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To achieve the nearly zero-field environment, demagnetization is an indispensable step for magnetic shields composed of high-permeability material, which adjusts the magnetization of the material to establish magnetic equilibrium with the environmental field and improve the shielding performance. The ideal demagnetization can make the high-permeability material on the anhysteretic magnetization curve to have a higher permeability than on the initial magnetization curve. However, inappropriate parameters of degaussing field cause the magnetization state to deviate from the anhysteretic magnetization curve. Therefore, this article proposes a new assessment criterion to analyze and evaluate the parameters of degaussing field based on the difference between the final magnetization state after demagnetization and theoretical anhysteretic state of the shielding material. By this way, the magnetization states after demagnetizations with different initial amplitude, frequency, period number and envelope attenuation function are calculated based on the dynamic Jiles-Atherton (J-A) model, and their magnetization curves under these demagnetization conditions are also measured and compared, respectively. The lower frequency, appropriate amplitude, sufficient period number and logarithmic envelope attenuation function can make the magnetization state after demagnetization closer to the ideal value, which is also consistent with the static magnetic-shielding performance of a booth-type magnetically shielded room (MSR) under different demagnetization condition.

The magnetic shielding device is used to provide an extreme weak magnetic field, which plays a key role in variety of fields. Since the high-permeability material constituting the magnetic shielding device determines the magnetic shielding performance, it is important to evaluate the property of the high-permeability material. In this paper, the relationship between the microstructure and the magnetic properties of the high-permeability material is analyzed using minimum free energy principle based on magnetic domain theory, and the test method of the material's microstructure including the material composition, the texture and the grain structure to reflect the magnetic properties is put forward. The test result shows that the grain structure is closely related to the initial permeability and the coercivity, which is highly consistent with the theory. As a result, it provides a more efficient way to evaluate the property of the high-permeability material. The test method proposed in the paper has important significance in the high efficiency sampling inspection of the high-permeability material.

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/Hz 1/2 and 0.10 fT/Hz 1/2 @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.

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 .

A single-beam spin-exchange relaxation-free atomic magnetometer is ultra-sensitive in the zero field, which has great potential for the detection of a magnetoencephalogram. The addition of a modulated magnetic field is an important approach to achieve high sensitivity for devices of this kind. In this study, we discovered that the amplitude and frequency of the modulated magnetic field (modulation index 0-3) both influence the light absorption. We defined this effect into a function by combining theoretical analysis and the results of experiments. It is discovered that the transmission intensity decreases with an increase in the modulation index. This effect is weakened under the application of a high modulation index. In addition, the transmission intensity and bias magnetic field no longer follow a strict Lorentz curve, while a high degree of fit can be achieved by applying the numerical solution of the Bloch function. A compact magnetometer with a volume of 10 cm 3 and a sensitivity of 20 fT/Hz is developed based on the single beam scheme for the proof of concept. Our study is crucial in two aspects: (1) Obtaining high sensitivity through a short measurement period and (2) alignment of the scale factor of the individual magnetometer in a detection array, which further pave the way for improvement in a magnetometer's performance under a variety of optics platforms.

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.

Electrical heating elements, which are widely used to heat the vapor cell of ultrasensitive atomic magnetometers, inevitably produce a magnetic field interference. In this paper, we propose a novel measurement method of the amplitude of electrical-heating-induced magnetic field for an atomic magnetometer. In contrast to conventional methods, this method can be implemented in the atomic magnetometer itself without the need for extra magnetometers. It can distinguish between different sources of magnetic fields sensed by the atomic magnetometer, and measure the three-axis components of the magnetic field generated by the electrical heater and the temperature sensor. The experimental results demonstrate that the measurement uncertainty of the heater's magnetic field is less than 0.2 nT along the x -axis, 1.0 nT along the y -axis, and 0.4 nT along the z -axis. The measurement uncertainty of the temperature sensor's magnetic field is less than 0.02 nT along all three axes. This method has the advantage of measuring the in-situ magnetic field, so it is especially suitable for miniaturized and chip-scale atomic magnetometers, where the cell is extremely small and in close proximity to the heater and the temperature sensor.