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Cylindrical ferrite shields consisting of multiple annuli can provide low-magnetic-noise environments. However, the gaps between different parts of the shield adversely affect the shielding performance. In this study, we numerically study the influence of the gaps on both the axial and radial magnetic noise of the multi-annular ferrite shield with different gap widths, permeabilities, and aspect ratios using the generalized Nyquist relation and the finite element method. Our study indicates that as the gap width increases, the axial magnetic noise decreases, while the radial magnetic noise increases. For the shield with a gap width of 0.10 mm and an aspect ratio of one in our study, the axial magnetic noise decreases by 5.2%, and the radial magnetic noise increases by 8.3%–33.5%. The difference in the increase is related to the permeability, and gaps have smaller effect on the radial magnetic noise of the shield with lower permeabilities. Therefore, compared with the no-gap shield, the multi-annular ferrite shield can provide an even better low-magnetic-noise environment along the axial direction. Although the gaps can induce an increase of the radial magnetic noise, this detrimental effect can be suppressed significantly by using a ferrite material with lower permeability and reducing the gap width. Our findings can aid in the application and optimization of low-noise ferrite shields. [ABSTRACT FROM AUTHOR]

We demonstrated a method for in-situ measurement of triaxial magnetic field coil constants of optically pumped magnetometer (OPM) operating in the spin-exchanged relaxation-free (SERF) regime based on higher-order parametric resonances. The triaxial coil constants play a vital role in achieving optimal operation of the OPM and amplitude calibration of weak signals such as magnetoencephalography (MEG). The measurement of the triaxial magnetic field coil constants is therefore particularly critical. Compared to the previous methods, our method is convenient and universal for practical application and commercialization. It does not require a complicated fitting process for measurements, and is applicable to both single- and dual-beam configurations of OPMs which are prevalent in current applications. The feasibility of the method is verified by simulation and experiment, and the average measurement errors of the triaxial coil constants of the OPM in single- and dual-beam configurations are 0.75 % and 1.74 %, respectively. This method holds substantial implications for calibrating and optimizing arrayed OPM systems, with the potential to enhance the measurement sensitivity and the accuracy of magnetic source localization in triaxial OPM-MEG systems. • Higher-order parametric resonances for measuring triaxial coil constants of OPMs. • Higher-order parametric resonances of two-mode OPMs were comprehensively analyzed. • Average measurement errors are 0.75% and 1.74% for coil constants of two-mode OPMs. [ABSTRACT FROM AUTHOR]

[Display omitted] • A two-dimensional (2D) biaxial magnetic field imaging technique with submillimeter spatial resolution and millisecond temporal resolution is demonstrated. • A time-sharing technique is adopted to solve the multi-axial dynamic magnetic field imaging problem. • Operation in the non-modulated SERF (spin-exchange relaxation-free) regime, the scanning imaging device achieves femto-Tesla sensitivity for single pixel. Multi-axial dynamic magnetic field imaging with femto-Tesla sensitivity paves a promising route for acquiring comprehensive information of the extremely-weak magnetic source. Here we propose a two-dimensional (2D) scanning imaging configuration that can realize rapid biaxial magnetic field measurement. Based on the Bragg diffraction, the configuration utilizes two orthogonally-arranged acousto-optic modulators to scan the probe laser temporally and spatially, realizing a 2D (7 × 7 pixels) magnetic field detection. To solve the multi-axial dynamic magnetic field imaging problem, a non-modulated time-sharing technique is theoretically and experimentally verified. Profiting from the non-modulated biaxial working mode that avoids long demodulation time, the magnetometer realizes millisecond temporal resolution (17.15 ms) for each sensitive axis. Operation in the spin-exchange relaxation-free regime, the single-pixel measurement sensitivity reaches around 2.6 fT/Hz1/2 (y -axis) and 7.5 fT/Hz1/2 (z -axis). Furthermore, weak pump and probe lasers power (500 μW and 350 μW) make it a low-power imaging device. [ABSTRACT FROM AUTHOR]

[Display omitted] • A novel in-situ method to measure complex magnetic permeability (CMP) based on the magnetic shielding mechanism is presented. • By measuring the magnetic field at the center of shielding, the effective CMP of a large dimensional ferrite shielding can be determined. • The addition of Co significantly improved the thermal stability of CMP by 6.62 times and reduce the magnetic noise. • This method ensures a real-time observation of CMP and magnetic noise under different temperatures. Magnetic shielding made of low noise ferrite materials is used in many ultra-sensitive measurements. The complex magnetic permeability (CMP) of ferrites directly affects the magnetic shielding performance, so the measurement of CMP is particularly important. Conventional measurements omit the effects of temperature on ferrites' magnetic properties and can only measure samples with specific shapes. Here a novel measurement method of CMP based on the magnetic shielding mechanism is presented. By in-situ measuring the magnetic field, the effective CMP of large dimensional ferrite shielding can be determined. Also, the intrinsic magnetic noise of a MnZn ferrite shielding was observed using the proposed method. Using the finite elements method (FEM), we identified the influencing factors of air gap in the CMP measurements. We also analyzed the influence of element doping on the thermal stability of CMP. This study ensures a real-time observation of CMP and magnetic noise under different temperatures. [ABSTRACT FROM AUTHOR]

This paper presents a novel synchronous micro-vibration suppression method on the basis of the small gain theorem to reduce the frequency-varying synchronous micro-vibration forces for a magnetically suspended flywheel (MSFW). The proposed synchronous micro-vibration suppression method not only eliminates the synchronous current fluctuations to force the rotor spinning around the inertia axis, but also considers the compensation caused by the displacement stiffness in the permanent-magnet (PM)-biased magnetic bearings. Moreover, the stability of the proposed control system is exactly analyzed by using small gain theorem. The effectiveness of the proposed micro-vibration suppression method is demonstrated via the direct measurement of the disturbance forces for a MSFW. The main merit of the proposed method is that it provides a simple and practical method in suppressing the frequency varying micro-vibration forces and preserving the nominal performance of the baseline control system. [ABSTRACT FROM AUTHOR]

A stable magnetic environment that is devoid of interference from ambient magnetic fields is crucial to precise measuring magnetic fields. In this study, a novel magnetic shield with a winding shape, similar to a spiral, is proposed to simultaneously increase the shielding coefficient and reduce the magnetic noise produced by the magnetic shield. In the winding-shaped magnetic shielding structure, an entire mu-metal strip is rolled into multiple layers to form a cylindrical barrel shape. Each layer is separated by insulating adhesives. The effects of the number of turns of the strip and the insulating adhesive on the shielding coefficient and the magnetic noise were analyzed. The simulation results demonstrated that the DC shielding coefficient of this novel structure increased by 123 % and the magnetic noise was reduced by 47 % compared to that of the conventional structures. In addition, the shielding coefficient and the magnetic noise of the two structures were experimentally measured, confirming the superiority of the proposed structure. [Display omitted] • A novel magnetic shielding structure with winding shape. • Improvement of magnetic shielding coefficient and reduction of magnetic noise. • Detailed analysis of shielding coefficient and magnetic noise of new winding-shaped magnetic shield. • Further promote the application of ultra-high sensitivity quantum sensing technology. [ABSTRACT FROM AUTHOR]

• An in situ method for simultaneously calibrating coil constants and nonorthogonal angles of triaxial coils in three-axis OPMs. • 12 error sources, i.e., nonorthogonal errors, proportional coefficient errors and zero-offset errors, have been corrected comprehensively. • A PSO algorithm has been used with higher accuracy, better convergence stability, faster convergence rate and less calibration uncertainty. • Suitable for most types of three-axis OPMs including the miniature magnetometers without any auxiliary calibration devices. A novel in situ method has been demonstrated for calibrating parameters (coil constants and nonorthogonal angles) of triaxial coils of a three-axis optically pumped magnetometer (OPM). In total, 12 error sources including nonorthogonal errors, proportional coefficient errors and zero-offset errors have been considered into the calibration model. We utilize a particle swarm optimization (PSO) algorithm to estimate the errors, and compare it with a regular Levenberg-Marquardt (LM) algorithm. The results demonstrate that the PSO algorithm has higher accuracy, better convergence stability, faster convergence rate and less calibration uncertainty. The calibration realizes the simultaneous measurement of the coil parameters and the correction of the 12 error sources. The coil constants are (88.93 ± 0.22) nT/mA, (88.78 ± 0.12) nT/mA, and (197.64 ± 0.29) nT/mA which deviate 1.2–1.4 % from the theoretical values, respectively. The nonorthogonal angles are (89.50 ± 0.06) °, (89.46 ± 0.04) ° and (89.40 ± 0.02) ° which correct the errors to 19.6–30.7 % of the original values, respectively. This study realizes in situ coil calibration without auxiliary devices and can be applied to most types of three-axis OPMs including the miniature magnetometers with higher accuracy. [ABSTRACT FROM AUTHOR]

The photoelastic modulator (PEM) is an optical modulation device which is widely used in optical detections. In this paper, we propose a high-precision and large-scale method for calibrating the peak retardations of PEM based on compound Bessel function. By applying compound Bessel function instead of the single Bessel function, the uncertainty of peak retardation calibration result decreases more than two times and the calibration scale expands nearly two times. Further, the second harmonic component is substituted for the DC component to reduce the random errors. In the experiment, a PEM is calibrated and the calibration result obtained for peak retardation is linear to the setting value in scale 0.15–2.5 rad. A dead zone appears in region 0 to 0.15 rad with value 0.233 rad. The experiment demonstrates that the relative uncertainty of peak retardation decreases from 2.5 % to less than 1 %. [ABSTRACT FROM AUTHOR]

An optical pumping scheme is proposed for reducing the gradient of electron spin polarization and suppressing light source noise in a spin-exchange relaxation-free magnetometer. This is achieved by modulating only the phase of a narrow-linewidth pump light field with external Gaussian noise. Compared to the absence of phase modulation, the uniformity of electron spin polarization was improved by over 40%, and the light-frequency noise suppression ratio of the magnetometer was enhanced by 4.3 times. Additionally, the response of the magnetometer was increased by 54%, resulting in a sensitivity of 0.34 fT/Hz 1/2 at 30 Hz. The applicability of this scheme can extend to other optical pumping experiments involving large atom ensembles requiring uniform electron spin polarization distribution, which is beneficial for developing ultra-high sensitivity and high stability magnetometers essential for magneto-cardiography and magneto-encephalography research applications.

The existence of an approximately uniform and unsaturated electron spin polarization distribution within a high-density alkali-metal vapor is considered of great importance for significantly improving the response amplitude and sensitivity properties of an atomic magnetometer. However, when a high-density alkali-metal vapor is formed, the optical depth is much larger than the value of one, resulting in the electron spin polarization gradient. In this work, it was demonstrated from both numerical simulations and experimental points of view, that by replacing the resonant pumping light with two off-resonant pumping light sources, the signal amplitude of the magnetometer can be doubled. By using this approach, the electron spin polarization gradient can be significantly suppressed and the sensitivity can be improved by more than 10%. The proposed scheme is generally applicable to various optical pumping high-density alkali-metal vapor systems, where a uniform electron spin polarization distribution is required, such as optical pumping co-magnetometers and atomic gyroscopes.

Rb optically pumped magnetometer (OPM) based on electron paramagnetic resonance (EPR) show advantages to measure the nuclear magnetization and have succeeded in fundamental physics and rotation sensing, etc. The magnetometry sensitivity is a key performance of these Rb OPMs which should be improved. In this study, a high sensitivity Rb OPM is demonstrated theoretically and experimentally. To improve the sensitivity, acousto-optic modulation based on balanced detection is applied to suppress the probe noises. Compared with the conventional optical rotation detection for this OPM configuration, the probe noise shows a significant suppression especially in low frequencies. Eventually, a simultaneous dual-axis transverse measurement with 30 fT/Hz 1/2 sensitivity is achieved in a 200 Hz bandwidth and a 250nT linear working range. In addition, we utilize a closed-loop feedback to improve the stability and enlarge the transverse measurement range to 10µT order of magnitude while maintain the open-loop performances. A quasi-static magnetic field measurement can also be achieved in the longitudinal direction in the closed-loop mode. This OPM can serve for the nuclear magnetization measurement with a high sensitivity especially in environments with a large magnitude of the external magnetic field.

This publisher's note contains a correction to Opt. Lett.47, 3908 (2022)10.1364/OL.465832.

The transient dynamics of atomic spins under oscillating and static magnetic fields have been studied in the spin-exchange relaxation-free (SERF) regime with a dual-beam configuration. The spin-relaxation rate can be accurately measured by detecting the transient response signal of the free induction decay (FID) process within several milliseconds. Leveraging this convenient method for measuring a large relaxation rate in a small cell volume, the dependence of the spin-relaxation rate on the probe intensity and ambient magnetic field was studied in the limit of low spin polarization. Moreover, by theoretical analysis of the dynamic evolution of the Rabi oscillation generated by a consecutive oscillating field and a small static magnetic field, we experimentally demonstrate that the amplitude of the Rabi oscillation is affected by the amplitude of the oscillating field in the SERF regime. According to the retrieved frequency of the FID signal and amplitude of relevant Rabi oscillation, the coil constants were 75.55 ± 0.78~nT/mA, 151.5 ± 0.9~nT/mA, and 116.6 ± 0.3~nT/mA along the x-, y-, and z-axes, respectively.

The emerging multi-channel spin-exchange relaxation-free (SERF) atomic magnetometer is a promising candidate for non-intrusive biomagnetism imaging. In this study, we propose a scanning 9-channel SERF magnetometer based on an acousto-optic modulator (AOM). Using the diffraction light of the AOM as the probe laser (with a low laser power of 1.7 mW), 9 channels were rapidly scanned by altering the diffraction angle. The scanning imaging scheme provides a new, to the best of our knowledge, approach for multi-channel magnetic field measurement and realizes a single-channel sensitivity of about 3 fT/Hz 1/2 , a spatial resolution of 0.6 mm, and a time resolution of about 2.7 ms, which is well suited for real-time extremely weak magnetic field imaging.

In the spin-exchange relaxation-free (SERF) magnetometer of a perpendicular pump-probe configuration, the pump and probe beam characteristics significantly affect the performance. In this paper, an efficient evaluation of optical parameters to improve the sensitivity of a miniature magnetometer has been presented. We have determined the pump light's optimal intensity and wavelength through theoretical analysis and the zero-field resonance experiments. Chirp signals are applied to measure the optical rotations at different probe intensities and frequencies. Through theoretical and experimental analysis of noise source characterization under different beam intensities and wavelengths, we demonstrate that dual-beam magnetometer performance is mainly limited by photon shot noise. Based on the optimum pump and probe beam parameters, we demonstrate magnetic field sensitivity of 6.3 fT/Hz in an 87 Rb vapor cell filled with nitrogen gas, with an active measurement volume of 3 × 3 × 3 mm 3 .

Broad-dynamic-range magnetometers are demanded in practical applications and fundamental research. We experimentally demonstrate a parametrically modulated atomic magnetometer with a large dynamic range by taking advantage of the high-order resonance effects. With the increase of the strength of the modulation field, both low-order and high-order resonances are well resolved and used to measure the DC or AC magnetic fields. The experimentally demonstrated sensitivity of the magnetometer based on the zeroth-order resonance is 1.5 pT/Hz, and those based on the high-order resonances are below 3 pT/Hz, making the measurement of high magnetic fields feasible under an open-loop operation. Moreover, we also demonstrated the measurement of high-frequency large AC magnetic field with the high-order resonances, and the sensitivity for the AC magnetic field based on the first-order resonance is 7 pT/Hz. Our scheme provides a new path for the development of broad-dynamic-range and miniaturized atomic magnetometers.

We analyze and suppress the magnetic noise response in optical rotation detection system (ORDS) in atomic magnetometers in this study. Because of the imperfections of the optical elements, the probe light is actually elliptically polarized in ORDS, which can polarize the atom ensemble and cause the responses to the three-axis magnetic noise. We theoretically analyze the frequency responses to the magnetic noise, and prove that the responses are closely associated with the DC magnetic field. The values of the DC magnetic fields are calculated with special frequency points, called 'break points', in the transverse responses. We reveal the relationships between the DC magnetic field and the sensitivities of ORDS, and effectively suppress the magnetic noise responses with the residual magnetic field compensation. Finally, the sensitivity of ORDS is improved by approximately two times at 10-20 Hz.

We present a theoretical and experimental study of a single-beam spin-exchange relaxation-free magnetometer in 87 Rb vapor cells under different nitrogen gas pressures. The spin relaxation rate is a key component to limit the magnetic sensitivity, and the zero-field resonance method was used to measure the spin relaxation rates of different alkali metal cells. Simultaneously, in a single-beam spin-exchange-relaxation-free (SERF) magnetometer, we demonstrated that the fundamental magnetic field sensitivity was also limited by the pumping light intensity. Based on our theoretical analysis and experimental results, we determined the optimal pumping light intensity and optimal gas pressure. We experimentally demonstrated that the magnetic field sensitivity was 8.89 fT/Hz in the single-beam configuration, with an active measurement volume of 3 × 3 × 3~mm 3 .

We demonstrate a single-beam atomic magnetometer (AM) capable of measuring a three-axis magnetic field with high-sensitivity, achieved by applying a small DC offset field and a high frequency modulation field. To satisfy the miniaturization demand of AMs, an elliptically polarized light detuned by 50 GHz from the resonance transition center is employed. The circularly polarized component is used to polarize the alkali-metal atoms, while the linearly polarized light is used to detect the dynamics of the polarized spin under a magnetic field. Based on theoretical analysis, parameters that significantly affect the performance are optimized, and a sensitivity of 20 fT/Hz 1/2 in x-axis, 25 fT/Hz 1/2 in y-axis, 30 fT/Hz 1/2 in z-axis is achieved with a miniature 4 × 4 × 4 mm 87 Rb vapor cell. Moreover, we also verify that the operation principle of AMs can be used to null background magnetic fields in-situ with isotropic compensation resolution of 6.7 pT, which provides an effectively precise method for zeroing ambient magnetic field. The high-sensitivity operating of an elliptically-polarized-laser-based magnetometer provides prospective futures for constructing a compact, low-cost AM, which is particularly applicable for non-invasive bio-magnetic imaging such as array-based magnetoencephalography (MEG) and magnetocardiography (MCG).

In this paper, we experimentally study transient dynamics of spin polarized atoms in the spin-exchange-relaxation-free (SERF) regime with a single-beam configuration. We pumped atoms with a weak detuning pumping beam, along with a sequence of magnetic field pulses orthogonal to the pumping beam were applied. The dynamics of atomic spin, which experiences Larmor precession under the perturbation of magnetic field, is detected by the transmitted pumping beam. Benefited from the long coherence time of atomic spin in the SERF regime, the dependence of precession frequency and decay rate, which is equal to the magnetic resonance linewidth of atomic spin, on magnetic fields is studied with the transient dynamics of atomic spin in the limit of low spin polarization. Moreover, we demonstrate that coil constants can be calibrated by analyzing the precession frequency of the transient dynamics of atomic spin. And the experimental results show that the coil constants are 114.25 ± 0.02 nT/mA and 114.12 ± 0.04 nT/mA in x- and y-axis, respectively. This method is particularly applicable to study the atomic spin dynamics and calibrate the coil constant in situ of a miniature single-beam SERF magnetometer.

In the spin-exchange relaxation-free (SERF) magnetometer, the probe noise is a consequential factor affecting the gradiometric measurement sensitivities. In this paper, we proposed a new characteristics model of the probe noise based on noise separation. Different from noise analysis on single noise source, we considered most of the noise sources influencing the probe system and realized noise sources level measurement experimentally. The results demonstrate that the major noise type changes with the signal frequency. Below 10 Hz, the probe noise mainly comes from the sources independent of light intensity such as the vibration, which accounts for more than 50%; while at 30 Hz, the photon shot noise and the magnetic noise are the main origins, with proportion about 43% and 32%, respectively. Moreover, the results indicate that the optimal probe light intensity with highest sensitivity appears when the response of the magnetic noise is equal to the sum of the electronic noise and half of the shot noise. The optimal intensity gets larger with higher signal frequency. The noise characteristics model could be applied in modulating or differential optical systems and helps sensitivity improvement in SERF magnetometer.

Background: The radiological differential diagnosis between tumor recurrence and radiation-induced necrosis (ie, pseudoprogression) is of paramount importance in the management of glioma patients., Objective: This research aims to develop a deep learning methodology for automated differentiation of tumor recurrence from radiation necrosis based on routine magnetic resonance imaging (MRI) scans., Methods: In this retrospective study, 146 patients who underwent radiation therapy after glioma resection and presented with suspected recurrent lesions at the follow-up MRI examination were selected for analysis. Routine MRI scans were acquired from each patient, including T1, T2, and gadolinium-contrast-enhanced T1 sequences. Of those cases, 96 (65.8%) were confirmed as glioma recurrence on postsurgical pathological examination, while 50 (34.2%) were diagnosed as necrosis. A light-weighted deep neural network (DNN) (ie, efficient radionecrosis neural network [ERN-Net]) was proposed to learn radiological features of gliomas and necrosis from MRI scans. Sensitivity, specificity, accuracy, and area under the curve (AUC) were used to evaluate performance of the model in both image-wise and subject-wise classifications. Preoperative diagnostic performance of the model was also compared to that of the state-of-the-art DNN models and five experienced neurosurgeons., Results: DNN models based on multimodal MRI outperformed single-modal models. ERN-Net achieved the highest AUC in both image-wise (0.915) and subject-wise (0.958) classification tasks. The evaluated DNN models achieved an average sensitivity of 0.947 (SD 0.033), specificity of 0.817 (SD 0.075), and accuracy of 0.903 (SD 0.026), which were significantly better than the tested neurosurgeons (P=.02 in sensitivity and P<.001 in specificity and accuracy)., Conclusions: Deep learning offers a useful computational tool for the differential diagnosis between recurrent gliomas and necrosis. The proposed ERN-Net model, a simple and effective DNN model, achieved excellent performance on routine MRI scans and showed a high clinical applicability., (©Yang Gao, Xiong Xiao, Bangcheng Han, Guilin Li, Xiaolin Ning, Defeng Wang, Weidong Cai, Ron Kikinis, Shlomo Berkovsky, Antonio Di Ieva, Liwei Zhang, Nan Ji, Sidong Liu. Originally published in JMIR Medical Informatics (http://medinform.jmir.org), 17.11.2020.)

The elimination of relaxation resulting from spin-exchange (SE) interaction is crucial for ultrasensitive atomic comagnetometers. In this study, we demonstrate the SE relaxation is only partially suppressed and significantly broadens the magnetic linewidth in the K-Rb- 21 Ne comagnetometer. The SE relaxation arises from the compensation magnetic field when operating in the self-compensation regime. We propose a new method to measure the SE relaxation in the self-compensation regime where the alkali-metal and noble-gas spin ensembles are coupled. In the presence of SE relaxation, we find the optimal alkali-metal polarization for maximizing the sensitivity is shifted from the typical value. Under various conditions, we present a detailed study of the SE relaxation and the scale factor as a function of alkali-metal polarization, which are further verified by the theoretical models. The reduction of SE relaxation and improvement of scale factor by using 87 Rb atoms is also studied.