Portable magnetometry for detection of biomagnetism in ambient environments
M. E. Limes, E. L. Foley, T. W. Kornack, S. Caliga, S. McBride, A. Braun, W. Lee, V. G. Lucivero, M. V. Romalis
PPortable magnetometry for detection of biomagnetism in ambient environments
M. E. Limes, E. L. Foley, and T. W. Kornack
Twinleaf LLC, 300 Deer Creek Dr., Plainsboro, New Jersey, 08536, USA
S. Caliga, S. McBride, and A. Braun
SRI International, 201 Washington Rd., Princeton, New Jersey, 08540, USA
W. Lee, V. G. Lucivero, and M. V. Romalis
Department of Physics, Princeton University, Princeton, New Jersey, 08544, USA (Dated: June 2, 2020)We present a method of optical magnetometry with parts-per-billion resolution that is able to de-tect biomagnetic signals generated from the human brain and heart in Earth’s ambient environment.Our magnetically silent sensors measure the total magnetic field by detecting the free-precession fre-quency of highly spin-polarized alkali metal vapor. A first-order gradiometer is formed from twomagnetometers that are separated by a 3 cm baseline. Our gradiometer operates from a laptopconsuming 5 W over a USB port, enabled by state-of-the-art micro-fabricated alkali vapor cells,advanced thermal insulation, custom electronics, and laser packages within the sensor head. Thegradiometer obtains a sensitivity of 16 fT/cm/Hz / outdoors, which we use to detect neuronalelectrical currents and magnetic cardiography signals. Recording of neuronal magnetic fields is oneof a few available methods for non-invasive functional brain imaging that usually requires extensivemagnetic shielding and other infractructure. This work demonstrates the possibility of a dense arrayof portable biomagnetic sensors that are deployable in a variety of natural environments. Magnetoenephalography (MEG) and electroen-cephalography (EEG) serve as important windows intohuman brain function by providing neuronal currentsource imaging with millisecond resolution—much fasterthan other noninvasive techniques, such as functionalmagnetic resonance imaging (fMRI) and positronemission tomography (PET) [1]. MEG also has sev-eral advantages over EEG, including improved sourcelocalization and non-contact measurements [2]. Com-mercially available MEG systems use superconductingquantum interference device (SQUID) magnetometersor gradiometers with sensitivity of 3-10 fT/Hz / .However, existing MEG systems require large, expensivemagnetically shielded rooms or human-scale magneticshields, as well as dewars and infrastructure for cryogenicoperation. Placing subjects in a magnetically shieldedroom restricts the range of behaviors and activitiesthat can potentially be studied. There are a fewdemonstrations of MEG detection using SQUIDs in anunshielded environment [3–5], but such recordings relyon third-order gradiometers that are primarily sensitiveto shallow neuronal current sources. SQUID gradiome-ters are fundamentally limited in the cancellation ofuniform magnetic fields by the fabrication tolerances oftheir pick-up coils.As an alternative to the cyrogenically cooled and bulkySQUID MEG systems, there has been a recent surge inresearch of optically pumped magnetometers for MEGdetection. Most sensitive atomic magnetoemters operateusing alkali vapors near zero field in a spin-exchange re-laxation free (SERF) regime [6]. SERF magnetometershave been used for detection [7–13] and localization [14– 17] of MEG signals, but still require magnetic shieldingor field cancellation because their operation relies on hav-ing a small total magnetic field. In addition, they requireindividual calibration and have inherently limited linear-ity and dynamic range. All measurements with wearableSERF magnetometers have been performed so far in mag-netically shielded rooms [16, 18].We present a method of operating a portable opticalgradiometric sensor that is able to detect MEG signals inEarth’s ambient magnetic field, all while exposed to nat-ural magnetic noise sources. Unlike all previous MEGsensors, our technique uses two total-field magnetome-ters that directly measure the Larmor precession fre-quency of alkali vapor electron spins in the magnetic field.Frequency measurements have a much greater dynamicrange and linearity compared to voltage measurementsassociated with other magnetic field sensors. Further-more, they do not require individual calibration, so wesimply subtract the frequencies recorded from two alkalivapor cells to find a first-order magnetic field gradient. Afirst-order gradiometer in principle allows for detection ofdeeper current sources. We demonstrate the performanceof our sensor by detecting MEG in Earth’s ambient envi-ronment, as well detecting human heartbeats in real timein magnetically noisy environments. Portable biomagnetic sensor.
Our portable gradiome-ter uses two 8 × × . Rb vapor cells separatedby 3 cm. These cells have anodically bonded glass win-dows with internal mirrors for 795 nm light [19]. Thecells are evacuated, baked, and filled with enriched Rband 650 torr N . In operation they are electrically heatedinside of a radiation shield that has low magnetic noise a r X i v : . [ phy s i c s . m e d - ph ] J un b O p t i c a l R o t a t i on (r ad ) π /4- π /4 Gradiometer dB/dx Rb Magnetometers0 0.2 0.4 0.6 0.8 1.0Time (s)0-1000100051.36651.36251.370 Total-field Gradiometer dB/dx = ( B - B )/3 cm S pe c t r a l D en s i t y G r ad . ( f T / c m H z ) d B / d x ( f T / c m ) B ( μ T ) B ( μ T ) S pe c t r a l D en s i t y M ag . ( f T / H z ) π /4- π /4 Single-shot Detection Time (ms) Rb 360 kHz Free Precession, B = 51.366 μ T 51.36251.370 Rb Cell 1 Rb Cell 2 Rb Cell 1 Mag. B c m B a s e li ne Rb Cell 1 Rb Cell 2 PumpPump Rb Cell 1 Rb Cell 2 ProbeProbe Rb Cell 1 Free Precession Rb Cell 2 Free Precession Rb Cell 2 Mag. B ac d B Fit 15.7 fT/cm Hz
FIG. 1.
Magnetic gradiometer operation. a) Two Rb vapor cells separated by a 3 cm baseline are optically pumped with alaser pulse train to near unity polarization. A quantum non-demolition measurement of the Rb polarization along the probeaxis occurs with a weak detuned laser undergoing optical rotation. Rb undergoes free precession about a total field B , leadingto a decaying sine wave signal for each magnetometer cell. The total field B , and quantization axis, is essentially determined bythe local Earth’s field B E . b) A custom frequency counter extracts a Rb free-precession frequency for each cell by detectingoptical-rotation zero crossings in a single-shot detection period of 2.3 ms. The counter then calculates a total field for each cell, B and B , by dividing by the Rb gyromagnetic ratio γ/ π ≈ µ T. c) The single-shot pump and probe measurementis repeated at a rate of 300 Hz. The total fields B and B are streamed to a laptop, and subtracted to obtain the first-ordertotal-field gradient dB/dx . d) We take the spectral densities of the total-field magnetometers and gradiometer time-domaindata to demonstrate the unshielded noise floor and common-mode rejection of the all-optical gradiometer in Earth’s ambientenvironment. The red line is a fit to the gradiometer noise floor giving 15.7 fT/cm √ Hz. [20]. The cells are attached to a glass substrate withlow-thermal-conduction supports and are placed into a6 . × . × . cuvette that is evacuated and sealedto maintain high vacuum, eliminating gas conduction andconvection. This assembly requires 30 mW/cell to heatto the operating temperature of 100 ◦ C, which gives a Rb density of about 5 × atoms/cm . The vac-uum packaging and low-power laser modules allow resultin the outside surface temperature of sensor to be 32 ◦ C,below body temperature.Shown in Fig. 1a, we form a magnetic gradiometer byorienting the two alkali vapor cells such that multi-passlaser beams optically pump and probe Rb in a planetransverse to Earth’s field B E ≈ . µ T. A multi-passpump is used due to geometrical constraints imposed bythe radiation shielding. Thus the high intensity pump pulses travel along the path of the probe beam, whichlimits the dead-zone to one dead axis. The total fieldseach vapor cell experiences, B and B , are dominatedby Earth’s field B E , and the direction of B E essentiallydetermines the quantization axis. Rb atoms are spin-polarized to near unity by an on-resonant (D1) 795 nmpulsed pump diode laser that is able to produce severalW for µ s pulses. The beam is sent through a polarizerand λ/ σ + light for optical pumping.We use a style of optical pumping similar to a conven-tional Bell-Bloom scheme [21, 22], obtaining a high initialatomic spin polarization by pumping synchronously witha pump pulse train at the Larmor precession rate activeonly during the state initialization period. Rb atomicspins are pumped in the transverse plane to near unitypolarization, which causes a suppression of the dominantspin-exchange relaxation mechanism between the F = 2and F = 1 hyperfine manifolds at these sizable magneticfields, and leads to an extension in Rb coherence time T [23, 24]. We then stop pumping and detect the mag-netic field during a Rb free-precession period in orderto eliminate frequency shifts associated with the pumplaser. A 0.1 mW linearly polarized VCSEL probe beamis far-detuned from resonance (D1) and undergoes para-magnetic Faraday rotation in a multi-pass configurationthat yields high signal-to-noise [25–27]. The probes ofeach cell are sent into balanced polarimeters that mea-sure signals corresponding to Rb free precession aboutthe total field, shown in Fig. 1b. After roughly 1 ms ofstate initialization and dead time, our acquisition timeis 2.3 ms per shot. The entirety of the optics and lasersare housed in a 3D-printed case along with a photodiodeamplifier (PDA) board.The electronics for the gradiometer consist of two6 . × . PCB boards each powered by 2.5 W froma USB laptop port (or a 5V battery). One board controlsthe sensor heating and probe laser, while the other con-tains a frequency counter and controls the pump-probesequence. We use 50 kHz for driving the heater, whichwe find to not add any additional noise to the measure-ment. The frequency counter streams two time-stampedfrequencies for each acquisition period to a Labview VIfor real-time analysis and logging. The power consump-tion of the boards is dominated by the microcontrollersand can be reduced with available lower-power versions.We use a shot-to-shot repetition rate of 300 Hz that alsodetermines that data rate of the fields of both magne-tometers streamed to the laptop. Subtracting the twomeasured fields B and B and dividing by the 3 cm base-line we find the total field gradient dB/dx . An exampleof data received by the computer is shown in Fig. 1c.To demonstrate the system’s potential for biomag-netic measurements, we show the spectral densities of thestreamed magnetometer and gradiometer data in Fig. 1dwith a human subject’s head near the sensor, in a naturalenvironment. The largest peaks observed by the sensorare 60 and 120 Hz components coming from power linesroughly 75 m away. Another prominent peak at 25 Hzwe find comes from a nearby New Jersey Transit/AmtrakRail line about 750 m away. Considering the 3 cm base-line, the 60 Hz peak suppression of the gradiometer indi-cates a common mode rejection ratio of at least 2000. Weobtain a similar noise level measured without a subject,and we note that it is difficult to separate real gradi-ent noise from the intrinsic noise floor of the gradiome-ter in an unshielded environment without multiple gra-diometers. Ignoring the 60 Hz peak in a least-squares fit,the gradiometer spectral density between 26 and 115 Hzgives 15.7 fT/cm √ Hz; this implies a magnetometer noisefloor of 33.3 fT/ √ Hz, which outperforms commerciallyavailable scalar atomic sensors operating unshielded inEarth’s field. Within magnetic shielding, the total-field gradiometer achieves 10 fT/cm √ Hz with a field of 50 µ Tapplied.
Ambient MEG.
Operating in a new regime enabled bythe first-order gradiometer, we demonstrate detection ofMEG signals in Earth’s ambient environment, choosingto focus on auditory evoked field responses. Here, 1 kHzaudio stimuli of duration 50 ms is generated with a de-livery time randomized in a 2 . ± B E is aligned to optimize the signal for acurrent dipole expected from auditory evoked responses,with an example of the subject’s orientation with respectto the sensor in Fig. 2b. Auditory evoked field data wasrecorded for four subjects in several 5-20 min trials, usingdifferent sensor positions and orientation.We show in Fig. 2c MEG data that is filtered and av-eraged over 462 epochs for a subject in a particular trial.For MEG data analysis we apply a 0.5-50 Hz bandpassfilter, along with 25, 60, and 120 Hz notch filters, andobserve P40m, N100m, and P150m evoked fields (therelatively fast N100m response is consistent with con-tralateral stimulation for a relatively short interstimulusinterval [28, 29]). Auditory evoked signals were detectedin all four subjects and the sign of the detected dB/dx peaks is consistent with the orientation of the currentdipole observed in previous studies of auditory evokedfields. The orientation of the sensor and head with re-spect to the Earth’s field is critical to MEG operation, astotal-field magnetometers are only sensitive to the com-ponent of the biomagnetic field parallel to the bias field.Field changes in the transverse plane B T appear only insecond order B / B E and are negligible. Thus when con-sidering arrays of this type of total-field sensor, additionalsignal processing will be required for making constraintson source localization methods.We briefly mention that another important medical ap-plication of sensitive magnetometers is magnetocardiog-raphy (MCG). Magnetic fields generated by the heart arestronger, but their detection in magnetically unshielded,noisy environments typical of a research laboratory orhosptial remains a challenge. A number of optically- T o t a l F i e l d G r ad i en t d B / d x ( f T / c m ) Time (s)100500-50-100 0.0-0.2 0.2 0.4 0.6 0.8 1.0
Stimulus N100mP40m P150m B E Controller/Counter (CC) Sync (S)Audio (A)Probe &Pump LasersPDA Rb Cell 1 & 2 (CC)(S)(A) a
462 Auditory Epoch Averages b c
Laptop
FIG. 2.
Auditory evoked fields detected unshielded in Earth’s field with a portable first-order gradiometer. a) The vacuum-packaged Rb vapor cells are optically pumped and probed by diode lasers integrated into the gradiometer head. Opticalrotation of the probe laser is detected with a photodiode amplifier assembly (PDA). The gradiometer is controlled by compactelectronics, including a custom counter streams the total fields B and B and gradient dB/dx to the laptop. The two Rbvapor cells are placed near a subject’s auditory cortex to measure the total-field gradient dB/dx with a 3 cm baseline. b) Apicture of the in-the-field MEG recording apparatus with a subject. c) For a given subject, data is recorded for roughly 20 minwhile time-randomized 1 kHz auditory stimuli are applied to the left ear of the subject. A filtered average of 462 epochs isshown for dB/dx gradient data taken above a subject’s right ear. Bands indicate the standard error of the mean. The auditoryevoked fields observed include the prominent N100m peak along with indication of P40m and P150m responses. pumped sensors are being developed for this application[30–33]. In Fig. 3 we show real-time in-the-field MCGsignals that are taken by simply walking up and present-ing the chest to the sensor, along with a 10 s averaging ofhuman heartbeats. Even in its current form our sensor isnot far from providing a practical MCG device that al-lows quick, electrode-free heart diagnostics for triage inambient environments.With this work, we have presented a method of oper-ating optical magnetometers in Earth’s natural environ-ment with unprecedented performance. We showed thepotential of this technique for biomagnetic measurementsthrough proof-of-principle detections of unshielded MEGand MCG signals using a portable first-order gradiome-ter. Wearable atomic sensors that do not require shield-ing will enable a greater variety of MEG research studies,as well as reduce their cost. They can eventually replaceEEG sensors currently being used in a variety of open-source EEG systems [34]. By using an all-optical designwe have eliminated cross-talk between sensors, which is adeficiency of sensors that require RF or microwave fields. This important feature allows for these types of sensorsto be formed into a scalable array, which is necessary forproper source localization, as well as to suppress mag-netic gradient noise from power lines and other nearbysources, and enables practical operation in a typical lab-oratory or hospital environment. We also note that thesensitivity of the gradiometer can be further improved[26] to compete with SQUID sensitivities, while retainingthe ability to measure closer to the biomagnetic sourcethan SQUID systems. We believe the development ofthese types of portable sensors for ambulatory subjects,that can be used in a cost-effective scalable array, will im-pact the scope of many MEG and MCG research studies,as well as the host of various other applications that canbenefit from a commercially available sensor for total-field magnetometry in Earth’s natural environment.Sensor development was funded by the DefenseAdvanced Research Projects Agency (DARPA) Mi-crosystems Technology Office (MTO) under ContractNo. 140D6318C0020. The views, opinions and/orfindings expressed are those of the authors and −
505 Time (s)0 1 2 3 4 5 6 7 8 9 10Real-time Filt. Grad.Filt. Grad. 10 second average bc QR S T
Time (s)-0.2 0 0.2 0.4 d B / d x G r ad . ( p T / c m ) d B / d x G r ad . ( p T / c m ) a FIG. 3.
Field-deployable magnetocardiography. a) A pictureof a next-generation gradiometer that is able to detect hu-man heartbeats in magnetically noisy environments. b) Asa subject presents their chest to the sensor, a real-time fil-ter (bandpass 0.1-50 Hz notch at 60/120 Hz) is applied to thetotal field gradient dB/dx to demonstrate heartbeat measure-ments. c) The result of averaging data for 10 s, triggered onthe R peak. should not be interpreted as representing the officialviews or policies of the Department of Defense orthe U.S. Government. Approved for Public Release,Distribution Unlimited. Proof-of-principle demon-strations of the sensor detecting biomagnetic signalswas supported by Princeton University and the FetzerFranklin Fund of the John E. Fetzer Memorial Trust. [1] M. H¨am¨al¨ainen, R. Hari, R. J. Ilmoniemi, J. Knuutila,and O. V. Lounasmaa, Rev. Mod. Phys. , 413 (1993).[2] S. Baillet, Nature Neuroscience , 327 EP (2017), re-view Article.[3] J. Vrba, B. Taylor, T. Cheung, A. A. Fife, G. Haid,P. R. Kubik, S. Lee, J. McCubbin, and M. B. Burbank,IEEE Transactions on Applied Superconductivity , 2118(1995).[4] Y. Okada, K. Pratt, C. Atwood, A. Mascarenas,R. Reineman, J. Nurminen, and D. Paulson, Re-view of Scientific Instruments , 024301 (2006),https://doi.org/10.1063/1.2168672.[5] Y. Seki, A. Kandori, K. Ogata, T. Miyashita, Y. Ku-magai, M. Ohnuma, K. Konaka, and H. Naritomi,Review of Scientific Instruments , 096103 (2010),https://doi.org/10.1063/1.3482154.[6] I. K. Kominis, T. W. Kornack, J. C. Allred, and M. V.Romalis, Nature , 596 (2003).[7] H. Xia, A. Ben-Amar Baranga, D. Hoffman, and M. V.Romalis, Applied Physics Letters , 211104 (2006),https://doi.org/10.1063/1.2392722.[8] C. Johnson, P. D. D. Schwindt, and M. Weisend,Applied Physics Letters , 243703 (2010),https://doi.org/10.1063/1.3522648.[9] T. H. Sander, J. Preusser, R. Mhaskar, J. Kitching,L. Trahms, and S. Knappe, Biomed. Opt. Express ,981 (2012).[10] C. N. Johnson, P. D. D. Schwindt, and M. Weisend,Physics in Medicine and Biology , 6065 (2013).[11] V. K. Shah and R. T. Wakai, Physics in Medicine &Biology , 8153 (2013).[12] O. Alem, A. M. Benison, D. S. Barth, J. Kitching, andS. Knappe, Journal of Neuroscience , 094304 (2017), https://doi.org/10.1063/1.5001730.[14] K. Kim, S. Begus, H. Xia, S.-K. Lee, V. Jazbinsek,Z. Trontelj, and M. V. Romalis, NeuroImage , 143(2014).[15] 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,NeuroImage , 404 (2017).[16] E. Boto, N. Holmes, J. Leggett, G. Roberts, V. Shah,S. S. Meyer, L. D. Mu˜noz, K. J. Mullinger, T. M. Tier-ney, S. Bestmann, G. R. Barnes, R. Bowtell, and M. J.Brookes, Nature , 657 EP (2018).[17] A. Borna, T. R. Carter, A. P. Colombo, Y.-Y. Jau,J. McKay, M. Weisend, S. Taulu, J. M. Stephen, andP. D. D. Schwindt, PLOS ONE , 1 (2020).[18] R. M. Hill, E. Boto, N. Holmes, C. Hartley, Z. A. Seedat,J. Leggett, G. Roberts, V. Shah, T. M. Tierney, M. W.Woolrich, C. J. Stagg, G. R. Barnes, R. R. Bowtell,R. Slater, and M. J. Brookes, Nature Communications , 4785 (2019).[19] N. Dural and M. V. Romalis, “Anodically bonded cellswith optical elements,” (2017), uS Patent 10345548.[20] H. B. Dang, A. C. Maloof, and M. V. Ro-malis, Applied Physics Letters , 151110 (2010),https://doi.org/10.1063/1.3491215. [21] W. E. Bell and A. L. Bloom, Physical Review Letters ,280 (1961).[22] V. Gerginov, S. Krzyzewski, and S. Knappe, J. Opt. Soc.Am. B , 1429 (2017).[23] M. V. Romalis, H. Dong, and A. Baranga, “Us20180356476a, pulsed scalar atomic magneometer,”(2018).[24] V. G. Lucivero and M. V. Romalis, In preparation.[25] S. Li, P. Vachaspati, D. Sheng, N. Dural, and M. V.Romalis, Phys. Rev. A , 061403 (2011).[26] D. Sheng, S. Li, N. Dural, and M. V. Romalis, Phys.Rev. Lett. , 160802 (2013).[27] W. Lee and M. V. Romalis, In preparation.[28] J. P. M¨akel¨a, A. Ahonen, M. H¨am¨al¨ainen, R. Hari, R. Ll-moniemi, M. Kajola, J. Knuutila, O. V. Lounasmaa,L. McEvoy, R. Salmelin, O. Salonen, M. Sams, J. Simola, C. Tesche, and J.-P. Vasama, Human Brain Mapping ,48 (1993).[29] A. Gutschalk, “Meg auditory research,” in Magnetoen-cephalography: From Signals to Dynamic Cortical Net-works , edited by S. Supek and C. J. Aine (Springer In-ternational Publishing, Cham, 2019) pp. 907–941.[30] G. Bison, R. Wynands, and A. Weis, Opt. Express ,904 (2003).[31] R. Wyllie, M. Kauer, R. T. Wakai, and T. G. Walker,Opt. Lett. , 2247 (2012).[32] O. Alem, T. H. Sander, R. Mhaskar, J. LeBlanc,H. Eswaran, U. Steinhoff, Y. Okada, J. Kitching,L. Trahms, and S. Knappe, Physics in Medicine & Biol-ogy , 4797 (2015).[33] M. Bai, Y. Huang, G. Zhang, W. Zheng, Q. Lin, andZ. Hu, Optics Express , 29534 (2019).[34] OpenBCI, https://openbci.com//. SUPPLEMENTARY INFORMATION
360 kHz sine wave at 300 HzFit 5.5 fT/cm Hz S pe c t r a l D en s i t y G r ad . f T / c m H z FIG. 1. The custom frequency counter is set up under the operating conditions used in the main text, triggered on 300 Hzand acquisition window of 2.3 ms. 360 kHz sine waves from a function generator are sent into the two channels. A fit to thewhite noise gives our reported portable detection noise floor of 5.5 fT/cm √ Hz. ‘‘ GradiometerFit 9.93 fT/cm Hz S pe c t r a l D en s i t y d B z / d z f T / c m H z FIG. 2. Spectral density of gradiometer in magnetic shielding (Twinleaf MS-2), taken with 49.3 µ T bias field. T o t a l f i e l d g r ad i en t d B z / d x ( p T / c m ) Randomized Auditory Stimuli
FIG. 3. The raw dB z /dx gradient data shown averaged in Fig. 3 of the main text. T o t a l F i e l d G r a d i e n t d B z / d x , ( f T / c m )
462 Avg. 0.2 0.0 0.2 0.4 0.6 0.8 1.0Time (s)10050050100 T o t a l F i e l d G r a d i e n t d B z / d x , ( f T / c m )
502 Avg.
A B
FIG. 4. Data for subject with (A) and without (B) auditory stimuli. T o t a l F i e l d G r a d i e n t d B z / d x , ( f T / c m ) Time (s)
10 avg. 20 avg.40 avg. 80 avg.
FIG. 5. Taking averages (10, 20, 40, and 80) of the data taken shown in Fig. 3 of the main text. T o t a l F i e l d G r a d i e n t d B z / d x , ( f T / c m ) Gen-2, 462 Avg. A T o t a l F i e l d G r a d i e n t d B z / d x , ( f T / c m )
460 Avg. 0.2 0.0 0.2 0.4 0.6 0.8 1.0Time (s)10050050100 T o t a l F i e l d G r a d i e n t d B z / d x , ( f T / c m )
360 Avg.0.2 0.0 0.2 0.4 0.6 0.8 1.0Time (s)10050050100 T o t a l F i e l d G r a d i e n t d B z / d x , ( f T / c m )
400 Avg.