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As a space application, the brushless dc motor (BLDCM) configured in a magnetically suspended control moment gyroscope has extremely high requirements for reliability and power consumption, where accurate commutation control is the key point. However, inevitable nonideal factors, especially the nonideal asymmetric back-electromotive force (back EMF) characteristics, would dramatically reduce commutation accuracy. In order to meet the requirements, this article proposes a fast self-correction commutation method for the sensorless BLDCMs with nonideal asymmetric back EMF. First, it analyzes the influence of nonideal asymmetrical back EMF characteristics on commutation accuracy and obtains the commutation point through the zero-crossing points of line-to-line voltages. Second, a novel phase shifter is proposed for the commutation error correction based on the amplitude transformation of back EMF. Finally, based on the relationship between the voltage difference and the commutation error, a closed-loop voltage adjuster with feedforward compensation is proposed to correct the commutation error using the phase shifter. Both simulation and experimental results validated the effectiveness of the proposed method.

Ferromagnetic boundary coupling is one key factor that limits the control accuracy of the residual magnetic field in the magnetic shielding room. Usually the image method is utilized to suppress the coupling, but the tolerance for door slit and holes of the image method is poor. Here, we propose the self-shielding method for suppressing the ferromagnetic boundary coupling with higher coupling suppression ability and better tolerance for door slit and holes. Two sets of biplane coils for one axis are designed for achieving uniform magnetic field in the target area and nearzero magnetic field in the shielding area near the passive metal shielding layer simultaneously. We have determined the analysis method and design process of the self-shielding method, and verified its feasibility by experimental test. The proposed method can provide new ideas for improving the control accuracy of the residual magnetic field in the magnetic shielding room, ensuring the smooth progress of magnetoencephalography measurement.

In this study, we demonstrate a three-axis synchronous sweeping field (TSSF) method for in situ magnetic field compensation under three-axis nonorthogonal conditions for optically pumped magnetometers (OPMs). The OPM operated in the spin-exchange relaxation-free (SERF) regime is gaining popularity as a promising substitute for the superconducting quantum interference device (SQUID) in biomagnetism measurements. Nevertheless, the three-axis nonorthogonality inherent in the OPM will give rise to residual magnetic field inaccuracies along the pumping axis while conducting the in situ magnetic field compensation procedure, consequently introducing supplementary OPM errors. The TSSF method can more proficiently rectify the residual magnetic field along the pumping axis and suppress the corresponding errors. In contrast to traditional methods, the TSSF method diminishes both the rotation angles of the sensitive axis and dual-axis coupling coefficients, which are introduced through compensation errors along the pumping axis, by more than 80%, and improves the measurement sensitivities by more than 30%. This effective magnetic field compensation method of the OPM holds promise for further improving the performance of OPM. It is expected to enhance the localization and calibration accuracy of multiple-channel OPM-based magnetoencephalography (OPM-MEG) systems.

Most magnetic shielding rooms (MSRs) are made of highly permeable permalloy. The limitation of such MSR is its intrinsic magnetic noise, which exceeds the sensitivity of magnetic sensors, impeding the further applications of ultrasensitive magnetic sensors, such as the magnetometers operated in the spin-exchange relaxation free (SERF) regime. In this article, a cubic ferrite magnetic shield with a low magnetic noise and magnetic field is proposed. The demagnetization model and magnetic noise calculation models are given. After optimizing several different coil structures and degaussing parameters, the magnetic field and the magnetic noises inside the cubic ferrite shield were measured. Within a distance of ±10 mm near the center, the residual magnetic field is below 0.5, 1.72, and 1.57 nT at the x-, y- and z- directions. The magnetic noise measurements at the center of the cubic ferrite magnetic shield reveal an averaged magnetic noise of 2.62 fT/Hz−1/2 from 20 to 100 Hz. Compared with the noise spectrum of permalloy shield, the noise level is reduced more than 133%. The results of this scaled-down cubic ferrite magnetic shield can be applied in larger sized shielding rooms. By assembling multiple ferrite panels together, it is possible to create a larger shielding space with a low magnetic field and low magnetic noise.

Biomagnetic field measurements necessitate magnetic shields of high performance, particularly for quasi-static and low-frequency fields. These largely rely on the magnetic properties of the shielding material. Magnetic shaking can enhance the material's permeability by reducing hysteresis loss, though this method introduces field interference into the shielding device, complicating the magnetic environment. In this study, an attenuation coefficient is introduced into the Jiles–Atherton model to quantify the suppression effect of magnetic shaking on hysteresis loss, based on measurements of magnetic properties under the shaking fields. To improve shielding performance while minimizing additional interference, the frequency of magnetic shaking is increased and applied only to the outermost layer of the shielding device. Through testing and fitting results, the impact of various magnetic shaking conditions on a cubic magnetic shielding device is examined. By applying a shaking field of 200 Hz solely to the outermost layer, the shielding factor (@0.01 Hz) of a three-layer device increases by 77.4% without additional magnetic noise. This method is also applied to a magnetically shielded room, enhancing its shielding factors by more than two times.

Optically pumped magnetometer (OPM) has gained popularity as a viable alternative to the superconducting quantum interference device (SQUID) for biomagnetic measurements. However, the presence of amplitude and phase errors in the OPM can degrade the signal quality of, e.g., magnetoencephalography (MEG) signals. This study presents a dual-PI closed-loop control (DPCC) method aimed at suppressing amplitude and phase errors of the OPM when operated in the spin-exchange relaxation-free (SERF) regime, thereby enhancing MEG localization accuracy. The main sources of the amplitude and phase errors in the OPM are identified through a theoretical analysis of the inertial element characteristics and static residual magnetic fields. The experimental results demonstrate that the utilization of DPCC for the OPM reduces the amplitude and phase errors in static MEG measurements by 94.2% and 95.6%, respectively. At a residual magnetic field of 6.5 nT, the amplitude and phase errors are further suppressed by 97.8% and 87.2%, respectively. Furthermore, the fluctuation of the residual magnetic field is reduced by a factor of 25, significantly enhancing the robustness of the OPM. This straightforward and effective arrangement of the OPM holds promise in the field of biomagnetism and is expected to enhance the localization and calibration accuracy of OPM-based MEG (OPM-MEG) systems.

A highly homogeneous and low-noise magnetic field is crucial for the development of devices based on optically pumped magnetometers (OPMs). However, the creation of a highly homogeneous and low-noise magnetic field in a large region remains a technical challenge. This work describes the development of a highly precise active magnetic field compensation system based on high-uniform magnetic field coils (H-UMFCs) with a small and adjustable coil constant. The H-UMFCs are designed with reference to a self-shielding coil based on the magnetic moment compensation strategy. The proportional magnification coefficient and the current scaling coefficient of the two sets of coils are optimized to obtain high uniformity in a large region. Compared with the traditional one set of planar coils, the uniformity of the ${B}_{x}$ coils is improved by more than six times in the same region. The active magnetic field compensation system was developed based on H-UMFCs with the coil constant reduced by controlling the current ratio of the two sets of wires in one wire slot. The performance of the compensation system was verified by experimental testing. A highly homogeneous and low-noise magnetic field environment was created with a noise of less than 10 fT/ $\sqrt {\text {Hz}}$ @1 Hz. The design strategy is important in the application of OPMs.

Accurate magnetoencephalography (MEG) localization of neural electrical activity requires registration between the MEG sensors and MRI. To reduce the geometric error of the sensor array and realize automatic registration, an array geometry calibration algorithm based on prior knowledge is proposed, which automatically completes the position and orientation calibration of optical pumped atomic magnetometer (OPM)-MEG array with the reference of the design model of MEG helmet. Full-process automatic coregistration based on optical scanning is realized. A position error of 0.23 ± 0.12 mm and orientation error of $0.34 \pm 0.14 ^{\circ }$ are obtained in the calibration results of 85 sensors on-scalp MEG system. The proposed array geometric calibration (AGC) algorithm is used to quantify the deviation between the manufactured array and the theoretical array for the first time. The results show a mean position deviation of 0.57 mm and an angle deviation of 0.68° in the manufactured array, with the maximum position deviation of 1.45 mm and the maximum orientation deviation of 2.13°. It is indicated that the replacement of the manufactured array by the theoretical array in previous research may introduce significant errors in the MEG source localization results.

In this article, the relationship between motion artifacts and magnetoencephalography (MEG) source localization errors was established for the MEG system based on array optically pumped magnetometers (OPMs). The influences of bias fields on OPM’s performances were first evaluated through theoretical and experimental analysis, whose results proved that the bias magnetic fields along the sensitive axis affect the gain and sensitivity of OPM, while the pumping axis bias magnetic fields affect the direction of the sensitive axis. The OPM with a large linewidth has better anti-interference ability but worse sensitivity. Then, MEG simulations were carried out on the basis of OPM performance testing. The relative error of the forward model proved that the rotated sensitive axis would affect the forward model, while the gain error and sensitivity directly affect the signal-to-noise ratio (SNR) of the MEG signal. The experiment and simulation also proved that it is recommended to use biaxial mode for OPM-MEG experiments and the motion artifact detected by OPMs should be reduced to less than 1nT at least. Moreover, the linewidth of the OPM’s cell is positively correlated with the anti-interference capability of OPM. Therefore, sensitivity and anti-interference capability must be simultaneously considered in the design of OPM by optimizing the cell’s linewidth to adapt to more scenarios.

The gyroscopic torque disturbances generated by base motion directly affects the stability of the high speed magnetically levitated centrifugal compressor (MLCC). This article explores a disturbance suppression method for the high-speed magnetically levitated rotor (MLR) system based on improved linear extended state observer (LESO). Firstly, the model of the high-speed MLR system with base motion is established, and the characteristics of the gyroscopic torque disturbance are analyzed. Then, a LESO with adaptive notch filter is designed for disturbance estimation and compensation of the magnetic bearing, and its convergence performance and disturbance tracking speed are deduced. Furthermore, due to the gain attenuation introduced by LESO, an innovative gain compensator is utilized to improve controller dynamic performance. Finally, simulation and experimental results demonstrate that the proposed method can effectively reject the gyroscopic torque disturbances in high speed MLCC.

We report on the geometric-phase (GP)-lens collimation of commercially available vertical-cavity surface-emitting laser (VCSEL), performed in the Rb D1 line spectroscopy experiments. The GP lens is fabricated by the direct-write approach and employed photopatterned liquid crystals in thin films to control the geometric phase shift. It generates the positive and negative first-order diffraction of laser beam, which are spatially separated to two focal points with one focused and the other one defocused. The diffraction efficiency at 794.9 nm is up to 99%. Changing the polarization state of the incident VCSEL laser continuously, the collimation and polarization conversion of divergent VCSEL laser is accomplished via GP lens. The $\sigma ^{+}$ and $\sigma ^{-}$ components of circularly polarized light are separated via different diffraction orders, which suppresses the light shift in atomic atoms. Then, a compact atomic magnetometer (AM) is constructed based on a Rb microcell. High sensitivity up to 30 fT/Hz $^{1/2}$ is achieved in the single-beam configuration. It is expected that directly fabricating the liquid crystal film on the surface of vapor cells can further reduce the sensor volume. This work extends integrated photonics to atomic spectroscopy and spin-based sensing and of great significance to promote the application of miniature AMs in biomagnetic measurements.

With the deepening research in atomic sensors, extremely weak magnetic detection has shown great advantages in the biomedical field. To achieve high detection sensitivity, the uniform field coil is used in the magnetic detection system to maintain a uniform and stable working environment for the atomic sensors. This article presents a design method for an asymmetric cylindrical uniform field coil based on the boundary element method (BEM) and optimized by the particle swarm optimization (PSO) algorithm. The BEM could find optimal coil paths on arbitrary geometries, which is fit for the asymmetric configuration in an optically pumped magnetometer-based magnetocardiogram (OPM-MCG) device. However, the BEM used in the coil design would cause an ill-posed mathematical problem. A Tikhonov regularization combined with a penalty function approach is proposed to solve the ill-posed problem and smooth the coil winding patterns, and the correction weights are optimized by PSO within constraints. The calculation results show that the absolute maximum relative error in the target region is optimized to 0.0124% by the proposed method when compared with the target field method (TFM) coil (0.023%). Meanwhile, it illustrates that the high uniformity region is enlarged through the utilization of asymmetric structure. In addition, through experiments, the test performance of the designed coil is verified to be consistent with the theory. As the proposed method contributes a high-performance uniform field coil on arbitrary structures, it has important significance in extremely weak magnetic field measuring devices such as the MCG and magnetoencephalogram (MEG).

The biplane coils (BCs) based on the inverse design method are crucial for creating the near-zero magnetic environment in magnetic shielding room (MSR), but multiparameter optimization remains a key factor that limits the performance of the BCs. This study proposes a funnel algorithm (FA) to solve the issue of multiparameter optimization in the design. The upper and lower limits of the parameters are dynamically adjusted based on the previous calculating step. By gradually reducing the upper and lower limits, we achieve the BCs with optimal performance. This method has been verified by both the theoretical analysis and experimental test. Compared with other methods, the designed coils show a higher space utilization ratio (SUR) and smaller relative errors, with the SUR improved from 1.6% to 3.75% and the relative errors all less than 2%. Based on the designed BCs, the total residual magnetic field is stabilized below 40.4 pT at the central point of the MSR, with the noise reaching the intrinsic noise of the flux-gate magnetometer in the frequency range of interest. The proposed method can significantly improve the performance of the BCs, thus reducing the space and construct cost of the MSR and promoting the magnetoencephalogram (MEG) measurement based on the quantum technology.

To calibrate induction magnetometer with high precision, a cylindrical uniform-field coil system design method is proposed, which combines forward method with reverse design method in this article. The optimized cost function of coil design is set to the average field error within the target region to minimize the error of induction magnetometer calibration caused by uniform-field coil system. The particle swarm algorithm is applied to solving each group of coil’s position and number of turns in the coil optimized design. According to the finite element analysis, the average error of the optimized coil in the target area is 0.009%, which is reduced by eight times than that of the Lee-Whiting coil system (0.075%). The experimental results of coil constant and magnetic fields along the axial were in good agreement with the simulation results. In addition, calibration experiments of three sets of induction magnetometers were carried out, whose experimental results show that the error of calibration using the optimized coil are all less than those of the Lee-Whiting coil system.

This article aims to deal with the speed control performance of the gimbal servo system at ultra-low speed to guarantee the accuracy of the output torque of the control moment gyroscope (CMG). The main factors leading to the speed fluctuation of the gimbal servo system are the speed measurement error and disturbance torque. This article proposes a composite controller that consists of the dual-sampling-rate reduced-order extended state observer (DSRESO) and sliding-mode controller (SMC) in the speed loop so as to improve the speed control performance at ultra-low speed. DSRESO is designed to deal with the speed measurement as well as the disturbance estimation in ultra-low speed conditions. Then, the SMC-based DSRESO is applied for speed closed-loop control so as to suppress the speed fluctuation of the gimbal servo system under ultra-low speed and disturbance torque conditions. The feasibility and effectiveness of the proposed control scheme have been verified by the simulations and experiments compared with other methods. Also, the resultant effect is that the speed tracking precision of the gimbal servo system at ultra-low speed is improved significantly.

We demonstrate a method for quickly and automatically detecting all three components of a remanent magnetic field around a shielded spin-exchange relaxation-free (SERF) atomic magnetometer (AM) using the trisection algorithm (TSA) for zero-field resonance (ZFR). To satisfy the measurement of AMs, a resonance light of the 87Rb D1 line with a spectral width of less than 1MHz is converted to circular polarization by a linear polarizer and a quarter-wave plate. After the light beam has passed through the alkali metal vapor cell, the residual magnetic field can be measured by searching for triaxial ZFR optical peaks. The TSA stably reduces the measurement time to 2.41 s on average and improves the measurement accuracy, significantly outpacing existing methods. The weighted averages of all measurements with corresponding uncertainties are (−15.437 ± 0.022)nT, (6.062 ± 0.021)nT, and (−14.158 ± 0.052)nT on the x-, y-, and z-axes, respectively. These improvements could facilitate more extremely weak magnetic studies in real time, such as magnetoencephalography (MEG) and magnetocardiography (MCG) measurements.