Magnetic field imaging with radio-frequency optically pumped magnetometers [Invited]

Xiyu Liu; Junlong Han; Wei Xiao; Teng Wu; Xiang Peng; Hong Guo

doi:10.3788/COL202422.060006

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Abstract

High-sensitivity radio-frequency optically pumped magnetometers (RF-OPMs), working without cryogenic condition, play a critical role in magnetic field imaging (MFI) at low frequencies (e.g., 100 Hz to 1 MHz). We introduce the principle of operation and recent developments of RF-OPMs and focus on reviewing the MFI applications in magnetic induction tomography, ultralow-field magnetic resonance imaging, and magnetic particle imaging. For the applications of RF-OPMs, ranging from industrial monitoring to medical imaging and security screening, the unshielded and portable RF-OPMs (and RF-OPM array) techniques are still under the further development for detecting and scanning over the target object for accomplishing the final three-dimensional imaging, and thus extremely require the abilities of active compensation of the ambient magnetic field and sensor miniaturization in the future.

Keywords

magnetic field imaging optically pumped magnetometer radio frequency

1. Introduction

Magnetic field imaging (MFI) is a valuable tool with significant importance in modern scientific research, proving useful across various domains. In the field of biomedical science, MFI serves as a noninvasive modality for acquiring the images of human anatomical structures and functions, thereby aiding in diagnostic procedures by employing the techniques including magnetic resonance imaging (MRI)^[1,2] and magnetic particle imaging (MPI)^[3]. Additionally, MFI enables the development of biomagnetism, such as the magnetocardiogram (MCG)^[4] and the magnetoencephalogram (MEG)^[5], thereby contributing to the investigation of biomagnetic fields. In materials science, MFI based on magnetic induction tomography (MIT) serves as a key tool for investigating the magnetic properties of materials^[6] and forms the foundation for the design and development of novel magnetic materials^[7], such as nondestructive testing (NDT)^[8]. In geophysics, MFI techniques contribute to probing the magnetic structures within the Earth, thereby advancing our understanding of the evolution of the Earth and geological formations^[9].

The research and development of high-sensitivity magnetometers have enabled the feasibility of various applications of MFI. The sensors for measuring magnetic fields include magnetoresistive sensors^[10], Hall effect magnetometers^[11], fluxgate magnetometers^[12], induction coil magnetometers^[13], superconducting quantum interference devices (SQUIDs)^[14], nitrogen-vacancy (NV) centers^[15], and optically pumped magnetometers (OPMs)^[16].

Among the magnetic field sensors mentioned above, the sensitivities of Hall effect magnetometers and magnetoresistive sensors are relatively low in the radio-frequency (RF) range, $nT / \sqrt{Hz}$ for Hall effect magnetometers^[17] and $μT / \sqrt{Hz}$ for magnetoresistive sensors^[18]. However, Hall effect magnetometers are portable and feature low power consumption. Additionally, small sensing volumes provide magnetoresistive sensors with the advantage of high spatial resolution in MFI. Fluxgate magnetometers have high sensitivity and resolution at low frequencies, but it is difficult to measure magnetic fields at frequencies above 1 kHz^[19]. As high-sensitivity RF magnetic field sensors, OPMs and NVs have the advantage of operating at room temperature, while SQUIDs require cryogens^[14]. Currently, the NV has become the emerging high-spatial-resolution sensor with the sensitivity of $70 fT / \sqrt{Hz}$ at 350 kHz^[20]. As the most sensitive sensor, the RF-OPMs behave with outstanding performance for MFI applications, with the potential for miniaturization and portability. As a conventional RF magnetometer, the induction coil magnetometers possess the advantage of a simple structure. However, its sensitivity is reduced particularly at lower frequencies (around 1–10 kHz)^[21].

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In this review, our primary emphasis is on the applications of RF-OPMs in MFI. The principle and current advancements of RF-OPMs are introduced in Sec. 2. In Sec. 3, we delve into three prominent high-frequency MFI applications, namely, NDT, MRI, and MPI. Ultimately, we summarize the advancements of RF-OPMs within the MFI applications and engage in a discussion regarding the prospective developments of RF-OPMs.

2. RF-OPMs

RF-OPMs are typically used for measuring magnetic fields in the kilohertz to megahertz frequency range, which have significant applications including unexploded ordnance^[22], geomagnetic surveys^[23], magnetic-inductive communication^[24], and nuclear magnetic resonance (NMR)^[21]. Additionally, RF-OPMs find utility in fundamental physics research for axions^[25] and noninvasive imaging techniques in biomedical applications^[26].

2.1. Principle

The traditional operational principle of RF-OPMs is based on magnetic resonance (MR) by detecting magnetically induced atomic coherences between neighboring Zeeman sublevels within the ground states of alkali metal atoms. In a typical configuration of RF-OPMs, a resonant pump light either circularly polarized or linearly polarized is applied to polarize atoms^[27], as shown in Fig. 1. A bias magnetic field $B_{0} = B_{0} \hat{z}$ is applied along the polarization direction of atoms. The RF magnetic field to be measured, $B_{rf} = \hat{x} B_{rf} \sin ω t + \hat{y} B_{rf} \cos ω t$ , is applied in the $x - y$ plane perpendicular to the bias field, where $ω$ is the frequency of the RF field. These atomic coherences are generated by $B_{rf}$ resonating with the energy splitting of adjacent Zeeman sublevels. The sublevels are brought into resonance with the RF field through the Zeeman effect, achieved by the bias magnetic field. The precessing atomic coherence can be detected by the probe light in the $x$ direction, typically achieved by measuring the optical rotation of a linearly polarized probe light using a balanced photodiode. Figure 1 shows the configuration that the pump light and probe light are orthogonal to each other. In addition, the pump light and the probe light can be combined and produced by the same laser to realize the compact sensor design^[28].

Figure 1.The basic principle of RF-OPMs. In the laboratory coordinate system, a z-axis pump light polarizes the atoms under a bias field B₀ applied in the same direction. When the frequency of the transverse RF field B_rf to be measured coincides with the Larmor frequency, magnetic resonances occur. This phenomenon can be easily understood in the rotating coordinate system.

For a more intuitive understanding of the principle of RF-OPMs, the system structure can be transformed into a rotating coordinate system, as illustrated in Fig. 1. An equivalent magnetic field along the $z$ direction in the rotating coordinate system exists due to the coordinate system transformation, with a magnitude of $ω / γ$ , where $γ$ is the atomic gyromagnetic ratio. When the bias field is in resonance with the RF field, the total magnetic field in the $z$ direction in the rotating coordinate system becomes zero. At this point, the magnetic moment component measured by the probe light is maximized. By scanning the amplitude of the bias field, the magnetic resonance signal can be obtained. Measuring the rotation angle of the probe light provides a proportional determination of the strength of the RF field, while the frequency of the RF field is simultaneously obtained.

In addition to the conventional MR-based operating principle mentioned above, an RF-OPM employing longitude parametric modulation has been proposed^[29]. By utilizing the pulse parametric resonances (PPRs), the spin-exchange relaxation is further suppressed and the sensitivity of the RF-OPM can be further improved. Additionally, Bevington et al. developed the RF-OPM based on a spin maser configuration that incorporated a positive feedback loop into the magnetometer configuration and enhanced the bandwidth of the system and signal-to-noise ratio (SNR)^[30]. In addition, Zheng et al. introduced an entanglement-enhanced quantum method by combining the conditional spin squeezing and stroboscopic backaction evasion^[31].

2.2. Development

In 2005, Savukov et al. first proposed the RF-OPM based on MR^[32]. The RF-OPM exhibited an exceptional sensitivity of $2 fT / \sqrt{Hz}$ at 99 kHz. Following, the RF-OPM had been applied to the detection of the ${}^{14}N$ nuclear quadrupole moments^[22]. To enhance the practicality of RF-OPMs, recent developments mainly focus on two aspects, which are the operation in unshielded environments and miniaturization while keeping higher sensitivity. Keder et al. achieved an unshielded RF-OPM by implementing a common-mode differential scheme for measuring two MR frequencies within the same atomic vapor cell^[33]. In 2022, they extended this technique to the RF gradiometer using a dual-chamber RF-OPM and exhibited superior sensitivity of $0.19 fT / \sqrt{Hz}$ at 1 MHz^[34]. In terms of miniaturization, Dhombridge et al. utilized a $1 {cm}^{3}$ natural rubidium atomic vapor cell, employing ${}^{87}{Rb}$ atoms for external field compensation while simultaneously detecting the RF magnetic field with ${}^{85}{Rb}$ atoms^[35]. This approach achieved a sensitivity of $9 fT / \sqrt{Hz}$ at 21.5 kHz. A summary of research for RF-OPMs based on the MR scheme is presented in Table 1. Since the ultimate spatial resolution usually depends on the cell size, we take the cell size as the spatial resolution in the table for reference.

Atomic cell	Sensitivity	Atoms	Environment	Reference
1 cm × 1 cm × 1 cm	$9 fT / \sqrt{Hz}$ @ 21.5 kHz	${}^{87}{Rb} - {}^{85}{Rb}$	Shielded	Dhombridge et al. (2022)^[35]
3.8 cm × 3.8 cm × 3.8 cm	$2 fT / \sqrt{Hz}$ @ 99 kHz	K	Shielded	Savukov et al. (2005)^[32]
4 cm × 4 cm × 6 cm	$0.3 fT / \sqrt{Hz}$ @ 0.5 MHz	K	Unshielded	Keder et al. (2014)^[33]
4 cm × 4 cm × 6 cm	$0.9 fT / \sqrt{Hz}$ @ 1.3 MHz	K	Unshielded	Keder et al. (2014)^[33]
4 cm × 4 cm × 6 cm	$0.24 fT / \sqrt{Hz}$ @ 423 kHz	K	Shielded	Lee et al. (2006)^[22]
5.2 cm × 2.1 cm × 2.6 cm	$0.19 fT / \sqrt{Hz}$ @ 1 MHz	${}^{87}{Rb}$	Unshielded	Cooper et al. (2022)^[34]

Table 1. Typical Studies of RF-OPMs Based on MR Scheme

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3. Applications in MFI

The applications of RF-OPMs in MFI mainly focus on biomedical diagnoses and industrial quality inspection. In the following, we will delve into three primary applications: NDT with MIT, ultralow-field magnetic resonance imaging (ULF-MRI), and MPI.

3.1. Nondestructive testing with MIT

NDT is a critical imaging methodology that has been used for evaluating the integrity of materials, components, or systems without causing damage or altering their functionality^[36]. This technique finds extensive applications across various sectors such as aerospace, construction, manufacturing, and energy industries for the detection of flaws^[37].

As one of the techniques in NDT, MIT emerges as an innovative imaging modality with promising applications in both the process industry and medical imaging^[38]. In MIT, a primary coil generates the primary magnetic field and induces the secondary magnetic field within the target material that is detected by RF-OPMs. By analyzing the characteristics of this secondary field, the internal structure and defects of the sample can be inferred^[39]. Compared to other methods shown in Table 2, in the context of NDT imaging, MIT by RF-OPMs exhibits advantages in terms of high sensitivity and spatial resolution.

Technique	Depth	Resolution	Characteristics
Radiography	Unlimited^[36]	$\sim μm$ ^[40]	Expensive, slow for thick samples, harmful to human body
Ultrasonic	10 mm^[41]	1 mm^[42]	Economical, fast, only for sound conductor
Thermography	∼mm^[43]	0.5 µm^[44]	Fast, portable, needing heated samples
MIT	Sub-mm^[45]	0.1 mm^[45]	Economical, contactless, only for electromagnetic conductors

Table 2. Methods Used in NDT Applications

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When RF-OPMs are used for NDT with MIT, the primary coil placed between the RF-OPM and the sample applies the primary magnetic field to the sample. The generation mechanism of the secondary magnetic field varies depending on the material properties of the sample, as shown in Fig. 2(a). In electrically conductive materials, the secondary field is produced by eddy currents induced by the primary magnetic field from the excitation coil. Conversely, in magnetically permeable materials, the secondary field arises from the local magnetization of the material. The secondary magnetic fields produced by these two mechanisms have opposite directions^[47]. The penetration depth of the oscillating magnetic field is determined by the skin depth of the eddy currents or the local magnetic fields. The skin depth is contingent upon the intrinsic properties of the material as well as the frequency of the magnetic field^[48].

Figure 2.(a) Imaging principles for conductive materials and magnetically permeable materials. The primary coil applies the primary magnetic field B_p to the test sample. The primary field induces eddy currents on the surface of materials with high conductivity, resulting in a secondary field opposite to the primary field. For materials with high magnetic permeability, the primary field induces local magnetization on the surface, leading to a secondary magnetic field in the same direction as the primary field. (b) Imaging of a square 90 mm stainless steel plate with a circular recess (diameter 25 mm) using an RF-OPM, capturing changes in amplitude and phase of the signal of the RF-OPM. Adapted from Bevington et al., 2020^[46].

The spatial resolution is dependent on the distribution of the RF magnetic field^[39]. A smaller diameter of the primary coil and the closer proximity to the sample result in a tighter radial distribution of the RF field, thereby enhancing the imaging resolution. Innovative coil geometries or magnetic flux guides may provide effective solutions to the issue of RF field divergence^[49].

In NDT, the amplitude and phase of secondary fields measured on the sample can be analyzed for imaging purposes. Figure 2(b) shows the amplitude and phase results of imaging of a steel plate with a circular recess. Due to the larger dynamic range of phase changes compared to amplitude changes, it can better capture the characteristics of grooves, as shown in Fig. 2(b). However, phase changes are unable to detect the secondary field generated by edges perpendicular to the magnetometer axis, showing directionality. Image information in any direction can be acquired through amplitude analysis. Nevertheless, the edge of the sample and the angle between the surface normal and the RF field significantly affect the amplitude, resulting in notable background signal fluctuations and diminished imaging contrast. Therefore, the choice between amplitude and phase imaging can be determined based on the characteristics and the location of defects^[39].

The typical results of NDT imaging using RF-OPMs in recent years are listed in Table 3. In addition to the traditional MR-based RF-OPM scheme, there have been new developments of RF-OPMs in the field of NDT. In 2019, Bevington et al. utilized an unshielded spin maser to image a thick carbon steel plate with defects, significantly reducing the imaging time from 12 h to just 25 min^[34]. Although the system may not fully replicate the shape of defects, it remains a viable solution for imaging magnetically permeable materials in unshielded environments. In terms of penetration depth, Maddox et al. proposed a two-photon RF transition method^[54]. By lowering the frequency of the RF field applied to the sample, the detection depth can be enhanced.

Volume	Frequency	Penetration depth	Resolution	Reference
5 cm × 5 cm × 5 cm	10 kHz	0.82 mm	30 mm	Wickenbrock et al. (2014)^[50]
2.5 cm × 2.5 cm × 2.5 cm	10 kHz		Sub-mm	Deans et al. (2016)^[51]
Φ 2.5 cm × 2.5 cm	250 kHz		Sub-mm	Wickenbrock et al. (2016)^[52]
1 cm × 1 cm × 1 cm	12.6 kHz	0.18 mm	0.1 mm	Bevington et al. (2018)^[45]
5 mm³	10.5 kHz	1 mm	7 mm	Rushton et al. (2022)^[53]

Table 3. Experimental Results of Applying RF Atomic Magnetometers for NDT on Materials with High Electrical Conductivity

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In the field of NDT, the RF-OPM is also advancing towards miniaturization, portability, and unshielded designs. Additionally, due to the nonlinear relationship between the strength of the secondary field and magnetization (characterized by the hysteresis loop phenomenon), conducting NDT on magnetically permeable materials is relatively complex, which is also an important research direction for RF-OPMs^[55].

3.2. ULF-MRI

MRI is widely known for its medical diagnostic capability and can also be used in anthropology^[56], paleontology^[57], evolution^[58], material analysis^[59], food quality^[60], and liquid explosives^[61]. Conventional MRI typically requires magnetic fields of up to several teslas to ensure an adequate signal intensity. The development of ultrasensitive magnetic field sensors such as SQUIDs and OPMs enables the application of MRI at ultralow-field (ULF) in the range of microtesla to millitesla^[62]. ULF-MRI does not require the use of a large magnet to generate a strong magnetic field at the tesla level, resulting in lower costs.

In ULF-MRI experiments based on RF-OPMs, the application of a prepolarization field of approximately several tens of microtesla induces the macroscopic polarization of atoms. In comparison to conventional MRI, the prepolarization field strength in ULF-MRI is relatively small. Subsequently, a pulsed measurement field that is orthogonal to the prepolarization field is applied to induce the precession of the atoms around it. Simultaneously, encoding gradient fields (frequency or phase encoding) are operated for two-dimensional imaging. The gradient fields for spatial encoding may induce the linewidth broadening of the RF-OPM, thereby degrading the sensitivity of the magnetometer.

To address the negative effect induced by the gradient field, various methods have been proposed, such as remote detection^[63], solenoid-based field separation^[64], and flux-transformer (FT) mediated detection^[65,66]. Among these methods, the FT-mediated detection method is currently the simplest and most convenient approach for decoupling the bias and gradient fields, and it is fully compatible with anatomical imaging. In 2009, Savukov et al. introduced the FT into the RF-OPM setup to decouple the bias field and the gradient field^[65]; the typical structure is shown in Fig. 3(a). Within the magnetic field, the dynamic magnetic flux resulting from the Larmor precession of the phantom atoms leads to the generation of alternating voltage in the FT input coil. The signals received by the FT input coil are transmitted through a capacitor box into the magnetic shield. The output coil of FT transfers the signals, which are then detected by the RF-OPM. Building upon this structure, they utilized the high gyromagnetic ratio of potassium atoms to achieve a precession frequency of 85 kHz in an ultralow bias field. This accomplishment led to a spatial resolution of approximately $1 mm \times 1 mm$ ^[68]. Moreover, they proposed a multichannel FT scheme to improve SNR, accelerate MRI scans, reduce the required bandwidth for each sensor, and increase the field of view (FOV) by a twofold magnitude^[66]. In 2022, Hori et al. successfully implemented ULF-MRI based on an RF-OPM in an unshielded environment, and the three-dimensional imaging resolution was demonstrated to be $3 mm \times 3 mm \times 3 mm$ ^[69]. Some of the main researches for ULF-MRI based on RF-OPMs are summarized in Table 4.

Sensitivity	Bias field	Environment	Resolution		Reference
Sensitivity	Bias field	Environment	Image plane^a	Slice direction^a	Reference
$80 fT / \sqrt{Hz}$ @ 0.1 Hz	3.1 mT	Shielded	4.5 mm × 4.5 mm	1.6 mm	Xu et al. (2006)^[62]
$24 fT / \sqrt{Hz}$ @ 1 kHz	117.5 µT	Shielded	8.9 mm × 8.9 mm	7.4 mm	Hilschenz et al. (2017)^[68]
$12 fT / \sqrt{Hz}$ @ 3.2 kHz	75 µT	Shielded	2 mm × 2 mm		Savukov et al. (2009)^[64]
$2 fT / \sqrt{Hz}$ @ 80 kHz	12 µT	Shielded	1.1 mm × 1.4 mm	4.5 mm	Savukov et al. (2013)^[66]
$14.7 fT / \sqrt{Hz}$ @ 300 kHz	42 µT	Unshielded	3 mm × 3 mm	3 mm	Hori et al. (2022)^[70]

Table 4. Imaging Results of ULF-MRI Based on RF-OPMs

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Figure 3.(a) Typical configuration of ULF-MRI with a flux transformer. Phantom is the test sample for ULF-MRI. (b) Comparison of ULF-MRI of the human head with traditional MRI. Adapted from Zotev et al., 2018^[67].

Figure 4.(a) Spatial encoding in MPI. After applying a modulation field to SPIONs, the magnetic field at the center (field-free point, FFP) of the inhomogeneous selection field becomes zero. The magnetization of SPIONs undergoes substantial oscillations due to the modulation field. At the edges of the selection field, where the magnetic field intensity is higher, the magnetization of SPIONs tends to saturate, resulting in a reduction in oscillation amplitude. The adjustment of the FFP is accomplished through the use of a focus field, facilitating spatial encoding. (b) In vivo overlays of MPI images (red) onto anatomical MRI images (gray) of mouse hearts and cardiovascular systems obtained using tracer materials. Adapted from Knopp et al., 2012^[83].

The technical challenges in ULF-MRI mainly come from attaining adequate SNR, contrast, and resolution within practical scanning timeframe due to relatively weak bias field, as seen in Fig. 3(b). Despite research demonstrating a high degree of consistency in diagnosing specific diseases between imaging results obtained from ULF-MRI and high-field MRI^[67], challenges persist in the clinical applications of ULF-MRI due to insufficient SNR and resolution^[71]. Replacing induction coil magnetometers with RF-OPMs can improve the SNR of ULF-MRI under low-frequency operating conditions with a weak bias field. However, the sensitivity of RF-OPMs would be reduced due to the gradient fields used for spatial encoding, leading to a decreased SNR. Although the FT has proven highly effective in decoupling gradient fields, using the FT at room temperature introduces Johnson noise, consequently diminishing the SNR of ULF-MRI^[66]. Hence, enhancing the SNR of ULF-MRI can be achieved by cooling the FT, coupled with geometric structure optimization. Moreover, the utilization of inhomogeneous dressing field serves as an alternative to the FT for mitigating the broadening effects induced by gradient fields. This allows RF-OPMs to operate effectively, even in the presence of strong gradient fields^[72].

The investigation and refinement of bias field stability, along with enhancing the interference resistance of RF-OPMs against external disruptions like magnetic field gradients, temperature gradients, and mechanical vibrations, are essential focal points for advancing the practical applications of RF-OPMs in ULF-MRI.

3.3. MPI

MPI is a tomographic imaging technique that detects superparamagnetic iron oxide nanoparticles (SPIONs) tracers, first proposed by Gleich and Weizenecker in 2005^[73]. SPIONs are composed of a magnetite or maghemite core surrounded by a nonmagnetic surface coating, which is detectable in biological fluids^[74]. At the same magnetic field strength, SPIONs exhibit a magnetization rate that is $10^{8}$ times higher than that of protons (the main signal source in MRI) and a relaxation speed that is $10^{4}$ times faster than MRI^[75]. The typical frequency range of MPI is 10 kHz to 100 kHz, with typical magnetic field strengths ranging from 10 to 100 mT^[74]. RF-OPMs could have higher sensitivity than induction coil magnetometers in the frequency range of 10–100 kHz^[74]. Therefore, it can reduce the magnetic field strength to tens of µT in MPI^[76].

In recent years, the application of RF-OPMs in MPI mostly focuses on imaging and tracking localization of SPIONs^[77], magnetic particle spectroscopy^[78], as well as research on magneto-relaxometry (MRX)^[79]. In 2010, Garcia et al. reported a miniaturized, room-temperature Cs-based RF-OPM, applied it to the measurement of magnetic particles^[80], and obtained preliminary one-dimensional scanning results with a resolution of 0.1 mm. Afterwards, Colombo et al. applied an RF-OPM to record the spatial distribution of fluid-suspended magnetic nanoparticles in one dimension, achieving a resolution of approximately 2.5 mm with the gradient field of about 1 T/m^[81]. The research on two-dimensional imaging using RF-OPMs in the context of MPI is still under development, as shown in Fig. 4(b).

MPI technology and RF-OPM usage are rapidly advancing. In the context of RF-OPMs in MPI, the challenge of gradient field broadening is met similarly to MRI methodologies, utilizing the FT to address sensitivity reduction^[82], as shown in Fig. 4(a). Ongoing investigations focus on establishing precise relationships among RF-OPM parameters, SPION properties, sensitivity, and spatial/temporal image resolution. Looking forward, potential applications of MPI may expand to include cell imaging, targeted imaging, and therapeutics, paving the way for clinical translation.

4. Conclusion

In conclusion, this review has provided a brief overview of MFI utilizing RF-OPMs, with a particular emphasis on their applications in NDT, ULF-MRI, and MPI. The advantages offered by RF-OPMs, such as low running costs, potential for miniaturization, and a broad operating frequency range with a flat response, underscore their significance in advancing MFI technologies.

In the future, the continued improvement of RF-OPM sensitivity and imaging resolution, along with efforts towards miniaturization, unshielded operation, and robustness at room temperatures, will broaden the scope of applications and unlock the full potential of RF-OPMs in MFI.

Additionally, further research is needed in NDT to explore the relationship between the optimal frequency of the RF field for imaging and factors such as sample thickness and the sensitivity of the RF-OPM. Furthermore, the majority of current researches in NDT are limited to materials with high electrical conductivity. There is a need for further investigation into imaging low electrical conductivity materials^[84,85] as well as materials with high magnetic permeability.

Moreover, given that the utilization of RF-OPMs in biomedical applications frequently involves spatial encoding through gradient magnetic fields, these gradients may cause broadening and diminished sensitivity of RF-OPMs. Hence, exploring novel spatial encoding methods or mitigating RF-OPM sensitivity to magnetic gradients could prove valuable in enhancing the performance in applications like ULF-MRI and MPI.

For conventional MR-based RF-OPMs, advancements in field stabilization techniques can enhance the stability of the bias field, consequently improving the practical stability of RF-OPMs.

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