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Naota Sekiguchi, Yuta Kainuma, Motofumi Fushimi, [Chikara Shinei](https://orcid.org/0000-0003-4926-8641), [Masashi Miyakawa](https://orcid.org/0000-0002-0838-8156), [Takashi Taniguchi](https://orcid.org/0000-0002-1467-3105), [Tokuyuki Teraji](https://orcid.org/0000-0002-7731-0547), Hiroshi Abe, Shinobu Onoda, Takeshi Ohshima, Mutsuko Hatano, Masaki Sekino, Takayuki Iwasaki

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This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in Naota Sekiguchi, Yuta Kainuma, Motofumi Fushimi, Chikara Shinei, Masashi Miyakawa, Takashi Taniguchi, Tokuyuki Teraji, Hiroshi Abe, Shinobu Onoda, Takeshi Ohshima, Mutsuko Hatano, Masaki Sekino, Takayuki Iwasaki; Performance evaluation of a diamond quantum magnetometer for biomagnetic sensing: A phantom study. Appl. Phys. Lett. 12 May 2025; 126 (19): 194001 and may be found at https://doi.org/10.1063/5.0254828.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Performance evaluation of a diamond quantum magnetometer for biomagnetic sensing: A phantom study](https://mdr.nims.go.jp/datasets/4988838e-f4ec-42ad-ba61-84ebee05d467)

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Performance Evaluation of a Diamond Quantum Magnetometer for Biomagnetic1Sensing: A Phantom Study2Naota Sekiguchi,1 Yuta Kainuma,1 Motofumi Fushimi,2 Chikara Shinei,3, 4 Masashi3Miyakawa,5 Takashi Taniguchi,5 Tokuyuki Teraji,3 Hiroshi Abe,6 Shinobu Onoda,64Takeshi Ohshima,6, 7 Mutsuko Hatano,1 Masaki Sekino,2 and Takayuki Iwasaki151)Department of Electrical and Electronic Engineering, Institute of Science Tokyo,6Meguro, Tokyo 152-8550, Japan72)Department of Bioengineering, The University of Tokyo, Bunkyo, Tokyo 113-8656,8Japan93)Research Center for Electronic and Optical Materials, National10Institute for Materials Science, Tsukuba, Ibaraki 305-0044,11Japan124)Department of Applied Physics, University of Tsukuba, Tsukuba, Ibaraki 305-8571,13Japan145)Research Center for Materials Nanoarchitectonics, National15Institute for Materials Science, Tsukuba, Ibaraki 305-0044,16Japan176)Takasaki Institute for Advanced Quantum Science, National Institutes18for Quantum Science and Technology, Takasaki, Gunma 370-1292,19Japan207)Department of Materials Science, Tohoku University, Sendai, Miyagi 980-8579,21Japan22(*sekiguchi.n.6ddd@m.isct.ac.jp)23(Dated: 25 March 2025)241mailto:sekiguchi.n.6ddd@m.isct.ac.jpWe employ a dry-type phantom to evaluate the performance of a diamond quantum mag-netometer with a high sensitivity of about 6 pT/√Hz from the viewpoint of practical mea-surement in biomagnetic sensing. The dry phantom is supposed to represent an equiv-alent current dipole (ECD) generated by brain activity, emulating an encephalomagneticfield. The spatial resolution of the magnetometer is evaluated to be sufficiently higher thanthe length of the variation in the encephalomagnetic field distribution. The minimum de-tectable ECD moment is evaluated to be 0.2 nA m by averaging about 8000 measurementsfor a standoff distance of 2.4 mm from the ECD. We also discuss the feasibility of detect-ing an ECD in the measurement of an encephalomagnetic field in humans. We concludethat it is feasible to detect an encephalomagnetic field from a shallow cortex area such asthe primary somatosensory cortex.2A diamond quantum magnetometer (DQM) based on nitrogen–vacancy (NV) center ensemble25in diamond is a fascinating tool for biomagnetic sensing due to its favorable characteristics1,2.26DQM can be operated at room temperature with a high sensitivity currently up to pT/√Hz27order3–5, which facilitates decreasing the distance to the measurement object. The short distance28leads to a better spatial resolution of the target activity6 and to a significantly larger signal because29the biomagnetic field typically decays faster than the −1 power of the distance7. The intrinsic30spatial resolution of DQM itself is determined by the optically-excited volume of NV centers and31can be decreased down to the sub-mm scale4,8,9. Additionally, a very wide dynamic range of32DQM10–12 provides the possibility of highly sensitive magnetometry in an ambient field outside a33magnetic shield.34Sensitivity improvement in DQM has been actively studied13 and actual application to biomag-35netic sensing has been reported8,9,14, while few studies have reported on the evaluation of DQM36from the viewpoint of biomagnetic sensing15. Many of those studies reported their field sensitiv-37ity achieved3–5,16–22, but discussions about the stability4 and the minimum detectable field in a38biomagnetic sensing have generally been limited. The stability is of great importance because the39current sensitivity around ∼ pT/√Hz in DQM generally requires a long measurement time in total40for accumulating a small signal. The minimum detectable field in this measurement depends on not41only the measurement bandwidth and the number of accumulation but also characteristics of noise.42Therefore, the evaluation of the minimum detectable field is essential to infer the performance of43a magnetometer in practical applications. Furthermore, the evaluation of the intrinsic spatial reso-44lution is important for a particular application including magnetoencephalography (MEG), where45the estimation of the source generating a biomagnetic field by solving an inverse problem6,7 would46be disturbed if the intrinsic spatial resolution is worse than the length of the variation in the field47distribution to be measured.48Here, we evaluate a DQM with a high sensitivity of about 6 pT/√Hz by using a dry type49of phantom for an encephalomagnetic field in small animals. The dry phantom can emulate an50encephalomagnetic field outside the brain and be considered as a representation of an equiva-51lent current dipole (ECD) generated by brain activity. The spatial distribution of the phantom’s52field was measured and agreed with the theoretical prediction, which indicates the intrinsic spatial53resolution was sufficiently higher than the length of the variation in the encephalomagnetic field54distribution. The minimum detectable field and the minimum detectable ECD in a typical mea-55surement of stimulus-evoked field were investigated. It was found that the ECD moment of about5630.70.2669.5O0zxzyNV centerdiamondddry phantomlenslaser(532 nm)aluminumblockpolycrystalline diamond plate MW guidecable from FG(a) (b)FIG. 1. (a) Experimental setup (not to scale) and (b) dimensions of the designed dry phantom.0.5 nA m and of 0.2 nA m can be detected with the unity signal-to-noise ratio by averaging about571500 and 8000 measurements, respectively, for a standoff distance of 2.4 mm. We also discuss the58feasibility of detecting an ECD in the measurement of an encephalomagnetic field in humans. We59conclude that it is feasible to detect a shallow ECD at, for example, the primary somatosensory60cortex area with our DQM.61A DQM used in this study is illustrated in Fig. 1(a). The DQM setup was almost the same62as that in our previous work4 and inside a magnetically-shielded room. We used a single-crystal63(111) diamond synthesized by a high-pressure and high-temperature method. The initial con-64centration of substitutional nitrogen (N0s ) was controlled by using a titanium additive to a metal65solvent as a nitrogen getter23. NV centers were fabricated by electron beam irradiation and high-66temperature annealing. An electron spin resonance measurement yielded [NV−] = 1.2 ppm and67[N0s ] = 2.3 ppm. The isotope ratio of 13C in the diamond was reduced to about 500 ppm. The68dephasing time, T ∗2 , of the NV− was estimated to be approximately 2 µs4.69An ensemble of NV− in the diamond was excited from a side face by a green laser at 532 nm70with the power of 0.39 W. The excitation laser beam was focused onto the diamond and had the71spot size of about 70 µm in diameter. The laser path length in the diamond was estimated to be721 mm. The intrinsic spatial resolution of this DQM was therefore estimated to be 70 µm and 1 mm73along the y and x direction, respectively. The laser-induced fluorescence from NV centers was74collected with a hemispherical lens and an elliptically-shaped inner wall of an aluminum block and75then detected by a photodiode. The intensity noise in the fluorescence due to the excitation-laser76intensity noise was reduced by a balanced detection technique4. Heat due to the laser illumination774was dissipated by attaching a polycrystalline diamond plate to the diamond.78We used a dry-type phantom that emulates an encephalomagnetic field from the brain of a79small animal. While modeling an actual magnetic field generated from a neuron is quite difficult80due to the complicated currents around the neuron, an analytical formula derived by Sarvas fairly81reproduces the encephalomagnetic field under the assumptions as follows24: a field source, which82is supposed to be an ensemble of intracellular currents at neurons, can be approximated as a single83ECD Q at r0 in the spherically symmetric conductor with its center at the origin of the coordinate.84The Sarvas’ formula computes a magnetic field B at the position r of a sensor as85B(r) =µ04πF2 [FQ×r0 −{(Q×r0) ·r}∇F ] , (1)where86F = |r−r0|(|r−r0||r|+ |r|2 −r0 ·r). (2)The dry phantom that consists of an isosceles-triangle current is known as a source generating a87magnetic field obeying the Sarvas’ formula25 and can emulate an encephalomagnetic field26. Our88dry phantom made on a PCB was placed below the DQM with the distance d from the excited NV89ensemble as shown in Fig. 1(a). The dimensions of the dry phantom [Fig. 1(b)] were determined90by considering the size of the head of a small animal such as a rat. We intended to realize an91isosceles-triangle coil with the base length l of 0.7 mm and the leg length of 9.5 mm, while the92actual legs were connected to parallel wires at 6-mm away from the base. The ECD is supposed93to be generated at the base with the moment Qy along the y direction, Qy = iDPl, where iDP is the94current flowing on the phantom. The dry phantom was mounted on a z stage to vary the distance95d and on a motorized xy stage for the two-dimensional scan. We applied a sinusoidal current at9633.33 Hz to this dry phantom to generate a test field. This frequency is within the primary band of97an encephalomagnetic field27,28.98We performed a continuous-wave optically-detected magnetic resonance by applying a mi-99crowave (MW) current through a MW guide on the other side of the polycrystalline diamond100plate. A bias magnetic field of about 1 mT along the z axis was applied to the NV center ensem-101ble by a permanent ring magnet. Here, the three possible resonances, which are associated with102the hyperfine manifold, between the electron ground states |0〉 ↔ |1〉 were simultaneously driven103by using a three-tone MW field8. The frequency of the three-tone field was modulated to employ104lock-in detection. During the measurement of a magnetic field, we stabilized the MW frequency to105the resonance frequency by monitoring the lock-in signal SLI and applying a slow (2 Hz) PID servo10652 10 100 500Frequency / Hz1101001000NSD / pT Hz1/29 pT Hz 1/2Magnetically sensitivePSN limitfltFIG. 2. Single-sided noise spectral density. The dashed line indicates the noise density floor of 9 pT Hz−1/2at 33.33 Hz.to an MW generator. The strength of the PID servo was optimized not to cause an increase in the107noise around the feedback frequency and to keep the resonance condition for a long period of mea-108surement. A magnetic field Bm faster than the PID servo was given as Bm = SLI/(dSLI/d f × γe),109where dSLI/d f is the zero-crossing slope around the resonance and γe = 28 GHz/T is the gy-110romagnetic ratio. The minimum distance between the excited NV ensemble and a measurement111object was estimated to be 0.8 mm, limited by the thicknesses of the NV center diamond, the heat112spreading plate, and the MW guide.113The single-sided noise spectral density in the DQM was obtained from the 5-s measurement114with the cut-off frequency of 500-Hz at the lock-in detection as shown in Fig. 2. The noise spectral115density determined by photon shot-noise was calculated to be 6.9 pT Hz−1/2 (black solid line). The116measured noise density was found to be almost limited by the photon shot noise. We also found117that no noise peaks other than the power-line noises at 50 Hz and its harmonics were observed118at the encephalomagnetic-field frequency band < 100 Hz27,28. The noise density floor around119the test-field frequency of 33.33 Hz was estimated to be 9 pT Hz−1/2 (dashed line). This noise120density floor corresponds to the field sensitivity of 9 pT Hz−1/2/√2 = 6 pT Hz−1/2 on the widely121used definition of the sensitivity as δB√T 8,19,29, where δB is the minimum detectable field for the122measurement time T .123We mapped the z component of the test field generated by the dry phantom by scanning the x124and y positions of the phantom at five different distances as shown in Fig. 3. The heatmaps show125the amplitude of the sinusoidal test field obtained by least square method for the current peak126amplitude of 7.19 mA. At some positions (the hatched points), the measurement failed because the127610 5 0 5X / mm10505Y / mm(a) d = 2.4(1) mm10 5 0 5X / mm(b)d = 4.4(3) mm10 5 0 5X / mm(c) d = 6.4(3) mm10 5 0 5X / mm(d)d = 8.4(3) mm10 5 0 5X / mm(e) d = 10.4(3) mm20 0 20Magnetic field / nT5 0 5Magnetic field / nT2.5 0.0 2.5Magnetic field / nT2 0 2Magnetic field / nT1 0 1Magnetic field / nTFIG. 3. Mapped magnetic field along the z axis with the different distance d. The measurement at thehatched regions failed due to a large noise from the motorized stage. The center of the phantom’s base wasaligned to the diamond center at (x,y) = (0,0) by the eye.motorized stage generated a magnetic field during the scanning that was larger than the applicable128range of the PID servo for the MW frequency. We observed two peaks with opposite polarity and129the sharper distribution for the closer distance, as expected from the ECD. The distance between130the two peaks approximately followed the distance d. The peak amplitude dependence on d shows131the decay faster than d−1.132The field profiles along x axis at y= 0 were extracted to compare the measured field with the nu-133merically calculated field by the Biot-Savart law and the Sarvas’ formula [Eq. (1)]. Figure 4(a)-(e)134corresponds to the profile for Fig. 3(a)-(e), respectively. We found that the numerically calculated135field (black solid line) by the Biot-Savart law with the current of 7.19 mA along the designed136phantom’s path agreed with the measured data (blue points) at all distances. This suggests that the137intrinsic spatial resolution of about 1 mm along the x direction was sufficient to resolve the peaks138of the phantom’s field at d = 2.4± 0.1 mm, which is comparable to or shorter than the typical139standoff distance from the cortex of a small animal such as a rat30. The discrepancy between the140numerically calculated field and the field given by the Sarvas’s formula (orange dashed line) at141larger distances indicates imperfection in our dry phantom. It was found by numerical calculation142that the discrepancy was attributed to two factors: the absence of the V-shaped wire compared to143the ideal isosceles triangle; and the presence of the slant wires from the parallel wire to pads for144connecting a cable [see Fig. 1(a)].145We investigated the minimum detectable magnetic field Bmd in a typical measurement of146stimulus-evoked encephalomagnetic field. The stimulus-evoked field has a characteristic response147725025(a) d = 2.4(1) mmSarvasNum. calc.Data505(b)d = 4.4(3) mmSarvasNum. calc.Data2.50.02.5(c) d = 6.4(3) mmSarvasNum. calc.Data202(d)d = 8.4(3) mmSarvasNum. calc.Data10 5 0 5X / mm101(e) d = 10.4(3) mmSarvasNum. calc.DataMagnetic field / nTFIG. 4. Magnetic field profile along the x axis at y = 0 for the different distance d. The measured fieldis shown by the blue circles. The black solid and orange dashed lines represent the numerically calculatedprofiles respectively by the Biot-Savart law and by the Sarvas’ formula. The colored bands about the linesindicate the uncertainty caused by the uncertainty in d.to a given stimulus, that is, its transient response to the stimulus is reproduced when the same148stimulus is applied. Typically, measurement of the evoked-field is repeated many times in syn-149chronization with the applied stimulus and averaged. In this evaluation of Bmd, we placed the150phantom at (x,y) = (2.0,0.0) mm with d = 2.4 mm and repeatedly acquired the time trace for a151period of 570 ms. The total number of measurements was 8000 times, corresponds to the measure-152ment time of 76 minutes. The cut-off frequency of the low-pass filter at the lock-in amplifier was153set to 100 Hz, which corresponds to the frequency band of an encephalomagnetic field27,28. The154sinusoidal test current at 33.33 Hz was sent at the time t = 200 ms for 8 periods to the phantom.155The peak amplitude of the current was iDP = 0.69 µA. The corresponding moment of an ECD156was roughly estimated to be Qy = 0.5 nA m. It is supposed that small animals like rats generate15780 100 200 300 400 500Time / ms6420246Magnetic field / pT(a)100101102103Number of averaging100101102Standard deviation / pT2.9 pT1.4 pT(b)FIG. 5. Time domain measurement at (x,y) = (2.0,0.0) mm. (a) Time trace averaged over 8000 measure-ments. The test field was generated at t = 200 ms for 8 periods (between the dashed lines). (b) The standarddeviation at t < 200 ms as a function of the number of averaging.such a small current dipole in the brain cortex by stimulation to, for example, auditory31. A type158of spontaneous brain activity including epilepsy should produce a stronger ECD32,33, but it is159difficult to average the field generated.160The time trace averaged over the 8000 acquisitions is shown in Fig. 5(a). The phantom’s test161field was clearly observed and measured to have the root-mean-square amplitude of 2.9 pT, while162the standard deviation (Bmd) at t < 200 ms was measured to be 1.4 pT. Furthermore, the minimum163detectable ECD moment for the 8000 times averaging and d = 2.4 mm can be estimated to be1640.5 nA m/2.1 ' 0.2 nA m.165We analyzed the decrease in the standard deviation in an averaged trace at t < 200 ms as the166number of averaging was increased, as shown in Fig. 5(b). The 50 Hz power line noise quickly167decreased and was negligible comparing to the white noise at the number of averaging > 10. It168was found that the standard deviation scales as the number of averaging to the power of −1/2,169which was enabled by the good noise performance. Since the standard deviation reached 2.9 pT at170around 1500 times averaging, we consider that our DQM can detect an ECD with Qy ∼ 0.5 nA m171by 15-minute measurement.172910 15 20 25 30 35 40Standoff distance / mm120406080100ECD moment / nA m1.4 pT0.5 pT1 pT2 pT5 pT10 pT101100101Peak field / pTFIG. 6. Simulated peak field as a function of the standoff distance and the ECD moment. The white linesare the contour lines of the peak field. The hatched circle represents the previously reported ECD momentand standoff distance34.Furthermore, we investigated the detectable ECD moment based on the Sarvas’ formula for the173case of encephalomagnetic-field measurement of a human. Here, it was assumed for simplicity174that the ECD was located on the z axis at z0 and oriented along the tangential direction (x-y plane).175Considering the size of a human brain, the distance between the center of the head-model sphere176and the DQM was fixed to 100 mm in this numerical calculation. The z component of the field was177numerically calculated by Eq. (1) and mapped by scanning the DQM position in the x-y plane. We178explored the field maximum Bz,max in the calculated field distribution for a given ECD moment179strength. Figure 6 shows Bz,max as a function of the standoff distance and the ECD moment.180The standoff distance may be limited by the depth of the ECD from the head surface, since the181measurement distance of the DQM can be decreased to about 1 mm and negligible compared182to the depth. The minimum detectable field Bmd = 1.4 pT for the case of 8000 averaging is183indicated by the white solid contour line. The other contours in dashed line are guides for the eye.184It is supposed that a typical moment of an ECD in MEG measurement would be on the order of18510 nA m7. The standoff distance largely varies on the activated region where the ECD is generated.186For example, for somatosensory stimulation, an ECD with the moment of about 15 nA m at the187depth of 15-20 mm (hatched circle) has been reported34. This simulation showed that the peak188field of the encephalomagnetic field that is generated by the previously reported ECD is stronger189than the minimum detectable field of 1.4 pT. Therefore, it is feasible for our DQM to detect an190encephalomagnetic field from such a shallow ECDs in humans.191We performed the measurement of a magnetic field generated by a dry-type phantom that em-192ulated an encephalomagnetic field in a small animal to evaluate a highly sensitive DQM from the19310viewpoint of biomagnetic sensing. The single-sided noise spectral density of the DQM showed the194very low noise floor of 9 pT Hz−1/2, which corresponds to the sensitivity of about 6 pT Hz−1/2.195The spatial distribution of the phantom’s field was measured by scanning the phantom relative to196the DQM. The intrinsic spatial resolution of about 1 mm along the x direction of the DQM enabled197us to observe the clear peaks of the phantom’s field without smearing. For the case of time domain198measurement, the minimum detectable field was found to be 1.4 pT with about 100-Hz bandwidth199by averaging signal 8000 times. It was found that the ECD moment of about 0.2 nA m can be200detected by averaging about 8000 measurements at the standoff distance of 2.4 mm. We also con-201sidered that it is feasible to detect an encephalomagnetic field from a shallow region of a human202brain like the primary somatosensory cortex area by using our DQM. 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