Multi-channel spin exchange relaxation free magnetometer towards two-dimensional vector magnetoencephalography

Guiying Zhang; Shengjie Huang; Feixiang Xu; Zhenghui Hu; Qiang Lin

doi:10.1364/OE.27.000597

1. Introduction

Bioelectromagnetic field measurement techniques, such as electroencephalography (EEG) and magnetoencephalography (MEG), can be used in basic and clinical research [1,2]. EEG has been used commonly for acquiring the physiological signal. However, MEG has not been used widely, although the magnetic signals are less affected by the human body tissues with nearly homogeneous permeability, and more suitable for determining the location of signal sources [3]. This is because the dominant technology for MEG measurement, superconducting quantum interference device (SQUID) magnetometers, still have many technical limitations [4]. For example, SQUID magnetometers require cryogenic cooling, making the installation and maintenance costs too high. Meanwhile, the liquid-helium-cooled dewar restricts the distance between the scalp surface and magnetometer to be 3-6 cm and makes the SQUID magnetometers inflexible.

To overcome these problems, non-cryogenic magnetometers have attracted increasing attentions. Optically pumped atomic magnetometers based on spin exchange relaxation free (SERF) regime have emerged as a most promising non-cryogenic alternative to the SQUID magnetometers [5]. By eliminating the relaxation due to rubidium-rubidium spin exchange collisions, SERF magnetometers have a sufficiently high sensitivity, but operate at near room temperature, and hence no liquid-helium-cooled equipment is required. Without the cooling dewar, SERF magnetometers can be moved closer to the scalp, the distinct advantages have been demonstrated by two recent simulation studies [4,6]. In addition, the size of SERF magnetometers can be much smaller than SQUID magnetometers, and hence only a small, cheap magnetically shielded room is required. For some applications, a person-sized shield is enough. SERF phenomena was firstly discovered by Happer group [7,8], and then Romalis group developed an ultra-sensitive magnetometer with 10 fT/Hz^1/2 level sensitivity [9]. Over the following decade, SERF magnetometers have achieved the 0.16 fT/Hz^1/2 level sensitivity with a measurement volume of 0.45 cm³, surpassing the sensitivity of SQUID magnetometers [10].

The SERF magnetometers with high enough sensitivity and small enough size are the only type of optically pumped atomic magnetometers that can be used to observe the MEG signals. In 2006, Romalis group demonstrated the detection and mapping of brain magnetic fields evoked by auditory stimulation with SERF magnetometers [11]. Progress since then has centered on developing the multi-channel system. Because multi-channel magnetic sensors are necessary in MEG measurements, in which the brain fields at multi locations need to be simultaneously measured. The present commercialized full-head MEG system based on SQUID magnetometers usually consists of multi-channel high sensitivity magnetic sensors, such as 306 SQUID sensor arrays. To construct the multi-channel SERF system, one technique is to arrange multiple independent modules, comprising a set of pump and probe beams irradiating a vapor cell. However, it is very difficult to make each vapor cell with the same characteristics exactly.

A large vapor cell with the broad pump and probe beam is proposed to solve the above problem [12,13]. The main idea is that the large vapor cell is usually filled with high pressure buffer gas to suppress the wall-rubidium collision relaxation by restricting the diffusion of rubidium atoms. This makes it possible to use different volume of the vapor cell as an independent local magnetic sensor. A broad pump beam polarizes the whole volume of the vapor cell. A broad probe beam measures the magnetic fields at multiple volumes with a two-dimensional photodiode array. However, the inherent restriction is that the probe beam measures the sum of all the magnetic fields along the probe beam direction, which means it is difficult to get the spatial magnetic field distribution.

Two methods have been proposed to get the spatial magnetic field distribution. In the first method, the pump beam is sliced into multiple sections and the vapor cell is repetitively pumped in successive layers. Using the temporal segmentation, one can get the two-dimensional spatial magnetic field distribution [14]. Subsequently, some improvements have been suggested to increase the magnetic field distribution measurement accuracy and accomplish simultaneous multilocation measurements [15,16]. Another method to distinguish these magnetic fields is based on the retro-reflected probe beam optical design [17–19]. The probe beam is reflected by a mirror to pass through the vapor cell twice. The head is positioned on the mirror surface. The two-dimensional multilocation magnetic fields of the tangential component can be measured simultaneously. However, compared to the tangential component, measuring the normal component is considered to be the optimal choice for MEG [6]. Because the tangential component is more affected by the volume currents, which makes more accurate head models and numerical methods are needed. In addition, measuring the tangential component requires more higher sensitivity due to the tangential component lower topography power. Furthermore, SQUID magnetometers traditionally measure the normal magnetic field, so the normal component data obtained with SERF magnetometers can follow the interpretation by others, which can provide many known information. But some tangential component data are very different from the traditional normal component data, which would introduce a profound change in the interpretation.

In this paper, a multi-channel new sensor module is designed and made to measure the normal magnetic field. In the new sensor module, the longitudinal parametric modulation [20] and retro-reflected probe beam optical configuration are used to accomplish the two-dimensional spatial distribution measurements of the normal magnetic field. Evoked brain magnetic fields perpendicular to the scalp resulting from the auditory stimulation are recorded with the four-channel SERF atomic magnetometer. In the longitudinal parametric modulation mode, the tangential magnetic field can be detected simultaneously. Some studies have demonstrated that the vector magnetic field information is useful for MEG applications [21,22].

2. Theory of four-channel SERF magnetometer

In the traditional operation mode, the circularly polarized pump beam optically pumps the atoms along the z direction, as shown in Fig. 1(a). A magnetic field $B_{y}$ perpendicular to the pump beam rotates the spin by an angle. A linearly polarized probe beam, perpendicular to the pump beam and the magnetic field, detects the spin polarization projection along the x direction, $P_{x}$ . According to the Bloch equation, $P_{x}$ is given by the following equation [23]:

P_{x} = - P_{0} \frac{γ B_{y} Γ}{{(γ B_{y})}^{2} + Γ^{2}},

where

P_{0}

is the spin polarization produced by optical pumping without the external magnetic field,

γ

is the is gyromagnetic ratio,

Γ

is the total transverse spin relaxation rate including relaxation processes, such as the optical pumping relaxation, spin destruction relaxation and diffusion wall relaxation. Equation (1) shows that a magnetic field

B_{y}

can be measured via detecting the spin polarization,

P_{x}

. However, as shown in Fig. 1(a),

B_{y}

is the sum of all y-direction magnetic fields along the x-axis. And thus only

B_{y}

magnetic fields of two measurement points along the z direction are measured. The position information along the x direction is lost.

Fig. 1 Four-channel operation of a single large vapor cell. (a) The traditional operation mode. It is difficult to distinguish the y-direction magnetic field along the probe beam. (b) The longitudinal parametric modulation mode. The normal magnetic fields of four locations can be measured simultaneously.

Download Full Size | PDF

In order to overcome this problem, a large longitudinal oscillating magnetic field is applied along the z direction, which forces the transverse spin polarization to precess about the z direction, as shown in Fig. 1(b). In this case, $P_{x}$ is expressed as follows [20]:

\begin{array}{l} P_{x} (ω_{z}) \approx \frac{γ B_{x} P_{0}}{Γ} 2 J_{0} (u) J_{1} (u) \sin (ω_{z} t) \\ P_{x} (2 ω_{z}) \approx \frac{γ B_{y} P_{0}}{Γ} 2 J_{0} (u) J_{2} (u) \cos (2 ω_{z} t), \end{array}

where

ω_{z}

is the longitudinal oscillating magnetic field frequency,

J_{0} (u)

,

J_{1} (u)

and

J_{2} (u)

are the Bessel functions of the first kind. The variable

u

is the modulation index given by

u = γ B_{\mod} / [(1 + ε) ω_{z}]

, where

B_{\mod}

is the modulation magnetic field amplitude and

1 + ε

is the slowing-down factor.

It can be seen from Eq. (2) that the magnetometer can detect the magnetic field in the x and y direction by the different harmonics. As shown in Fig. 1(b), the probe beam is reflected to pass through the vapor cell twice. In this case, the head rests against the sensor from the mirror side, the normal (x direction) and tangential (y direction) magnetic field components of four measurement points in the y-z plane can be measured simultaneously.

3. Design of four-channel SERF magnetometer

The schematic and photograph of our four-channel SERF magnetometer are shown in Fig. 2. The core of the SERF magnetometer is a cubic borosilicate glass cell of side length 20 mm, which contains enriched ⁸⁷Rb and approximately 730 torr helium as buffer gas and 30 torr N₂ as quenching gas. The vapor cell is housed in a boron nitride oven, which is surrounded by a 2 mm thick microporous ceramic insulation at all surfaces except for the locations of three embedded vacuum cells. This design reduces heat loss due to convection, meanwhile, allows the probe and pump beam to pass through. It is then electrically heated to approximately 150 ${}^{°}C$ with a 43 kHz ac voltage. At this temperature, a rubidium density of 10¹⁴ cm⁻³ is obtained. The twisted pair high resistance nichrome wire and high frequency heating voltage minimize the heating effect during measurement. A three-axis Helmholtz coil system is wrapped around the oven to cancel the residual magnetic fields and produces the longitudinal oscillating magnetic field.

Fig. 2 Sensor schematic (a) and photograph (b). The optics for the pump beam (top) and the optics for the probe beam (bottom) in (a). A longitudinal oscillating magnetic field is applied along the pump beam. The circularly polarized pump beam optically pumps the atoms along the z direction. The linearly polarized probe beam passes through the vapor cell twice by reflection, and then is focused onto the polarization analyzer to extract the normal magnetic field. With the high temperature resistant polyformaldehyde plastic housing, the dimension of the sensor module head is 40 × 50 × 200 mm³.

Download Full Size | PDF

Two ECL lasers are coupled to the sensor via the polarization maintaining fibers. The pump beam passes through a linear polarizer and a quarter-wave plate, and then is expanded to about 18 mm by a lens to pump as many atoms as possible. The frequency is detuned by 0.2 nm from the D1 line to reduce the spatial inhomogeneity of spin polarization due to the resonance absorption of the pump beam. The probe beam is incident at a small angle of about 3° on the vapor cell, and then is reflected by a mirror to pass through the vapor cell twice. The frequency is detuned by 0.5 nm from the D1 line. The beam diameter is expanded to 13 mm by a lens, and then is reshaped by another lens to match the size of the polarization analyzer. The analyzer consists of a Wollaston prism and two 2 × 2 photodiode matrixes. The amount of light on each quadrant can be made nearly equal with 3% deviation by adjusting the y-z position of photodiode matrix. A half-wave plate is used to balance the light power of the two 2x2 photodiode matrixes. The magnetic field information of each sensing volume of the vapor cell can be obtained by the differential signal of the corresponding quadrant of two photodiodes. In this way, the normal magnetic fields of the four brain locations can be measured simultaneously via the optical rotation of the single linearly polarized probe beam.

In our experiment, the channel signal comes from the average magnetic field within the volume set by the overlap of the pump and probe beams. The diameters of the pump and probe beams are 18 mm and 13 mm, respectively. Therefore, the whole sensing volume is a cylinder with a diameter of probe beam (13 mm) in the y-z plane and a length of the pump beam diameter (18 mm) in the x direction as shown in Fig. 3. Each sensing volume is one quadrant of the cylinder.

Fig. 3 Schematic of the sensing volume. The pink cylinder is the whole sensing volume and each sensing volume is one quadrant of the cylinder. The cyan area is the diffusion volume. The gray cube represents the vapor cell.

Download Full Size | PDF

However, the cross-talk between adjacent channels caused by the atom diffusion must be considered. If the rubidium atoms do not diffuse from one channel to another during the spin coherence time, the cross-talk between adjacent channels does not happen. The diffusion distance $l_{D}$ is given as follows:

l_{D} = \sqrt{\frac{D}{Γ}},

where

D

is the diffusion constant. In our experiment, the diffusion constant of rubidium atom in the buffer gas is about 0.40 cm²/s [17], the total transverse spin relaxation rate

Γ

is equal to 2π × 100 Hz. The diffusion distance is then equal to 0.25 mm.

Atom diffusion leads to the exchange of atoms between adjacent sensing volumes. Large atom diffusion distance can even make the average magnetic field of adjacent sensing volumes indistinguishable. As shown in Fig. 3, assume that $B_{1}$ , $B_{2}$ , $B_{3}$ , $B_{4}$ are the homogenous magnetic field in each quadrant of the cylinder. Due to the diffusion, some atoms carrying the magnetic field information of $B_{1}$ will diffuse into the volume of $B_{2}$ , and vise verse. And hence the magnetic field difference of adjacent sensing volumes is changed. In this case, the magnetic field difference

\bar{Δ B} = \bar{B_{1}} - \bar{B_{2}} = Δ B (1 - 0.5 V_{r a t i o}),

where

V_{r a t i o}

is the ratio of the diffusion volume

V_{d i f f u s i o n}

in one quadrant to the one quadrant volume

V

.

Δ B = B_{1} - B_{2} = B_{4} - B_{3}

is the magnetic field difference of up-down adjacent channel.

\bar{B_{1}} = B_{1} - 0.25 V_{r a t i o} (B_{1} - B_{2}) - 0.25 V_{r a t i o} (B_{1} - B_{4})

and

\bar{B_{2}} = B_{2} - 0.25 V_{r a t i o} (B_{2} - B_{1}) - 0.25 V_{r a t i o} (B_{2} - B_{3})

.

In our case, the diffusion distance is equal to 0.25 mm. Considering the extreme situation that the atoms diffuse a distance of 0.25 mm in each quadrant. The diffusion volume $V_{d i f f u s i o n} = 2 \times 0.25 \times 6.5 \times 18$ mm³, and thus $V_{r a t i o}$ is equal to 0.1. The magnetic field difference $\bar{Δ B}$ is only reduced by five percent of the original value. Therefore, the atom diffusion doesn’t severely affect the sensing volume decided by the geometry. Each channel of the magnetometer can be regarded as an independent sensor.

4. Magnetometer characterization and MEG measurements

The four-channel magnetometer is positioned in a person-sized four-layer permalloy magnetic shield, the residual magnetic field in the shield is less than 10 nT. The very weak magnetic field plus high vapor density of rubidium atoms can keep the magnetometer in the SERF regime, where the spin exchange rate is much larger than the Larmor precession frequency, so the spin exchange relaxation can be eliminated.

The longitudinal oscillating magnetic field modulates the transverse spin polarization at a frequency of 2 kHz, so we demodulate the polarization analyzer output with the lock-in amplifier at this modulation frequency to extract the first and second harmonic components. Considering the modulation frequency, and meanwhile in order to record the relatively fast brain signals, the time constant and roll-off of the lock-in amplifier are set to be 300 μs and 24 dB/octave, respectively. And then the fast Fourier transform with Blackman window is performed on the lock-in amplifier output to yield the amplitude noise power spectral density (PSD) with the Stanford FFT analyzer. The light shift can cause the degrading of the magnetometer sensitivity. In general, the effect can be cancelled by applying a compensating magnetic field. But in our experiment, the sensitivity is high enough for human MEG measurements, so the effects of light shift have not been considered.

Figure 4(a) shows the magnetic field sensitivities of the four sensor channels in the x direction. The magnetic noise spectrum is obtained by applying a small sinewave calibration magnetic field at frequencies below 400 Hz, where the amplitude at each frequency is a constant, about 31 pT. Each noise spectrum in Fig. 4 is normalized via dividing the amplitude noise spectrum by the ratio of the corresponding frequency response amplitude to the applied calibration field. It is shown that the noise floor is 6-15 fT/Hz^1/2 between 7 Hz and 200 Hz, except for a few spikes at discrete frequencies. Below 7 Hz, the sensitivity is degraded, which may be due to the fluctuations of the light polarization in the fiber. The frequency response of human brain on the auditory stimulation is usually below 40 Hz, so we should emphatically consider the average sensitivity at this frequency range. The average noise level of channels 1-4 over 2-40 Hz are 14.46, 14.44, 13.85 and 13.38 fT/Hz^1/2, respectively. The sensitivity is high enough for human MEG measurements. The gradient measurements are performed by taking the difference between two adjacent channels. And then the data are divided by 2^1/2 to show the equivalent single-channel sensitivity. Because the gradiometer can remove the common-mode noise, it represents the intrinsic sensitivity of the sensor module. The gradient noise spectrum in Fig. 4(a) shows the gradient sensitivities of 5 fT/Hz^1/2 between 10 Hz and 100 Hz are achieved in the horizontal and vertical directions. Figure 4(b) shows the sensitivities in the y direction. A sensitivity of 20-30 fT/Hz^1/2 between 5 Hz and 100 Hz is achieved in this direction. The work to get the high sensitivities for simultaneous two-axis detection by further optimizing the setup is currently in progress.

Fig. 4 Magnetic noise spectrum of the magnetometer. (a) The sensitivities of the four channels in the x direction are nearly identical and approximately 10 fT/Hz^1/2. For the horizontal gradiometer (Ch1 - Ch4) and the vertical gradiometer (Ch3 - Ch4), the intrinsic sensitivities of 5 fT/Hz^1/2 are achieved. (b) The average sensitivities of the four channels in the y direction are approximately 25 fT/Hz^1/2.

Download Full Size | PDF

The normalized frequency responses of the four channels in the x direction are shown in Fig. 5. The high pumping rate can increase the frequency response, but also results in the loss of the sensitivity, so an optimized pumping rate is chosen in our magnetometer. The frequency response of each sensor channel can be well fitted by the combination of a first-order low-pass filter caused by the atom and a fourth-order low-pass filter of the lock-in amplifier. The fitting formula is given as follows [24]:

\frac{1}{{(1 + {(2 π τ_{c} f)}^{2})}^{2} \sqrt{1 + {(f / f_{3 dB})}^{2}}},

where

τ_{c}

is the time constant of the lock-in amplifier low-pass filter. In our case, the – 3dB cut-off frequency of the lock-in amplifier is 230 Hz for a time constant of 300 μs when using a 24 dB/octave filter.

f_{3 dB}

is the bandwidth of the atom. Figure 5 shows the – 3dB bandwidths of the atoms for the four sensor channels are 105.3, 114.3, 123.3 and 129.8 Hz, respectively. The frequency responses of the four channels below 50 Hz are nearly identical. Therefore, the atomic bandwidth is desirable, which is fast enough to observe the evoked brain magnetic signals by auditory simulation.

Fig. 5 The normalized frequency responses of the four channels. The measured response amplitudes are obtained by changing the frequency of the calibration field while maintaining the amplitude of the calibration field constant.

Download Full Size | PDF

To further observe the performance of the frequency response, we set the frequency of the calibration field as 10 Hz. The frequency response amplitudes of channels 1-4 in the x direction are shown in Fig. 6(a). The measured voltage amplitudes at 10 Hz are 1.17, 1.15, 1.15 and 1.14 V, respectively. The peak deviation from the mean of the amplitude is only 1%. In order to demonstrate experimentally that the four channels are truly independent, a loop coil with a diameter of 14 mm is used to as a signal source. The coil is located about 10 cm away from the sensing volume along the x-axis, and about 3 cm along the y-axis. A sinewave magnetic field at a frequency of 10 Hz is generated by the loop coil. As shown in Fig. 6(b), the clear different readings from the four channels are obtained. It is a clear demonstration that the four channels are truly independent.

Fig. 6 The measured frequency response waveform at 10 Hz. (a) The measured amplitudes of the four channels are nearly identical, when a homogeneous calibration magnetic field is applied. (b) The inhomogeneous magnetic field generated by the loop coil is measured. The four different readings are obtained clearly.

Download Full Size | PDF

Auditory evoked response MEG measurements are performed in a person-sized shield with the four-channel SERF magnetometer. The diameter and length of the innermost shield are 0.8 m and 2.4 m, respectively. The MEG signals are from a healthy male (age 23). The human subject is a volunteer in our institute. The relevant ethical guidelines have been followed. The subject lays in the shield and rests his head close to the position-fixed sensor. The front surface of the sensor module facing the subject head is maintained at 45 °C by attaching a 1.5 mm thick microporous ceramic insulation, which is only higher than body temperature by several degrees. The distance between the center of the vapor cell and the scalp is about 20 mm. Auditory stimuli are applied to the subject to evoke brain magnetic fields. Each auditory stimulus consists of 0.25 s 1000 Hz tones presented to both ears. The interval between tones is varied randomly, either 0.9 s or 1.0 s. The evoked magnetic fields perpendicular to the scalp are recorded by the four channels. The signals are then filtered with a 2-40 Hz bandpass fast Fourier transform (FFT) filter and are averaged for 250 auditory stimuli. The auditory evoked magnetic field signals of the four adjacent locations are shown in Fig. 7. A clear M100 peak is observed at approximately 100 ms after auditory stimuli for all four channels, which is consistent with the typical M100 peak measured by the SQUID magnetometers.

Fig. 7 Auditory evoked response recorded by the four-channel SERF magnetometer. Each curve is an average of 250 auditory stimuli. Bandpass filtering from 2 to 40 Hz is performed. A M100 peak is observed clearly.

Download Full Size | PDF

5. Conclusions and discussions

In this study, a four-channel SERF magnetometer is designed and constructed. The four-channel operation is realized with a single vapor cell, two broad beams and two 2 × 2 photodiode matrixes. The longitudinal parametric modulation and a reflection optical design are proposed to accomplish the multilocation normal magnetic field measurements. The noise level of approximately 10 fT/Hz^1/2 is achieved, and −3dB bandwidth is roughly 100 Hz. Using the four-channel magnetometer, auditory evoked response MEG recordings are achieved.

Some improvements of the sensor module are possible. Firstly, the sensitivity at below 7 Hz may be improved by stabilizing the light polarization in the fiber. Secondly, to further increase the relative uniformity of the bandwidths of the four channels, a hybrid vapor cell may be used instead of the individual species vapor cell [25,26]. Hybrid optical pumping can have a more homogeneous optical pumping rate inside the vapor cell due to the suppression of pump beam absorption. Thirdly, at the buffer gas of about one atmosphere, the atom diffusion distance is only 0.25 mm. Therefore, the number of channels can be further increased to improve the spatial resolution. Finally, since the normal magnetic field plus the additional tangential magnetic field can help the source location, the work to get the vector magnetic field information by further optimizing the setup is currently in progress.

Funding

National Key R&D Program of China (2017YFC0601602); National Natural Science Foundation of China (NSFC) (11704335, 61727821 and 61475139).

Acknowledgments

We thank the Hangzhou Chinmagnetics Technology Co., Ltd for assistance with funding.

References

1. D. Cheyne, A. C. Bostan, W. Gaetz, and E. W. Pang, “Event-related beamforming: a robust method for presurgical functional mapping using MEG,” Clin. Neurophysiol. 118(8), 1691–1704 (2007). [CrossRef] [PubMed]

2. A. J. Colon, P. Ossenblok, L. Nieuwenhuis, K. J. Stam, and P. Boon, “Use of routine MEG in the primary diagnostic process of epilepsy,” J. Clin. Neurophysiol. 26(5), 326–332 (2009). [CrossRef] [PubMed]

3. D. Cohen and B. N. Cuffin, “Demonstration of useful differences between magnetoencephalogram and electroencephalogram,” Electroencephalogr. Clin. Neurophysiol. 56(1), 38–51 (1983). [CrossRef] [PubMed]

4. E. Boto, S. S. Meyer, V. Shah, O. Alem, S. Knappe, P. Kruger, T. M. Fromhold, M. Lim, P. M. Glover, P. G. Morris, R. Bowtell, G. R. Barnes, and M. J. Brookes, “A new generation of magnetoencephalography: Room temperature measurements using optically-pumped magnetometers,” Neuroimage 149, 404–414 (2017). [CrossRef] [PubMed]

5. E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah, S. S. Meyer, L. D. Muñoz, K. J. Mullinger, T. M. Tierney, S. Bestmann, G. R. Barnes, R. Bowtell, and M. J. Brookes, “Moving magnetoencephalography towards real-world applications with a wearable system,” Nature 555(7698), 657–661 (2018). [CrossRef] [PubMed]

6. J. Iivanainen, M. Stenroos, and L. Parkkonen, “Measuring MEG closer to the brain: Performance of on-scalp sensor arrays,” Neuroimage 147, 542–553 (2017). [CrossRef] [PubMed]

7. W. Happer and A. C. Tam, “Effect of rapid spin exchange on the magnetic-resonance spectrum of alkali vapors,” Phys. Rev. A 16(5), 1877–1891 (1977). [CrossRef]

8. W. Happer and H. Tang, “Spin-exchange shift and narrowing of magnetic resonance lines in optically pumped alkali vapors,” Phys. Rev. Lett. 31(5), 273–276 (1973). [CrossRef]

9. J. C. Allred, R. N. Lyman, T. W. Kornack, and M. V. Romalis, “High-sensitivity atomic magnetometer unaffected by spin-exchange relaxation,” Phys. Rev. Lett. 89(13), 130801 (2002). [CrossRef] [PubMed]

10. H. B. Dang, A. C. Maloof, and M. V. Romalis, “Ultrahigh sensitivity magnetic field and magnetization measurements with an atomic magnetometer,” Appl. Phys. Lett. 97(15), 151110 (2010). [CrossRef]

11. H. Xia, A. B. A. Baranga, D. Hoffman, and M. V. Romalis, “Magnetoencephalography with an atomic magnetometer,” Appl. Phys. Lett. 89(21), 211104 (2006). [CrossRef]

12. K. Nishi, Y. Ito, and T. Kobayashi, “High-sensitivity multi-channel probe beam detector towards MEG measurements of small animals with an optically pumped K-Rb hybrid magnetometer,” Opt. Express 26(2), 1988–1996 (2018). [CrossRef] [PubMed]

13. Y. J. Kim and I. Savukov, “Highly sensitive multi-channel atomic magnetometer,” in 2018 IEEE Sensors Applications Symposium (SAS) (2018), pp. 1–4.

14. Y. Ito, D. Sato, K. Kamada, and T. Kobayashi, “Measurements of magnetic field distributions with an optically pumped K-Rb hybrid atomic magnetometer,” IEEE Trans. Magn. 50(11), 1–3 (2014). [CrossRef]

15. Y. Mamishin, Y. Ito, and T. Kobayashi, “A novel method to accomplish simultaneous multilocation magnetic field measurements based on pump-beam modulation of an atomic magnetometer,” IEEE Trans. Magn. 53(5), 1–6 (2017). [CrossRef]

16. A. Gusarov, A. B. A. Baranga, D. Levron, and R. Shuker, “Accuracy enhancement of magnetic field distribution measurements with a large cell Spin-Exchange Relaxation Free magnetometer,” Meas. Sci. Technol. 29(4), 045209 (2018). [CrossRef]

17. K. Kim, S. Begus, H. Xia, S. K. Lee, V. Jazbinsek, Z. Trontelj, and M. V. Romalis, “Multi-channel atomic magnetometer for magnetoencephalography: a configuration study,” Neuroimage 89, 143–151 (2014). [CrossRef] [PubMed]

18. C. Johnson, P. D. D. Schwindt, and M. Weisend, “Magnetoencephalography with a two-color pump-probe, fiber-coupled atomic magnetometer,” Appl. Phys. Lett. 97(24), 243703 (2010). [CrossRef]

19. C. N. Johnson, P. D. D. Schwindt, and M. Weisend, “Multi-sensor magnetoencephalography with atomic magnetometers,” Phys. Med. Biol. 58(17), 6065–6077 (2013). [CrossRef] [PubMed]

20. Z. Li, R. T. Wakai, and T. G. Walker, “Parametric modulation of an atomic magnetometer,” Appl. Phys. Lett. 89(13), 235755 (2006). [CrossRef] [PubMed]

21. V. Diekmann, W. Becker, B. Grözinger, R. Jürgens, and C. Kornhuber, “A comparison of normal and tangential magnetic field component measurements in biomagnetic investigations,” Clin. Phys. Physiol. Meas. 12(Suppl A), 55–59 (1991). [PubMed]

22. J. Nurminen, S. Taulu, J. Nenonen, L. Helle, J. Simola, and A. Ahonen, “Improving MEG performance with additional tangential sensors,” IEEE Trans. Biomed. Eng. 60(9), 2559–2566 (2013). [CrossRef] [PubMed]

23. M. P. Ledbetter, I. M. Savukov, V. M. Acosta, D. Budker, and M. V. Romalis, “Spin-exchange-relaxation-free magnetometry with Cs vapor,” Phys. Rev. A 77(3), 033408 (2008). [CrossRef]

24. A. P. Colombo, T. R. Carter, A. Borna, Y. Y. Jau, C. N. Johnson, A. L. Dagel, and P. D. D. Schwindt, “Four-channel optically pumped atomic magnetometer for magnetoencephalography,” Opt. Express 24(14), 15403–15416 (2016). [CrossRef] [PubMed]

25. M. V. Romalis, “Hybrid optical pumping of optically dense alkali-metal vapor without quenching gas,” Phys. Rev. Lett. 105(24), 243001 (2010). [CrossRef] [PubMed]

26. Y. Ito, H. Ohnishi, K. Kamada, and T. Kobayashi, “Sensitivity Improvement of spin-exchange relaxation free atomic magnetometers by hybrid optical pumping of potassium and rubidium,” IEEE Trans. Magn. 47(10), 3550–3553 (2011). [CrossRef]

Multi-channel spin exchange relaxation free magnetometer towards two-dimensional vector magnetoencephalography

Abstract

1. Introduction

2. Theory of four-channel SERF magnetometer

3. Design of four-channel SERF magnetometer

4. Magnetometer characterization and MEG measurements

5. Conclusions and discussions

Funding

Acknowledgments

References

Cited By

Figures (7)

Equations (5)

Optics Express