with To ensure the error is zero, the corresponding preset total magnetic field magnitude is determined by solving the equation. Let b be the target magnetic field matrix. The weighted stream function coefficient matrix is ​​obtained by solving the equation: Based on the distance from the target field point to the origin, different weights are added to better balance the magnetic field uniformity in the uniform field region and the magnetic field attenuation in the self-shielding region; Step 4, perform SVD decomposition on WA: U w It is a left singular vector matrix, S w It is a singular value matrix. It is the transpose of the right singular vector matrix. Let k be the truncation coefficient. Then, the SVD decomposition of WA is truncated to obtain... WA k It is a truncated weighted intermediate computation matrix, obtained from WA through truncated singular value decomposition, U w_k It is a truncated left singular vector matrix, S w_k It is a truncated singular value matrix. It is the transpose of the truncated right singular vector matrix, from which we obtain the new P. mn Solve the equation: Step 5, P mn Substituting the values ​​into the stream function yields the stream function curve. The surface current is discretized into multiple conductor segments, which serve as the design result, i.e., the conductor winding shape, and then fabricated onto a flexible PCB. For the design result of the self-shielded shimming coil system, based on the magnetic field magnitudes of the shimming region and the self-shielding region, the magnetic field uniformity of the shimming region and the magnetic field attenuation of the self-shielding region are calculated to evaluate the coil performance.

[0053] The selection method for the 216 uniform field target points in step 1 is as follows: Divide the target into 6 overlapping squares with a vertical spacing of 0.4D. In each square, divide the rows and columns into 6 parts to obtain 36 points. The 6 squares yield 216 uniformly distributed uniform field target points. The selection method for the 1116 shielding target points is as follows: Cut out 31 circles radially and take 36 points evenly on each circle to obtain 1116 uniformly distributed shielding target points in the self-shielding area.

[0054] Step 3 includes the following expression:

[0055]

[0056] Where d is the distance from the target field point to the source point, and x tThe x-axis coordinate of the target field point, y t It is the y-axis coordinate of the target field point, z t It is the z-axis coordinate of the target field point.

[0057] The weighted matrix design method in step 3 is as follows: W is a diagonal matrix, and different weights are assigned according to the target field point position. A distance threshold is set, and d is compared with the threshold to determine the weight magnitude. In the uniform field region, when d ≤ λ in When d > λ, the weight w1 = w1_1; when d > λ in At that time, the weight w1 = w1_2. In the self-shielding region, when d ≤ λ out When d > λ, the weight w2 = w2_1; when d > λ out At that time, the weight w1 = w2_2.

[0058] Where w1 is the weight of the target field point in the shimming region, w2 is the weight of the target field point in the shielding region, w1_1 is the weight value of the near point in the shimming region, w1_2 is the weight value of the far point in the shimming region, w2_1 is the weight value of the near point in the self-shimming region, w2_2 is the weight value of the far point in the self-shimming region, and λ in λ is the distance threshold of the target field point in the uniform field region. out The distance threshold for the target field point in the self-shielded area is taken.

[0059] Step 5 includes the following expression:

[0060]

[0061]

[0062] Where ε1 is the relative error of inhomogeneity in the uniform field region, used to evaluate the uniformity of the target magnetic field, and ε2 is the magnetic field attenuation in the self-shielding region. The magnitude of the source magnetic field. The magnitude of the magnetic field at the target point in the uniform field region. x represents the magnitude of the magnetic field in the self-shielding region. t The x-axis coordinate of the target field point, y t It is the y-axis coordinate of the target field point, z t ε1 is the z-axis coordinate of the target field point; the smaller ε1 is, the better the uniformity of the magnetic field in the shimming region generated by the self-shimming coil; the smaller ε2 is, the better the attenuation of the magnetic field in the self-shimming region generated by the self-shimming coil.

[0063] The self-shielded shimming coil system and its design method in a chip-based atomic magnetometer include two pairs of dual-plane coils: one pair of inner dual-plane coils and one pair of outer dual-plane coils. The inner dual-plane coils consist of an inner negative-direction plane coil and an inner positive-direction plane coil, located in the z=-a1 and z=a1 planes, respectively. The outer dual-plane coils consist of an outer negative-direction plane coil and an outer positive-direction plane coil, located in the z=-a2 and z=a2 planes, respectively. The combined effect of these four coils generates a uniform magnetic field in the cubic shimming region (D is half the side length of the cube) and rapidly attenuates the magnetic field in the cylindrical self-shielded region (H is the half-height of the self-shielded region, and R is the radius of the self-shielded region), thus preventing magnetic field crosstalk from affecting coil performance.

[0064] The self-shielded shimming coil system and its design method in a chip-based atomic magnetometer include the following steps:

[0065] Step 1: Determine the center position of the self-shielded shimming coil system and use it as the origin to set up the coordinate system. Define two square inner double-plane coils, where L1 is the side length of the inner double-plane coil. The inner double-plane coil consists of an inner negative-direction plane coil and an inner positive-direction plane coil, located in the z=-a1 and z=a1 planes respectively, where a1 is the half-space between the inner double-plane coils. Define two square outer double-plane coils, where L2 is the side length of the outer double-plane coil. The outer double-plane coil consists of an outer negative-direction plane coil and an outer positive-direction plane coil, located in the z=-a2 and z=a2 planes respectively, where a2 is the half-space between the outer double-plane coils. Set up a cubic shimming region, where D is half the side length of the cube, and select shimming target points. Preset the target magnetic field size for each shimming target point to B_target. Set up a cylindrical self-shielding region, where H is the half-height of the self-shielding region, R is the radius of the self-shielding region, and select shielding target points. Preset the target magnetic field size for each self-shielding target point to 0.01. B_target.

[0066] Step 2: Obtain the current density function based on the stream function and its symmetry, and then calculate the magnitude of the magnetic field according to the Biot-Savart law.

[0067] Step 3, Design the error function To make the error zero, we can obtain the solution equation: A is the intermediate function coefficient matrix, P mn is the stream function coefficient matrix, and b is the target magnetic field matrix. Multiplying both sides of the equation by the weighted diagonal matrix W on the left yields the weighted stream function coefficient matrix. Solving the equation, i.e., W is a weighted diagonal matrix, and WA is a weighted intermediate calculation matrix, obtained by multiplying the weighted diagonal matrix W and the intermediate function coefficient matrix A. Different weights are added based on the distance from the target field point to the origin, allowing the coil performance to better balance the uniformity of the magnetic field in the uniform field region and the attenuation of the magnetic field in the self-shielding region.

[0068] Step 4, perform SVD decomposition on WA: Decompose WA into U w S w and The product of three matrices. U w It is a left singular vector matrix, S w It is a singular value matrix. It is the transpose of the right singular vector matrix. Let k be the truncation coefficient, and truncate the SVD decomposition of WA to obtain... WA k It is a truncated weighted intermediate computation matrix, obtained from WA through truncated singular value decomposition. U w_k It is a truncated left singular vector matrix, S w_k It is a truncated singular value matrix. It is the transpose of a truncated right singular vector matrix. This yields a new P. mn Solve the equation: .

[0069] Step 5, the final matrix P is obtained. mn Substituting into the stream function, the stream function curve is obtained. The surface current is discretized into multiple conductor segments, the shape of which represents the final design result of the coil, i.e., the conductor winding shape. The inner and outer double-plane coils have different winding methods. Their respective winding data are processed on a flexible PCB to obtain an inner negative-direction plane coil, an inner positive-direction plane coil, an outer negative-direction plane coil, and an outer positive-direction plane coil. The distance between the inner and outer negative-direction plane coils is a2-a1, and they are placed in the negative direction of the target area. The distance from the origin to the inner negative-direction plane coil is a1. The distance between the inner and outer positive-direction plane coils is a2-a1, and they are placed in the positive direction of the target area. The distance from the origin to the origin to the inner negative-direction plane coil is a1. The inner negative-direction plane coil, the inner positive-direction plane coil, the outer negative-direction plane coil, and the outer positive-direction plane coil constitute a self-shielded shimming coil system. Calculate the magnetic field magnitudes in the shimming region and the self-shimming region under this self-shimming coil system, calculate the relative error of magnetic field non-uniformity in the shimming region and the magnetic field attenuation in the self-shimming region, and evaluate the coil design effect.

[0070] This invention provides a self-shielded shimming coil system and design method for a chip-based atomic magnetometer. It employs a combination of weighted algorithms and SVD decomposition to design a uniform magnetic field coil with self-shielding effect. As shown in Figure 1, the self-shielded shimming coil system in this design consists of two pairs of biplane coils. The inner biplane coil consists of an inner negative-direction plane coil and an inner positive-direction plane coil, located in the z=-a1 and z=a1 planes respectively, where a1 is half the spacing between the inner biplane coils. Each coil is square, and L1 is the side length of the inner negative-direction plane coil and the inner positive-direction plane coil. The outer biplane coil consists of an outer negative-direction plane coil and an outer positive-direction plane coil, located in the z=-a2 and z=a2 planes respectively, where a2 is half the spacing between the outer biplane coils. Each coil is square, and L2 is the side length of the outer negative-direction plane coil and the outer positive-direction plane coil.

[0071] The shimming region involved in this invention is the gas chamber of a chip-based atomic magnetometer, which is cubic in shape, where D is half the side length of the cube. The method of selecting the shimming target field points is shown in Figure 2. It is divided into 6 overlapping squares with a vertical spacing of 0.4D. In each square, the rows and columns are divided into 6 parts, resulting in 36 points. In this way, 216 uniformly distributed shimming target points are obtained in the shimming region, and the target magnetic field size of each shimming target point is preset to B_target.

[0072] The self-shielding region involved in this invention is a cylindrical surface, where H is the half-height of the self-shielding region and R is the radius of the self-shielding region. The method for selecting the shielding target field points is shown in Figure 3. Within the cylindrical self-shielding region, 31 circles are radially cut out, and 36 points are evenly selected on each circle, thus obtaining 1116 evenly distributed shielding target field points within the self-shielding region. The target magnetic field magnitude for each self-shielding target point is preset to 0.01. B_target.

[0073] The magnitude of a magnetic field can be calculated using the Biot-Savart law, which is expressed as follows:

[0074]

[0075] The total magnetic field of the four self-shielded shim coils relative to the magnetic field in the X direction at a target field point is:

[0076]

[0077] in,

[0078]

[0079]

[0080] Set the flow function design order M=N=3.

[0081] Design error function To make the error zero, we can solve the equation. A is the intermediate function coefficient matrix, and A is derived from A... mn and B mn Composition. P mn It is the stream function coefficient matrix, P mn By P mn1 and P mn2 Composition. b is the target magnetic field matrix. Multiplying W on the left and right sides of the above solution equation yields the weighted stream function coefficient matrix. Solution equation: W is a weighted diagonal matrix. Different weights are added based on the distance from the target field point to the origin, so that the coil performance can better balance the magnetic field uniformity in the uniform field region and the magnetic field attenuation in the self-shielding region.

[0082] The weighted matrix structure and weighting coefficient setting method are as follows: the weighted matrix W is a diagonal matrix, and different weights are assigned according to the location of the target field point. The specific weight allocation is shown in Table 1.

[0083] Distance formula d:

[0084]

[0085] In the formula, d is the distance from each target point to the source point, and x is the distance from each target point to the source point. t The x-axis coordinate of the target field point, y t It is the y-axis coordinate of the target field point, z t It is the z-axis coordinate of the target field point.

[0086] A distance threshold is set, and d is compared with the threshold to determine the weight, as shown in Table 1. In the shimming region, when d ≤ λ in When d > λ, the weight w1 = w1_1; when d > λ in At that time, the weight w1 = w1_2. In the self-shielding region, when d ≤ λ out When d > λ, the weight w2 = w2_1; when d > λ out At that time, the weights w1 = w2_2. w1_1 is the near-point weight value of the shimming region, w1_2 is the far-point weight value of the shimming region, w2_1 is the near-point weight value of the self-shimming region, and w2_2 is the far-point weight value of the self-shimming region. λ in λ is the distance threshold of the target field point in the uniform field region. out The distance threshold for the target field point in the self-shielded area is taken.

[0087] Table 1 Weighting Matrix Weight Division Table

[0088]

[0089] Solving the equation WAP using the convection function coefficient matrix mn =The WA in Wb is decomposed using SVD, and WA is decomposed into U w S w and Product of three matrices:

[0090]

[0091] In the formula, WA is the weighted intermediate calculation matrix, U w It is a left singular vector matrix, S w It is a singular value matrix. It is the transpose of the right singular vector matrix.

[0092] Due to S w The phenomenon that some singular values ​​in U are extremely small indicates that this information is not a major influencing factor. A positive integer k is chosen, where k is the cutoff coefficient, for U... w S w and Truncate the matrix to generate a new matrix WA that can represent WA. k ,

[0093]

[0094] In the formula, WA k It is a truncated weighted intermediate calculation matrix; U w_k It is the truncated left singular vector matrix, taking U w The first k columns; S w_k It is a truncated singular value matrix, taking S w The first k singular values; It is the transpose of the truncated right singular vector matrix, taking... The first k rows.

[0095] A new P can be obtained. mn Solve the equation:

[0096] .

[0097] matrix P mnSubstituting into the stream function, the surface current is discretized into multiple conductor segments, the shape of which represents the final design of the coil. The magnetic field magnitudes in the shimming and self-shimming regions are calculated under this self-shimming coil. The relative error of magnetic field inhomogeneity in the shimming region and the magnetic field attenuation in the self-shimming region are calculated to evaluate the coil design effectiveness. The formulas for the relative error ε1 of magnetic field inhomogeneity in the shimming region and the magnetic field attenuation ε2 in the self-shimming region are:

[0098]

[0099]

[0100] In the formula, The magnitude of the source magnetic field. The magnitude of the magnetic field at the target point in the uniform field region. x represents the magnitude of the magnetic field in the self-shielding region. t The x-axis coordinate of the target field point, y t It is the y-axis coordinate of the target field point, z t It is the z-axis coordinate of the target field point.

[0101] The smaller ε1 is, the better the uniformity of the magnetic field in the shimming region generated by the self-shimming coil; the smaller ε2 is, the better the attenuation of the magnetic field in the self-shimming region generated by the self-shimming coil.

[0102] This paper presents a self-shielded shimming coil system and its design method in a chip-based atomic magnetometer. The physical parameters of the coil, including coil size, coil spacing, shimming region size, and self-shielding region size, are designed based on the volume and requirements of the chip-based atomic magnetometer. Target shimming points and their magnitudes are defined, as are target shielding points and their magnitudes. The magnetic field is calculated using the Biot-Savart law, and the flow function coefficient matrix is ​​solved. Weighted matrices are added according to distance, and SVD decomposition is used to reduce the dimensionality of the matrices, improving the uniformity of the magnetic field in the shimming region and the attenuation of the magnetic field in the self-shielding region. The designed coil provides a uniform magnetic field in the target region and attenuates the magnetic field in the self-shielding region.

[0103] The self-shielded shimming coil system and design method in a chip-based atomic magnetometer include the following steps:

[0104] Step 1: Consider the configuration of the self-shielded shimming coil system, which consists of two pairs of biplane coils: an inner pair and an outer pair. Establish an xyz rectangular coordinate system with the center of the chip-based atomic magnetometer cell as the origin. The inner biplane coils consist of an inner negative-direction plane coil and an inner positive-direction plane coil. Each coil is a square with a side length of L1. The inner negative-direction plane coil is located in the z=-a1 plane, and the inner positive-direction plane coil is located in the z=a1 plane, where a1 is half the spacing between the inner biplane coils. The outer biplane coils consist of an outer negative-direction plane coil and an outer positive-direction plane coil. Each coil is a square with a side length of L2. The outer negative-direction plane coil is located in the z=-a2 plane, and the outer positive-direction plane coil is located in the z=a2 plane, where a2 is half the spacing between the outer biplane coils. The gas chamber of the chip-based atomic magnetometer is simplified into a cubic region, which is then used as the target shimming region. D is the half-side length of the cube. Target field points are uniformly selected for shimming, and the target magnetic field of each point is preset to B_target. A cylindrical self-shielding region is set, where H is the half-height of the self-shielding region and R is its radius. Shielding target field points are uniformly selected on the side of the cylinder, and the target magnetic field of each point is preset to 0.01. B_target.

[0105] Step 2: Obtain the current density function based on the stream function and its symmetry, and calculate the magnetic field magnitude using the Biot-Savart law. Taking the design of the magnetic field in the X direction as an example, the magnitude of the magnetic field generated by the inner positive-direction planar coil in the X direction is: The magnitude of the magnetic field generated by the inner negative direction planar coil in the X direction is The magnitude of the magnetic field generated by the outer positive plane coil in the X direction is The magnitude of the magnetic field generated by the outer negative direction planar coil in the X direction is A mn1 A is the magnetic field response parameter of the inner positive direction planar coil. mn2 B is the magnetic field response parameter of the inner negative direction planar coil. mn1 B is the magnetic field response parameter of the outer positive direction planar coil. mn2 P is the magnetic field response parameter of the outer negative direction planar coil. mn1 P is the current function coefficient of the inner double-plane coil. The inner positive-direction plane coil and the inner negative-direction plane coil have the same current function coefficient. mn2 These are the current function coefficients of the inner dual-plane coils. The inner positive-direction plane coil and the inner negative-direction plane coil have the same current function coefficients. M is the mode order in the X direction, and N is the mode order in the Y direction.

[0106] The combined effect of four self-shielded shim coils on the magnetic field in the X direction at a target field point is: B x Let the total magnetic field magnitude at a target point in the X direction be denoted as , which can be simplified to . A mn These are the magnetic field response parameters of the inner double-plane coil. B mn These are the magnetic field response parameters of the outer two-plane coil. Set the flow function design order M=N=3

[0107] Step 3, Design the error function To make the error zero, we can obtain the solution equation. A is the intermediate function coefficient matrix, and A is derived from A... mn and B mn Composition. P mn It is the stream function coefficient matrix, P mn By P mn1 and P mn2 Composition. b is the target magnetic field matrix. Multiplying W on the left and right sides of the above solution equation yields the weighted stream function coefficient matrix. Solution equation: W is a weighted diagonal matrix. Different weights are added based on the distance from the target field point to the origin, so that the coil performance can better balance the magnetic field uniformity in the uniform field region and the magnetic field attenuation in the self-shielding region.

[0108] Step 4, solve the equations obtained in Step 3: WA is a weighted intermediate computation matrix, obtained by multiplying the weighted diagonal matrix W and the intermediate function coefficient matrix A. SVD decomposition is performed on WA: Decompose WA into U w S w and The product of three matrices. U w It is a left singular vector matrix, S w It is a singular value matrix. It is the transpose of the right singular vector matrix. Let k be the truncation coefficient, and truncate the SVD decomposition of WA to obtain... WA k It is a truncated weighted intermediate computation matrix, obtained from WA through truncated singular value decomposition, U w_k It is a truncated left singular vector matrix, S w_k It is a truncated singular value matrix. It is the transpose of a truncated right singular vector matrix. This yields a new P. mn Solve the equation: .

[0109] Step 5, based on the stream function coefficient matrix P obtained in Step 4 mnSubstituting into the stream function, the stream function curve is obtained. The surface current is discretized into multiple conductor segments, the shape of which represents the final design result of the coil, i.e., the conductor winding shape. The inner and outer double-plane coils have different winding methods. Their respective winding data are processed on a flexible PCB to obtain an inner negative-direction plane coil, an inner positive-direction plane coil, an outer negative-direction plane coil, and an outer positive-direction plane coil. The distance between the inner and outer negative-direction plane coils is a2-a1, and they are placed in the negative direction of the target area. The distance from the origin to the inner negative-direction plane coil is a1. The distance between the inner and outer positive-direction plane coils is a2-a1, and they are placed in the positive direction of the target area. The distance from the origin to the origin to the inner negative-direction plane coil is a1. The inner negative-direction plane coil, the inner positive-direction plane coil, the outer negative-direction plane coil, and the outer positive-direction plane coil constitute a self-shielded shimming coil system. Calculate the magnetic field magnitudes in the shimming region and the self-shimming region under this self-shimming coil system, calculate the relative error of magnetic field non-uniformity in the shimming region and the magnetic field attenuation in the self-shimming region, and evaluate the coil design effect.

[0110] The selection scheme for the shimming target field points in step 1 is as follows: The cubic region of the chip-based atomic magnetometer chamber is selected as the shimming region, where D is half the side length of the cube. It is divided into 6 overlapping squares with a vertical spacing of 0.4D. Within each square, rows and columns are equally divided into 6 parts, resulting in 36 points. This yields 216 uniformly distributed shimming target field points within the shimming region. The selection scheme for the shielding target field points is as follows: A cylindrical self-shimming region is set up, where H is the half-height of the self-shimming region and R is the radius. 31 circles are radially cut out, and 36 points are uniformly selected on each circle. This yields 1116 uniformly distributed shielding target field points within the self-shimming region.

[0111] The SVD decomposition truncation method for WA described in step 4 is as follows:

[0112]

[0113] In the formula, WA is the weighted intermediate calculation matrix; U w It is a left singular vector matrix; S w It is a singular value matrix, with the diagonal elements being singular values ​​that represent importance; It is the transpose of the right singular vector matrix.

[0114] Due to S w The phenomenon that some singular values ​​in U are extremely small indicates that this information is not a major influencing factor. A positive integer k is chosen, where k is the cutoff coefficient, for U... w S w and Truncate the matrix to generate a new matrix WA that can represent WA.k :

[0115]

[0116] In the formula, WA k It is a truncated weighted intermediate calculation matrix; U w_k It is the truncated left singular vector matrix, taking U w The first k columns; S w_k It is a truncated singular value matrix, taking S w The first k singular values; It is the transpose of the truncated right singular vector matrix, taking... The first k rows.

[0117] Contents not described in detail in this specification are prior art known to those skilled in the art. It is hereby indicated that the above description is intended to help those skilled in the art understand this invention, but does not limit the scope of protection of this invention. Any equivalent substitutions, modifications, improvements, and / or simplifications of the above descriptions that do not depart from the essential content of this invention fall within the scope of protection of this invention.

Claims

1. A self-shielded shimming coil system in a chip-based atomic magnetometer, characterized in that, include: The chip-based atomic magnetometer chamber is simplified into a cube model with side length D. A coordinate system XYZ is established with the center point of the chip-based atomic magnetometer chamber as the origin. The chip-based atomic magnetometer chamber is used as the target shimming region. A cube-shaped shimming target region is constructed with the origin as the center point. Half of the cube's side length is D. A cylindrical self-shielding region is constructed with the y-axis as the central axis. The radius of the cylindrical surface is R, and the half-height of the cylindrical surface is H. The cube is placed within the inner dual-plane coil, which is located within the outer dual-plane coil. The inner dual-plane coil is a square with side length L1. The inner dual-plane coil includes an inner negative direction plane coil and an inner positive direction plane coil. The inner negative direction plane coil is located in the z=-a1 plane, and the inner positive direction plane coil is located in the z=a1 plane, where a1 is the distance between the inner negative direction plane coil and the outer positive direction plane coil. The inner positive direction plane coil has a half-spacing. The outer double-plane coil is a square with a side length of L2. The outer double-plane coil includes an outer negative direction plane coil and an outer positive direction plane coil. The outer negative direction plane coil is located in the z=-a2 plane, and the outer positive direction plane coil is located in the z=a2 plane, where a2 is the half-spacing between the outer negative direction plane coil and the outer positive direction plane coil. A uniform field target point distribution is set in the cube, and a self-shielding target point distribution is set on the cylindrical surface. The weighted intermediate calculation matrix WA is obtained by multiplying the weighted diagonal matrix W and the intermediate function coefficient matrix A. The stream function coefficient matrix P is obtained by performing SVD decomposition and truncation on WA. mn Using P mn The flow function curve of the dual-plane coil is obtained, and the surface current is discretized into multiple wire segments to obtain the design result of the dual-plane coil.

2. The design method of the self-shielded shimming coil system in the chip-based atomic magnetometer as described in claim 1, characterized in that, Includes the following steps: Step 1: Uniformly select 216 target field points in the cube, and preset the target magnetic field of each target field point as B_target; uniformly select 1116 shielding target field points on the cylindrical surface, and preset the target magnetic field of each shielding target field point as 0.

01. B_target; Step 2, obtain the current density function based on the stream function and its symmetry, and calculate the magnetic field magnitude according to the Biot-Savart law, as shown in the following formula: in M is the magnitude of the magnetic field generated by the inner positive-direction planar coil in the X direction, where M is the mode order in the X direction, m is the index, N is the mode order in the Y direction, n is the index, and A is the magnetic field. mn1 P is the magnetic field response parameter of the inner positive direction planar coil. mn1 These are the current function coefficients of the inner dual-plane coils. The inner positive-direction plane coil and the inner negative-direction plane coil have the same current function coefficients. A is the magnitude of the magnetic field generated by the inner negative direction planar coil in the X direction. mn2 These are the magnetic field response parameters of the inner negative direction planar coil. B is the magnitude of the magnetic field generated by the outer positive-direction planar coil in the X direction. mn1 P is the magnetic field response parameter of the outer positive direction planar coil. mn2 These are the current function coefficients of the inner dual-plane coils. The inner positive-direction plane coil and the inner negative-direction plane coil have the same current function coefficients. B is the magnitude of the magnetic field generated by the outer negative-direction planar coil in the X direction. mn2 B is the magnetic field response parameter of the outer negative direction planar coil. x Let A be the total magnetic field magnitude of a target point in the X direction. mn B is the magnetic field response parameter of the inner double-plane coil. mn These are the magnetic field response parameters of the outer double-plane coil; Step 3, design the error function. ， Is with To ensure the error is zero, the corresponding preset total magnetic field magnitude is determined by solving the equation. Let b be the target magnetic field matrix. The weighted stream function coefficient matrix is ​​obtained by solving the equation: Based on the distance from the target field point to the origin, different weights are added to better balance the magnetic field uniformity in the uniform field region and the magnetic field attenuation in the self-shielding region; Step 4, perform SVD decomposition on WA: U w It is a left singular vector matrix, S w It is a singular value matrix. It is the transpose of the right singular vector matrix. Let k be the truncation coefficient. Then, the SVD decomposition of WA is truncated to obtain... WA k It is a truncated weighted intermediate computation matrix, obtained from WA through truncated singular value decomposition, U w_k It is a truncated left singular vector matrix, S w_k It is a truncated singular value matrix. It is the transpose of the truncated right singular vector matrix, from which we obtain the new P. mn Solve the equation: Step 5, the final matrix P is obtained. mn Substituting into the stream function, the stream function curve is obtained. The surface current is discretized into multiple conductor segments, the shape of which represents the final design result of the coil, i.e., the conductor winding shape. The inner and outer double-plane coils have different winding methods. Their respective winding data are processed on a flexible PCB to obtain an inner negative direction plane coil, an inner positive direction plane coil, an outer negative direction plane coil, and an outer positive direction plane coil. The inner and outer negative direction plane coils are spaced a2-a1 apart and placed in the negative direction of the target area, with the distance from the inner negative direction plane coil to the origin being a1. The inner and outer positive direction plane coils are also spaced a2-a1 apart and placed in the positive direction of the target area, with the distance from the inner negative direction plane coil to the origin being a1. The inner negative direction plane coil, inner positive direction plane coil, outer negative direction plane coil, and outer positive direction plane coil constitute a self-shielded shimming coil system. Calculate the magnetic field magnitudes in the shimming region and the self-shimming region under this self-shimming coil system, calculate the relative error of magnetic field non-uniformity in the shimming region and the magnetic field attenuation in the self-shimming region, and evaluate the coil design effect.

3. The design method of the self-shielded shimming coil system in the chip-based atomic magnetometer according to claim 2, characterized in that, The selection method for the 216 uniform field target points in step 1 is as follows: Divide the target into 6 overlapping squares with a vertical spacing of 0.4D. In each square, divide the rows and columns into 6 parts to obtain 36 points. The 6 squares yield 216 uniformly distributed uniform field target points. The selection method for the 1116 shielding target points is as follows: Cut out 31 circles radially and take 36 points evenly on each circle to obtain 1116 uniformly distributed shielding target points in the self-shielding area.

4. The design method of the self-shielded shimming coil system in the chip-based atomic magnetometer according to claim 2, characterized in that, Step 3 includes the following expression: Where d is the distance from the target field point to the source point, and x t The x-axis coordinate of the target field point, y t It is the y-axis coordinate of the target field point, z t This refers to the z-axis coordinate of the target field point. The weighting matrix design method in step 3 is as follows: W is a diagonal matrix, and different weights are assigned based on the target field point's location. A distance threshold is set, and d is compared with the threshold to determine the weight magnitude. In the uniform field region, when d ≤ λ... in When d > λ, the weight w1 = w1_1; when d > λ in At that time, the weight w1 = w1_2. In the self-shielding region, when d ≤ λ out When d > λ, the weight w2 = w2_1; when d > λ out At that time, the weight w1 = w2_2; Where w1 is the weight of the target field point in the shimming region, w2 is the weight of the target field point in the shielding region, w1_1 is the weight value of the near point in the shimming region, w1_2 is the weight value of the far point in the shimming region, w2_1 is the weight value of the near point in the self-shimming region, w2_2 is the weight value of the far point in the self-shimming region, and λ in λ is the distance threshold of the target field point in the uniform field region. out The distance threshold for the target field point in the self-shielded area is taken.

5. The design method for a micro self-shielding shimming coil system based on weighted SVD decomposition according to claim 2, characterized in that, The SVD decomposition truncation method for WA described in step 4 is as follows: In the formula, WA is the weighted intermediate calculation matrix; U w It is a left singular vector matrix; S w It is a singular value matrix, with the diagonal elements being singular values ​​and the remaining elements being 0, representing importance; It is the transpose of the right singular vector matrix; since S w The phenomenon that some singular values ​​in U are extremely small indicates that this information is not a major influencing factor. A positive integer k is chosen, where k is the cutoff coefficient, for U... w S w and Truncate the matrix to generate a new matrix WA that can represent WA. k : In the formula, WA k It is a truncated weighted intermediate calculation matrix; U w_k It is the truncated left singular vector matrix, taking U w The first k columns are set to 0, and the rest of the columns are set to 0; S w_k It is a truncated singular value matrix, taking S w The first k singular values, and the remaining diagonal elements are 0; It is the transpose of the truncated right singular vector matrix, taking... The first k lines are 0, and the rest are 0.

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