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Magnetoencephalography (MEG) is a non-invasive neuroimaging technique that can detect whole-brain neuroelectromagnetic signals in real-time in a single measurement. Due to excellent temporal and spatial resolution and integration of computed tomography or magnetic resonance imaging data, MEG allows signal source analysis. It can pinpoint epileptic foci as well as functional brain regions, reducing the necessity for invasive electrode implantation.

The combination of high-permeability ferrite and coils is often used to nullify ambient magnetic fields and is widely used in applications such as magnetic resonance imaging and high-sensitivity magnetic sensors. We propose the design method of transverse gradient coils based on the target field method in a high-permeability shield considering sidewall apertures (TFM-HPSCSA), which are installed in the ferrite shield to zero the residual magnetic field gradient. TFM-HPSCSA coils enable an innovative combination of magnetic field gradient linearity and structural luminescence. The coil current density distribution is set to avoid the central sidewall apertures. As a result, the contour distribution of the stream function under the optimized weight coefficients is calculated to obtain the wire alignments of the dBy/dx, dBy/dy and dBy/dz gradient coils. The deviations of the experimentally measured values from the finite element simulations of the three types coils are 0.63%, 1.17% and 0.48%, respectively, which verified the validity and the accuracy of the proposed method. In comparison to the traditional saddle gradient coil designed under the free space condition, the proposed dBy/dx coil produces a 30.5% improvement in the percentage range of regions with 5% magnetic field gradient nonlinearity. The increased linear range of the gradient magnetic field contributes to the improvement of the residual field nulling range in magnetic sensors and magnetic shielding systems in practical applications.

Alkali-metal vapor cells are key elements of atomic sensors. The temperature uniformity in the vapor cell is important for the sensitivity of the atomic sensors especially highly-sensitive SERF atomic magnetometers. This study proposes a novel double-layer cylindrical oven to improve the heating performance and the temperature uniformity of the vapor cell. We use the finite element method to build the thermal simulation models of the conventional square oven and the novel double-layer cylindrical oven. The performances of two ovens are compared. Then we build the experimental system to carry out the measurement experiment of heating temperature of the conventional and novel ovens and the in-situ measurement experiment of temperature distribution of the vapor cell using different ovens. We also measure the change of output signal amplitude of the SERF atomic magnetometer with frequency, i.e. the frequency response R(f) using the conventional and novel ovens respectively to evaluate the performance of the SERF atomic magnetometer using different ovens. The experimental results demonstrate that the proposed oven structure can improve the temperature uniformity of the alkali-metal vapor cell by 63.63% and the amplitude of R(f) using the novel oven increases by 24.7% on average. The novel double-layer cylindrical oven improves the temperature uniformity in the alkali-metal vapor cell and increases amplitude of the output signal of the SERF atomic magnetometer. The study is of great significance for improving the sensitivity of the atomic sensors especially SERF atomic magnetometers.

Ferrites are promising nonmetallic materials used for the fabrication of low-noise magnetic shields because they possess high permeability and high electrical resistivity. However, large-sized ferrite components are difficult to fabricate or machine. In this study, we develop a cylindrical ferrite shield that consists of five annuli and two lids with an inner volume of φ11.2 cm × 22.5 cm. Although this structure contains gaps between different components, it eases considerably the fabrication and machining process as compared to the entire module. The magnetic noise is measured by a spin-exchange relaxation-free atomic magnetometer, and the detrimental effects of the gaps are analyzed quantificationally using the finite element method. Our research results indicate that compared with the ferrite shield without gaps, the magnetization noise increases by 34.1%. Nonetheless, the magnetic noise at the center of the ferrite shield achieves 5.5f -1/2 fT, which is much lower than that of μ-metal shields with a similar size. If the gap width can be reduced to be smaller than 0.01 mm, the increase of the magnetization noise will be less than 4.9%, which can be negligible in practical applications. Our study provides a low-cost, readily available, and low-noise ferrite shield structure.

The magnetic noise generated by the ferrite magnetic shield affects the performance of ultra-sensitive atomic sensors. Differential measurement can effectively suppress the influence of common-mode (CM) magnetic noise, but the limit of suppression capability is not clear at present. In this paper, a finite element analysis model using power loss to calculate differential-mode (DM) magnetic noise under a ferrite magnetic shield is proposed. The experimental results confirm the feasibility of the model. An ultrahigh-sensitive magnetometer was built, the single channel magnetic noise measured and the differential-mode (DM) magnetic noise are 0.70 fT/Hz1/2 and 0.10 fT/Hz1/2 @30 Hz. The DM magnetic noise calculated by the proposed model is less than 5% different from the actual measured value. To effectively reduce DM magnetic noise, we analyze and optimize the structure parameters of the shield on the DM magnetic noise. When the outer diameter is fixed, the model is used to analyze the influence of the ratio of ferrite magnetic shielding thickness to outer diameter, the ratio of length to outer diameter, and the air gap between magnetic annuli on DM magnetic noise. The results show that the axial DM magnetic noise and radial DM magnetic noise reach the optimal values when the thickness to outer diameter ratio is 0.08 and 0.1. The ratio of length to outer diameter is negatively correlated with DM magnetic noise, and the air gap (0.1–1 mm) is independent of DM magnetic noise. The axial DM magnetic noise is less than that of radial DM magnetic noise. These results are useful for suppressing magnetic noise and breaking through the sensitivity of the magnetometer.

This study proposes a high-performance magnetic shielding structure composed of MnZn ferrite and mu-metal film. The use of the mu-metal film with a high magnetic permeability restrains the decrease in the magnetic shielding coefficient caused by the magnetic leakage between the gap of magnetic annuli. The 0.1–0.5 mm thickness of mu-metal film prevents the increase of magnetic noise of composite structure. The finite element simulation results show that the magnetic shielding coefficient and magnetic noise are almost unchanged with the increase in the gap width. Compared with conventional ferrite magnetic shields with multiple annuli structures under the gap width of 0.5 mm, the radial shielding coefficient increases by 13.2%, and the magnetic noise decreases by 21%. The axial shielding coefficient increases by 22.3 times. Experiments verify the simulation results of the shielding coefficient of the combined magnetic shield. The shielding coefficient of the combined magnetic shield is 16.5%. It is 91.3% higher than the conventional ferrite magnetic shield. The main difference is observed between the actual and simulated relative permeability of mu-metal films. The combined magnetic shielding proposed in this study is of great significance to further promote the performance of atomic sensors sensitive to magnetic field.

The atomic magnetometer in the application of simultaneous multichannel biomagnetic field measurement has gained increasing attention in recent researches. In this paper, a novel asymmetrical heating method for improving the temperature spatial homogeneity of the vapor cell in atomic magnetometer based on the finite element method was investigated. The homogeneity of temperature spatial distribution and the consistency of output signal from multilocation in a large vapor cell were numerically analyzed considering multichannel magnetic field measurement. With this asymmetrical heating method, the multilocation measurement signal regularity in the large vapor cell has been improved and the minimum variation coefficient of nine sensing areas' measurement signals decrease over 70% compared with the common heating method with the same heating temperature for the quadrate cell. This method is of great interest for the applications in miniaturing magnetometers of multichannel biomagnetic field measurement.

In this study, we demonstrate a non-modulated triaxial magnetic field compensation method for spin-exchange relaxation-free (SERF) atomic magnetometers. We realize simultaneous compensation of the magnetic field along the pump and probe directions by maximizing the first order differential value of the zero-field resonance signal. The magnetic field perpendicular to the pump-probe plane is compensated by zeroing the DC response of the magnetometer. The zero-field resonance is obtained by applying a linearly changed magnetic field along the direction perpendicular to that of the pump-probe plane. The first order differential of the zero-field resonance is acquired using the second order central difference method in real time. Compared with the conventional compensation methods, this method does not involve modulation and demodulation. Therefore, it requires no lock-in amplifier, thus making it more applicable in miniature atomic devices. Moreover, this method compensates the magnetic field along the pump and probe directions using only one criterion. It avoids the cross-talk effect between the pump and probe directions in the presence of non-orthogonal coils. The experiment results show that the compensation resolution is 9 pT, 7 pT and 0.05 pT for the probe, pump, and direction perpendicular to the pump-probe plane, respectively.

The ferrite magnetic shield can provide a low-noise magnetic environment for various ultrahigh-sensitivity measurements. The low-frequency complex permeability, which determines the magnetic hysteresis noise and the shielding factor, is a key parameter of the ferrite shield and thus should be measured accurately. In this paper, the measurement error of conventional coil method is analyzed at low frequency, and an improved method is proposed which could eliminate the measurement error introduced by the wire resistance. Using this method, four ferrite samples made of PC40 and PC47 materials are measured. The measurement accuracy of the low-frequency complex permeability has improved by two orders of magnitude. On the basis of the measurement results, magnetic hysteresis noise and the shielding factor of ferrite shields are calculated. The calculated results of the noise analysis indicate that the PC40 material has lower magnetic hysteresis noise. This study can help select the ferrite materials and estimate the performance for low-noise magnetic shield design.

Abstract We propose an in-situ method to calibrate the coil constants of the optical atomic magnetometer. This method is based on measuring the Larmor precession of spin polarized alkali metal atoms and has been demonstrated on a K-Rb hybrid atomic magnetometer. Oscillation fields of different frequencies are swept on the transverse coil. By extracting the resonance frequency through phase-frequency analysis of electron spin projection, the coil constants are calibrated to be 323.1 ± 0.28 nT/mA, 108 ± 0.04 nT/Ma, and 185.8 ± 1.03 nT/mA along the X, Y, and Z directions, respectively.

The alkali number density inside the sealed vapor cell restricts the fundamental sensitivity of the atomic magnetometer and may decrease in the long term, thus motivating the investigation of an in situ density determination method on atomic magnetometers. This paper presents a method to measure the alkali number density, which is proportional to the spin-exchange relaxation rate, through phase-frequency analysis. The magnetic resonance response of the atomic magnetometer was actively strengthened at low polarization by increasing the oscillating field amplitude. To downplay the side effect of the transverse field broadening, phase-frequency analysis was applied to extract the transverse relaxation time limited by spin-exchange collisions. The experimental results coincided well with the saturated vapor pressure curve ranging from 413 K to 463 K. Calculated densities were approximately 0.779–0.992 times those of predictions. The density measurement accuracy was improved compared to traditional methods. [ABSTRACT FROM AUTHOR]