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Page 1: Optimization of Flux Transformer for Optically Pumped Atomic Magnetometer in Ultra-Low Field MRI Systems

3074 IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011

Optimization of Flux Transformer for Optically Pumped AtomicMagnetometer in Ultra-Low Field MRI Systems

T. Oida, Y. Kawamura, and T. Kobayashi

Department of Electrical Engineering, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan

An ultra-low field (ULF) magnetic resonance imaging (MRI) system with an optically pumped atomic magnetometer (AM) has re-cently been proposed. Because AM does not require cryogenic cooling, it can easily measure extremely small magnetic fields. However, tomeasure magnetic resonance (MR) signals with high sensitivity in ULF-MRI systems with AMs, the resonant frequencies of the sampleand alkali metal in the AM must be same. To satisfy this requirement, a flux transformer (FT) has been proposed to detect MR sig-nals. In this study, the simulations in the output coil of the FT and pseudo-MR signal measurements were performed to improve thesignal-to-noise ratio (SNR) in the remote detection of MR signals by using AM with FT. The simulations and measurement results indi-cate that, to improve the SNR of the detector, the output coil of the FT should be placed in the vicinity of a glass cell, and the number ofturns and radius of the output coil need to be optimized.

Index Terms—Flux transformer (FT), nuclear magnetic resonance (NMR), optically pumped atomic magnetometer, ultra-low field(ULF) magnetic resonance imaging (MRI).

I. INTRODUCTION

M AGNETIC RESONANCE IMAGING (MRI) is mostuseful diagnostic imaging system, which enables the

visualization of the anatomy and function of the human body.In general, a high magnetic field is utilized to achieve a highsignal-to-noise ratio (SNR) in MRI measurements. However,the conventional high-magnetic-field scanner has limitationssuch as high cost, a large chassis, and risk for patients withmetal implants.To measure magnetic resonance (MR) signals without these

limitations, ultra-low field (ULF) MRI systems that rely on su-perconducting quantum interference devices (SQUIDs) have at-tracted attention in recent years [1]. More recently, a ULF-MRIsystem with an optically pumped atomic magnetometer (AM)has been proposed by Savukov et al. [2]. In this system, remotedetection of MR signals by using an AMwith a flux transformer(FT) was proposed.When magnetic signals are measured by AM, the magneto-

optical effect of optically pumped alkali metal vapor is utilizedfor measuring magnetic fields with high sensitivity [3], [4]. Ingeneral, AM consists of alkali metal vapor in a glass cell withpump and probe lasers, as shown in Fig. 1; it has magnetic sen-sitivity in the region where the pump and probe lasers cross eachother. However, because the gyromagnetic ratio of alkali metalis different from that of protons, which are used most frequentlyin MRI measurements, the sensitivity for measuring MR signalsis reduced when the same magnetic field is applied to a sampleas well as the magnetometer.The flux transformer consists of two coils and a capacitor that

is used to tune the resonant frequency of the FT circuit to thefrequency of the MR signals (see Fig. 2). The two coils in theFT are used to input and output signals, respectively.

Manuscript received February 21, 2011; revised April 23, 2011; acceptedMay 09, 2011. Date of current version September 23, 2011. Corresponding au-thor: T. Oida (e-mail: [email protected]).Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TMAG.2011.2156765

Fig. 1. Schematic of optically pumped AM with FT.

Fig. 2. Flux transformer used in the experiments.

In this study, simulations and pseudo-MR signal measure-ments were performed to optimize the parameters of the FT,e.g., number of turns and radius of the output coil, in order toimprove SNR.

0018-9464/$26.00 © 2011 IEEE

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OIDA et al.: OPTIMIZATION OF FLUX TRANSFORMER FOR OPTICALLY PUMPED ATOMIC MAGNETOMETER 3075

II. MATERIALS AND METHODS

In the simulations, MR signals with 1 kHz frequency weredetected by an AM with an FT. When the MR signals were de-tected by the FT input coil, voltage signals were generated atboth ends of the input coil causing a current to flow in the outputcoil. Then, the magnetic fields produced by the output coil of theFT can be calculated by the Biot–Savart law as follows:

(1)

where is the magnetic field strength per unit voltage in themagnetic sensitivity region of the AM, generated by the FToutput coil. In this study, because the output coil is assumed tobe circular with parameters such as radius , number of turns

, and distance from the center of a glass cell can becalculated from , and the resistance value of the cir-cuit . Here is the sum of the resistance of the input coil,output coil, and cable connecting both coils. The resistance ofthe output coil is proportional to and .On the other hand, the Johnson–Nyquist noise in V Hz,

generated by the thermal agitation of the charge carriers insidean FT circuit, is calculated according to the equation

(2)

where is Boltzmann’s constant and is the circuit’s absolutetemperature [5], [6]. Here, the noise level in T Hz ofMR signal detector using AM and FT is expressed as

(3)

where is the noise level of the AM.Therefore, the SNRs in the MR signal detector using AM and

FT are calculated as follows:

(4)

In this study, SNRs were simulated and measured usingpseudo-MR signals to examine the influence of the output-coilparameters on the SNR. In these simulations, SNR simulationswere performed with varying radii , number of turnsof output coil in FT, and distances of output coil from the centerof a glass cell . It is assumed that a circular coil having240 turns and a radius of 45 mm was used, and inter-linkagemagnetic fluxes of Wb passed through the inputcoil. The minimum distance of output coil from the center ofthe glass cell was 30 mm, which was constrained by the heat-in-sulating box. The noise level of the AM was 51.9 fT Hz,the electrical resistivity of the copper wire used in the FT was

m, and the wire was 0.5 mm in diameter. Inaddition, the temperature of the FT circuit was 300 K.In pseudo-MR signal measurements, pseudo-MR signals with

Wb magnetic fluxes and 1 kHz frequency weredetected by a solenoidal input coil having 240 turns and a 45mmradius. These magnetic fluxes were about 5000 times greaterthan those in simulations, which were selected to reduce theeffect of the environmental magnetic noise. On the other hand,seven output coils were used to evaluate the SNRs of the MR

TABLE IPARAMETERS FOR FT OUTPUT COIL

Fig. 3. SNR map obtained by simulations as functions of both number of turnsand radius of output coil.

signal detector using AM and FT, whose parameters are shownin Table I. The output coil was placed on the heat-insulatingbox, and its position was more than 65 mm from the center ofthe glass cell. In addition, capacitors were tuned to the resonantcircuit with a resonant frequency of 1 kHz in all FTs.

III. RESULTS

The SNR map obtained by the simulations as functions ofboth number of turns and radius of the output coil is shown inFig. 3. In these simulations, the distance of the output coil fromthe center of the glass cell was fixed to 30 mm. This simulationresult indicates that the SNR of the MR signal detector with AMand FT is improved by selecting optimum radius and number ofturns of the output coil in FT. However, with greater number ofturns than the optimum, there would be no significant change inthe SNR.ThemaximumSNRs plotted against the distance of the output

coil from the center of the glass cell are shown in Fig. 4. Thissimulation result indicates that the SNR with the detector isimproved by reducing the distance of the output coil from thecenter of the glass cell.The SNRs in measuring pseudo-MR signals (dots) and the

simulated SNRs (lines) as a function of the number of turns isshown in Fig. 5. In these measurements, output coils of Nos. 1,2, 3, and 4, whose radius is 30 mm, were utilized and placed 65mm from the center of the glass cell. Fig. 5 shows that the SNRwith the detector is improved by increasing the number of turns

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3076 IEEE TRANSACTIONS ON MAGNETICS, VOL. 47, NO. 10, OCTOBER 2011

Fig. 4. Maximum SNR as a function of distance of output coil from the centerof a glass cell.

Fig. 5. Result of SNRs in measuring pseudo-MR signals as a function of thenumber of turns of output coil.

of the output coil. However, the improvement rate of the SNRdecreases with increase in the number of turns.Fig. 6 shows the SNRs when measuring pseudo-MR signals

(dots) with output coils of Nos. 1, 5, 6, and 7 and the simulatedSNRs (lines) as a function of radius. In these measurements,the number of turns of the output coil was fixed at 40, and thecoil was placed 65 mm from the center of the glass cell. Fromthe results of the measurement, it was determined that the SNRwith the detector is improved by increasing the radius of theoutput coil. However, because the output coil was farther fromthe center of the glass cell in the measurements than in the simu-lations mentioned above, the SNR did not achieve the maximumvalue even though the output coil was 62.5 mm in radius.The SNRs in measuring the pseudo-MR signals with dis-

tances of 65, 75, 85, 95, and 105 mm from the center of theglass cell (dots) and the simulated SNRs (lines) as a function ofdistance is shown in Fig. 7. In these measurements, the outputcoil of No. 1 was utilized. Fig. 7 shows that the SNR with thedetector is improved by reducing the distance of the output coil

Fig. 6. Result of SNRs in measuring pseudo-MR signals as a function of theradius of output coil.

Fig. 7. Result of SNRs in measuring pseudo-MR signals as a function of dis-tance of output coil from the center of a glass cell.

from the center of the glass cell, which is similar to the simula-tion results.By comparing the SNRs in simulations represented as lines in

Figs. 5–7 and those in Figs. 3 and 4, it was found that the SNRsin Figs. 5–7 were three orders of magnitude greater than those inFigs. 3 and 4. These differences were caused by the differenceof interlinkage magnetic fluxes used in the simulations.

IV. DISCUSSION

In this study, to improve the SNR of an MR signal detectorusing AM with FT, simulations and pseudo-MR signal mea-surements with varying output coil parameters were performed.From the simulation results and pseudo-MR signal measure-ments, it was determined that the output coil of FT using AMwith FT, simulations and pseudo-MR signal can be placed inthe vicinity of the glass cell to improve the SNR of the detector.However, the output-coil position is constrained by the path ofthe pump and probe laser beams, and the heat-insulating box of

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OIDA et al.: OPTIMIZATION OF FLUX TRANSFORMER FOR OPTICALLY PUMPED ATOMIC MAGNETOMETER 3077

the AM. This constraint of alignment can be overcome by im-proving the modularization [7] and the downsizing of the AM.It is expected that this will contribute to the improvement of theSNR of the detector.On the other hand, the simulation results shown in Fig. 4 indi-

cate that the number of turns and radius of the output coil need tobe optimized to improve the SNR of the detector. This optimiza-tion corresponds to that of in (3). In addition, from the resultsof the pseudo-MR signal measurements shown in Figs. 5 and 6,it is determined that the SNR of the detector can be improved byselecting the optimum number of turns and radius of the outputcoil. However, the optimum number of turns and radius werenot confirmed clearly in the pseudo-MR signal measurements.Here, the noise level expressed as magnetic field strength in

the magnetic sensitivity region of AM, that is, , varies withthe optimization in the number of turns and radius of the outputcoil. From the relationship between this noise level and the noiselevel of AM, the SNR of the detector is expressed as follows:

(5)

In the case of , the SNR of the detector is lowerthan that of the FT. Therefore, the SNR of the detector is limitedby that of the FT, that is, . From the discussion mentionedabove, to improve the SNR of the detector, it is important toutilize both AM and FT with lower noise level. Here a low-re-sistance wire, which has low electrical resistivity, reduces theresistance in (2), so that the noise level of FT decreases aswell. In addition, because reduction in the number of turns andradius of output coil shorten the wire length of FT, where theresistance in (2) is proportional to the wire length of FT, thenoise level of FT can be decreased by their reductions. There-fore, to make an FT with a lower noise level, a low-resistancewire and/or reduction in the number of turns and radius of outputcoil are required.In Figs. 5–7, the errors of the SNR between simulations and

pseudo-MR signal measurements are approximately 50% atmaximum. In the simulations, to simplify the calculation ofthe magnetic field using the Biot-Savart law, the width andthickness of coils were not assumed. However, actual outputcoils have width and thickness as shown in Table I. In addition,the resistances of FT circuits shown in Table I are higher thanthose assumed in the simulations. It is considered that these arethe major reasons for the SNR errors between the simulationsand pseudo-MR signal measurements.

V. CONCLUSION

In this study, simulations with the output coil of the FT, andpseudo-MR signal measurements were performed to improvethe SNR in the remote detection of MR signals using AM withFT. The simulations and measurement results indicate that theoutput coil of the FT should be placed in the vicinity of a glasscell to improve the SNR of the detector. In addition, it is im-portant to utilize a low-resistance wire for FT and reduce thenumber of turns and radius of the output coil. On the other hand,the simulation result indicates that the number of turns and ra-dius of the output coil need to be optimized to improve the SNRof the detector.In this study, a single circular output coil was used in the

simulations and pseudo-MR signal measurements. This coil wasselected on the basis of the constraints of the pump and probelaser beams and the heat-insulating box. However, progress inmodularization and downsizing of the AM will allow the use ofa Helmholtz coil and a solenoid coil as the output coil. In thefuture, the coil type mentioned above and the coil shape shouldalso be investigated.

ACKNOWLEDGMENT

This work was supported in part by a Grant-in-Aid for chal-lenging exploratory research (22650116) from the Ministry ofEducation, Culture, Sports, Science, and Technology (MEXT),Japan.

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