Photomagnetic modulation method and device for enhancing single-beam free precession atom magnetometer signal

Abstract

The invention discloses an optomagnetic modulation method and device for enhancing a single-beam free precession atom magnetometer signal, which is based on a synchronous optical pumping technology and a radio frequency magnetic field pulse control technology, controls the spin polarization of atoms through optomagnetic modulation and excites a free precession signal, so that more spin polarization components participate in free precession, and the free precession of the atoms is enhanced. And all-around signal enhancement of the single-beam free procession atom magnetometer is realized. The free precession signal is enhanced, the signal-to-noise ratio is improved, further improvement of the sensitivity of the single-beam free precession atom magnetometer is facilitated, and further application of the single-beam free precession atom magnetometer in the field of quantum precision magnetic field measurement in the future is facilitated.

Description

Technical Field

[0001] The invention relates to the field of magnetic field measurement technology, and in particular to an optical magnetic modulation method and device for enhancing a single-beam free precession atomic magnetometer signal. Background Art

[0002] Optically pumped atomic magnetometers have the characteristics of miniaturization, high sensitivity, and low cost, and are widely used in the fields of biomagnetic measurement and space magnetic detection. The free precession atomic magnetometer based on the free precession mechanism is a typical representative of optically pumped atomic magnetometers. With its high accuracy, large dynamic range, and simple circuit structure, it has become a hot spot in the research and development of optically pumped atomic magnetometers in recent years. Compared with the dual-beam configuration, the single-beam free precession atomic magnetometer is easier to achieve miniaturization and low cost, but its sensitivity is lower than that of the dual-beam configuration.

[0003] An important factor limiting the sensitivity of the free precession atomic magnetometer is the intensity of the free precession signal generated by the magnetometer. A high-intensity free precession signal can achieve a high signal-to-noise ratio, and thus achieve high sensitivity of the magnetometer. In the prior art, the single-beam free precession optically pumped atomic magnetometer using all-optical modulation realizes spin polarization preparation through synchronous optical pumping, but only the transverse spin polarization component participates in the free precession, which limits the improvement of the signal intensity and thus affects the sensitivity of the magnetometer. Therefore, enhancing the signal intensity of the single-beam free precession atomic magnetometer is a very important research issue. Summary of the invention

[0004] The purpose of the present invention is to provide a method and device for optical magnetic modulation to enhance the signal of a single-beam free precession atomic magnetometer. After synchronous optical pumping is completed, a transverse radio frequency magnetic field pulse is applied to manipulate the atomic spin polarization to rotate to a plane perpendicular to the magnetic field direction, so that both the transverse component and the longitudinal component of the spin polarization can participate in the free precession, thereby achieving all-round signal enhancement of the single-beam free precession atomic magnetometer.

[0005] To achieve the above object, the present invention provides a method for enhancing the optical magnetic modulation signal of a single-beam free precession atomic magnetometer, comprising the following steps:

[0006] S1, turn on the laser, adjust the laser light wavelength to the alkali metal atom D1 line, the laser forms circularly polarized light through the optical path and passes through the alkali metal gas chamber;

[0007] S2. Use a light intensity modulator to adjust the intensity of circularly polarized light to achieve synchronous optical pumping and prepare atomic spin polarization;

[0008] S3, after completing synchronous optical pumping, applying a transverse radio frequency magnetic field pulse to manipulate the atomic spin polarization to a plane perpendicular to the magnetic field direction;

[0009] S4. Atomic spin polarization undergoes free precession. Free precession signal detection is achieved through low-intensity laser, and the magnetic field is measured by collecting and processing signals through a data acquisition and processing system.

[0010] Preferably, the adjustment of the laser in step S1 specifically includes the following steps:

[0011] S11, turn on the laser and drive the light intensity modulator;

[0012] S12, adjusting the frequency of the laser emitted by the laser to the center of the alkali metal atomic spectrum line D1;

[0013] S13, adjusting the polarization device so that the laser generates circularly polarized light after passing through the laser and passes through the alkali metal gas chamber.

[0014] Preferably, the synchronous optical pumping in step S2 specifically includes the following steps:

[0015] S21, inputting a square wave pulse sequence with a period of milliseconds and a certain duty cycle into the light intensity modulator through a signal generator, wherein the duty cycle of the square wave pulses in the sequence is 50%, and the pulse repetition frequency is the Larmor precession frequency corresponding to the magnetic field;

[0016] S22, fine-tuning the repetition frequency of the square wave pulse in the sequence until the output signal of the magnetometer reaches the maximum at the end of the square wave pulse sequence, thereby realizing synchronous optical pumping.

[0017] Preferably, in step S3, controlling the atomic spin polarization to a plane perpendicular to the magnetic field direction specifically comprises the following steps:

[0018] S31, at the moment of removing the input to the light intensity modulator in each cycle, inputting a transverse radio frequency magnetic field pulse perpendicular to the laser direction to the radio frequency coil through a signal generator, the oscillation frequency of the input radio frequency magnetic field is the same as the repetition frequency of the square wave pulse in step S22, and the duration is much shorter than the free precession period;

[0019] S32. Control other parameters unchanged and adjust the size of the radio frequency magnetic field pulse so that the signal output by the magnetometer reaches a maximum. At this time, the spin polarization is controlled to a plane orthogonal to the magnetic field.

[0020] Preferably, the collection and processing of the free precession signal in step S4 specifically includes the following steps:

[0021] S41. After optical magnetic modulation, the spin polarization undergoes free precession. The signal generator inputs a DC signal with a low amplitude to the light intensity modulator to ensure a certain light intensity of the laser, and detects the free precession signal of the spin polarization.

[0022] S42, collecting the signal output by the magnetometer after passing through the transimpedance amplifier and the bandpass filter through the data acquisition and processing system;

[0023] S43, processing the collected free precession signal, extracting the oscillation frequency of each periodic signal, dividing it by the gyromagnetic ratio to obtain the magnetic field to be measured, wherein the oscillation frequency is the Larmor precession frequency.

[0024] Preferably, in step S4, the spin polarization performs free precession, and the evolution of the spin polarization in the laser propagation direction can be expressed as:

[0025]

[0026] The first term of the formula is the expression of the slow-varying DC term caused by optical pumping, and the second term is the expression of the free precession of spin polarization, S z (t) is the spin polarization component in the laser direction, t is time, is the pumping rate in the free precession phase, R r1 is the longitudinal relaxation rate in the free precession phase, R r2 is the transverse relaxation rate in the free precession stage, θ is the angle between the magnetic field to be measured and the laser propagation direction, γ is the gyromagnetic ratio, B0 is the magnitude of the magnetic field to be measured, is the signal phase, P1 is the spin polarization longitudinal component, P2 is the spin polarization transverse component, and the expressions of P1 and P2 are as follows:

[0027]

[0028] Where t1 is the duration of synchronous pumping, t3 is the duration of the free precession phase, and R p0 is the peak optical power P in the synchronous optical pumping stage p The corresponding pumping rates are: R1 is the longitudinal relaxation rate during the synchronous optical pumping stage, and R2 is the transverse relaxation rate during the synchronous optical pumping stage.

[0029] Preferably, in step S4, after the circularly polarized light signal passes through the photodetector, the transimpedance amplifier and the bandpass filter, the slowly varying DC term is filtered out, and the signal collected by the data acquisition and processing system is expressed as:

[0030]

[0031] Among them, V0 is the voltage signal amplitude output by the bandpass filter.

[0032] The present invention also provides a device for enhancing the signal of a single-beam free-precession atomic magnetometer, comprising a laser, a light intensity modulator, a polarization-maintaining optical fiber, a collimator, a half-wave plate, a polarizer, a quarter-wave plate, an alkali metal gas chamber and a photodetector connected in sequence, wherein the output end of the photodetector is connected to the input end of a data acquisition and processing system through a transimpedance amplifier and a bandpass filter, the alkali metal gas chamber is wrapped and heated by an oven and a non-magnetic electric heating coil to achieve a high atomic density, a radio frequency coil and a magnetometer support shell are arranged on the outside of the alkali metal gas chamber, the input end of the light intensity modulator is connected to the output end of a signal generator, and the radio frequency coil is connected to the other output end of the signal generator through an axis perpendicular to the laser direction.

[0033] Preferably, the frequency range of the bandpass filter is centered on the Larmor precession frequency corresponding to the magnetic field to be measured.

[0034] Therefore, the present invention adopts the above-mentioned optical magnetic modulation method and device for enhancing the signal of a single-beam free precession atomic magnetometer, which has the following beneficial effects:

[0035] (1) Conventional single-beam all-optical modulated free precession atomic magnetometers realize free precession signals through synchronous optical pumping, while the present invention adds transverse radio frequency magnetic field pulses to manipulate the atomic spin polarization rotation, so that more spin polarization components participate in free precession, thereby enhancing the free precession signal.

[0036] (2) The present invention realizes the all-round enhancement of the free precession signal and the improvement of the signal-to-noise ratio of the single-beam free precession atomic magnetometer, thereby realizing the improvement of the sensitivity of the magnetometer, which facilitates the further research and development of the single-beam free precession atomic magnetometer in the field of quantum precision magnetic field measurement.

[0037] (3) The present invention achieves all-round enhancement of the free precession signal of the magnetometer without increasing the complexity of the single-beam free precession atomic magnetometer system.

[0038] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 This is a flow chart of a method for enhancing optical magnetic modulation signals of a single-beam free precession atomic magnetometer according to an embodiment of the present invention;

[0040] Figure 2 It is a schematic structural diagram of a device for enhancing a single-beam free precession atomic magnetometer signal according to an embodiment of the present invention;

[0041] Figure 3 A signal timing diagram of the optical-magnetic modulation method according to an embodiment of the present invention;

[0042] Reference numerals

[0043] 1. Laser; 2. Light intensity modulator; 3. Polarization-maintaining fiber; 4. Collimator; 5. Half-wave plate; 6. Polarizer; 7. Quarter-wave plate; 8. Alkali metal gas chamber; 9. Photodetector; 10. Transimpedance amplifier; 11. Bandpass filter; 12. Data acquisition and processing system; 13. Signal generator; 14. Oven; 15. Non-magnetic electric heating coil; 16. Radio frequency coil; 17. Magnetometer support shell. DETAILED DESCRIPTION

[0044] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but merely represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0045] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, further definition and explanation thereof is not required in subsequent drawings.

[0046] Example

[0047] like Figure 1 and Figure 3 As shown, the present invention provides a method for enhancing the optical magnetic modulation signal of a single-beam free precession atomic magnetometer, comprising the following steps:

[0048] S1, turn on the laser 1, adjust the wavelength of the light emitted by the laser 1 to the alkali metal atom D1 line, and the laser forms circularly polarized light through the optical path and passes through the alkali metal gas chamber 8.

[0049] In this embodiment, the adjustment of the laser in step S1 specifically includes the following steps:

[0050] S11, turn on the laser 1 and drive the light intensity modulator 2 and other devices;

[0051] S12, adjusting the frequency of the laser emitted by laser 1 to the center of the alkali metal atomic spectrum line D1;

[0052] S13, adjusting the polarization device so that the laser generates circularly polarized light after passing through the laser, and passes through the alkali metal gas chamber 8.

[0053] S2. Use light intensity modulator 2 to adjust the intensity of circularly polarized light to achieve synchronous optical pumping and prepare atomic spin polarization.

[0054] In this embodiment, the synchronous optical pumping in step S2 specifically includes the following steps:

[0055] S21, inputting a square wave pulse sequence with a period of millisecond level and a certain duty cycle into the light intensity modulator 2 through the signal generator 13, wherein the duty cycle of the square wave pulses in the sequence is 50%, and the pulse repetition frequency is approximately the Larmor precession frequency corresponding to the magnetic field;

[0056] S22, fine-tuning the repetition frequency of the square wave pulse in the sequence until the output signal of the magnetometer reaches a maximum at the end of the square wave pulse sequence, thereby realizing synchronous optical pumping.

[0057] S3. After completing synchronous optical pumping, a transverse radio frequency magnetic field pulse is applied to manipulate the atomic spin polarization to a plane perpendicular to the magnetic field direction.

[0058] In this embodiment, in step S3, controlling the atomic spin polarization to a plane perpendicular to the magnetic field direction specifically includes the following steps:

[0059] S31, at the moment of removing the input to the light intensity modulator 2 in each cycle, the signal generator 13 is used to input to the radio frequency coil 16 to generate a transverse radio frequency magnetic field pulse perpendicular to the laser direction, the oscillation frequency of the input radio frequency magnetic field is the same as the repetition frequency of the square wave pulse in step S22, and the duration is much shorter than the free precession period;

[0060] S32. Control other parameters unchanged and adjust the size of the RF magnetic field pulse signal so that the output signal of the magnetometer reaches the maximum. At this time, the spin polarization is controlled to a plane orthogonal to the magnetic field, and the free precession signal reaches the maximum.

[0061] S4. Atomic spin polarization undergoes free precession, and free precession signal detection is achieved through low-intensity laser, and the data acquisition and processing system 12 collects and processes the signal to achieve measurement of the magnetic field.

[0062] In this embodiment, the collection and processing of the free precession signal in step S4 specifically includes the following steps:

[0063] S41, after optical magnetic modulation, the spin polarization undergoes free precession, and the signal generator 13 inputs a DC signal with a lower amplitude to the light intensity modulator 2 to ensure a certain light intensity of the laser, and detects the free precession signal of the spin polarization;

[0064] S42, collecting the signal output by the magnetometer after passing through the transimpedance amplifier 10 and the bandpass filter 11 through the data acquisition and processing system 12;

[0065] S43, processing the collected free precession signal, extracting the oscillation frequency of each periodic signal, namely the Larmor precession frequency, and dividing it by the gyromagnetic ratio to obtain the magnetic field to be measured.

[0066] In step S4 of this embodiment, the spin polarization undergoes free precession, and the evolution of the spin polarization in the laser propagation direction can be expressed by the following formula:

[0067]

[0068] The first term of the formula is the expression of the slow-varying DC term caused by optical pumping, and the second term is the expression of the free precession of spin polarization, S z (t) is the spin polarization component in the laser direction, t is time, is the pumping rate in the free precession phase, R r1 is the longitudinal relaxation rate in the free precession phase, R r2 is the transverse relaxation rate in the free precession stage, θ is the angle between the magnetic field to be measured and the laser propagation direction, γ is the gyromagnetic ratio, B0 is the magnitude of the magnetic field to be measured, is the signal phase, P1 is the spin polarization longitudinal component, P2 is the spin polarization transverse component, and the expressions of P1 and P2 are as follows:

[0069]

[0070] Where t1 is the duration of synchronous pumping, t2 is the duration of the RF pulse, t3 is the duration of the free precession phase, and R p0 is the peak optical power P in the synchronous optical pumping stage p The corresponding pumping rates are: R1 is the longitudinal relaxation rate during the synchronous optical pumping stage, and R2 is the transverse relaxation rate during the synchronous optical pumping stage.

[0071] It can be seen from the free precession expression that when the optical magnetic modulation method of the present invention is implemented, the transverse component and the longitudinal component of the atomic spin polarization both participate in the free precession after being manipulated by the radio frequency pulse magnetic field, thereby achieving single-beam free precession atomic magnetometer signal enhancement.

[0072] In step S4 of this embodiment, after the circularly polarized light signal passes through the photodetector 9, the transimpedance amplifier 10 and the bandpass filter 11, the slowly varying DC term is filtered out, and the signal collected by the data acquisition and processing system 12 can be expressed as:

[0073]

[0074] Wherein, V0 is the voltage signal amplitude output by the bandpass filter 11. The data acquisition and processing system 12 analyzes the acquired signal, extracts the oscillation component in the signal to obtain the Larmor precession frequency, and thus obtains the magnetic field information to be measured.

[0075] refer to Figure 2 , xyz in the figure is the three axes (x-axis, y-axis, z-axis) of the Cartesian coordinate system established with the laboratory pump light direction as the z-axis. The present invention also provides a device for enhancing the signal of a single-beam free precession atomic magnetometer, comprising a laser 1, a light intensity modulator 2, a polarization-maintaining optical fiber 3, a collimator 4, a half-wave plate 5, a polarizer 6, a quarter-wave plate 7, an alkali metal gas chamber 8 and a photodetector 9 connected in sequence, and the output end of the photodetector 9 is connected to the input end of a data acquisition and processing system 12 through a transimpedance amplifier 10 and a bandpass filter 11. The frequency range of the bandpass filter 11 is centered on the Larmor precession frequency corresponding to the magnetic field to be measured. The half-wave plate 5, the polarizer 6 and the quarter-wave plate 7 make the pump light form circularly polarized light and have maximum optical power before passing through the alkali metal gas chamber 8. The alkali metal gas chamber 8 is wrapped and heated by an oven 14 and a non-magnetic electric heating coil 15 to achieve a high atomic density, and a radio frequency coil 16 and a magnetometer support shell 17 are arranged outside the alkali metal gas chamber 8. The input end of the light intensity modulator 2 is connected to the output end of the signal generator 13 , and the RF coil 16 is connected to the other output end of the signal generator 13 along one axis perpendicular to the laser direction.

[0076] Therefore, the present invention adopts the above-mentioned optical magnetic modulation method and device for enhancing the signal of a single-beam free precession atomic magnetometer. First, atomic spin polarization is prepared by synchronous optical pumping technology, and then a transverse radio frequency magnetic field pulse is applied to manipulate the atomic spin polarization to a plane perpendicular to the magnetic field direction. During the spin-polarized free precession stage, the pumping light maintains a low light intensity output to realize the detection of the free precession signal. The magnetic field information can be obtained by collecting and processing the signal through a data acquisition and processing system.

[0077] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for enhancing the optical magnetic modulation signal of a single-beam free precession atomic magnetometer, characterized in that: The following steps are involved: S1, turn on the laser, adjust the laser light wavelength to the alkali metal atom D1 line, the laser forms circularly polarized light through the optical path and passes through the alkali metal gas chamber; S2. Use a light intensity modulator to adjust the intensity of circularly polarized light to achieve synchronous optical pumping and prepare atomic spin polarization; S3, after completing synchronous optical pumping, applying a transverse radio frequency magnetic field pulse to manipulate the atomic spin polarization to a plane perpendicular to the magnetic field direction; S4. Atomic spin polarization undergoes free precession. Free precession signal detection is achieved through low-intensity laser, and the magnetic field is measured by collecting and processing signals through a data acquisition and processing system.

2. The optical magnetic modulation method for enhancing the signal of a single-beam free precession atomic magnetometer according to claim 1, characterized in that: The adjustment of the laser in step S1 specifically includes the following steps: S11, turn on the laser and drive the light intensity modulator; S12, adjusting the frequency of the laser emitted by the laser to the center of the alkali metal atomic spectrum line D1; S13, adjusting the polarization device so that the laser generates circularly polarized light after passing through the laser and passes through the alkali metal gas chamber.

3. The optical magnetic modulation method for enhancing the signal of a single-beam free precession atomic magnetometer according to claim 1, characterized in that: The synchronous optical pumping in step S2 specifically includes the following steps: S21, inputting a square wave pulse sequence with a period of milliseconds and a certain duty cycle into the light intensity modulator through a signal generator, wherein the duty cycle of the square wave pulses in the sequence is 50%, and the pulse repetition frequency is the Larmor precession frequency corresponding to the magnetic field; S22, fine-tuning the repetition frequency of the square wave pulse in the sequence until the output signal of the magnetometer reaches the maximum at the end of the square wave pulse sequence, thereby realizing synchronous optical pumping.

4. The optical magnetic modulation method for enhancing the signal of a single-beam free precession atomic magnetometer according to claim 1, characterized in that: In step S3, controlling the atomic spin polarization to a plane perpendicular to the magnetic field direction specifically includes the following steps: S31, at the moment of removing the input to the light intensity modulator in each cycle, inputting a transverse radio frequency magnetic field pulse perpendicular to the laser direction to the radio frequency coil through a signal generator, the oscillation frequency of the input radio frequency magnetic field is the same as the repetition frequency of the square wave pulse in step S22, and the duration is much shorter than the free precession period; S32. Control other parameters unchanged and adjust the size of the RF magnetic field pulse so that the output signal of the magnetometer reaches a maximum. At this time, the spin polarization is controlled to a plane orthogonal to the magnetic field.

5. The optical magnetic modulation method for enhancing the signal of a single-beam free precession atomic magnetometer according to claim 1, characterized in that: The collection and processing of the free precession signal in step S4 specifically includes the following steps: S41. After optical magnetic modulation, the spin polarization undergoes free precession. The signal generator inputs a DC signal with a low amplitude to the light intensity modulator to ensure a certain light intensity of the laser, and detects the free precession signal of the spin polarization. S42, collecting the signal output by the magnetometer after passing through the transimpedance amplifier and the bandpass filter through the data acquisition and processing system; S43, processing the collected free precession signal, extracting the oscillation frequency of each periodic signal, and dividing it by the gyromagnetic ratio to obtain the magnetic field to be measured, wherein the oscillation frequency is the Larmor precession frequency.

6. The optical magnetic modulation method for enhancing the signal of a single-beam free precession atomic magnetometer according to claim 5, characterized in that: In step S4, the spin polarization undergoes free precession, and the evolution of the spin polarization in the laser propagation direction can be expressed as: The first term of the formula is the expression of the slow-varying DC term caused by optical pumping, and the second term is the expression of the free precession of spin polarization, S z (t) is the spin polarization component in the laser direction, t is time, is the pumping rate in the free precession phase, R r1 is the longitudinal relaxation rate in the free precession phase, R r2 is the transverse relaxation rate in the free precession stage, θ is the angle between the magnetic field to be measured and the laser propagation direction, γ is the gyromagnetic ratio, B0 is the magnitude of the magnetic field to be measured, is the signal phase, P1 is the spin polarization longitudinal component, P2 is the spin polarization transverse component, and the expressions of P1 and P2 are as follows: Where t1 is the duration of synchronous pumping, t3 is the duration of the free precession phase, and R p0 is the peak optical power P in the synchronous optical pumping stage p The corresponding pumping rates are: R1 is the longitudinal relaxation rate during the synchronous optical pumping stage, and R2 is the transverse relaxation rate during the synchronous optical pumping stage.

7. The optical magnetic modulation method for enhancing the signal of a single-beam free precession atomic magnetometer according to claim 6, characterized in that: In step S4, after the circularly polarized light signal passes through the photodetector, the transimpedance amplifier and the bandpass filter, the slowly varying DC term is filtered out, and the signal collected by the data acquisition and processing system is expressed as: Among them, V0 is the voltage signal amplitude output by the bandpass filter.

8. A device for enhancing the signal of a single-beam free precession atomic magnetometer, applied to the optical magnetic modulation method for enhancing the signal of a single-beam free precession atomic magnetometer as claimed in any one of claims 1 to 7, characterized in that: The invention comprises a laser, a light intensity modulator, a polarization-maintaining optical fiber, a collimator, a half-wave plate, a polarizer, a quarter-wave plate, an alkali metal gas chamber and a photodetector connected in sequence. The output end of the photodetector is connected to the input end of a data acquisition and processing system through a transimpedance amplifier and a bandpass filter. The alkali metal gas chamber is wrapped and heated by an oven and a non-magnetic electric heating coil to achieve high atomic density. A radio frequency coil and a magnetometer supporting shell are arranged on the outside of the alkali metal gas chamber. The input end of the light intensity modulator is connected to the output end of a signal generator. The radio frequency coil is connected to the other output end of the signal generator at an axis perpendicular to the laser direction.

9. The device for enhancing the signal of a single-beam free precession atomic magnetometer according to claim 8, characterized in that: The frequency range of the bandpass filter is centered on the Larmor precession frequency corresponding to the magnetic field to be measured.

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