Method and device for accurately measuring geomagnetic field based on optical detection helium-3

Abstract

The invention discloses a geomagnetic field accurate measurement method and device based on optical detection helium-3, and the method comprises the steps: achieving nuclear spin polarization through optical pumping and metastable state spin exchange, applying a pulse magnetic field to excite a helium-3 nuclear spin FID signal, and detecting the frequency and relaxation rate of the helium-3 nuclear spin FID signal; a theoretical model is constructed, parameters such as helium 3 atomic number density and relaxation rate in a gas chamber are measured in combination with spin exchange frequency shift and a relaxation phenomenon, a conversion formula of FID frequency and helium 3 ground state Larmor frequency is established based on the parameters, and frequency shift caused by spin exchange is corrected; the residual magnetism of the probe is inversed through multi-angle measurement, errors introduced by the residual magnetism are eliminated, and finally accurate measurement of the geomagnetic field is achieved. The invention provides a geomagnetic field accurate measurement method and device based on optical detection helium-3, which are used for carrying out complete system error correction and elimination aiming at spin exchange and probe residual magnetism system errors in an optical detection type geomagnetic field helium-3 magnetometer, and can solve the problem that the accuracy and the sensitivity of geomagnetic field measurement are difficult to consider at the same time.

Description

Technical Field

[0001] This invention relates to the technical field of magnetic field measurement, and in particular to an accurate method and apparatus for measuring the geomagnetic field based on optical detection of helium-3. Background Technology

[0002] Accurate magnetic field measuring instruments enable traceable measurements of magnetic field strength, correlating results with International System of Units (SI) standards and ensuring consistency in parameter evaluations across magnetic field applications, thus possessing significant metrological importance. Since the reform of the SI, magnetic field measurement technology has shifted from the traditional induction coil method to a scheme based on the physical constant—the gyromagnetic ratio (γ). This directly defines and transmits standard magnetic field values ​​through the relationship between frequency and the gyromagnetic ratio (f = γB). Alkali metal and helium-4 atomic magnetometers exhibit high sensitivity (~20 fT / Hz) in the Earth's magnetic field. 1 / 2 However, the gyromagnetic ratio of alkali metals and helium-4 atoms is not a physical constant due to limited measurement data. Furthermore, alkali metal and helium-4 atomic magnetometers suffer from various systematic errors, such as optical frequency shift, spin-exchange frequency shift, and nonlinear Zeeman effects, making accurate magnetic field measurements based on alkali metals and helium-4 atoms quite difficult. The nuclear spin gyromagnetic ratio of helium-3 nuclei is a physical constant, offering high measurement accuracy. Moreover, helium-3 nuclear spin-based magnetometers have fewer sources of systematic errors, making them an ideal medium for constructing high-accuracy magnetometers. Existing atomic magnetometers and coil techniques for detecting the precession of the helium-3 nuclear magnetic moment involve polarizing the helium-3 nuclear spin to induce precession in a magnetic field, then using an atomic magnetometer or coil to detect the alternating magnetic field signal generated by the precession, obtaining its frequency information, and combining this with the helium-3 gyromagnetic ratio to obtain an accurate value of the magnetic induction intensity.

[0003] The helium-3 nuclear magnetic moment precession detection scheme based on atomic magnetometers and coil pickup can achieve high-accuracy measurements in both strong magnetic field (~1.45T) and weak magnetic field (~1μT) environments. However, in the geomagnetic field, at approximately 50μT, the nuclear spin precession frequency is on the order of kHz, outside the measurement range of these two schemes. This significantly reduces the ability of these two schemes to extract nuclear spin signals, limiting their sensitivity. Therefore, in summary, within the geomagnetic field range, existing magnetometer technology struggles to simultaneously meet the dual requirements of accuracy and sensitivity for magnetic field measurements. Summary of the Invention

[0004] This invention provides a method and apparatus for accurately measuring the geomagnetic field based on optical detection of helium-3, in order to solve the problem of balancing the accuracy and sensitivity of geomagnetic field measurements.

[0005] To achieve the above objectives, the present invention provides a method for accurately measuring the geomagnetic field based on optical detection of helium-3, comprising:

[0006] The FID frequency and FID relaxation rate were obtained by polarizing and probing the helium-3 nuclear spin;

[0007] The measurement establishes a first relationship between radio frequency power and the FID frequency, and a second relationship between the FID relaxation rate and the FID frequency under different radio frequency powers; wherein the first relationship is a spin-switched frequency shift, and the second relationship is a spin-switched relaxation.

[0008] Based on the preset spin-exchange frequency shift expression and spin-exchange relaxation expression, the first change relationship and the second change relationship, a set of parameters including the number density and relaxation rate of helium-3 particles in the gas chamber is calculated.

[0009] Based on the spin-exchange frequency shift expression and the parameter set, establish the conversion formula between the FID frequency and the helium-3 ground-state Larmor frequency;

[0010] The ground-state Larmor frequency of helium-3 is calculated based on the FID frequency according to the conversion formula, the spin exchange frequency shift is eliminated, and the remanence is corrected by inverting the remanence vector of the probe. The accurate geomagnetic field value after system error correction is obtained by combining the helium-3 nucleus spin gyromagnetic ratio.

[0011] This invention, based on the spin-exchange frequency shift and spin-exchange relaxation expressions, combined with the first relationship between radio frequency power and FID frequency, and the second relationship between FID frequency and relaxation rate, calculates a set of key parameters such as the helium-3 particle number density and relaxation rate in the gas chamber. It then establishes a precise mathematical mapping between the FID frequency and the ground-state Larmor frequency. By using a quantitative conversion formula to invert the FID frequency, it not only accurately eliminates the systematic error introduced by the spin-exchange frequency shift but also enables the measurement of particle number density and other parameters within the gas chamber. Furthermore, the superposition effect of the probe's remanent magnetization can cause the amplitude and direction of the magnetic field signal measured by the helium-3 magnetometer to differ from the signal to be measured, resulting in systematic errors. This invention, by inverting the probe's remanent magnetization vector and constructing a vector relationship equation, can accurately remove the vector superposition effect of the probe's remanent magnetization on the measurement results. Combining the above-mentioned optically probed geomagnetic field helium-3 magnetometer construction scheme and systematic error correction scheme, this invention achieves accurate and sensitive measurement of the magnetic field.

[0012] Compared to existing technologies, this invention improves the sensitivity of nuclear spin magnetometers by utilizing a light-detecting helium-3 geomagnetic field magnetometer. It comprehensively corrects and eliminates system errors related to spin exchange and probe remanence in the light-detecting helium-3 geomagnetic field magnetometer. Compared to traditional proton magnetometers, the light-detecting helium-3 geomagnetic field magnetometer proposed in this invention achieves higher accuracy in geomagnetic field measurements, thus solving the problem of balancing accuracy and sensitivity in geomagnetic field measurements.

[0013] As a preferred embodiment, the spin-exchange frequency shift expression and the spin-exchange relaxation expression are obtained by solving the metastable spin-exchange theoretical model of Helium-3. The metastable spin-exchange theoretical model of Helium-3 is obtained by modeling the process of Helium-3 under the influence of spin exchange, external magnetic field, and relaxation. Specifically:

[0014] Based on the spin exchange interaction between helium-3 ground-state and metastable atoms, and the influence of the external magnetic field on the spin evolution of ground-state and metastable helium-3 atoms, the spin density matrix of helium-3 ground-state and metastable atoms is transformed into observable angular momentum evolution values. Combined with the relaxation of spin polarization, the theoretical model of helium-3 metastable spin exchange is established.

[0015] Based on the metastable spin exchange theory model of Helium-3, a set of time evolution equations for the ground state and metastable transverse angular momentum are established, and the set of time evolution equations is solved to obtain the spin exchange frequency shift expression and the spin exchange relaxation expression.

[0016] This preferred scheme transforms the spin density matrix into observable angular momentum evolution relationships, realizing the logical transformation from abstract theoretical description to concrete physical quantities, and making the chain from theory to experimental observability more coherent in the modeling process. By combining the relaxation of spin polarization, the incorporation of relaxation effects into the model is clarified, forming a multi-dimensional influencing factor with spin exchange and external magnetic field effects, thus fully describing the objective physical process.

[0017] As a preferred approach, based on the spin exchange interaction between helium-3 ground-state and metastable atoms, and the influence of the external magnetic field on the spin evolution of ground-state and metastable helium-3 atoms, the spin density matrices of helium-3 ground-state and metastable atoms are transformed into observable angular momentum evolution values. Combined with the relaxation of spin polarization, the theoretical model of the helium-3 metastable spin exchange is established, specifically as follows:

[0018] Establish the first density matrix equation describing the spin exchange process between helium-3 ground-state atoms and metastable atoms;

[0019] Based on the Liouville equation, an external magnetic field is introduced to establish the second density matrix equation for the ground-state and metastable-state atoms of helium-3 under the influence of the external magnetic field.

[0020] By combining the first density matrix equation and the second density matrix equation, we obtain the combined equation;

[0021] Based on the preset irreducible tensor and angular momentum operator relation, the combined equation is projected onto the transverse angular momentum direction to obtain the evolution equation of the mean transverse angular momentum of the ground state and metastable state over time.

[0022] A transverse relaxation mechanism is introduced between helium-3 ground-state and metastable atoms in spin-exchange collisions. Based on the exponential decay characteristics of the transverse angular momentum components of the ground state and metastable state over time, a set of relaxation equations for the transverse angular momentum of the ground state and metastable state is established.

[0023] Based on the mean angular momentum equation and the relaxation equations, a metastable spin exchange theoretical model for helium-3 is established.

[0024] This preferred scheme relies on the first and second density matrix equations to describe spin state evolution, accurately capturing the spin exchange interaction between ground-state and metastable atoms and the influence of external magnetic fields. Simultaneously, it introduces the Liouville equation to handle dynamic evolution, utilizing irreducible tensors and angular momentum operator relations to achieve physical quantity transformation. Furthermore, it first describes the independent effects of spin exchange and external magnetic fields using the first and second density matrix equations separately, then couples these two effects through equation merging, and finally projects the equations onto the transverse angular momentum direction to focus on experimentally observable objects. This decomposition and integration approach effectively overcomes the complexity of multi-physics coupling, ensuring the model fully covers key influencing factors while avoiding the descriptive chaos caused by the direct superposition of multiple effects.

[0025] As a preferred embodiment, a set of time evolution equations for the ground state and metastable transverse angular momentum is established based on the helium-3 metastable spin exchange theory model, and the set of time evolution equations is solved to obtain the spin exchange frequency shift expression and the spin exchange relaxation expression, specifically:

[0026] Based on the helium-3 metastable spin exchange theory model, the mean angular momentum equation and the relaxation equations are solved simultaneously to obtain the time evolution equations of the ground state and metastable transverse angular momentum.

[0027] The time evolution equations are transformed into coefficient matrices and the eigenvalues ​​are solved to obtain the spin-exchange frequency shift expression and the spin-exchange relaxation expression; wherein, the spin-exchange frequency shift expression is an odd-degree polynomial relationship between the FID frequency and the ground-state Larmor frequency, and the spin-exchange relaxation expression is an even-degree polynomial relationship between the FID relaxation rate and the FID frequency.

[0028] This preferred scheme integrates the interrelated angular momentum evolution and relaxation decay into a unified time evolution equation system by simultaneously solving the mean angular momentum equation and the relaxation equation system. This overcomes the limitations of solving single equations in isolation, fully capturing the dynamic coupling of the transverse angular momentum between the ground state and metastable state, ensuring that the results reflect the overall characteristics of the system, and improving the systematicity and accuracy of the model. The time evolution equation system is transformed into a coefficient matrix and its eigenvalues ​​are solved. These eigenvalues ​​physically correspond to the system's intrinsic frequencies and decay rates. This method transforms the solution of complex differential equation systems into matrix operations, simplifying the process.

[0029] As a preferred embodiment, the first relationship between the RF power and the FID frequency, and the second relationship between the FID relaxation rate and the FID frequency under different RF powers are measured, specifically as follows:

[0030] Within a constant external magnetic field, the helium-3 FID frequency under different radio frequency powers is measured, and the relationship between different radio frequency powers and corresponding FID frequencies is recorded to obtain the first relationship of FID frequency variation.

[0031] The relaxation rate and frequency of the helium-3 FID signal under different radio frequency powers were measured in external magnetic fields of different magnitudes. By fitting the relationship curves of relaxation rate and frequency under different radio frequency powers, the second variation relationship between the FID relaxation rate and the FID frequency under different radio frequency powers was obtained.

[0032] This preferred solution, when measuring the first variation relationship, eliminates environmental interference by stabilizing the external magnetic field and measures the FID frequency using only RF power as a variable, thus accurately capturing the independent variation law of FID frequency with RF power. When measuring the second variation relationship, by changing the external magnetic field and RF power, corresponding data of relaxation rate and frequency are obtained within a wide parameter range. Curve fitting of the data transforms discrete values ​​into a continuous quantitative expression, which can intuitively present the intrinsic relationship between relaxation rate and frequency.

[0033] As a preferred embodiment, a conversion formula between the FID frequency and the helium-3 ground-state Larmor frequency is established based on the spin-exchange frequency shift expression and the parameter set, specifically as follows:

[0034] As a preferred embodiment, based on the preset spin-exchange frequency shift expression and spin-exchange relaxation expression, the first change relationship and the second change relationship, a parameter set including the helium-3 particle number density and relaxation rate in the gas chamber is calculated, specifically as follows:

[0035] Based on the measured first and second variation relationships, the ground-state particle number density, metastable particle number density, and ground-state relaxation rate in the gas chamber are obtained by fitting the spin-exchange frequency shift expression and the spin-exchange relaxation expression.

[0036] As a preferred embodiment, a conversion formula between the FID frequency and the helium-3 ground-state Larmor frequency is established based on the spin-exchange frequency shift expression and the parameter set, specifically as follows:

[0037] Substitute the parameters of the parameter set into the spin-exchange frequency shift expression for calculation, establish a quantitative conversion relationship between the FID frequency and the helium-3 ground-state Larmor frequency, and obtain the conversion formula.

[0038] As a preferred embodiment, the probe's remanent magnetization vector is obtained by solving a system of vector relationship equations, specifically:

[0039] The FID frequency of helium-3 was measured at different angles by changing the angle between the probe of the helium-3 magnetometer and the external magnetic field.

[0040] Based on the measured values ​​of the helium 3 magnetometer obtained by converting the FID frequency of helium 3 at different angles, a set of vector relationship equations between the measured values ​​of the helium 3 magnetometer, the probe remanence, and the external magnetic field are established. The set of vector relationship equations is solved to invert the magnitude and direction of the probe remanence and obtain the probe remanence vector.

[0041] In this preferred scheme, the probe's remanence and the external magnetic field are vector superpositions. This multi-angle sampling can acquire multi-dimensional resultant magnetic field data, providing constraints for the vector relationship equations, avoiding multivalued solutions, and ensuring that the magnitude and direction of the remanence are uniquely determined. Using vector relationship equations instead of scalar calculations aligns with the physical nature of both being vectors, capturing directional coupling, avoiding the loss of directional information, and ensuring that the solution fully reflects the vector characteristics of the probe's remanence.

[0042] As a preferred embodiment, the ground-state Larmor frequency of Helium-3 is calculated based on the FID frequency according to the conversion formula to eliminate the spin exchange frequency shift. The remanence is then corrected by retrieving the remanence vector from the inversion probe. Combined with the spin-gyromagnetic ratio of the Helium-3 nucleus, the accurate geomagnetic field value after system error correction is obtained. Specifically:

[0043] Based on the FID frequency, an inversion calculation is performed according to the conversion formula to eliminate the systematic error introduced by the spin exchange frequency shift, and the ground state Larmor frequency of Helium-3 is obtained.

[0044] Based on the magnetic field value corresponding to the ground state Larmor frequency of Helium-3 and the remanent magnetization vector of the probe, the systematic error introduced by subtracting the remanent magnetization vector of the probe from the magnetic field value corresponding to the ground state Larmor frequency of Helium-3 is obtained by constructing a vector relationship equation, and then combining the spin gyromagnetic ratio of the Helium-3 nucleus to obtain the accurate geomagnetic field value after systematic error correction.

[0045] This preferred approach first obtains the ground-state Larmor frequency of Helium-3 through conversion formula inversion, thus eliminating the inherent error originating from atomic interactions. The second step targets the probe's remanence, an independent error source—the vector interference inherent in the hardware—by subtracting its contribution separately using vector relation equations. This step-by-step processing method precisely isolates and targets different types of errors, avoiding the chaotic correction caused by error superposition. It ensures that each correction step focuses on a specific error source, thereby improving overall correction efficiency.

[0046] The present invention also provides a helium-3 geomagnetic field measuring device based on optical detection, including a signal module, a relation module, a parameter module, a conversion module and a correction module;

[0047] The signal module is used to obtain the FID frequency and FID relaxation rate by polarizing and probing the helium-3 nucleus spin;

[0048] The relationship module is used to measure a first relationship between radio frequency power and the FID frequency, and a second relationship between the FID relaxation rate and the FID frequency under different radio frequency powers; wherein, the first relationship is a spin-switched frequency shift, and the second relationship is a spin-switched relaxation.

[0049] The parameter module is used to calculate a set of parameters, including the number density and relaxation rate of helium-3 particles in the gas chamber, based on preset spin-exchange frequency shift expressions and spin-exchange relaxation expressions, the first change relationship and the second change relationship.

[0050] The conversion module is used to establish a conversion formula between the FID frequency and the helium-3 ground state Larmor frequency based on the spin-exchange frequency shift expression and the parameter set.

[0051] The correction module is used to calculate the ground-state Larmor frequency of helium-3 based on the FID frequency according to the conversion formula, eliminate the spin exchange frequency shift, correct the remanence by inverting the remanence vector of the probe, and obtain the accurate geomagnetic field value after system error correction by combining the helium-3 nucleus spin gyromagnetic ratio.

[0052] The present invention also provides a storage medium storing a computer program, which is called and executed by a computer to realize the above-described method for accurate measurement of the geomagnetic field based on optical detection of helium-3. Attached Figure Description

[0053] Figure 1 This is a flowchart illustrating an accurate geomagnetic field measurement method based on optical detection of helium-3 provided in an embodiment of the present invention.

[0054] Figure 2 This is a data conversion diagram provided in an embodiment of the present invention;

[0055] Figure 3 This is a schematic diagram of the structure of the helium-3 magnetometer system based on optical detection provided in an embodiment of the present invention;

[0056] Figure 4 This is a schematic diagram of the measurement results of the relationship between Helium 3 FID frequency and radio frequency power provided in an embodiment of the present invention;

[0057] Figure 5 This is a schematic diagram of the first measurement and fitting results provided in an embodiment of the present invention;

[0058] Figure 6 This is a schematic diagram of the second measurement and fitting results provided in an embodiment of the present invention;

[0059] Figure 7 This is a schematic diagram of the structure of a helium-3 geomagnetic field measuring device based on optical detection provided in an embodiment of the present invention;

[0060] Figure 8 This is a schematic diagram of the structure of a high-accuracy geomagnetic field measuring device based on helium-3 provided in an embodiment of the present invention. Detailed Implementation

[0061] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0062] In the description of this invention, it should be understood that the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first," "second," and "third" may explicitly or implicitly include one or more of that feature.

[0063] The present invention provides an accurate geomagnetic field measurement method based on optically detected helium-3, which aims to improve the sensitivity and accuracy of geomagnetic field measurement through technological innovation. It theoretically models and corrects key system errors such as spin exchange and probe remanence in optically detected helium-3 FID magnetometers, thereby constructing a high-accuracy helium-3 measurement system suitable for geomagnetic field environments.

[0064] Example 1:

[0065] Please see Figure 1 The present invention provides an accurate method for measuring the geomagnetic field based on optical detection of helium-3, comprising steps S1 to S5, and the specific implementation steps are as follows:

[0066] S1. By polarizing and probing the spin of helium-3 nuclei, the FID frequency and FID relaxation rate are obtained.

[0067] In this embodiment of the invention, step S1 includes S1.1 to S1.3; wherein, S1.1 is the process of magnetic field measurement, S1.2 is the process of establishing a metastable spin exchange theoretical model of helium-3, and S1.3 is the process of solving for the spin exchange frequency shift expression, the spin exchange relaxation expression, and f based on the metastable spin exchange theoretical model of helium-3. g '(f g ,n g ,b (0) ,b (0) The process is as follows:

[0068] S1.1 Construct a helium-3 FID magnetometer system based on optical detection. This system is used to acquire FID signals under specific radio frequency power and external magnetic field conditions, and extract their frequency and relaxation rate through signal processing. Furthermore, the core components of this system include: a helium-3 gas chamber, a probe light source, a pump light source, a magnetic field pulse coil, a photodetector, a main magnetic field coil, a main magnetic field current source, a radio frequency power source, and various optical components.

[0069] Based on a photodetector-type helium-3 FID magnetometer system, external magnetic fields of varying magnitudes are generated. Macroscopic longitudinal polarization is formed by polarizing the helium-3 nuclear spin, providing initial conditions for the subsequent precession signal generation. A magnetic field pulse perpendicular to the external magnetic field is used to transfer the longitudinal polarization to the transverse direction, allowing the nuclear spin to acquire a component perpendicular to the external magnetic field, thus precessing around the magnetic field direction under the influence of the external magnetic field's magnetic torque. Finally, magnetic field information is acquired by detecting the FID signal, obtaining the FID frequency and FID relaxation rate of helium-3 under the external magnetic field. The specific steps are as follows:

[0070] ① Based on the optically detected helium-3 FID magnetometer system, external magnetic fields of different magnitudes are generated: In the optically detected helium-3 FID magnetometer system, the current source is connected to the main magnetic field coil, and the constant current output by it can generate a stable main magnetic field in the main magnetic field coil; while the instrument control and signal processing terminal can flexibly change the intensity of the main magnetic field by adjusting the output parameters of the current source to adapt to the measurement scenario requirements of different external magnetic field magnitudes.

[0071] ② Based on the optically probed helium-3 FID magnetometer system, the helium-3 nuclear spin is polarized: the pump light (wavelength 1083.327nm, power about 300mW) that resonates with the helium-3 C9 energy level interacts with the helium-3 gas cell in the radio frequency discharge state along the longitudinal direction (i.e. the direction of the external magnetic field to be measured), and completes the polarization of the metastable helium-3 atom; then, by means of the spin exchange effect between the ground state and metastable atoms in the gas cell, the polarization characteristics of the metastable state are transferred to the ground state, and finally the polarization of the helium-3 ground state energy level nuclear spin is realized.

[0072] ③ Based on the optical detection type helium-3 FID magnetometer system, the transverse polarization of helium-3 nuclear spin is formed: using a magnetic field pulse (frequency close to the helium-3 ground state Larmor frequency) perpendicular to the direction of the external magnetic field, the longitudinal polarization of the atom is transferred to the transverse direction, that is, perpendicular to the direction of the external magnetic field.

[0073] ④ Detecting FID signals, including physical detection methods and parameter extraction methods for FID signals:

[0074] (1) Based on the optical detection type helium-3 FID magnetometer system, the FID signal of helium-3 nucleus spin precessing around an external magnetic field is detected and its frequency and relaxation rate are obtained: using a detection light with a wavelength of 1083.331nm and a power of 1mW, the light interacts with the helium-3 cell in the radio frequency discharge state in the transverse direction to detect the FID signal of the helium-3 cell, and then obtain its frequency and relaxation rate, that is, the FID frequency and FID relaxation rate of helium-3 under an external magnetic field are obtained.

[0075] (2) Based on the optically probed helium-3 FID magnetometer system, the frequency and relaxation rate of the helium-3 FID signal are obtained, specifically including:

[0076] The helium-3 FID signal was recorded using the acquisition card of a photodetector-type helium-3 FID magnetometer system. The signal format was as follows:

[0077]

[0078] Where A is the amplitude of the helium-3 nuclear spin FID signal, Γ g ' is the relaxation rate of the helium-3 nuclear spin FID signal, f g ' is the frequency of the helium-3 nuclear spin FID signal, φ is the initial phase of the helium-3 nuclear spin FID signal, b is the DC quantity in the helium-3 nuclear spin FID signal, e is the natural constant, and t is the time variable.

[0079] By fitting the FID signal using the above formula, the frequency and relaxation rate of the FID signal can be obtained, which means the FID frequency and FID relaxation rate of helium-3 under an external magnetic field can be obtained.

[0080] S1.2 Establish the first density matrix equation describing the spin exchange process between the ground-state and metastable helium-3 atoms;

[0081] Based on the Liouville equation, an external magnetic field is introduced to establish the second density matrix equation for helium-3 ground-state and metastable atoms under the influence of an external magnetic field.

[0082] By combining the first density matrix equation and the second density matrix equation, we obtain the combined equation;

[0083] Based on the pre-defined irreducible tensor and angular momentum operator relations, the combined equations are projected onto the transverse angular momentum direction to obtain the evolution equations of the mean transverse angular momentum of the ground state and metastable state over time.

[0084] A transverse relaxation mechanism is introduced between helium-3 ground-state and metastable atoms in spin-exchange collisions. Based on the exponential decay characteristics of the transverse angular momentum components of the ground state and metastable state over time, a set of relaxation equations for the transverse angular momentum of the ground state and metastable state is established.

[0085] Based on the mean angular momentum equation and the relaxation equations, a metastable spin exchange theoretical model of helium-3 is established.

[0086] The specific process of establishing the above metastable spin exchange theory model of helium-3 is as follows:

[0087] ① Establish the first density matrix equation describing the spin exchange process between helium-3 ground-state and metastable-state atoms. Specifically, model the process of helium-3 under the influence of spin exchange, external magnetic field, and relaxation to obtain the first density matrix equation (Equation 2-3):

[0088]

[0089] Among them, for 1 / T MEC1 and 1 / T MEC2 have:

[0090]

[0091] Where, ρ g and ρ m Let Tr represent the density matrices of the ground-state and metastable atoms, respectively. n With Tr e The operators represent the traces of the neutron and electron components in the density matrix, respectively. (i = 1, 2, F1 = 1 / 2, F2 = 3 / 2) represents the projection onto the hyperfine structure, while 1 / T MEC1 and 1 / T MEC2 These are the collision exchange rates of the ground state and metastable state, respectively; n m and n g These represent the atomic number densities in the metastable and ground states, respectively. Where k... ME =154×10 -18 (T / 300) 1.09 m 3 / s is the collision coefficient of metastable spin exchange. T is the Kelvin temperature.

[0092] Furthermore, the physical meaning of the above equation is that the spin exchange frequency of the ground state is directly proportional to the number density of metastable particles, and the spin exchange frequency of the metastable state is directly proportional to the number density of ground state particles; while during the collision process, the ground state atom and the metastable atom will exchange the state of their extranuclear electrons.

[0093] ② Based on the Liouville equation, an external magnetic field is introduced to establish the second density matrix equation for helium-3 ground-state and metastable atoms under the influence of an external magnetic field. Specifically, based on the Liouville equation, the second density matrix equation for the helium-3 ground-state and metastable state density matrices under the influence of an external magnetic field is established (Equation 6):

[0094]

[0095] in, It is the density matrix describing the spins of helium-3 atoms in the ground state (g) and metastable state (m). The external magnetic field to be measured, and These are the magnetic moments of the outer electrons and the atomic nucleus, respectively, g s It is the Lande g factor of electron spin in a helium-3 atom, g I It is the Lande g-factor of the nuclear spin in a helium-3 atom, μ B It is the Bohr magneton, where i is the imaginary unit. It is the reduced Planck constant.

[0096] ③ By combining the first density matrix equation and the second density matrix equation, the effects of spin exchange and external magnetic field are superimposed into the complete Liouville equation, resulting in the combined equation.

[0097] ④ Based on the pre-defined irreducible tensor and angular momentum operator relations, the combined equations are projected onto the transverse angular momentum direction to obtain the evolution equations of the mean transverse angular momentum over time for the ground state and metastable state. Specifically:

[0098] Using the irreducible tensor to represent the density matrix, the third density matrix is ​​obtained (Equation 7); based on the relationship between the first-order irreducible tensor operator and the angular momentum operator, the relation of the angular momentum operator is established (Equation 8):

[0099]

[0100] in, Let represent an irreducible tensor formed by the coupling of two angular momentum particles with spin I, with order κ and components p. Indicates transpose; <> is the mean operator; It is a spin angular momentum operator The p-component.

[0101] By projecting the combined equations onto the transverse angular momentum direction using the third density matrix (Equation 7) and the angular momentum operator relation (Equation 8) and simplifying them, we obtain the evolution equations of the mean transverse angular momentum over time for the ground state and metastable state. That is, the density matrix equations of Helium 3 under the influence of spin exchange and external magnetic field (Equations 2-3, 6) are expressed as the evolution equations of the mean transverse angular momentum over time for the ground state and metastable state (Equations 9-11):

[0102]

[0103] in, and These are the expected values ​​of the transverse angular momentum of the atoms in the ground state, metastable states F1 = 1 / 2, and F2 = 3 / 2, which are generated by projecting the density matrix onto the space of the first-order irreducible tensor operator. g It is the precession frequency of the expected value of the transverse angular momentum of a ground-state helium-3 atom under an external magnetic field. and These are the gyromagnetic ratios of helium-3 atoms in the metastable F1 = 1 / 2 and F2 = 3 / 2 energy levels, respectively, and γ g It is the ground-state gyromagnetic ratio, and i is the imaginary unit.

[0104] ⑤ Introducing the transverse relaxation mechanism of helium-3 ground-state and metastable atoms in spin-exchange collisions, and based on the exponential decay characteristics of the transverse angular momentum components of the ground state and metastable state over time, a set of relaxation equations for the transverse angular momentum of the ground state and metastable state are established. Specifically:

[0105] Due to the relaxation phenomenon of polarized atomic spins, the mean angular momentum perpendicular to the external magnetic field in the metastable state and ground state is affected by the relaxation effect. Its evolution can be described by the equations shown in Equations 12-14:

[0106]

[0107] The relaxation process within the helium-3 chamber is mainly affected by two factors: first, the transition from the ground state dominated by nonpolar electrons generated by radio frequency power to the metastable state (corresponding to the relaxation rate Γ). g Secondly, the metastable state transition to the ground state, dominated by the metastable level lifetime (corresponding to the relaxation rate Γ), is another factor. m Under the dominance of these two types of processes, the correlation of the relaxation process is shown in Equation 15:

[0108] Γ m n m =Γ g n g (15)

[0109] Equations 12-15 constitute the relaxation equations for the transverse angular momentum of the ground state and metastable state.

[0110] For an explanation of the embodiments of the present invention, please refer to [link / reference]. Figure 2 , Figure 2 This is a data conversion diagram provided in an embodiment of the present invention, which illustrates the relationship between two types of relaxation transition processes: one is the transition from the ground state to a metastable state dominated by nonpolar electrons generated by radio frequency power (corresponding to relaxation rate Γ). g Another type is the metastable-to-ground state transition dominated by the lifetime of the metastable energy level (corresponding to the relaxation rate Γ). m ).

[0111] ⑥ Based on the mean angular momentum equation and the relaxation equations, a metastable spin exchange theoretical model of helium-3 is established.

[0112] This embodiment, S1.2, relies on the first and second density matrix equations to describe spin state evolution, accurately capturing the spin exchange interaction between ground-state and metastable atoms and the influence of the external magnetic field. Simultaneously, the Liouville equation is introduced to handle dynamic evolution, utilizing irreducible tensors and angular momentum operator relations to achieve physical quantity transformation. Furthermore, the independent effects of spin exchange and the external magnetic field are first described using the first and second density matrix equations respectively, then the coupling of the two effects is achieved through equation merging, and finally projected onto the transverse angular momentum direction to focus on the experimentally observable object. This decomposition and integration method effectively overcomes the complexity of multi-physics coupling, ensuring the model fully covers key influencing factors while avoiding the descriptive chaos caused by the direct superposition of multiple effects.

[0113] S1.3. Based on the metastable spin exchange theory model of Helium-3, the mean angular momentum equation (Equation 9-11) and the relaxation equations (Equation 12-15) are solved simultaneously to obtain the time evolution equations of the transverse angular momentum in the ground state and metastable state (Equation 16-18). Specifically, by simultaneously solving Equations 9-11 and 12-15, the relaxation effect is superimposed into the angular momentum evolution equation, thus constructing a quantitative correlation bridge between experimental parameters and the theoretical model. On this basis, intermediate variables are eliminated, and core physical factors such as spin exchange, external magnetic field influence, and relaxation effect are integrated to obtain the time evolution equations of the transverse angular momentum in the ground state and metastable state—Equation 16-18.

[0114] The time evolution equations (Equations 16-18) are transformed into a coefficient matrix (Equation 19) and the eigenvalues ​​are solved to obtain the spin-exchange frequency shift expression (Equation 20) and the relaxation rate-ground state Larmor frequency relationship (Equation 24).

[0115] Based on the spin-exchange frequency shift expression (Equation 20) and the relaxation rate-ground state Larmor frequency relationship (Equation 24), the spin-exchange relaxation expression (Equation 28) is derived, and f is obtained by inverse solution. g '(f g ,n g ,b (0) ,b (2) That is, to obtain the helium-3 FID frequency f g Regarding the ground state particle number density n g The ground-state Larmor frequency f of Helium-3 g And the quadratic function of degree 0, b (0) 2 times b (2) The coefficients are functions. The spin-exchange frequency shift expression is an odd-degree polynomial relationship between the FID frequency and the ground-state Larmor frequency, and the spin-exchange relaxation expression is an even-degree polynomial relationship between the FID relaxation rate and the FID frequency.

[0116] The time evolution equations are (Equations 16-18):

[0117]

[0118] Among them, 1 / T MEC1 =n m k ME and 1 / T MEC2 =n g k ME These are the collision exchange rates of the ground state and metastable state, respectively, n m and n g These are the atomic number densities in the metastable and ground states, respectively, k ME =154×10 -18 (T / 300) 1.09 m 3 / s is the collision cross section of metastable spin exchange. T is the Kelvin temperature. and These are the expected values ​​of the transverse angular momentum of the atoms in the ground state, metastable state, F1 = 1 / 2, and F2 = 3 / 2.

[0119] Among them, the coefficient matrix (Equation 19) is first written out to solve the three first-order differential equations in equations 16-18 using the characteristic root method:

[0120]

[0121] The coefficient matrix has three eigenvalues, and this invention focuses on the eigenvalue "2πif" of the ground state precession frequency. g '+Γ g '". Under an external magnetic field of 8000 nT, f g The expression for ' is (the spin-transformation frequency shift expression, Equation 20):

[0122] f g '=f g +a (1) f g +a (3) f g 3 +a (5) f g 5 +O(10 -5 Hz)(20)

[0123] Among them, f g =γ g B is the ground-state Larmor frequency of Helium-3 without spin exchange. The physical meaning of Equation 20 is that the frequency shift introduced by spin exchange is an odd-degree polynomial of the ground-state Larmor frequency; the coefficients of this spin exchange frequency shift expression are (Equations 21-23):

[0124]

[0125] Γ' gThe expression is (relaxation rate-ground state Larmor frequency relationship, Equation 24):

[0126] Γ g '=c (0) +c (2) f g 2 +c (4) f g 4 +O(10 -5 s -1 ),(twenty four)

[0127] Among them, the relaxation rate Γ of the FID signal g 'and the Larmor frequency f of the ground state of Helium-3 g Given the even-degree polynomial relationship, the coefficients of this spin-exchange relaxation expression are (Equation 25-27):

[0128]

[0129] Based on the spin-exchange frequency shift expression (Equation 20) and the relaxation rate-ground state Larmor frequency relationship (Equation 24), the spin-exchange relaxation expression (Equation 28) is derived, and f is obtained by inverse solution. g '(f g ,n g ,b (0) ,b (2) That is, to obtain the helium-3 FID frequency f g Regarding the ground state particle number density n g The ground-state Larmor frequency f of Helium-3 g And the quadratic function of degree 0, b (0) 2 times b (2) The function of the coefficients is specifically:

[0130] ① Combining the spin-exchange frequency shift expression (Equation 20) and the relaxation rate-ground state Larmor frequency relationship (Equation 24), the relaxation rate Γ of the FID signal is established. g 'and frequency f g From the relationship between the two, we obtain the expression for the relationship between the 0th and 2nd order coefficients of spin exchange relaxation (equation 28 for spin exchange relaxation):

[0131] Γ g '=b (0) +b (2) f g ' 2 +b (4) f g ' 4 +O(10 -5 s -1 ), (28)

[0132] Among them, b (0) b (2) and b (4) They are respectively (Equations 29-31):

[0133]

[0134] ②The metastable particle number density n m and ground state relaxation rate Γ g Expressed as ground-state particle number density, helium-3 ground-state Larmor frequency, and quartic function (excluding tertiary) 0th order b. (0) 2 times b (2) A function of coefficients, i.e., based on b (0) and b (2) The expression (Equation 29-30) can be used to solve for the metastable particle number density n. m and ground state relaxation rate Γ g (Equation 32):

[0135]

[0136] ③ Substituting equation 32 into equation 20, we can obtain f g '(f g ,n g ,b (0) ,b (2) That is, we get: Helium-3 FID frequency f g Regarding the ground state particle number density n g The ground-state Larmor frequency f of Helium-3 g And the quadratic function of degree 0, b (0) 2 times b (2) The coefficients are functions, and their specific expressions can be obtained through computation using the Mathematica symbolic computation software.

[0137] In this embodiment, S1.3 integrates the interrelated angular momentum evolution and relaxation decay into a unified time evolution equation system by simultaneously solving the mean angular momentum equation and the relaxation equation system. This overcomes the limitation of solving a single equation in isolation, fully capturing the dynamic coupling of the transverse angular momentum between the ground state and metastable state, ensuring that the results reflect the overall characteristics of the system, and improving the systematicity and accuracy of the model. The time evolution equation system is transformed into a coefficient matrix and its eigenvalues ​​are solved. These eigenvalues ​​physically correspond to the system's intrinsic frequencies and decay rates. This method transforms the solution of complex differential equation systems into matrix operations, simplifying the process.

[0138] In summary, S1.2-S1.3 of this embodiment transforms the spin density matrix into observable angular momentum evolution relationships, realizing the logical transformation from abstract theoretical description to specific physical quantities, making the chain from theory to experimental observability more coherent in the modeling process. By combining the relaxation of spin polarization, the incorporation of relaxation effects into the model is clarified, forming a multi-dimensional influencing factor with spin exchange and external magnetic field effects, thus fully describing the objective physical process.

[0139] S2. Measure the first relationship between RF power and FID frequency, and the second relationship between FID relaxation rate and FID frequency under different RF powers; wherein, the first relationship is spin-switched frequency shift, and the second relationship is spin-switched relaxation.

[0140] Step S2 in this embodiment of the invention is specifically as follows:

[0141] Based on a photodetector-type helium-3 FID magnetometer system, the frequency f of the helium-3 FID signal under different radio frequency powers is measured within a generated constant external magnetic field (time-domain peak-to-peak value less than 10 pT). g (i.e., spin-switching frequency shift phenomenon), and record the relationship between different radio frequency powers and corresponding FID frequencies to obtain the first relationship of FID frequency variation. Specifically: the optically probed helium-3 FID magnetometer system is equipped with a radio frequency power source, whose function is to generate metastable helium-3 atoms in the helium-3 chamber. Under a constant external magnetic field environment of approximately 8000 nT, by changing the radio frequency power (P... RF The frequency (f) of the helium-3 FID signal under different radio frequency power conditions was measured and recorded. g From this, the first variation relationship of FID frequency (f) is obtained. g '-P RF ).

[0142] In one possible implementation, the optically detected helium-3 FID magnetometer system includes a magnetic field generation module (shielding cylinder, main magnetic field coil, constant current source), a helium-3 FID signal generation module (laser source, optical components, helium-3 atom gas chamber, radio frequency excitation source, signal generator, Pi / 2 pulse coil), and a helium-3 FID signal acquisition module (photodetector, preamplifier, analog-to-digital converter signal acquisition card, rubidium clock, terminal equipment). The shielding cylinder, main magnetic field coil, and constant current source are used to shield external magnetic fields and generate a stable axial main magnetic field. The laser source is used to generate linearly polarized probe light and circularly polarized pump light. The optical elements include a polarizing beam splitter (PBS), a quarter-wave plate, a half-wave plate, and a convex lens, used to adjust the optical path and laser polarization state. The atomic gas chamber includes a pure helium-3 atomic gas chamber (approximately 10 torr). The radio frequency excitation source is used to generate metastable atoms in the helium-3 gas chamber, and the number density of metastable atoms changes with the radio frequency power. The signal generator and Pi / 2 pulse coil are used to generate Pi / 2 pulses, which generate transverse atomic spin polarization in the helium-3 gas chamber. The photodetector, preamplifier, analog-to-digital converter, rubidium clock, and terminal equipment are used to receive the helium-3 FID signal in the light, amplify and fit it sequentially to obtain its frequency and relaxation rate.

[0143] Specifically, in one embodiment, the acquisition of the helium-3 FID signal frequency under different radio frequency (RF) powers is automated using a MatLab program. The frequency of the helium-3 FID signal under different RF power conditions is measured and recorded. The steps include: First, setting the RF power to a specific value using a control terminal; second, controlling the pump laser emission using the control terminal to form macroscopic atomic longitudinal polarization within the helium-3 gas chamber; third, controlling a signal generator to generate an AC pulse with near-resonance and the Larmor frequency of the helium-3 ground state, and inputting the AC pulse into a Pi / 2 pulse coil to form macroscopic atomic transverse polarization within the helium-3 gas chamber; finally, using a control analog-to-digital converter signal acquisition card, reading the helium-3 FID signal carried by the probe light passing through the gas chamber, and fitting the signal in MatLab to obtain the helium-3 FID signal frequency and relaxation rate under that RF power. The above steps are repeated for each RF power to obtain the helium-3 FID signal frequency under different RF powers.

[0144] For an explanation of the embodiments of the present invention, please refer to [link / reference]. Figure 3 , Figure 3 This is a schematic diagram of the structure of a helium-3 magnetometer system based on optical detection provided in an embodiment of the present invention, showing the structure of the optical detection type helium-3 FID magnetometer system.

[0145] Based on a photodetector-type helium-3 FID magnetometer system, the relaxation rate and frequency of the helium-3 FID signal are measured under different radio frequency (RF) powers within generated external magnetic fields of varying magnitudes, thus obtaining the FID frequency and relaxation rate. By fitting the relationship curves of relaxation rate and frequency under different RF powers, the curve of the helium-3 FID signal relaxation rate versus its frequency is obtained, representing a second relationship between the FID relaxation rate and FID frequency under different RF powers. Based on this second relationship, the 0th and 2nd order spin-exchange relaxation coefficients of the curves under different RF powers are obtained using a quartic function (excluding cubic). Specifically, a specific RF power is selected, and the photodetector-type helium-3 FID magnetometer system is operated under this power condition. The curves of the helium-3 FID signal relaxation rate versus its frequency (f) under different external magnetic fields are measured and recorded. g '-Г g 'atP RF Furthermore, the above measurement and recording steps are repeated under different radio frequency powers to obtain a second relationship between the relaxation rate and the FID frequency of the helium-3 FID signal. This process can be automated by a MatLab program.

[0146] In one embodiment, the 0th and 2nd order coefficients of spin-exchange relaxation under different radio frequency (RF) powers are measured using automated control via a MATLAB program. The relationship between the relaxation rate and frequency of the helium-3 FID signal under different RF power conditions is measured and recorded, and the 0th and 2nd order coefficients are obtained through fitting. The steps include: first, setting the RF power to a specific value using a control terminal; second, setting the current source current to a specific value using a control terminal, which generates a magnetic field of a specific magnitude in the main magnetic field coil; and third, obtaining and recording the frequency and relaxation rate of the helium-3 FID signal under the same RF power and magnetic field, based on the same steps described above. The above steps are repeated for each RF power and each magnetic field value to obtain the relationship between the relaxation rate and frequency of the helium-3 FID signal under different RF powers, and then fitting it with a quadratic function, as shown in the figure. Figure 4 As shown.

[0147] For an explanation of the embodiments of the present invention, please refer to [link / reference]. Figure 4 , Figure 4 This is a schematic diagram of the measurement results of the relationship between the frequency and radio frequency power of Helium 3FID provided in the embodiment of the present invention. It shows the relationship between the relaxation rate and frequency of the Helium 3FID signal under different radio frequency powers, and the results obtained by fitting it with a quadratic function.

[0148] The first change relationship is spin-exchange frequency shift, and the second change relationship is spin-exchange relaxation.

[0149] In this embodiment S2, when measuring the first variation relationship, environmental interference is eliminated by stabilizing the external magnetic field, and FID frequency is measured using only radio frequency power as a variable. This allows for accurate capture of the independent variation law of FID frequency with radio frequency power. When measuring the second variation relationship, by changing the external magnetic field and radio frequency power, corresponding data of relaxation rate and frequency are obtained within a wide parameter range. Curve fitting is performed on the data, transforming discrete values ​​into a continuous quantitative expression, which can intuitively present the intrinsic relationship between relaxation rate and frequency.

[0150] S3. Based on the preset spin-exchange frequency shift expression and spin-exchange relaxation expression, the first change relationship and the second change relationship, calculate the parameter set including the number density and relaxation rate of helium-3 particles in the gas chamber.

[0151] Step S3 in this embodiment of the invention is specifically as follows:

[0152] Based on the measured first and second variation relationships, according to the spin-exchange frequency shift expression (Equation 20) and the spin-exchange relaxation expression (Equation 28), and the 0th and 2nd order spin-exchange relaxation coefficients of the curves under different RF powers obtained by fitting according to the second variation relationship, the f is fitted. g '(f g ,n g ,b (0) ,b (2) The curve yields the ground-state particle number density n in the helium-3 chamber. g Among them, "f" g '(f g ,n g ,b (0) ,b (2) The process of establishing “)” is described in detail in Example S1;

[0153] Furthermore, based on the metastable particle number density n m and ground state relaxation rate Γ g The expression (Equation 32), combined with the already obtained n g and b at various RF powers (0) b (2) The coefficient was used to calculate the metastable particle number density n under different radio frequency powers. m and ground state relaxation rate Γ g The ground-state particle number density n obtained from the calculation g Metastable particle number density n m and ground state relaxation rate Γ g This constitutes a parameter set.

[0154] For an explanation of the embodiments of the present invention, please refer to [link / reference]. Figure 5-6 , Figure 5This is a schematic diagram of the first measurement and fitting results provided in an embodiment of the present invention, showing the measurement and fitting results of the relationship between the helium-3 FID frequency and relaxation rate as a function of radio frequency power.

[0155] Figure 6 This is a schematic diagram of the second measurement and fitting results provided in an embodiment of the present invention, showing the measurement and fitting results of the helium-3 FID frequency and the 0th and 2nd order coefficients of spin exchange relaxation.

[0156] S4. Establish the conversion formula between FID frequency and Lamoir frequency of helium-3 ground state based on the spin-exchange frequency shift expression and parameter set.

[0157] Step S4 of this embodiment of the invention is specifically as follows:

[0158] The ground-state particle number density n in the helium-3 chamber of the parameter set. g Metastable particle number density n under different radio frequency powers m and ground state relaxation rate Γ g Substituting the spin-exchange frequency shift expression (Equation 20) into the equation, a quantitative conversion relationship between the FID frequency and the helium-3 ground-state Larmor frequency is established, yielding the FID frequency f. g 'and the ground state Larmor frequency f of Helium-3 g The conversion formula.

[0159] Among them, f g ' is the measured frequency of the helium-3 FID signal, that is, the spin precession frequency of the helium-3 nucleus detected experimentally. It is affected by systematic errors such as spin exchange and is not the true frequency corresponding to the external magnetic field. f g It is the Larmor frequency (f) of the ground state of Helium-3. g =Bγ g , where γ g (where B is the ground-state gyromagnetic ratio of helium-3 and B is the external magnetic field), representing the true frequency corresponding to the external magnetic field, unaffected by errors such as spin exchange, and requires f to be used. g 'Physical quantities derived from data.' g ' is the relaxation rate of the helium-3 nuclear spin FID signal, representing the rate at which the FID signal decays over time during precession. Г g It is the ground state relaxation rate, which is affected by the ground state to metastable state transition process dominated by nonpolar electrons generated by the radio frequency power in the helium-3 chamber.

[0160] S5. Calculate the ground-state Larmor frequency of Helium-3 based on the conversion formula and FID frequency, eliminate the spin exchange frequency shift, and correct the remanence by inverting the probe remanence vector. Combine the Helium-3 nucleus spin gyromagnetic ratio to obtain the accurate geomagnetic field value after system error correction.

[0161] Step S5 in this embodiment of the invention includes S5.1 to S5.2, specifically as follows:

[0162] S5.1 Based on the optically probed helium-3 FID magnetometer system, the FID frequency of helium-3 is measured at different probe angles by changing the angle between the probe of the helium-3 FID magnetometer and the external magnetic field. After converting the FID frequency of helium-3 at different probe angles into the measured value of the helium-3 magnetometer, a set of vector relationship equations between the measured value of the helium-3 magnetometer, the remanence of the probe, and the external magnetic field is established. The set of vector relationship equations is solved to invert the magnitude and direction of the remanence of the probe and obtain the remanence vector of the probe.

[0163] The vector relation equations are given by equation (33):

[0164] B 2 read =B 2 residual +B 2 -|B residual ||B|Cosθ,(33)

[0165] Among them, B read These are measurements from a helium-3 magnetometer, B. residual It is remanence, B is the magnitude of the external magnetic field to be measured, and θ is the remanence of B. residual The angle between B and B, bolded to indicate that the variable is a vector.

[0166] In this embodiment S5.1, the probe's remanence and the external magnetic field are in a vector superposition relationship. This multi-angle sampling can acquire multi-dimensional resultant magnetic field data, providing constraints for the vector relationship equations, avoiding multi-valued solutions, and ensuring that the magnitude and direction of the remanence are uniquely determined. Using a vector relationship equation system instead of scalar calculations aligns with the physical nature of both being vectors, capturing directional coupling relationships, avoiding the loss of directional information, and ensuring that the solution fully reflects the vector characteristics of the probe's remanence.

[0167] S5.2 Based on the measured FID frequency, perform inversion calculation according to the conversion formula to eliminate the systematic error introduced by the spin exchange frequency shift and obtain the ground state Larmor frequency of Helium-3;

[0168] Based on the magnetic field value corresponding to the ground state Larmor frequency of Helium-3 and the probe remanent magnetization vector, the systematic error introduced by subtracting the probe remanent magnetization vector from the magnetic field value corresponding to the ground state Larmor frequency of Helium-3 by constructing a vector relationship equation, and combining the spin gyromagnetic ratio of the Helium-3 nucleus, the accurate geomagnetic field value after systematic error correction is obtained.

[0169] In this embodiment, S5.2 firstly, the ground-state Larmor frequency of Helium-3 is obtained through conversion formula inversion, which eliminates the inherent error originating from atomic interactions. Secondly, for the independent error source of probe remanence, namely the vector interference inherent in the hardware, its contribution is subtracted separately using vector relationship equations. This step-by-step processing method allows different types of errors to be precisely isolated and targeted for correction, avoiding the correction chaos caused by error superposition, ensuring that each correction step focuses on a specific error source, thereby improving the overall correction efficiency.

[0170] It should be noted that the derivation and calculation processes involved in this embodiment can all be systematically automated and accurately executed using MATLAB programs.

[0171] Overall, this embodiment has the following beneficial effects:

[0172] This invention, based on the spin-exchange frequency shift and spin-exchange relaxation expressions, combined with the first relationship between radio frequency power and FID frequency, and the second relationship between FID frequency and relaxation rate, calculates a set of key parameters such as the helium-3 particle number density and relaxation rate in the gas chamber. It then establishes a precise mathematical mapping between the FID frequency and the ground-state Larmor frequency. By using a quantitative conversion formula to invert the FID frequency, it not only accurately eliminates the systematic error introduced by the spin-exchange frequency shift but also enables the measurement of particle number density and other parameters within the gas chamber. Furthermore, the superposition effect of the probe's remanent magnetization can cause the amplitude and direction of the magnetic field signal measured by the helium-3 magnetometer to differ from the signal to be measured, resulting in systematic errors. This invention, by inverting the probe's remanent magnetization vector and constructing a vector relationship equation, can accurately remove the vector superposition effect of the probe's remanent magnetization on the measurement results. Combining the above-mentioned optically probed geomagnetic field helium-3 magnetometer construction scheme and systematic error correction scheme, this invention achieves accurate and sensitive measurement of the magnetic field.

[0173] In summary, this invention measures the FID signal of the helium-3 cell and uses an automated control program to measure and record the frequency of the helium-3 cell FID signal at different radio frequency powers, as well as the 0th and 2nd order spin exchange relaxation coefficients of the helium-3 cell at different radio frequency powers. Numerical fitting and calculation are used to obtain the helium-3 particle number density and relaxation rate parameters within the cell, and based on these parameters, the numerical relationship between the helium-3 FID signal frequency and the ground-state Larmor frequency is derived. Furthermore, by measuring the FID signal frequency of the helium-3 probe at different angles, the magnitude and direction of the probe's remanence are calculated. Finally, by combining the elimination of the two types of systematic errors mentioned above, accurate measurement of the geomagnetic field based on a photodetector-type helium-3 magnetometer is achieved. Compared with traditional methods for accurate magnetic field measurement using proton magnetometers, this invention, relying on a photodetector-type helium-3 nuclear spin magnetometer and comprehensive systematic error analysis, significantly improves the sensitivity and accuracy of accurate geomagnetic field measurement.

[0174] Example 2:

[0175] Please see Figure 7 The present invention provides a helium-3 geomagnetic field measuring device based on optical detection, including a signal module 10, a relation module 20, a parameter module 30, a conversion module 40 and a correction module 50;

[0176] Among them, the signal module 10 is used to obtain the FID frequency and FID relaxation rate by polarizing and probing the spin of helium-3 nuclei;

[0177] The relationship module 20 is used to measure the first relationship between RF power and FID frequency, and the second relationship between FID relaxation rate and FID frequency under different RF powers; wherein, the first relationship is spin-switched frequency shift, and the second relationship is spin-switched relaxation.

[0178] The parameter module 30 is used to calculate a set of parameters, including the number density and relaxation rate of helium-3 particles in the gas chamber, based on the preset spin-exchange frequency shift expression and spin-exchange relaxation expression, the first change relationship and the second change relationship.

[0179] The conversion module 40 is used to establish the conversion formula between the FID frequency and the ground state Larmor frequency of helium-3 based on the spin-exchange frequency shift expression and parameter set.

[0180] The correction module 50 is used to calculate the ground state Larmor frequency of helium-3 based on the conversion formula and the FID frequency, eliminate the spin exchange frequency shift, and correct the remanence by inverting the remanence vector of the probe. Combined with the spin gyromagnetic ratio of the helium-3 nucleus, the accurate geomagnetic field value after system error correction is obtained.

[0181] In one embodiment, the signal module 10 includes a data unit, a model unit, and a solution unit; wherein, the data unit is for the process of magnetic field measurement, the model unit is for the process of establishing a metastable spin exchange theory model of helium-3, and the solution unit is for solving the spin exchange frequency shift expression, the spin exchange relaxation expression, and f based on the helium-3 metastable spin exchange theory model. g '(f g ,n g ,b (0) ,b (0) The process;

[0182] The data unit is used to build a photodetector-based helium-3 FID magnetometer system. This system is used to acquire FID signals under specific radio frequency power and external magnetic field conditions, and extract their frequency and relaxation rate through signal processing. Furthermore, the core components of this system include: a helium-3 gas chamber, a probe light source, a pump light source, a magnetic field pulse coil, a photodetector, a main magnetic field coil, a main magnetic field current source, a radio frequency power source, and various optical components.

[0183] The data unit is also used to generate external magnetic fields of different magnitudes based on a photodetector-type helium-3 FID magnetometer system; to form macroscopic longitudinal polarization by polarizing the helium-3 nuclear spin, providing initial conditions for the subsequent precession signal generation; to transfer the longitudinal polarization to the transverse direction using a magnetic field pulse perpendicular to the external magnetic field, so that the nuclear spin acquires a component perpendicular to the external magnetic field, and then precesses around the magnetic field direction under the action of the magnetic torque of the external magnetic field; finally, magnetic field information is acquired by detecting the FID signal to obtain the FID frequency and FID relaxation rate of helium-3 under the external magnetic field. The specific steps are as follows:

[0184] ① Based on the optically detected helium-3 FID magnetometer system, external magnetic fields of different magnitudes are generated: In the optically detected helium-3 FID magnetometer system, the current source is connected to the main magnetic field coil, and the constant current output by it can generate a stable main magnetic field in the main magnetic field coil; while the instrument control and signal processing terminal can flexibly change the intensity of the main magnetic field by adjusting the output parameters of the current source to adapt to the measurement scenario requirements of different external magnetic field magnitudes.

[0185] ② Based on the optically probed helium-3 FID magnetometer system, the helium-3 nuclear spin is polarized: the pump light (wavelength 1083.327nm, power about 300mW) that resonates with the helium-3 C9 energy level interacts with the helium-3 gas cell in the radio frequency discharge state along the longitudinal direction (i.e. the direction of the external magnetic field to be measured), and completes the polarization of the metastable helium-3 atom; then, by means of the spin exchange effect between the ground state and metastable atoms in the gas cell, the polarization characteristics of the metastable state are transferred to the ground state, and finally the polarization of the helium-3 ground state energy level nuclear spin is realized.

[0186] ③ Based on the optical detection type helium-3 FID magnetometer system, the transverse polarization of helium-3 nuclear spin is formed: using a magnetic field pulse (frequency close to the helium-3 ground state Larmor frequency) perpendicular to the direction of the external magnetic field, the longitudinal polarization of the atom is transferred to the transverse direction, that is, perpendicular to the direction of the external magnetic field.

[0187] ④ Detecting FID signals, including physical detection methods and parameter extraction methods for FID signals:

[0188] (1) Based on the optical detection type helium-3 FID magnetometer system, the FID signal of helium-3 nucleus spin precessing around an external magnetic field is detected and its frequency and relaxation rate are obtained: using a detection light with a wavelength of 1083.331nm and a power of 1mW, the light interacts with the helium-3 cell in the radio frequency discharge state in the transverse direction to detect the FID signal of the helium-3 cell, and then obtain its frequency and relaxation rate, that is, the FID frequency and FID relaxation rate of helium-3 under an external magnetic field are obtained.

[0189] (2) Based on the optically probed helium-3 FID magnetometer system, the frequency and relaxation rate of the helium-3 FID signal are obtained, specifically including:

[0190] The helium-3 FID signal was recorded using the acquisition card of a photodetector-type helium-3 FID magnetometer system. The signal format was as follows:

[0191]

[0192] Where A is the amplitude of the helium-3 nuclear spin FID signal, Γ g ' is the relaxation rate of the helium-3 nuclear spin FID signal, f g ' is the frequency of the helium-3 nuclear spin FID signal, φ is the initial phase of the helium-3 nuclear spin FID signal, b is the DC quantity in the helium-3 nuclear spin FID signal, e is the natural constant, and t is the time variable.

[0193] By fitting the FID signal using the above formula, the frequency and relaxation rate of the FID signal can be obtained, which means the FID frequency and FID relaxation rate of helium-3 under an external magnetic field can be obtained.

[0194] The model unit is used to establish the first density matrix equation describing the spin exchange process between helium-3 ground-state atoms and metastable atoms.

[0195] The model unit is also used to establish the second density matrix equation of helium-3 ground-state atoms and metastable atoms under the influence of an external magnetic field based on the Liouville equation;

[0196] The model unit is also used to merge the first density matrix equation and the second density matrix equation to obtain the merged equation;

[0197] The model unit is also used to project the merging equations onto the transverse angular momentum direction based on the preset irreducible tensor and angular momentum operator relations, so as to obtain the evolution equations of the mean transverse angular momentum of the ground state and metastable state over time.

[0198] The model unit is also used to introduce the transverse relaxation mechanism of helium-3 ground-state and metastable atoms in spin-exchange collisions. Based on the exponential decay characteristics of the transverse angular momentum components of the ground state and metastable state over time, a set of relaxation equations for the transverse angular momentum of the ground state and metastable state is established.

[0199] The model unit is also used to establish a metastable spin exchange theory model of helium-3 based on the mean angular momentum equation and the relaxation equations.

[0200] The specific process of establishing the above metastable spin exchange theory model of helium-3 is as follows:

[0201] ① Establish the first density matrix equation describing the spin exchange process between helium-3 ground-state and metastable-state atoms. Specifically, model the process of helium-3 under the influence of spin exchange, external magnetic field, and relaxation to obtain the first density matrix equation (Equation 2-3):

[0202]

[0203] Among them, for 1 / T MEC1 and 1 / T MEC2 have:

[0204]

[0205] Where, ρ g and ρ m Let Tr represent the density matrices of the ground-state and metastable atoms, respectively. n With Tr e The operators represent the traces of the neutron and electron components in the density matrix, respectively. (i = 1, 2, F1 = 1 / 2, F2 = 3 / 2) represents the projection onto the hyperfine structure, while 1 / T MEC1 and 1 / T MEC2 These are the collision exchange rates of the ground state and metastable state, respectively; n m and n g These represent the atomic number densities in the metastable and ground states, respectively. Where k... ME =154×10 -18 (T / 300) 1.09 m 3 / s is the collision coefficient of metastable spin exchange. T is the Kelvin temperature.

[0206] Furthermore, the physical meaning of the above equation is that the spin exchange frequency of the ground state is directly proportional to the number density of metastable particles, and the spin exchange frequency of the metastable state is directly proportional to the number density of ground state particles; while during the collision process, the ground state atom and the metastable atom will exchange the state of their extranuclear electrons.

[0207] ② Based on the Liouville equation, an external magnetic field is introduced to establish the second density matrix equation for helium-3 ground-state and metastable atoms under the influence of an external magnetic field. Specifically, based on the Liouville equation, the second density matrix equation for the helium-3 ground-state and metastable state density matrices under the influence of an external magnetic field is established (Equation 6):

[0208]

[0209] in, It is the density matrix describing the spins of helium-3 atoms in the ground state (g) and metastable state (m). The external magnetic field to be measured, and These are the magnetic moments of the outer electrons and the atomic nucleus, respectively, g s It is the Lande g factor of electron spin in a helium-3 atom, g I It is the Lande g-factor of the nuclear spin in a helium-3 atom, μ B It is the Bohr magneton, where i is the imaginary unit. It is the reduced Planck constant.

[0210] ③ By combining the first density matrix equation and the second density matrix equation, the effects of spin exchange and external magnetic field are superimposed into the complete Liouville equation, resulting in the combined equation.

[0211] ④ Based on the pre-defined irreducible tensor and angular momentum operator relations, the combined equations are projected onto the transverse angular momentum direction to obtain the evolution equations of the mean transverse angular momentum over time for the ground state and metastable state. Specifically:

[0212] Using the irreducible tensor to represent the density matrix, the third density matrix is ​​obtained (Equation 7); based on the relationship between the first-order irreducible tensor operator and the angular momentum operator, the relation of the angular momentum operator is established (Equation 8):

[0213]

[0214] in, Let represent an irreducible tensor formed by the coupling of two angular momentum particles with spin I, with order κ and components p. Indicates transpose; <> is the mean operator; It is a spin angular momentum operator The p-component.

[0215] By projecting the combined equations onto the transverse angular momentum direction using the third density matrix (Equation 7) and the angular momentum operator relation (Equation 8) and simplifying them, we obtain the evolution equations of the mean transverse angular momentum over time for the ground state and metastable state. That is, the density matrix equations of Helium 3 under the influence of spin exchange and external magnetic field (Equations 2-3, 6) are expressed as the evolution equations of the mean transverse angular momentum over time for the ground state and metastable state (Equations 9-11):

[0216]

[0217] in, and These are the expected values ​​of the transverse angular momentum of the atoms in the ground state, metastable states F1 = 1 / 2, and F2 = 3 / 2, which are generated by projecting the density matrix onto the space of the first-order irreducible tensor operator. g It is the precession frequency of the expected value of the transverse angular momentum of a ground-state helium-3 atom under an external magnetic field. and These are the gyromagnetic ratios of helium-3 atoms in the metastable F1 = 1 / 2 and F2 = 3 / 2 energy levels, respectively, and γ g It is the ground-state gyromagnetic ratio, and i is the imaginary unit.

[0218] ⑤ Introducing the transverse relaxation mechanism of helium-3 ground-state and metastable atoms in spin-exchange collisions, and based on the exponential decay characteristics of the transverse angular momentum components of the ground state and metastable state over time, a set of relaxation equations for the transverse angular momentum of the ground state and metastable state are established. Specifically:

[0219] Due to the relaxation phenomenon of polarized atomic spins, the mean angular momentum perpendicular to the external magnetic field in the metastable state and ground state is affected by the relaxation effect. Its evolution can be described by the equations shown in Equations 12-14:

[0220]

[0221] The relaxation process within the helium-3 chamber is mainly affected by two factors: first, the transition from the ground state dominated by nonpolar electrons generated by radio frequency power to the metastable state (corresponding to the relaxation rate Γ). g Secondly, the metastable state transition to the ground state, dominated by the metastable level lifetime (corresponding to the relaxation rate Γ), is another factor. m Under the dominance of these two types of processes, the correlation of the relaxation process is shown in Equation 15:

[0222] Γ m n m =Γ g n g (15)

[0223] Equations 12-15 constitute the relaxation equations for the transverse angular momentum of the ground state and metastable state.

[0224] For an explanation of the embodiments of the present invention, please refer to [link / reference]. Figure 2 , Figure 2 This is a data conversion diagram provided in an embodiment of the present invention, which illustrates the relationship between two types of relaxation transition processes: one is the transition from the ground state to a metastable state dominated by nonpolar electrons generated by radio frequency power (corresponding to relaxation rate Γ). g Another type is the metastable-to-ground state transition dominated by the lifetime of the metastable energy level (corresponding to the relaxation rate Γ). m ).

[0225] ⑥ Based on the mean angular momentum equation and the relaxation equations, a metastable spin exchange theoretical model of helium-3 is established.

[0226] In this embodiment, the model unit relies on the first and second density matrix equations to describe spin state evolution, accurately capturing the spin exchange interaction between ground-state and metastable atoms and the influence of the external magnetic field. Simultaneously, the Liouville equation is introduced to handle dynamic evolution, and physical quantity transformations are achieved using irreducible tensors and angular momentum operator relations. Furthermore, the independent effects of spin exchange and the external magnetic field are first described using the first and second density matrix equations respectively, then the coupling of the two effects is achieved through equation merging, and finally projected onto the transverse angular momentum direction to focus on the experimentally observable object. This decomposition and integration method effectively overcomes the complexity of multi-physics coupling, ensuring the model fully covers key influencing factors while avoiding the descriptive chaos caused by the direct superposition of multiple effects.

[0227] The solution unit is used to solve the mean angular momentum equation (Equation 9-11) and the relaxation equations (Equation 12-15) simultaneously based on the metastable spin exchange theory model of Helium-3, thereby obtaining the time evolution equations of the transverse angular momentum in the ground state and metastable state (Equation 16-18). Specifically, by simultaneously solving Equations 9-11 and 12-15, the relaxation effect is superimposed into the angular momentum evolution equation, thus constructing a quantitative correlation bridge between experimental parameters and the theoretical model. On this basis, intermediate variables are eliminated, and core physical factors such as spin exchange, external magnetic field influence, and relaxation effect are integrated to obtain the time evolution equations of the transverse angular momentum in the ground state and metastable state—Equation 16-18.

[0228] The solving unit is also used to transform the time evolution equations (Equations 16-18) into a coefficient matrix (Equation 19) and solve for the eigenvalues ​​to obtain the spin-exchange frequency shift expression (Equation 20) and the relaxation rate-ground state Larmor frequency relationship (Equation 24).

[0229] The solver unit is also used to derive the spin-exchange relaxation expression (Equation 28) based on the spin-exchange frequency shift expression (Equation 20) and the relaxation rate-ground state Larmor frequency relationship (Equation 24), and to inversely solve for f. g '(f g ,n g ,b (0) ,b (2) That is, to obtain the helium-3 FID frequency f g Regarding the ground state particle number density n g The ground-state Larmor frequency f of Helium-3 g And the quadratic function of degree 0, b (0) 2 times b (2) The coefficients are functions. The spin-exchange frequency shift expression is an odd-degree polynomial relationship between the FID frequency and the ground-state Larmor frequency, and the spin-exchange relaxation expression is an even-degree polynomial relationship between the FID relaxation rate and the FID frequency.

[0230] The time evolution equations are (Equations 16-18):

[0231]

[0232] Among them, 1 / T MEC1 =n m k ME and 1 / T MEC2 =n g k ME These are the collision exchange rates of the ground state and metastable state, respectively, n m and n g These are the atomic number densities in the metastable and ground states, respectively, k ME =154×10 -18 (T / 300) 1.09 m3 / s is the collision cross section of metastable spin exchange. T is the Kelvin temperature. and These are the expected values ​​of the transverse angular momentum of the atoms in the ground state, metastable state, F1 = 1 / 2, and F2 = 3 / 2.

[0233] Among them, the coefficient matrix (Equation 19) is first written out to solve the three first-order differential equations in equations 16-18 using the characteristic root method:

[0234]

[0235] The coefficient matrix has three eigenvalues, and this invention focuses on the eigenvalue "2πif" of the ground state precession frequency. g '+Γ g '". Under an external magnetic field of 8000 nT, f g The expression for ' is (the spin-transformation frequency shift expression, Equation 20):

[0236] f g '=f g +a (1) f g +a (3) f g 3 +a (5) f g 5 +O(10 -5 Hz)(20)

[0237] Among them, f g =γ g B is the ground-state Larmor frequency of Helium-3 without spin exchange. The physical meaning of Equation 20 is that the frequency shift introduced by spin exchange is an odd-degree polynomial of the ground-state Larmor frequency; the coefficients of this spin exchange frequency shift expression are (Equations 21-23):

[0238]

[0239]

[0240] Γ g The expression for ' is (relaxation rate - ground state Larmor frequency relationship, Equation 24):

[0241] Γ g '=c (0) +c (2) f g 2 +c (4) f g 4 +O(10 -5 s -1 ),(twenty four)

[0242] Among them, the relaxation rate Γ of the FID signal g 'and the Larmor frequency f of the ground state of Helium-3 g Given the even-degree polynomial relationship, the coefficients of this spin-exchange relaxation expression are (Equation 25-27):

[0243]

[0244] Based on the spin-exchange frequency shift expression (Equation 20) and the relaxation rate-ground state Larmor frequency relationship (Equation 24), the spin-exchange relaxation expression (Equation 28) is derived, and f is obtained by inverse solution. g '(f g ,n g ,b (0) ,b (2) That is, to obtain the helium-3 FID frequency f g Regarding the ground state particle number density n g The ground-state Larmor frequency f of Helium-3 g And the quadratic function of degree 0, b (0) 2 times b (2) The function of the coefficients is specifically:

[0245] ① Combining the spin-exchange frequency shift expression (Equation 20) and the relaxation rate-ground state Larmor frequency relationship (Equation 24), the relaxation rate Γ of the FID signal is established. g 'and frequency f g From the relationship between the two, we obtain the expression for the relationship between the 0th and 2nd order coefficients of spin exchange relaxation (equation 28 for spin exchange relaxation):

[0246] Γ g '=b (0) +b (2) f g ' 2 +b (4) f g ' 4 +O(10 -5 s -1 ), (28)

[0247] Among them, b (0) b (2) and b (4) They are respectively (Equations 29-31):

[0248]

[0249]

[0250] ②The metastable particle number density n m and ground state relaxation rate Γ gExpressed as ground-state particle number density, helium-3 ground-state Larmor frequency, and quartic function (excluding tertiary) 0th order b. (0) 2 times b (2) A function of coefficients, i.e., based on b (0) and b (2) The expression (Equation 29-30) can be used to solve for the metastable particle number density n. m and ground state relaxation rate Γ g (Equation 32):

[0251]

[0252] ③ Substituting equation 32 into equation 20, we can obtain f g '(f g ,n g ,b (0) ,b (2) That is, we get: Helium-3 FID frequency f g Regarding the ground state particle number density n g The ground-state Larmor frequency f of Helium-3 g And the quadratic function of degree 0, b (0) 2 times b (2) The coefficients are functions, and their specific expressions can be obtained through computation using the Mathematica symbolic computation software.

[0253] In this embodiment, the solution unit integrates the interrelated angular momentum evolution and relaxation decay into a unified time evolution equation system by simultaneously solving the mean angular momentum equation and the relaxation equation system. This overcomes the limitations of solving single equations in isolation, fully capturing the dynamic coupling of the transverse angular momentum between the ground state and metastable state, ensuring that the results reflect the overall characteristics of the system, and improving the systematicity and accuracy of the model. The time evolution equation system is transformed into a coefficient matrix and its eigenvalues ​​are solved. These eigenvalues ​​physically correspond to the system's intrinsic frequencies and decay rates. This method transforms the solution of complex differential equation systems into matrix operations, simplifying the process.

[0254] In summary, the model unit and solution unit in this embodiment realize the transformation logic from abstract theoretical description to specific physical quantities by converting the spin density matrix into observable angular momentum evolution values, making the chain from theory to experimental observability more coherent in the modeling process. By combining the relaxation of spin polarization, the incorporation method of relaxation effect in the model is clarified, forming a multi-dimensional influencing factor with spin exchange and external magnetic field, thus fully describing the objective physical process.

[0255] In one embodiment, the relationship module 20 specifically comprises:

[0256] Based on a photodetector-type helium-3 FID magnetometer system, the frequency f of the helium-3 FID signal under different radio frequency powers is measured within a generated constant external magnetic field (time-domain peak-to-peak value less than 10 pT).g (i.e., spin-switching frequency shift phenomenon), and record the relationship between different radio frequency powers and corresponding FID frequencies to obtain the first relationship of FID frequency variation. Specifically: the optically probed helium-3 FID magnetometer system is equipped with a radio frequency power source, whose function is to generate metastable helium-3 atoms in the helium-3 chamber. Under a constant external magnetic field environment of approximately 8000 nT, by changing the radio frequency power (P... RF The frequency (f) of the helium-3 FID signal under different radio frequency power conditions was measured and recorded. g From this, the first variation relationship of FID frequency (f) is obtained. g '-P RF ).

[0257] In one possible implementation, the optically detected helium-3 FID magnetometer system includes a magnetic field generation module (shielding cylinder, main magnetic field coil, constant current source), a helium-3 FID signal generation module (laser source, optical components, helium-3 atom gas chamber, radio frequency excitation source, signal generator, Pi / 2 pulse coil), and a helium-3 FID signal acquisition module (photodetector, preamplifier, analog-to-digital converter signal acquisition card, rubidium clock, terminal equipment). The shielding cylinder, main magnetic field coil, and constant current source are used to shield external magnetic fields and generate a stable axial main magnetic field. The laser source is used to generate linearly polarized probe light and circularly polarized pump light. The optical elements include a polarizing beam splitter (PBS), a quarter-wave plate, a half-wave plate, and a convex lens, used to adjust the optical path and laser polarization state. The atomic gas chamber includes a pure helium-3 atomic gas chamber (approximately 10 torr). The radio frequency excitation source is used to generate metastable atoms in the helium-3 gas chamber, and the number density of metastable atoms changes with the radio frequency power. The signal generator and Pi / 2 pulse coil are used to generate Pi / 2 pulses, which generate transverse atomic spin polarization in the helium-3 gas chamber. The photodetector, preamplifier, analog-to-digital converter, rubidium clock, and terminal equipment are used to receive the helium-3 FID signal in the light, amplify and fit it sequentially to obtain its frequency and relaxation rate.

[0258] Specifically, in one embodiment, the acquisition of the helium-3 FID signal frequency under different radio frequency (RF) powers is automated using a MatLab program. The frequency of the helium-3 FID signal under different RF power conditions is measured and recorded. The steps include: First, setting the RF power to a specific value using a control terminal; second, controlling the pump laser emission using the control terminal to form macroscopic atomic longitudinal polarization within the helium-3 gas chamber; third, controlling a signal generator to generate an AC pulse with near-resonance and the Larmor frequency of the helium-3 ground state, and inputting the AC pulse into a Pi / 2 pulse coil to form macroscopic atomic transverse polarization within the helium-3 gas chamber; finally, using a control analog-to-digital converter signal acquisition card, reading the helium-3 FID signal carried by the probe light passing through the gas chamber, and fitting the signal in MatLab to obtain the helium-3 FID signal frequency and relaxation rate under that RF power. The above steps are repeated for each RF power to obtain the helium-3 FID signal frequency under different RF powers.

[0259] For an explanation of the embodiments of the present invention, please refer to [link / reference]. Figure 3 , Figure 3 This is a schematic diagram of the structure of a helium-3 magnetometer system based on optical detection provided in an embodiment of the present invention, showing the structure of the optical detection type helium-3 FID magnetometer system.

[0260] Based on a photodetector-type helium-3 FID magnetometer system, the relaxation rate and frequency of the helium-3 FID signal are measured under different radio frequency (RF) powers within generated external magnetic fields of varying magnitudes, thus obtaining the FID frequency and relaxation rate. By fitting the relationship curves of relaxation rate and frequency under different RF powers, the curve of the helium-3 FID signal relaxation rate versus its frequency is obtained, representing a second relationship between the FID relaxation rate and FID frequency under different RF powers. Based on this second relationship, the 0th and 2nd order spin-exchange relaxation coefficients of the curves under different RF powers are obtained using a quartic function (excluding cubic). Specifically, a specific RF power is selected, and the photodetector-type helium-3 FID magnetometer system is operated under this power condition. The curves of the helium-3 FID signal relaxation rate versus its frequency (f) under different external magnetic fields are measured and recorded. g '-Г g 'atP RF Furthermore, the above measurement and recording steps are repeated under different radio frequency powers to obtain a second relationship between the relaxation rate and the FID frequency of the helium-3 FID signal. This process can be automated by a MatLab program.

[0261] In one embodiment, the 0th and 2nd order coefficients of spin-exchange relaxation under different radio frequency (RF) powers are measured using automated control via a MATLAB program. The relationship between the relaxation rate and frequency of the helium-3 FID signal under different RF power conditions is measured and recorded, and the 0th and 2nd order coefficients are obtained through fitting. The steps include: first, setting the RF power to a specific value using a control terminal; second, setting the current source current to a specific value using a control terminal, which generates a magnetic field of a specific magnitude in the main magnetic field coil; and third, obtaining and recording the frequency and relaxation rate of the helium-3 FID signal under the same RF power and magnetic field, based on the same steps described above. The above steps are repeated for each RF power and each magnetic field value to obtain the relationship between the relaxation rate and frequency of the helium-3 FID signal under different RF powers, and then fitting it with a quadratic function, as shown in the figure. Figure 4 As shown.

[0262] For an explanation of the embodiments of the present invention, please refer to [link / reference]. Figure 4 , Figure 4 This is a schematic diagram of the measurement results of the relationship between the frequency and radio frequency power of Helium 3FID provided in the embodiment of the present invention. It shows the relationship between the relaxation rate and frequency of the Helium 3FID signal under different radio frequency powers, and the results obtained by fitting it with a quadratic function.

[0263] The first change relationship is spin-exchange frequency shift, and the second change relationship is spin-exchange relaxation.

[0264] In this embodiment, the relationship module 20, when measuring the first change relationship, eliminates environmental interference by stabilizing the external magnetic field and measures the FID frequency using only the radio frequency power as a variable, thus accurately capturing the independent variation of the FID frequency with the radio frequency power. When measuring the second change relationship, by changing the external magnetic field and the radio frequency power, corresponding data of relaxation rate and frequency are obtained within a wide parameter range. Curve fitting is performed on the data, transforming discrete values ​​into a continuous quantitative expression, which can intuitively present the intrinsic relationship between relaxation rate and frequency.

[0265] In one embodiment, parameter module 30 specifically comprises:

[0266] Based on the measured first and second variation relationships, according to the spin-exchange frequency shift expression (Equation 20) and the spin-exchange relaxation expression (Equation 28), and the 0th and 2nd order spin-exchange relaxation coefficients of the curves under different RF powers obtained by fitting according to the second variation relationship, the f is fitted. g '(f g ,n g ,b (0) ,b (2) The curve yields the ground-state particle number density n in the helium-3 chamber. g Among them, "f" g '(f g ,ng ,b (0) ,b (2) The process of establishing ")" is described in detail in the signal module 10 of the embodiment;

[0267] Furthermore, based on the metastable particle number density n m and ground state relaxation rate Γ g The expression (Equation 32), combined with the already obtained n g and b at various RF powers (0) b (2) The coefficient was used to calculate the metastable particle number density n under different radio frequency powers. m and ground state relaxation rate Γ g The ground-state particle number density n obtained from the calculation g Metastable particle number density n m and ground state relaxation rate Γ g This constitutes a parameter set.

[0268] For an explanation of the embodiments of the present invention, please refer to [link / reference]. Figure 5-6 , Figure 5 This is a schematic diagram of the first measurement and fitting results provided in an embodiment of the present invention, showing the measurement and fitting results of the relationship between the helium-3 FID frequency and relaxation rate as a function of radio frequency power.

[0269] Figure 6 This is a schematic diagram of the second measurement and fitting results provided in an embodiment of the present invention, showing the measurement and fitting results of the helium-3 FID frequency and the 0th and 2nd order coefficients of spin exchange relaxation.

[0270] In one embodiment, the conversion module 40 specifically comprises:

[0271] The ground-state particle number density n in the helium-3 chamber of the parameter set. g Metastable particle number density n under different radio frequency powers m and ground state relaxation rate Γ g Substituting the spin-exchange frequency shift expression (Equation 20) into the equation, a quantitative conversion relationship between the FID frequency and the helium-3 ground-state Larmor frequency is established, yielding the FID frequency f. g 'and the ground state Larmor frequency f of Helium-3 g The conversion formula.

[0272] Among them, f g ' is the frequency of the helium-3 FID signal, that is, the spin precession frequency of the helium-3 nucleus detected experimentally. It is affected by systematic errors such as spin exchange and is not the true frequency corresponding to the external magnetic field. f g It is the Larmor frequency (f) of the ground state of Helium-3. g =Bγ g , where γ g(where B is the ground-state gyromagnetic ratio of helium-3 and B is the external magnetic field), representing the true frequency corresponding to the external magnetic field, unaffected by errors such as spin exchange, and requires f to be used. g 'Physical quantities derived from data.' g ' is the relaxation rate of the helium-3 nuclear spin FID signal, representing the rate at which the FID signal decays over time during precession. Г g It is the ground state relaxation rate, which is affected by the ground state to metastable state transition process dominated by nonpolar electrons generated by the radio frequency power in the helium-3 chamber.

[0273] In one embodiment, the correction module 50 includes a vector unit and an elimination unit;

[0274] The vector unit is used in a light-detection-based helium-3 FID magnetometer system to measure the FID frequency of helium-3 at different probe angles by changing the angle between the probe of the helium-3 FID magnetometer and the external magnetic field. After converting the FID frequency of helium-3 at different probe angles into the measured values ​​of the helium-3 magnetometer, a set of vector relationship equations between the measured values ​​of the helium-3 magnetometer, the probe remanence, and the external magnetic field are established. By solving the set of vector relationship equations, the magnitude and direction of the probe remanence are inverted to obtain the probe remanence vector.

[0275] The vector relation equations are given by equation (33):

[0276] B 2 read =B 2 residual +B 2 -|B residual ||B|Cosθ,(33)

[0277] Among them, B read These are measurements from a helium-3 magnetometer, B. residual It is remanence, B is the magnitude of the external magnetic field to be measured, and θ is the remanence of B. residual The angle between B and B, bolded to indicate that the variable is a vector.

[0278] In this embodiment, the probe's remanent magnetization and the external magnetic field are vector superpositions. This multi-angle sampling can acquire multi-dimensional resultant magnetic field data, providing constraints for the vector relationship equations, avoiding multivalued solutions, and ensuring that the magnitude and direction of the remanent magnetization are uniquely determined. Using vector relationship equations instead of scalar calculations aligns with the physical nature of both being vectors, capturing directional coupling relationships, avoiding the loss of directional information, and ensuring that the solution fully reflects the vector characteristics of the probe's remanent magnetization.

[0279] The elimination unit is used to perform inversion calculations based on the measured FID frequency and the conversion formula to eliminate the systematic error introduced by the spin exchange frequency shift and obtain the ground state Larmor frequency of Helium-3.

[0280] The elimination unit is also used to subtract the systematic error introduced by the probe's residual magnetism vector from the magnetic field value corresponding to the ground state Larmor frequency of Helium-3 by constructing a vector relationship equation, based on the magnetic field value corresponding to the ground state Larmor frequency of Helium-3 and the probe's remanent magnetization vector, and to obtain the accurate geomagnetic field value after systematic error correction by combining the spin gyromagnetic ratio of the Helium-3 nucleus.

[0281] In this embodiment, the elimination unit first obtains the ground-state Larmor frequency of Helium-3 through conversion formula inversion, which eliminates the inherent error originating from atomic interactions. The second step targets the probe's remanence, an independent error source—the vector interference inherent in the hardware—and deducts its contribution separately using vector relationship equations. This step-by-step processing method ensures that different types of errors are precisely isolated and targeted for correction, avoiding the correction chaos caused by error superposition, and ensuring that each correction step focuses on a specific error source, thereby improving the overall correction efficiency.

[0282] It should be noted that the derivation and calculation processes involved in this embodiment can all be systematically automated and accurately executed using MATLAB programs.

[0283] Overall, this embodiment has the following beneficial effects:

[0284] This invention, based on the spin-exchange frequency shift and spin-exchange relaxation expressions, combined with the first relationship between radio frequency power and FID frequency, and the second relationship between FID frequency and relaxation rate, calculates a set of key parameters such as the helium-3 particle number density and relaxation rate in the gas chamber. It then establishes a precise mathematical mapping between the FID frequency and the ground-state Larmor frequency. By using a quantitative conversion formula to invert the FID frequency, it not only accurately eliminates the systematic error introduced by the spin-exchange frequency shift but also enables the measurement of particle number density and other parameters within the gas chamber. Furthermore, the superposition effect of the probe's remanent magnetization can cause the amplitude and direction of the magnetic field signal measured by the helium-3 magnetometer to differ from the signal to be measured, resulting in systematic errors. This invention, by inverting the probe's remanent magnetization vector and constructing a vector relationship equation, can accurately remove the vector superposition effect of the probe's remanent magnetization on the measurement results. Combining the above-mentioned optically probed geomagnetic field helium-3 magnetometer construction scheme and systematic error correction scheme, this invention achieves accurate and sensitive measurement of the magnetic field.

[0285] In summary, this invention measures the FID signal of the helium-3 cell and uses an automated control program to measure and record the frequency of the helium-3 cell FID signal at different radio frequency powers, as well as the 0th and 2nd order spin exchange relaxation coefficients of the helium-3 cell at different radio frequency powers. Numerical fitting and calculation are used to obtain the helium-3 particle number density and relaxation rate parameters within the cell, and based on these parameters, the numerical relationship between the helium-3 FID signal frequency and the ground-state Larmor frequency is derived. Furthermore, by measuring the FID signal frequency of the helium-3 probe at different angles, the magnitude and direction of the probe's remanence are calculated. Finally, by combining the elimination of the two types of systematic errors mentioned above, accurate measurement of the geomagnetic field based on a photodetector-type helium-3 magnetometer is achieved. Compared with traditional methods for accurate magnetic field measurement using proton magnetometers, this invention, relying on a photodetector-type helium-3 nuclear spin magnetometer and comprehensive systematic error analysis, significantly improves the sensitivity and accuracy of accurate geomagnetic field measurement.

[0286] Example 3:

[0287] See Figure 8 , Figure 8 This is a schematic diagram of an embodiment of the high-accuracy geomagnetic field measuring device based on helium-3 provided by the present invention. Figure 8 As shown, the device includes a helium-3 FID magnetometer system based on optical detection 201, a helium-3 spin exchange model construction module 202, a spin exchange frequency shift measurement module 203, a spin exchange relaxation curve 0th and 2nd order coefficient measurement module 204, a gas cell parameter calculation module 205, a spin exchange frequency shift calculation module 206, a probe remanence measurement module 207, and a system error correction module 208;

[0288] The helium-3 FID magnetometer system 201 based on optical detection is used to measure the helium-3 FID signal under specific radio frequency power and external magnetic field, and to obtain its frequency and relaxation rate through data processing, such as... Figure 3 As shown.

[0289] The helium-3 spin exchange model construction module 202 is used to construct the spin exchange model of the ground state and metastable state of helium-3 atoms in the gas chamber. Based on the spin exchange model, the expression for the relationship between the spin exchange frequency shift and the 0th and 2nd order coefficients of spin exchange relaxation is obtained.

[0290] The spin-switched frequency shift measurement module 203 is used to measure the frequency f of the helium-3 FID signal under different radio frequency powers within a constant external magnetic field (time-domain peak-to-peak value less than 10 pT). g (i.e., the spin-switching frequency shift phenomenon).

[0291] The spin-exchange relaxation curve 0th and 2nd order coefficient measurement module 204 is used to measure the relaxation rate and frequency relationship of the helium-3FID signal under different radio frequency power (i.e., spin-exchange relaxation phenomenon) in an external magnetic field of different magnitudes, and to fit the 0th and 2nd order coefficients of the spin-exchange relaxation curve under different radio frequency power.

[0292] The gas chamber parameter calculation module 205, based on the expression and experimental measurement results relating the spin exchange frequency shift and the 0th and 2nd order coefficients of spin exchange relaxation, fits f... g '(f g ,n g ,b (0) ,b (2) The curve yields the particle number density n of the ground state of helium-3. g The metastable particle number density n under different radio frequency powers was calculated using equation (32). m and ground state relaxation rate Γ g '.

[0293] The spin-exchange frequency shift calculation module 206, combined with the ground-state particle number density n in the helium-3 gas chamber... g Metastable particle number density n m and ground state relaxation rate Γ g Calculate the numerical relationship between the helium-3 FID frequency and the ground-state Larmor frequency.

[0294] The probe remanence measurement module 207 measures the helium-3 FID frequency at different probe angles and constructs a set of vector relationship equations between the helium-3 magnetometer measurement value and the probe remanence and external magnetic field, and calculates the magnitude and direction of the probe remanence.

[0295] The system error correction module 208 calculates the ground state Larmor frequency based on the measured FID frequency, eliminates the system error introduced by spin exchange, and then calculates the magnitude of the helium-3 magnetometer measurement value without the influence of remanent magnetization by combining the magnitude and direction of the probe's remanent magnetization, ultimately realizing accurate measurement of the geomagnetic field based on the optically detected helium-3 magnetometer.

[0296] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working process of the device described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0297] It should be noted that the above-described embodiment of the high-accuracy geomagnetic field measurement device based on helium-3 is merely illustrative. The modules described as separate components may or may not be physically separate, and the components shown as modules may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs.

[0298] Based on the above-described embodiments of the high-accuracy geomagnetic field measurement device based on helium-3, another embodiment of the present invention provides a high-accuracy geomagnetic field measurement terminal device based on helium-3. The high-accuracy geomagnetic field measurement terminal device based on helium-3 includes a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor. When the processor executes the computer program, it implements the high-accuracy geomagnetic field measurement method based on helium-3 according to any embodiment of the present invention.

[0299] For example, in this embodiment, the computer program can be divided into one or more modules, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules can be a series of computer program instruction segments capable of performing specific functions, which describe the execution process of the computer program in the helium-3-based high-accuracy geomagnetic field measurement terminal device.

[0300] The high-accuracy geomagnetic field measurement terminal device based on helium-3 can be a desktop computer, laptop, handheld computer, or cloud server, etc. The high-accuracy geomagnetic field measurement terminal device based on helium-3 may include, but is not limited to, a processor and a memory.

[0301] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor. This processor is the control center of the helium-3-based high-accuracy geomagnetic field measurement terminal equipment, connecting all parts of the equipment via various interfaces and lines.

[0302] The memory can be used to store the computer programs and / or modules. The processor implements various functions of the high-accuracy geomagnetic field measurement terminal device based on Helium-3 by running or executing the computer programs and / or modules stored in the memory, and by calling the data stored in the memory. The memory may mainly include a program storage area and a data storage area. The program storage area may store the operating system, at least one application program required for a function, etc.; the data storage area may store data created based on the use of the mobile phone, etc. In addition, the memory may include high-speed random access memory, and may also include non-volatile memory, such as hard disk, memory, plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, at least one disk storage device, flash memory device, or other volatile solid-state storage device.

[0303] Example 4:

[0304] This invention provides a computer-readable storage medium including a stored computer program, wherein the computer program, when running, controls the device where the computer-readable storage medium is located to execute the aforementioned method for accurately measuring the geomagnetic field based on optical detection of helium-3.

[0305] The method for accurately measuring the geomagnetic field based on optical detection of helium-3, when implemented as a software functional unit and used as an independent product, can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the above embodiments of the present invention can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc.

[0306] The above are preferred embodiments of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A method for accurately measuring the geomagnetic field based on optical detection of helium-3, characterized in that, include: The FID frequency and FID relaxation rate were obtained by polarizing and probing the helium-3 nuclear spin; The measurement establishes a first relationship between radio frequency power and the FID frequency, and a second relationship between the FID relaxation rate and the FID frequency under different radio frequency powers; wherein the first relationship is a spin-switched frequency shift, and the second relationship is a spin-switched relaxation. Based on the preset spin-exchange frequency shift expression and spin-exchange relaxation expression, the first change relationship and the second change relationship, a set of parameters including the number density and relaxation rate of helium-3 particles in the gas chamber is calculated. Based on the spin-exchange frequency shift expression and the parameter set, establish the conversion formula between the FID frequency and the helium-3 ground-state Larmor frequency; The ground-state Larmor frequency of helium-3 is calculated based on the FID frequency according to the conversion formula, the spin exchange frequency shift is eliminated, and the remanence is corrected by inverting the remanence vector of the probe. The accurate geomagnetic field value after system error correction is obtained by combining the helium-3 nucleus spin gyromagnetic ratio.

2. The method for accurately measuring the geomagnetic field based on optical detection of helium-3 as described in claim 1, characterized in that, The spin-exchange frequency shift expression and the spin-exchange relaxation expression are obtained by solving the metastable spin-exchange theoretical model of helium-3. The metastable spin-exchange theoretical model of helium-3 is obtained by modeling the process of helium-3 under the influence of spin exchange, external magnetic field, and relaxation. Specifically: Based on the spin exchange interaction between helium-3 ground-state and metastable atoms, and the influence of the external magnetic field on the spin evolution of ground-state and metastable helium-3 atoms, the spin density matrix of helium-3 ground-state and metastable atoms is transformed into observable angular momentum evolution values. Combined with the relaxation of spin polarization, the theoretical model of helium-3 metastable spin exchange is established. Based on the metastable spin exchange theory model of Helium-3, a set of time evolution equations for the ground state and metastable transverse angular momentum are established, and the set of time evolution equations is solved to obtain the spin exchange frequency shift expression and the spin exchange relaxation expression.

3. The method for accurately measuring the geomagnetic field based on optical detection of helium-3 as described in claim 2, characterized in that, Based on the spin exchange interaction between helium-3 ground-state and metastable atoms, and the influence of an external magnetic field on the spin evolution of ground-state and metastable helium-3 atoms, the spin density matrices of helium-3 ground-state and metastable atoms are transformed into observable angular momentum evolution values. Combined with the relaxation of spin polarization, the theoretical model of the helium-3 metastable spin exchange is established, specifically as follows: Establish the first density matrix equation describing the spin exchange process between helium-3 ground-state atoms and metastable atoms; Based on the Liouville equation, an external magnetic field is introduced to establish the second density matrix equation for the ground-state and metastable-state atoms of helium-3 under the influence of the external magnetic field. By combining the first density matrix equation and the second density matrix equation, we obtain the combined equation; Based on the preset irreducible tensor and angular momentum operator relation, the combined equation is projected onto the transverse angular momentum direction to obtain the evolution equation of the mean transverse angular momentum of the ground state and metastable state over time. A transverse relaxation mechanism is introduced between helium-3 ground-state and metastable atoms in spin-exchange collisions. Based on the exponential decay characteristics of the transverse angular momentum components of the ground state and metastable state over time, a set of relaxation equations for the transverse angular momentum of the ground state and metastable state is established. Based on the mean angular momentum equation and the relaxation equations, a metastable spin exchange theoretical model for helium-3 is established.

4. The method for accurately measuring the geomagnetic field based on optical detection of helium-3 as described in claim 3, characterized in that, Based on the helium-3 metastable spin exchange theory model, a set of time evolution equations for the ground state and metastable transverse angular momentum are established, and the time evolution equations are solved to obtain the spin exchange frequency shift expression and the spin exchange relaxation expression, specifically: Based on the helium-3 metastable spin exchange theory model, the mean angular momentum equation and the relaxation equations are solved simultaneously to obtain the time evolution equations of the ground state and metastable transverse angular momentum. The time evolution equations are transformed into coefficient matrices and the eigenvalues ​​are solved to obtain the spin-exchange frequency shift expression and the spin-exchange relaxation expression; wherein, the spin-exchange frequency shift expression is an odd-degree polynomial relationship between the FID frequency and the ground-state Larmor frequency, and the spin-exchange relaxation expression is an even-degree polynomial relationship between the FID relaxation rate and the FID frequency.

5. The method for accurately measuring the geomagnetic field based on optical detection of helium-3 as described in claim 1, characterized in that, The measurement of the first relationship between RF power and the FID frequency, and the second relationship between the FID relaxation rate and the FID frequency under different RF powers, are specifically as follows: Within a constant external magnetic field, the helium-3 FID frequency under different radio frequency powers is measured, and the relationship between different radio frequency powers and corresponding FID frequencies is recorded to obtain the first relationship of FID frequency variation. The relaxation rate and frequency of the helium-3 FID signal under different radio frequency powers were measured in external magnetic fields of different magnitudes. By fitting the relationship curves of relaxation rate and frequency under different radio frequency powers, the second variation relationship between the FID relaxation rate and the FID frequency under different radio frequency powers was obtained.

6. The method for accurately measuring the geomagnetic field based on optical detection of helium-3 as described in claim 1, characterized in that, Based on the preset spin-exchange frequency shift expression and spin-exchange relaxation expression, the first change relationship and the second change relationship, a parameter set including the helium-3 particle number density and relaxation rate in the gas chamber is calculated, specifically as follows: Based on the measured first and second variation relationships, the ground-state particle number density, metastable particle number density, and ground-state relaxation rate in the gas chamber are obtained by fitting the spin-exchange frequency shift expression and the spin-exchange relaxation expression.

7. The method for accurately measuring the geomagnetic field based on optical detection of helium-3 as described in claim 1, characterized in that, Based on the spin-exchange frequency shift expression and the parameter set, a conversion formula is established between the FID frequency and the helium-3 ground-state Larmor frequency, specifically as follows: Substitute the parameters of the parameter set into the spin-exchange frequency shift expression for calculation, establish a quantitative conversion relationship between the FID frequency and the helium-3 ground-state Larmor frequency, and obtain the conversion formula.

8. The method for accurately measuring the geomagnetic field based on optical detection of helium-3 as described in claim 1, characterized in that, The residual magnetism vector of the probe is obtained by solving a system of vector relationship equations, specifically: The FID frequency of helium-3 was measured at different angles by changing the angle between the probe of the helium-3 magnetometer and the external magnetic field. Based on the measured values ​​of the helium 3 magnetometer obtained by converting the FID frequency of helium 3 at different angles, a set of vector relationship equations between the measured values ​​of the helium 3 magnetometer, the probe remanence, and the external magnetic field are established. The set of vector relationship equations is solved to invert the magnitude and direction of the probe remanence and obtain the probe remanence vector.

9. The method for accurately measuring the geomagnetic field based on optical detection of helium-3 as described in claim 1, characterized in that, The ground-state Larmor frequency of helium-3 is calculated based on the FID frequency using the conversion formula, the spin-exchange frequency shift is eliminated, and the remanence is corrected by inverting the probe's remanence vector. Combined with the helium-3 nucleus spin-gyromagnetic ratio, the accurate geomagnetic field value after system error correction is obtained, specifically: Based on the FID frequency, an inversion calculation is performed according to the conversion formula to eliminate the systematic error introduced by the spin exchange frequency shift, and the ground state Larmor frequency of Helium-3 is obtained. Based on the magnetic field value corresponding to the ground state Larmor frequency of Helium-3 and the remanent magnetization vector of the probe, the systematic error introduced by subtracting the remanent magnetization vector of the probe from the magnetic field value corresponding to the ground state Larmor frequency of Helium-3 is obtained by constructing a vector relationship equation, and then combining the spin gyromagnetic ratio of the Helium-3 nucleus to obtain the accurate geomagnetic field value after systematic error correction.

10. A device for accurately measuring the geomagnetic field based on optical detection of helium-3, characterized in that, It includes a signal module, a relation module, a parameter module, a conversion module, and a correction module; The signal module is used to obtain the FID frequency and FID relaxation rate by polarizing and probing the helium-3 nucleus spin; The relationship module is used to measure a first relationship between radio frequency power and the FID frequency, and a second relationship between the FID relaxation rate and the FID frequency under different radio frequency powers; wherein, the first relationship is a spin-switched frequency shift, and the second relationship is a spin-switched relaxation. The parameter module is used to calculate a set of parameters, including the number density and relaxation rate of helium-3 particles in the gas chamber, based on preset spin-exchange frequency shift expressions and spin-exchange relaxation expressions, the first change relationship and the second change relationship. The conversion module is used to establish a conversion formula between the FID frequency and the helium-3 ground state Larmor frequency based on the spin-exchange frequency shift expression and the parameter set. The correction module is used to calculate the ground-state Larmor frequency of helium-3 based on the FID frequency according to the conversion formula, eliminate the spin exchange frequency shift, correct the remanence by inverting the remanence vector of the probe, and obtain the accurate geomagnetic field value after system error correction by combining the helium-3 nucleus spin gyromagnetic ratio.

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