Magnetic field closed-loop tracking measurement method based on CPT magnetometer

Abstract

Based on CPT magnetometer magnetic field closed loop tracking measurement method, using voltage controlled oscillator and PID control to achieve the tracking of the external magnetic field to achieve real-time magnetic field measurement, to ensure the feasibility of real-time tracking measurement of magnetic field, the stability of the closed loop output signal is analyzed by transfer function and the effectiveness of the magnetic field tracking measurement is qualitatively analyzed. As the probe part of the coherent layout trapped CPT vector magnetometer, the modulated vertical cavity surface emitting laser VCSEL generates polychromatic light input into the cell, and the light signal carrying the magnetic field information is obtained after photoelectric conversion and lock-in amplifier modulation and demodulation to obtain multiple dispersion signals. Further adjust the center frequency and frequency scanning range of VCSEL modulation signal to make the obtained light signal only contain the dispersion signal of the magnetic field information, and the scanning center coincides with the zero crossing point of the dispersion signal. Input the error signal into the closed loop measurement system composed of VCO and PID control to realize real-time measurement of magnetic field.

Description

Technical Field

[0001] This invention relates to a closed-loop tracking measurement method for magnetic fields based on a CPT magnetometer, belonging to the field of light-alkali metal atom interaction and automatic control technology. Background Technology

[0002] The Coherent Population Trapping (CPT) effect is a quantum coherence effect. Using the CPT and Zeeman effects, a CPT magnetometer can be established to perform absolute measurements of external magnetic fields. Generally, the magnitude of the magnetic field in a CPT magnetometer is calculated by measuring the frequency detuning Δν of the CPT manifold and then using the relationship between the frequency detuning Δν and the magnitude of the external magnetic field B0.

[0003] Δν=γ0|B0| (1)

[0004] Where γ0 is the gyromagnetic ratio of the alkali metal atom.

[0005] To obtain the frequency detuning of the CPT manifold, the frequency of the two-color light field is often modulated by trigonometric wave function signals and sine wave function signals. Multiple CPT dispersion signals are obtained by using a photodetector and a lock-in amplifier. The frequency of the laser at the zero-crossing point between each dispersion signal is calibrated, and then the frequency detuning Δν of the CPT manifold is obtained.

[0006] However, this method struggles to achieve high-frequency magnetic field measurements, primarily due to limitations in the scanning range and frequency of the dual-color laser field. When the external magnetic field is large, the frequency detuning is significant, increasing the laser frequency scanning range. However, due to the instrument's inherent resolution and bandwidth, further increasing the scanning frequency may result in peak leakage or misalignment. Conversely, a lower scanning frequency will drastically reduce the magnetic field measurement signal acquisition rate. When the external magnetic field is small, the frequency detuning is minimal, the laser frequency scanning range is small, and the scanning frequency can be slightly increased. However, the scanning process itself makes real-time continuous magnetic field measurement difficult. Since magnetometers measure not only constant magnetic field magnitude but, more importantly, changes and even abrupt changes in the magnetic field, achieving real-time continuous magnetic field output is crucial. Summary of the Invention

[0007] The problem solved by this invention is as follows: This invention proposes a closed-loop tracking measurement method for magnetic fields based on a CPT magnetometer. A radio frequency (RF) signal generated by an RF signal generator is injected into a VCSEL laser through a T-type biaser (Bias-T). The output laser is half-wave modulated to obtain a multicolor laser. An intensity modulation device is used to reduce the light intensity and change the laser polarization state. An adder is used to superimpose the signals generated by a triangular wave signal generator and a sine wave signal generator to modulate the RF signal, achieving scanning and modulation of the multicolor light field. Multiple CPT dispersion signals (CPT, Coherent Population Trapping) are obtained by demodulating the optical signal through a lock-in amplifier in an alkali metal gas chamber. A suitable magnetically sensitive CPT dispersion signal is selected as the closed-loop tracking object. The center frequency and scanning range of the RF signal are adjusted to make the optical frequency scanning center coincide as closely as possible with the zero-crossing point of the magnetically sensitive CPT dispersion signal. The triangular wave signal generator is turned off to obtain the setpoint for closed-loop feedback compensation control. This signal is input into a closed-loop control measurement system composed of PID control and a VCO (Voltage Control Unit). A voltage-controlled oscillator (VCO) is a device that uses a proportional-integral-derivative (PID) converter to measure the magnetic field strength in real time by observing the input voltage signal of the VCO.

[0008] The technical solution of the present invention is as follows:

[0009] A closed-loop tracking measurement method for magnetic fields based on a CPT magnetometer is characterized by the following steps: A mixed signal, consisting of a modulated radio frequency signal and a DC signal, is input to the laser of the CPT magnetometer system. This causes the multicolor laser emitted by the laser to form an optical signal carrying magnetic field information after passing through an atomic gas cell. The optical signal is converted into a CPT signal by a photodetector amplifier and then modulated and demodulated in a lock-in amplifier to obtain multiple dispersion signals. A magnetically sensitive dispersion signal is selected from these multiple dispersion signals as the closed-loop tracking object. A PI controller or PID controller generates an input voltage change for a voltage-controlled oscillator (VCO) based on the frequency offset of the zero-crossing point of the magnetically sensitive dispersion signal. The VCO provides a clock signal to a radio frequency signal generator that generates the modulated radio frequency signal. The change in the magnetic field to be measured is determined by the input voltage change.

[0010] The laser is a vertical-cavity surface-emitting laser (VCSEL). The laser is connected to the output of a T-type bias to obtain the mixed signal. The first input of the T-type bias is connected to a VCSEL laser controller to obtain the DC signal. The second input of the T-type bias is connected to the radio frequency (RF) signal generator to obtain the modulated RF signal. The RF signal generator is connected to the output of an adder to modulate the RF signal. The first input of the adder is connected to a triangular wave signal generator. The second input of the adder is connected to a sine wave signal generator. The sine wave signal generator is connected to the lock-in amplifier to use the sine wave signal as a reference signal for demodulating the dispersive signal. The PI controller or PID controller is connected to an input voltage data acquisition system.

[0011] The mixed signal passes sequentially through a λ / 2 waveplate, a polarization beam splitter prism, an optical fiber coupler, a polarization-maintaining fiber, and a laser collimator before entering the atomic gas chamber. The atomic gas chamber is located inside an oven, which is located inside a magnetic field coil. The magnetic field coil is located inside a ferrite shielding layer, which is located inside a permalloy shielding layer.

[0012] Including the following relations:

[0013] Δν Ref =k T ·ΔV in

[0014] Where Δν Ref It is the change in the clock signal output by the voltage-controlled oscillator (VCO), k T It is a coefficient, with units of V / Hz. The magnitude of the coefficient depends on the performance of the voltage-controlled oscillator (VCO), ΔV. in It is the change in the input voltage of the voltage-controlled oscillator (VCO).

[0015] Including the following relations:

[0016] Δν′=γ·ΔB

[0017] Where Δν′ is the frequency offset, γ is the gyromagnetic ratio of alkali metal atoms in the atomic gas cell, and ΔB is the change in the measured magnetic field.

[0018] Including the following relations:

[0019]

[0020] Where ΔB is the change in the measured magnetic field, γ is the gyromagnetic ratio of the alkali metal atoms in the atomic gas cell, and k T It is a coefficient, ΔV in It is the change in the input voltage of the voltage-controlled oscillator (VCO).

[0021] Includes the following steps:

[0022] (1) Generation of multicolor lasers

[0023] Based on the principle of CPT magnetometer, two laser frequencies need to be generated to satisfy the frequency difference of 6.834 GHz between the two hyperfine energy levels of the D1 line of Rb87 atom. The VCSEL laser is locked on the D1 line, and a 3.417 GHz signal is generated by an RF signal generator. The RF signal is modulated into the DC signal of the VCSEL laser through a T-type bias to obtain multicolor laser. The basic clock signal of the RF signal generator is provided by an external voltage-controlled oscillator (VCO) to ensure closed-loop control.

[0024] (2) Modulate and demodulate the CPT signal to obtain a dispersive signal

[0025] The signal generated by the radio frequency signal generator is frequency modulated by a triangular wave function and a sine wave function. The triangular wave function is used to achieve frequency scanning, and the sine wave function modulates the optical signal. The sine wave function signal is used as the reference signal input of the lock-in amplifier, and the corresponding dispersive signal is obtained by demodulation. Since there is a one-to-one correspondence between the dispersive signal and the CPT signal, and the zero-crossing point of the dispersive signal coincides with the peak point of the CPT signal, the dispersive signal is used to measure the magnetic field. Under the condition of an external magnetic field, multiple CPT resonances are formed due to the Zeeman multiplicity of the ground state. For the magnetic quantum number m of alkali metal atoms... F The frequency difference between the Zeeman sublevels of ±1 changes with the magnetic field, resulting in a frequency shift; therefore, the generated dispersive signal is called a magnetically susceptible dispersive signal, and m F The frequency difference of the Zeeman sublevels with a value of 0 remains unchanged and is always equal to the frequency difference of the hyperfine level; this is called the magnetically insensitive dispersion signal.

[0026] (3) Implementation of dispersive signal selection and modulation signal adjustment

[0027] Closed-loop measurement requires sensing of the external magnetic field; therefore, the magnetically sensitive dispersive signal is chosen as the object of closed-loop tracking. 3.417 GHz is used as the radio frequency modulation center, and the center of the resulting dispersive signal is m. F =0 indicates a magnetically insensitive signal; therefore, the center frequency is adjusted so that the center position of the obtained dispersive signal corresponds to m. F =1 or m F = -1 The zero-crossing point of the magnetic susceptibility dispersion signal is selected based on the peak value in the experiment. During this process, the scanning range of the radio frequency signal is adjusted to achieve more precise alignment.

[0028] (4) Implementation of closed-loop system control

[0029] The atomic magnetometer system is equivalent to a first-order inertial element. The open-loop system behaves as a first-order low-pass filter in the frequency domain response, where the input is the magnetic field to be measured and the output is the signal voltage, with a chromaticity relationship between them. The open-loop transfer function G(s) is:

[0030]

[0031] Where G0 is the DC gain, obtained from the slope of the dispersion curve at zero; ω c The cutoff frequency is the measurement bandwidth of the magnetometer, which is related to (R... op +R rel It is directly proportional to R, where R rel R is the relaxation rate. op Let be the pumping rate, and the sum of the two is obtained by the distance between the two poles of the dispersion curve. s is a complex variable in the Laplace transform.

[0032] The bandwidth is further increased through negative feedback, exceeding the amplifier's characteristic bandwidth to improve its linearity. Therefore, negative feedback is applied to the CPT atomic magnetometer to improve the linearity of the output signal and extend the magnetic resonance bandwidth. A PI or PID controller is used for feedback control, with a transfer function G... PID Represented as:

[0033]

[0034] Among them, K P K I and K D These represent the proportional, integral, and derivative coefficients, respectively. Using a PI controller can improve stability and eliminate steady-state errors in the system. The feedback loop keeps the magnetic field experienced by the magnetometer during its movement at zero, thus expanding the dynamic range.

[0035] Based on the transfer functions of equations (1) and (2), the closed-loop transfer function G between the feedback magnetic field and the input can be obtained. closed (s) and amplitude-frequency response A closed (ω) is:

[0036]

[0037] Where η=G0·K P ·ω c η is an intermediate quantity, obtained by transferring the PI controller's transfer function G. PI When (s) is adjusted to a larger value, the amplitude-frequency response of the closed-loop magnetometer is close to 1. This means that the amplitude of the closed-loop magnetometer will not attenuate when measuring magnetic signals in the low-frequency range, which can improve the bandwidth of the system and increase its stability, thus verifying the feasibility of the magnetic field closed-loop control system.

[0038] Since the peak value of the CPT signal corresponds to the zero-crossing point of the dispersive signal, and magnetic flux density is usually measured by measuring the Zeeman frequency shift of the CPT resonance, the magnetic field measurement is transformed into a measurement of the frequency offset of the zero-crossing point of the dispersive signal. The frequency scanning of the RF modulation signal is turned off, and the output of the lock-in amplifier at this time is used as the setpoint for the PI negative feedback. When the external magnetic field changes, the center of the magnetically sensitive dispersive signal shifts, and the output of the lock-in amplifier is no longer 0. The input voltage of the VCO is controlled by the PI negative feedback to change the center frequency of the RF modulation signal, causing the output of the lock-in amplifier to return to 0, thus keeping the output of the lock-in amplifier always at the zero-crossing point of the dispersive signal. When the magnetic field stabilizes, the closed-loop measurement state described above is returned.

[0039] (5) Magnetic field measurement is achieved by observing the VCO input voltage.

[0040] The input voltage of the VCO will change the fundamental clock signal frequency of the crystal oscillator within a very small range; for the VCO used in this scheme, the change in its input voltage ΔV in The change in frequency of the output clock signal Δν Ref The relationship is:

[0041] Δν Ref =k T ·ΔV in (5)

[0042] Where, k T The voltage change ΔV in The change in frequency of the output clock signal Δν Ref The proportionality coefficient, in units of V / Hz;

[0043] When the frequency of the basic clock signal changes, the output frequency of the RF signal generator will change due to the characteristics of the clock signal. Specifically, if the RF signal input is set to 3.417 GHz, when the VCO output frequency decreases by 1 Hz due to the decrease in input voltage, the RF signal output will decrease by 341.7 Hz.

[0044] The output of the lock-in amplifier is always controlled at the zero-crossing point of the dispersive signal by PID control; the shift of the zero-crossing frequency of the magnetically sensitive dispersive signal Δν' can be obtained by observing the change of the input voltage of the VCO and using equation (4); the frequency shift Δν' and the change of the magnetic field ΔB can be expressed as:

[0045] Δν′=γ·ΔB (6)

[0046] Where γ = 7Hz / nT is the gyromagnetic ratio of rubidium 87; using equations (4) and (5), the magnetic field change ΔB and the input voltage change ΔV of VCO are obtained. in The relationship is:

[0047]

[0048] This enables real-time measurement of the magnetic field.

[0049] The advantages of this invention compared to existing technologies are as follows: While using a scanning method to obtain the frequency difference between CPT magnetometer dispersive signals results in a delayed and single-point output magnetic field signal, lacking real-time performance and stability, making it difficult to capture high-frequency changes in the magnetic field. This invention proposes a closed-loop tracking measurement method for magnetic fields based on a CPT magnetometer. A VCSEL laser is half-wave modulated to obtain a multi-color laser, and the intensity is reduced using an intensity adjustment device. An RF signal is modulated to achieve scanning and modulation of the multi-color light field. A lock-in amplifier is used to demodulate the optical signal to obtain multiple CPT dispersive signals. A suitable CPT dispersive signal is selected as the closed-loop tracking object, and the center frequency and scanning range of the RF signal are adjusted until the optical frequency scanning center coincides with the zero-crossing point of the dispersive signal. The triangular wave signal generator is turned off to obtain the setpoint for closed-loop feedback compensation control. This signal is input into a closed-loop control measurement system composed of PID control and a VCO, and the input voltage signal of the VCO is observed to achieve real-time measurement of the magnetic field magnitude. Attached Figure Description

[0050] Figure 1 This is a flowchart illustrating the implementation of the magnetic field closed-loop tracking measurement method based on a CPT magnetometer according to the present invention. Figure 1 The process includes: Step 1, generating a multicolor laser; Step 2, modulating the multicolor laser and demodulating it through a gas cell probe located in a fixed magnetic field using a lock-in amplifier to obtain multiple CPT dispersion signals (CPT, Coherent Population Trapping); Step 3, selecting a suitable magnetically sensitive dispersion signal, adjusting the center frequency and frequency scanning range of the modulation signal received by the laser to obtain a single magnetically sensitive CPT dispersion signal, whose zero-crossing point basically coincides with the scanning center; Step 4, turning off the modulation signal scanning frequency, and using PID control to adjust the input voltage of the VCO (Voltage Controlled Oscillator; PID, Proportional Integral Derivative) to stabilize the output of the lock-in amplifier; Step 5, observing the input voltage of the VCO to achieve real-time measurement of the magnetic field.

[0051] Figure 2 This is a schematic diagram of the CPT magnetometer system structure involved in the magnetic field closed-loop tracking measurement method based on the CPT magnetometer of this invention.

[0052] The following are the annotations for the attached figures: 1-VCSEL laser (VCSEL, Vertical-Cavity Surface-Emitting Laser); 2-λ / 2 waveplate; 3-Polarization beam splitter prism; 4-Fiber coupler; 5-Polarization-maintaining fiber; 6-Laser collimator; 7-Atomic gas cell; 8-Photodetector amplifier; 9-Lock-in amplifier; 10-PID controller (PID, Proportional-Integral-Derivative); 11-Voltage-Controlled Oscillator (VCO). 12-RF signal generator; 13-T-type biaser (Bias-T, used to mix DC and RF signals into the same path, DC is direct current, RF is radio frequency, T-type biaser outputs RF+DC signal); 14-Input voltage data acquisition system; 15-Sine wave signal generator; 16-Triangle wave signal generator; 17-VCSEL laser controller; 18-Oven; 19-Magnetic field coil; 20-Ferrite shielding layer; 21-Permalloy shielding layer; 22-Adder; xyz-Cartesian coordinate system three axes (i.e., x-axis, y-axis and z-axis). Detailed Implementation

[0053] The following is in conjunction with the attached diagram ( Figures 1-2 The invention will be described in the following sections and examples.

[0054] Figure 1 This is a flowchart illustrating the implementation of the magnetic field closed-loop tracking measurement method based on a CPT magnetometer according to the present invention. Figure 2 This is a schematic diagram of the CPT magnetometer system structure involved in the magnetic field closed-loop tracking measurement method based on the CPT magnetometer of this invention. (Reference) Figures 1 to 2 As shown, the magnetic field closed-loop tracking measurement method based on a CPT magnetometer includes inputting a mixed signal (e.g., a VCSEL laser 1) of the CPT magnetometer system into the laser (e.g., a VCSEL laser 1), which is a mixture of a modulated radio frequency signal and a DC signal, so that the multicolor laser emitted by the laser forms an optical signal carrying magnetic field information after passing through the atomic gas cell 7. The optical signal is converted into a CPT signal by a photodetector amplifier 8 and then modulated and demodulated in a lock-in amplifier 9 to obtain multiple dispersion signals. A magnetically sensitive dispersion signal is selected from the multiple dispersion signals as the closed-loop tracking object. A PI controller or PID controller 10 generates an input voltage change provided to a voltage-controlled oscillator (VCO) 11 based on the frequency offset of the zero-crossing point of the magnetically sensitive dispersion signal. The VCO 11 provides a clock signal to the radio frequency signal generator 12 that generates the modulated radio frequency signal. The change in the magnetic field to be measured is determined by the input voltage change.

[0055] The laser is a vertical cavity surface-emitting laser 1. The laser is connected to the output of a T-type bias 13 to obtain the mixed signal. The first input of the T-type bias 13 is connected to a VCSEL laser controller 17 to obtain the DC signal. The second input of the T-type bias 13 is connected to an RF signal generator 12 to obtain the modulated RF signal. The RF signal generator 12 is connected to the output of an adder 22 to modulate the RF signal. The first input of the adder 22 is connected to a triangular wave signal generator 16. The second input of the adder 22 is connected to a sine wave signal generator 15. The sine wave signal generator 15 is connected to a lock-in amplifier 9 to use the sine wave signal as a reference signal for demodulating the dispersive signal. The PI controller or PID controller 10 is connected to an input voltage data acquisition system 14.

[0056] The mixed signal passes sequentially through a λ / 2 waveplate 2, a polarization beam splitter prism 3, an optical fiber coupler 4, a polarization-maintaining fiber 5, and a laser collimator 6 before entering the atomic gas chamber 7. The atomic gas chamber 7 is located inside an oven 18, which is located inside a magnetic field coil 19. The magnetic field coil 19 is located inside a ferrite shielding layer 20, which is located inside a permalloy shielding layer 21.

[0057] Including the following relations:

[0058] Δν Ref =k T ·ΔV in

[0059] Where Δν Ref It is the change in the clock signal output by the voltage-controlled oscillator (VCO), k T It is a coefficient, with units of V / Hz. The magnitude of the coefficient depends on the performance of the voltage-controlled oscillator (VCO), ΔV. in It is the change in the input voltage of the voltage-controlled oscillator (VCO).

[0060] Including the following relations:

[0061] Δν′=γ·ΔB

[0062] Where Δν′ is the frequency offset, γ is the gyromagnetic ratio of alkali metal atoms in the atomic gas cell, and ΔB is the change in the measured magnetic field.

[0063] Including the following relations:

[0064]

[0065] Where ΔB is the change in the measured magnetic field, γ is the gyromagnetic ratio of the alkali metal atoms in the atomic gas cell, and k T It is a coefficient, ΔV in It is the change in the input voltage of the voltage-controlled oscillator (VCO).

[0066] This invention relates to a closed-loop magnetic field tracking measurement method based on a CPT magnetometer. A voltage-controlled oscillator (VCO) and PID control are used to track the external magnetic field for real-time measurement. To ensure the feasibility of real-time magnetic field tracking measurement, the stability of the closed-loop output signal is analyzed using transfer function analysis, and the effectiveness of the magnetic field tracking measurement is qualitatively analyzed. As the probe part of a Coherent Population Trapping (CPT) vector magnetometer, multicolor light generated by a modulated vertical-cavity surface-emitting laser (VCSEL) is input into a gas chamber. The resulting optical signal carrying magnetic field information is converted into a voltage signal by a photodiode and modulated and demodulated by a lock-in amplifier to obtain multiple dispersive signals. The center frequency and frequency scanning range of the VCSEL modulation signal are further adjusted so that the obtained optical signal contains only the dispersive signal with magnetic field information, and the scanning center coincides with the zero-crossing point of the dispersive signal. This error signal is input to the closed-loop measurement system composed of VCO and PID control, achieving real-time magnetic field measurement. This method can improve the sampling rate of CPT magnetometers, enabling real-time measurement of the magnetic field. Furthermore, because it utilizes dispersive linear measurements for correlation analysis, it can also be applied to optical pumping (OP) magnetometers, spin-exchange relaxation-free SERF magnetometers, nonlinear magneto-optical rotation (NMOR) magnetometers, CPT atomic clocks, and other fields, demonstrating strong applicability and high practical value.

[0067] A closed-loop tracking measurement method for magnetic fields based on a CPT magnetometer is proposed: The laser frequency is modulated, and multiple dispersive signals are observed through a lock-in amplifier. The center frequency of the modulation signal is adjusted to select the magnetically sensitive dispersive signal. Frequency scanning of the modulation signal is turned off, and PID control is used to analyze the feasibility and effectiveness of closed-loop measurement. The accuracy of real-time magnetic field measurement is qualitatively analyzed. Through closed-loop feedback compensation control, the input voltage of the VCO directly reflects the frequency offset of the magnetically sensitive dispersive signal, further enabling real-time measurement of the magnetic field magnitude using the VCO input voltage.

[0068] CPT magnetometers utilize the interference effect between atomic energy levels. For rubidium-87 atoms, it is necessary to generate multicolor light that satisfies the hyperfine energy level frequency difference. This paper uses a VCSEL laser to generate laser light from the D1 line of Rb87 atoms. A 3.417 GHz electrical signal generated by an RF signal generator is injected into the DC control signal via a Bias-T method to half-wave modulate the laser frequency. The resulting frequency difference between the two sidebands is equal to 6.834 GHz, which roughly satisfies the hyperfine energy level difference. The RF signal generator uses an external voltage-controlled oscillator (VCO) as its basic clock signal to ensure closed-loop compensation control. Simultaneously, an adder is used to superimpose the signals generated by a triangular wave signal generator and a sine wave signal generator, inputting them into the RF signal generator to modulate the RF signal to achieve a small-range scan (MHz) and modulation of the multicolor light field. When the laser passes through a gas cell containing Rb87 atoms, the CPT phenomenon due to the Zeeman effect can be observed. The magnetically sensitive dispersion signal is selected as the closed-loop tracking object. The center frequency and scanning range of the RF signal are adjusted so that the center position of the obtained dispersion signal corresponds to m F =1 or m F = -1 The zero-crossing point of the magnetic susceptibility dispersion signal is selected based on the peak value in the experiment. During this process, the scanning range of the radio frequency signal is adjusted to achieve more precise alignment.

[0069] An atomic magnetometer system can be equivalently represented as a first-order inertial element. The open-loop system behaves as a first-order low-pass filter in the frequency domain response, where the input is the magnetic field to be measured and the output is the signal voltage, with a chromaticity relationship between them. The open-loop transfer function G(s) is:

[0070]

[0071] Where G0 is the DC gain, which can be obtained from the slope of the dispersion curve at zero; ω c The cutoff frequency is the measurement bandwidth of the magnetometer, which is related to (R... op +R rel It is directly proportional to R, where R rel R is the relaxation rate. op The pumping rate is the sum of the two values, which can be obtained by the distance between the two poles of the dispersion curve.

[0072] Based on this setting, the bandwidth can be further increased through negative feedback. Negative feedback exceeds the characteristic bandwidth of the amplifier, thus improving its linearity. Therefore, negative feedback can be applied to CPT atomic magnetometers to improve the linearity of the output signal and extend the magnetic resonance bandwidth. A simple and highly stable PID controller is used for feedback control, and its transfer function can be expressed as:

[0073]

[0074] Among them, KP K I and K D These represent the proportional, integral, and derivative coefficients, respectively. Typically, a PI controller is sufficient because it improves stability and eliminates steady-state errors. The feedback loop keeps the magnetic field experienced by the magnetometer during its movement at zero, thus expanding the dynamic range.

[0075] Based on the transfer functions of equations (1) and (2), the closed-loop transfer function G between the feedback magnetic field and the input can be obtained. closed (s) and amplitude-frequency response A closed (ω) is:

[0076]

[0077] Where η=G0·K P ·ω c By G PI When (s) is adjusted to a larger value, the amplitude-frequency response of the closed-loop magnetometer is close to 1. This means that the amplitude of the closed-loop magnetometer will not attenuate when measuring magnetic signals in the low-frequency range, which can improve the bandwidth of the system and increase its stability, thus verifying the feasibility of the magnetic field closed-loop control system.

[0078] Since the peak value of the CPT signal corresponds to the zero-crossing point of the dispersive signal, and magnetic flux density is usually measured by measuring the Zeeman frequency shift of the CPT resonance, the magnetic field measurement is transformed into a measurement of the frequency offset of the dispersive signal's zero-crossing point. With the frequency scanning of the RF modulation signal turned off, the output of the lock-in amplifier at this point is used as the setpoint for the PI negative feedback. When the external magnetic field changes, the center of the magnetically sensitive dispersive signal shifts, and the output of the lock-in amplifier is no longer zero. The PI negative feedback controls the input voltage of VOC, changing the center frequency of the RF modulation signal, causing the lock-in amplifier's output to return to zero, thus keeping the output of the lock-in amplifier always controlled at the zero-crossing point of the dispersive signal; when the magnetic field stabilizes, it returns to the closed-loop measurement state described above.

[0079] The input voltage of the VCO will change the fundamental clock signal frequency of the crystal oscillator within a very small range. For the VCO used in this scheme, the input voltage change ΔV in The change in frequency of the output clock signal Δν Ref The relationship is:

[0080] Δν Ref =k T ·ΔV in (4)

[0081] Where, k T The voltage change ΔV in The change in frequency of the output clock signal Δν RefThe proportionality coefficient, expressed in V / Hz. The proportionality coefficient k is typically varied depending on the performance of the VCO. T The values ​​are also different; the value in this experiment is 3.5V / Hz.

[0082] When the frequency of the basic clock signal changes, the output frequency of the RF signal generator will change due to the characteristics of the clock signal. Specifically, if the RF signal input is set to 3.417 GHz, when the VCO output frequency decreases by 1 Hz due to a decrease in input voltage, the RF signal output will decrease by 341.7 Hz.

[0083] The output of the lock-in amplifier is always controlled at the zero-crossing point of the dispersive signal by PID control. By observing the change in the input voltage of the VCO, the offset Δν' of the zero-crossing frequency of the magnetically sensitive dispersive signal can be obtained using equation (4). The frequency offset Δν' and the change in magnetic field ΔB can be expressed as:

[0084] Δν′=γ·ΔB (5)

[0085] Where γ = 7Hz / nT is the gyromagnetic ratio of rubidium 87. Using equations (4) and (5), the magnetic field change ΔB and the input voltage change ΔV of the VCO can be obtained. in The relationship is:

[0086]

[0087] This enables real-time measurement of the magnetic field.

[0088] This method requires five steps to implement a closed-loop tracking measurement method for magnetic fields based on a CPT magnetometer.

[0089] Step 1: Generation of multicolor lasers

[0090] To meet the requirements of the CPT magnetometer, two laser frequencies need to be generated to satisfy the frequency difference (6.834 GHz) between the two hyperfine energy levels of the D1 line of the Rb87 atom. Typically, a 3.417 GHz signal is generated using an RF signal generator. This RF signal is then modulated into the DC control signal of the VCSEL laser using a Bias-T method to obtain a multicolor laser. The basic clock signal for the RF signal generator is provided by an external voltage-controlled oscillator (VCO), ensuring closed-loop control.

[0091] Step 2: Modulate and demodulate the CPT signal to obtain the dispersive signal

[0092] The signal generated by the radio frequency signal generator is frequency modulated by a triangular wave function and a sine wave function. The triangular wave function is used to achieve frequency scanning; the sine wave function modulates the optical signal, and the sine wave function signal is used as the reference signal input to the lock-in amplifier to demodulate the corresponding dispersive signal. Since there is a one-to-one correspondence between the dispersive signal and the CPT signal, and the zero-crossing point of the dispersive signal coincides with the peak point of the CPT signal, the dispersive signal can be used to measure the magnetic field. Under the condition of an external magnetic field, multiple CPT resonances are formed due to the Zeeman multiplicity of the ground state. For the magnetic quantum number m of alkali metal atoms... F The frequency difference between the Zeeman sublevels of ±1 changes with the magnetic field, resulting in a frequency shift; therefore, the generated dispersive signal is called a magnetically susceptible dispersive signal, and m F The frequency difference of the Zeeman sublevels with a value of 0 remains constant and is always equal to the frequency difference of the hyperfine sublevels; this is known as the magnetically insensitive dispersion signal.

[0093] Step 3: Implementation of Dispersion Signal Selection and Modulation Signal Adjustment

[0094] Closed-loop measurement requires sensing of the external magnetic field; therefore, a magnetically sensitive dispersive signal must be selected as the object of closed-loop tracking. Using 3.417 GHz as the RF modulation center, the center of the resulting dispersive signal is m. F The magnetically insensitive signal has a value of 0. Therefore, it is necessary to adjust the center frequency so that the center position of the obtained dispersive signal corresponds to m. F =1 or m F = -1 The zero-crossing point of the magnetic susceptibility dispersion signal is selected based on the peak value in the experiment. During this process, the scanning range of the radio frequency signal is adjusted to achieve more precise alignment.

[0095] Step 4: Implementation of Closed-Loop System Control

[0096] An atomic magnetometer system can be equivalently represented as a first-order inertial element. The open-loop system behaves as a first-order low-pass filter in the frequency domain response, where the input is the magnetic field to be measured and the output is the signal voltage, with a chromaticity relationship between them. The open-loop transfer function G(s) is:

[0097]

[0098] Where G0 is the DC gain, which can be obtained from the slope of the dispersion curve at zero; ω c The cutoff frequency is the measurement bandwidth of the magnetometer, which is related to (R... op +R rel It is directly proportional to R, where R rel R is the relaxation rate. op The pumping rate is the sum of the two values, which can be obtained by the distance between the two poles of the dispersion curve.

[0099] Based on this setting, the bandwidth can be further increased through negative feedback. Negative feedback exceeds the characteristic bandwidth of the amplifier, thus improving its linearity. Therefore, negative feedback can be applied to CPT atomic magnetometers to improve the linearity of the output signal and extend the magnetic resonance bandwidth. A simple and highly stable PID controller is used for feedback control, and its transfer function can be expressed as:

[0100]

[0101] Among them, K P K I and K D These represent the proportional, integral, and derivative coefficients, respectively. Typically, a PI controller is sufficient because it improves stability and eliminates steady-state errors. The feedback loop keeps the magnetic field experienced by the magnetometer during its movement at zero, thus expanding the dynamic range.

[0102] Based on the transfer functions of equations (1) and (2), the closed-loop transfer function G between the feedback magnetic field and the input can be obtained. closed (s) and amplitude-frequency response A closed (ω) is:

[0103]

[0104] Where η=G0·K P ·ω c By G PI When (s) is adjusted to a larger value, the amplitude-frequency response of the closed-loop magnetometer is close to 1. This means that the amplitude of the closed-loop magnetometer will not attenuate when measuring magnetic signals in the low-frequency range, which can improve the bandwidth of the system and increase its stability, thus verifying the feasibility of the magnetic field closed-loop control system.

[0105] Since the peak value of the CPT signal corresponds to the zero-crossing point of the dispersive signal, and magnetic flux density is usually measured by measuring the Zeeman frequency shift of the CPT resonance, the magnetic field measurement is transformed into a measurement of the frequency offset of the dispersive signal's zero-crossing point. With the frequency scanning of the RF modulation signal turned off, the output of the lock-in amplifier at this point is used as the setpoint for the PI negative feedback. When the external magnetic field changes, the center of the magnetically sensitive dispersive signal shifts, and the output of the lock-in amplifier is no longer zero. The PI negative feedback controls the input voltage of VOC, changing the center frequency of the RF modulation signal, causing the lock-in amplifier's output to return to zero, thus keeping the output of the lock-in amplifier always controlled at the zero-crossing point of the dispersive signal; when the magnetic field stabilizes, it returns to the closed-loop measurement state described above.

[0106] Step 5: Observe the VCO input voltage to achieve magnetic field measurement

[0107] The input voltage of the VCO will change the fundamental clock signal frequency of the crystal oscillator within a very small range. For the VCO used in this scheme, the input voltage change ΔV in The change in frequency of the output clock signal Δν Ref The relationship is:

[0108] Δν Ref =k T ·ΔV in (4)

[0109] Where, k T The voltage change ΔV in The change in frequency of the output clock signal Δν Ref The proportionality coefficient, expressed in V / Hz. The proportionality coefficient k is typically varied depending on the performance of the VCO. T The values ​​are also different; the value in this experiment is 3.5V / Hz.

[0110] When the frequency of the basic clock signal changes, the output frequency of the RF signal generator will change due to the characteristics of the clock signal. Specifically, if the RF signal input is set to 3.417 GHz, when the VCO output frequency decreases by 1 Hz due to a decrease in input voltage, the RF signal output will decrease by 341.7 Hz.

[0111] The output of the lock-in amplifier is always controlled at the zero-crossing point of the dispersive signal by PID control. By observing the change in the input voltage of the VCO, the offset Δν' of the zero-crossing frequency of the magnetically sensitive dispersive signal can be obtained using equation (4). The frequency offset Δν' and the change in magnetic field ΔB can be expressed as:

[0112] Δν'=γ·ΔB (5)

[0113] Where γ = 7Hz / nT is the gyromagnetic ratio of rubidium 87. Using equations (4) and (5), the magnetic field change ΔB and the input voltage change ΔV of the VCO can be obtained. in The relationship is:

[0114]

[0115] This enables real-time measurement of the magnetic field.

[0116] Contents not described in detail in this specification are prior art known to those skilled in the art. It is hereby indicated that the above description is intended to help those skilled in the art understand this invention, but does not limit the scope of protection of this invention. Any equivalent substitutions, modifications, improvements, and / or simplifications of the above descriptions that do not depart from the essential content of this invention fall within the scope of protection of this invention.

Claims

1. A closed-loop tracking measurement method for magnetic fields based on a CPT magnetometer, characterized in that, The method includes inputting a mixed signal, consisting of a modulated radio frequency signal and a DC signal, into the laser of the CPT magnetometer system. This causes the multicolor laser emitted by the laser to form an optical signal carrying magnetic field information after passing through an atomic gas cell. The optical signal is converted into a CPT signal by a photodetector amplifier and then modulated and demodulated in a lock-in amplifier to obtain multiple dispersive signals. A magnetically sensitive dispersive signal is selected from the multiple dispersive signals as the closed-loop tracking object. A PI controller or PID controller generates an input voltage change for a voltage-controlled oscillator (VCO) based on the frequency offset of the zero-crossing point of the magnetically sensitive dispersive signal. The VCO provides a clock signal to the radio frequency signal generator that generates the modulated radio frequency signal. The change in the magnetic field to be measured is determined by the input voltage change. Includes the following steps: (1) Generation of multicolor lasers Based on the principle of CPT magnetometer, two laser frequencies need to be generated to satisfy the frequency difference of 6.834 GHz between the two hyperfine energy levels of the D1 line of Rb87 atom. The VCSEL laser is locked on the D1 line, and a 3.417 GHz signal is generated by an RF signal generator. The RF signal is modulated into the DC signal of the VCSEL laser through a T-type bias to obtain multicolor laser. The basic clock signal of the RF signal generator is provided by an external voltage-controlled oscillator (VCO) to ensure closed-loop control. (2) Modulate and demodulate the CPT signal to obtain a dispersive signal The signal generated by the radio frequency signal generator is frequency modulated by a triangular wave function and a sine wave function. The triangular wave function is used to achieve frequency scanning, and the sine wave function modulates the optical signal. The sine wave function signal is used as the reference signal input of the lock-in amplifier, and the corresponding dispersive signal is obtained by demodulation. Since there is a one-to-one correspondence between the dispersive signal and the CPT signal, and the zero-crossing point of the dispersive signal coincides with the peak point of the CPT signal, the dispersive signal is used to measure the magnetic field. Under the condition of an external magnetic field, multiple CPT resonances are formed due to the Zeeman multiplicity of the ground state. For the magnetic quantum number m of alkali metal atoms... F The frequency difference between the Zeeman sublevels (±1) changes with the magnetic field, resulting in a frequency shift; the resulting dispersive signal is called a magnetically susceptible dispersive signal. F The frequency difference of the Zeeman sublevels with =0 remains unchanged and is always equal to the frequency difference of the hyperfine level, which is called the magnetically insensitive dispersion signal. (3) Implementation of dispersive signal selection and modulation signal adjustment Closed-loop measurement requires sensing of the external magnetic field; therefore, the magnetically sensitive dispersive signal is chosen as the object of closed-loop tracking. 3.417 GHz is used as the radio frequency modulation center, and the center of the resulting dispersive signal is m. F =0 magnetically insensitive signal; therefore, the center frequency is adjusted so that the center position of the obtained dispersive signal corresponds to m. F =1 or m F =-1 The zero-crossing point of the magnetic susceptibility dispersion signal is selected based on the peak value in the experiment. During this process, the scanning range of the radio frequency signal is adjusted to achieve more precise alignment. (4) Implementation of closed-loop system control The atomic magnetometer system is equivalent to a first-order inertial element. The open-loop system behaves as a first-order low-pass filter in the frequency domain response, where the input is the magnetic field to be measured and the output is the signal voltage, with a chromaticity relationship between them. The open-loop transfer function G(s) is: （1） Where G0 is the DC gain, which is obtained from the slope of the dispersion curve at zero; The cutoff frequency is the measurement bandwidth of the magnetometer, which is related to (R... op +R rel It is directly proportional to R, where R rel R is the relaxation rate. op Let be the pumping rate, and the sum of the two is obtained by the distance between the two poles of the dispersion curve. s is a complex variable in the Laplace transform. The bandwidth is further increased through negative feedback, exceeding the amplifier's characteristic bandwidth to improve its linearity. Therefore, negative feedback is applied to CPT atomic magnetometers to improve the linearity of the output signal and extend the magnetic resonance bandwidth. A PI or PID controller is used for feedback control, and the transfer function... Represented as: （2） Among them, K P K I and K D These represent the proportional, integral, and derivative coefficients, respectively. Using a PI controller can improve stability and eliminate steady-state errors in the system. The feedback loop keeps the magnetic field experienced by the magnetometer during its movement at zero, thus expanding the dynamic range. Based on the transfer functions of equations (1) and (2), the closed-loop transfer function G between the feedback magnetic field and the input can be obtained. closed (s) and amplitude-frequency response A closed ( )for: （3） in , It is an intermediate quantity, obtained by transferring the PI controller's transfer function G. PI When (s) is adjusted to a larger value, the amplitude-frequency response of the closed-loop magnetometer is close to 1. This means that the amplitude of the closed-loop magnetometer will not attenuate when measuring magnetic signals in the low-frequency range, which can improve the bandwidth of the system and increase its stability, thus verifying the feasibility of the magnetic field closed-loop control system. Since the peak value of the CPT signal corresponds to the zero-crossing point of the dispersion signal, the frequency scanning of the RF modulation signal is turned off, and the output of the lock-in amplifier at this time is used as the set value of the PI negative feedback. When the external magnetic field changes, the center of the magnetically sensitive dispersion signal shifts, and the output of the lock-in amplifier is no longer 0. The input voltage of the VCO is controlled by the PI negative feedback to change the center frequency of the RF modulation signal, so that the output of the lock-in amplifier returns to 0, and the output of the lock-in amplifier is always controlled at the zero-crossing point of the dispersion signal. When the magnetic field stabilizes, it returns to the closed-loop measurement state described above. (5) Magnetic field measurement is achieved by observing the VCO input voltage. The input voltage of the VCO will change the frequency of the crystal oscillator's fundamental clock signal within a very small range; for the VCO used in this scheme, the change in its input voltage... The change in the frequency of the output clock signal The relationship is: （4） Where, k T The frequency change of the output clock signal With voltage change The proportionality coefficient, in units of Hz / V; When the frequency of the basic clock signal changes, the output frequency of the RF signal generator will change due to the characteristics of the clock signal. Specifically, if the RF signal input is set to 3.417 GHz, when the VCO output frequency decreases by 1 Hz due to the decrease in input voltage, the RF signal output will decrease by 341.7 Hz. By using PID control, the output of the lock-in amplifier is always controlled at the zero-crossing point of the dispersive signal; by observing the change in the input voltage of the VCO, the offset of the zero-crossing frequency of the magnetically sensitive dispersive signal can be obtained using equation (4). Frequency offset Changes in magnetic field It can be represented as: （5） in It is the gyromagnetic ratio of rubidium 87; the change in magnetic field is obtained using equations (4) and (5). The change in input voltage of the VCO The relationship is: （6） This enables real-time measurement of the magnetic field.

2. The closed-loop tracking measurement method for magnetic field based on a CPT magnetometer according to claim 1, characterized in that, The laser is a vertical-cavity surface-emitting laser (VCSEL). The laser is connected to the output of a T-type bias to obtain the mixed signal. The first input of the T-type bias is connected to a VCSEL laser controller to obtain the DC signal. The second input of the T-type bias is connected to the radio frequency (RF) signal generator to obtain the modulated RF signal. The RF signal generator is connected to the output of an adder to modulate the RF signal. The first input of the adder is connected to a triangular wave signal generator. The second input of the adder is connected to a sine wave signal generator. The sine wave signal generator is connected to the lock-in amplifier to use the sine wave signal as a reference signal for demodulating the dispersive signal. The PI controller or PID controller is connected to an input voltage data acquisition system.

3. The closed-loop tracking measurement method for magnetic field based on a CPT magnetometer according to claim 1, characterized in that, The mixed signal passes sequentially through a λ / 2 waveplate, a polarization beam splitter prism, an optical fiber coupler, a polarization-maintaining fiber, and a laser collimator before entering the atomic gas chamber. The atomic gas chamber is located inside an oven, which is located inside a magnetic field coil. The magnetic field coil is located inside a ferrite shielding layer, which is located inside a permalloy shielding layer.

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