Experimental estimation of the accuracy of modern scalar quantum magnetometers in measurements of the Earth's magnetic field

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Physics of the Earth and Planetary Interiors 166 (2008) 147–152

Experimental estimation of the accuracy of modern scalar quantum magnetometers in measurements of the Earth’s magnetic field V.Ya. Shifrin a,∗ , V.N. Khorev a , V.N. Kalabin a , P.G. Park b a

b

D.I. Mendeleyev Institute for Metrology (VNIIM), VNIIM, 19, Moskovsky pr., St. Petersburg 198005, Russia Korean Research Institute of Standards and Science (KRISS), P.O. Box 102, Yuseong, Daejeon 305-600, South Korea Received 2 July 2007; received in revised form 7 December 2007; accepted 30 December 2007

Abstract The results of calibration of proton, cesium, potassium and helium–cesium scalar magnetometers in the range 20–100 ␮T are discussed. The calibration made it possible to estimate errors and to apply corrections to reduce the uncertainty of measurements. Experimental data have been obtained using a standard calibration system designed in the Russian Mendeleyev Metrology Institute (VNIIM). The systematic uncertainty in the reproduction of the magnetic flux density is estimated to be 1.8 × 10−7 , the random standard deviation being 0.001 nT. The experimental data can be used for the proper selection of measuring instruments and prediction of their uncertainty when studying the Earth’s magnetic field. © 2008 Elsevier B.V. All rights reserved. Keywords: Magnetometer; Magnetic resonance; Measurement; Calibration; Uncertainty

1. Introduction Quantum proton and atom magnetic resonance magnetometers that have been improved for many decades are essential instruments in investigations of the Earth’s magnetic field. However, in spite of the vast experience gained, no reliable data on accuracies in the realization of SI units by these instruments have been obtained to date. At the same time, there is a need for global scientific geomagnetic research, for which it is necessary to reduce the systematic component of the uncertainty to values below 0.1–0.2 nT in scalar magnetic flux density measurements carried out at geomagnetic observatories, while the random standard deviation (RSTD) should be reduced to a level of 0.001–0.01 nT. The latter is especially important for the purpose of exploration of low-magnetized mineral resources. Traditional comparisons of different magnetic resonance magnetometers usually show a disagreement of 1–2 nT (1 × 10−4 to 1 × 10−5 ), resulting in errors that are much worse

∗

Corresponding author. Fax: +7 812 2517602. E-mail addresses: [email protected] (V.Ya. Shifrin), [email protected] (P.G. Park). 0031-9201/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.pepi.2007.12.003

than the uncertainty of the conversion coefficient. Such rigid requirements for reducing systematic components of the uncertainty to relative values of about 1 × 10−6 to 1 × 10−5 and to values of about 1 × 10−7 to 1 × 10−8 for its random components in the geomagnetic range of 20–100 ␮T, to necessitate closer attention to the use of calibration methods and standards than actually occurs in current practice. As is well known, a factor that restricts the accuracy in measurements of magnetic field parameters is the uncertainty of the shielded proton gyromagnetic ratio value γP in terms of SI. The latest recommendation of the International Committee on Data for Science and Technology (CODATA) based on the last adjustment of fundamental physical constants was published in 2005 (Mohr and Taylor, 2005) and specifies the value γP = 2.67515333 × 108 c−1 T−1 with the uncertainty of 8.6 × 10−8 . Gyromagnetic ratios for other microparticles that are also used in quantum magnetometers (e.g., cesium, helium) are determined theoretically and experimentally through γP . The prevailing practice among geophysicists – the consumers of quantum geomagnetometers – is to estimate instruments’ serviceability using comparison devices having equivalent accuracy in the limited range (or points) of measurements of the Earth’s background magnetic field and its variations. Metrolog-

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ical characteristics obtained in this way are extended to a wide range of measurements, generally from 20 to 100 ␮T. Proton magnetometers have the reputation of being “absolute” instruments based on the proton gyromagnetic ratio γP as a conversion factor from scalar magnetic flux density to an AC voltage frequency. The specific factors forming a signal from magnetic resonance in different coverages, affect the stability and uncertainty of measurement results and also demand an adequate metrological approach for maintenance of the required accuracy. In practice, the errors of real instruments can exceed by hundreds of times the uncertainty of γP determination and the RSTD of measurements, because the methods used have some specific limitations affecting the systematic part of the uncertainty. With proton magnetometers, these limitations are associated with the phase shifts caused by NMR signal damping, the magnetization of the windings and other parts of the sensor, and the low signal-to-noise ratio affecting the frequency of the feedback system. This paper describes results of metrological investigations of serial proton and cesium magnetometers using the improved standard calibration system (Shifrin et al., 2000) developed in Russia at the Mendeleyev Metrology Institute (VNIIM) on the basis of an experimental measuring system for determination of the proton gyromagnetic ratio in water at low fields (Shifrin et al., 1998). 2. Standard calibration system for geomagnetometers In comparison with reference Shifrin et al. (2000), since the last publication, the accuracy of the standard has been improved and additional systems have been developed. As a result, it has become possible to expand the range of reproduced magnetic flux densities of lower fields down to 100 nT and of stronger fields up to 1 mT with the same random uncertainty as in the base range of 20–100 ␮T. The scope of application of this system has extended not only to the calibration of instruments for outer space but also to precision current-carrying highly uniform field coil systems used in fundamental and applied research. The measuring system is based on a new type of large-volume three-component coil system (Shifrin et al., 2000) with active control of the coil currents by external and internal optically pumped atomic magnetic resonance converters. The apparatus can operate in two modes depending on the reproduced parameters. In the first mode, the field control is realized by a converter installed inside the main three-component coil system (one-volume system). In the second mode, separate outside compensation of the three-component Earth magnetic field variation is realized through the control of the main system using converters placed inside three auxiliary coil systems (three-volume system). A one-volume magnetic field stabilizer ensures high stability of the scalar magnetic field by three factors: the use of the potassium narrow-line magnetic-resonance converter with enhanced sensitivity and stability; reduction of the distance between the sensor of the magnetic field controller and the measuring mag-

netometer, and expansion of the uniform working volume of the new design of the three-component coil. For calibration of different kinds of optical pumping magnetometers in this system, in addition to potassium, also rubidium and cesium magnetic-resonance converters are used for field stabilization. A field stabilizer sensor that is different from the sensor of the optical pumping magnetometer being calibrated is always used, to exclude any interference between them. The new three-component coil system is cube shaped; it is based on a four-section coil with square windings and square cross-section. Each of the two perpendicular components of the coil has two coaxial symmetrical groups of sections placed in parallel planes attached to opposite facets of the base coil. Therefore, the axial entrance is completely free for access to the three-component system. The coils have cube face dimensions of about 2 m, making it possible to place several magnetic field sensors separated by 0.3–0.4 m in its working volume. A multidipole complementary coil system fixed on the base three-component coil system allows reproduction and control of the magnetic field with a non-uniformity below 0.1 nT at the edges of a spherical working volume 100 mm in diameter in the range 0.1–110 ␮T. A special AC field control system compensates for the variable component from the power lines (50 Hz nominal). It consists of an induction AC magnetic field converter that controls the amplitude and phase of the AC current source loaded on a separate winding of the main three-component coil system. The one-volume magnetic field stabilizer provides a random standard uncertainty (RSTD) of 0.001 nT for 1 s intervals, and the long-term drift is less than 0.01 nT for at least 10 h. The systematic uncertainty of the system depends mainly on the errors in the standard magnetometer and the uniformity of the main coil at the magnetometer sensor location. The standard magnetometer is based on the method of He-4 metastable 23 S1 spin polarization with high-frequency heating of plasma by spin-exchange collisions with optically pumped Cs-133 atoms (Blinov et al., 1982; Blinov and Kuleshov, 1987). The basic metrological examination of this method was made in (Blinov et al., 1986; Shifrin et al., 1998). These authors reported that the He-4 magnetic resonance frequency is (at the limit of the random uncertainty level) independent of all significant physical factors forming the magnetic resonance signal: the kind of polarizing alkaline metal (Cs, Rb, K); He-4 pressure; temperature; pulse discharge intensity; polarizing light intensity; radio frequency; modulation amplitudes. The random standard uncertainty is 0.003 nT for a measurement time of 1 s. This does not depend on the value of the magnetic flux density in the range from 100 nT to 1.3 mT. Special measures were taken with the standard magnetometer to avoid any magnetic field distortion caused by magnetization of the sample environment and the resonance line shape because of a phase-shift effect in the phase-sensitive detector. The full uncompensated contribution of the sensor magnetization does not exceed 0.05 nT in the whole range of measurements, and it is completely excluded by a corrective action or averaging by turning the sensor axis 180◦ with respect to the direction of the magnetic field.

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The experimental determination of the He-4 atom’s gyromagnetic ratio using this method was made by the authors in γP and γ 4He /γ 3He determination experiments (Shifrin et al., 1997). Thus, the conversion constant of the standard magnetometer has been determined in the calculable standard quartz solenoid through the basic SI units—the meter and the ampere. The constants of the solenoid were calculated for precisely measured dimensions of the winding (diameter and pitch), and the current was measured using Josephson and Hall quantum standards. The results were reported in references Shifrin et al. (1998, 1997) and were taken into consideration by the CODATA group in the adjustment of fundamental constants reported in reference Mohr and Taylor (2005). The ratio γ 4He (23 S1 )/γ 3He (1S0 ) = 864.02276 was measured with a standard deviation of 3 × 10−8 . Combining this result with (Flowers et al., 1993) for γ3He /γP ) and using the value recommended by CODATA in 2002 of γP = 2.67515333 × 108 s−1 T−1 (9 × 10−8 ) we obtain: γ4He = 1760.787408 × 108 s−1 T−1 (9 × 10−8 ) This constant has been taken as the conversion factor for the standard helium–cesium magnetometer. For the calibration system as a whole, the uncertainty component associated with the field uniformity depends on the volume and the shape of the magnetometer’s sensitive element. This error does not exceed 1 × 10−7 in the whole reproduced range from 20 to 100 ␮T for the aspheric volume of diameter 10 cm around the coil center. Table 1 gives the latest relative systematic uncertainty estimates for the value of the reproduced total magnetic field. At the probability of 0.95, it corresponds to the uncertainty in the absolute form of 0.01–0.04 nT in the range 20–100 ␮T. 3. Metrological characteristics of the calibrated quantum magnetometers The above magnetic field density standards with one-volume and three-volume reproduction systems were used for calibration of high-sensitivity scalar quantum magnetometers. The sensor of the magnetic field controller was placed at a distance of 30 cm from the coil center, where a vol-

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Table 1 The uncertainty estimate for the value of the total reproduced magnetic field density Item

Relative uncertainty, 1 × 10−7

He-4 gyromagnetic ratio Magnetic field non-uniformity He-4 magnetic resonance frequency determination He-4 sample environment magnetic susceptibility Magnetic field stability Total relative uncertainty (one standard deviation)

0.9 1.0 1.0 0.5 0.5 1.8

ume with the most uniform field was intended for the sensors of the standard magnetometer or of one to be calibrated. Compensation for the difference in the coil constants of the field-controlling and field-measuring sensors, and also the field gradient, was made by additional windings. These windings were fixed on the sensor of the magnetic field controller. The direction of the base between the sensor positions was selected to have a minimal gradient of the local outside magnetic field source. The uniformity of the magnetic flux density in the working volume of the coils was corrected and controlled immediately before calibration using a multidipole coil system and the standard magnetometer readings. Computer control was used at two stages of calibration: (1) self-calibration of the magnetic-field reproducing system using a standard 4 He–Cs magnetometer and (2) precise magnetic field reproduction for scalar magnetometer calibration. The first stage is carried out twice, before and after calibration of a magnetometer, to estimate probable drift. The computer sets the output parameters of current sources connected to the windings of the coils and to the frequency synthesizers of the field controller to ascertain the values of the stabilized MFD. It also addresses the standard magnetometer to determine values of magnetic flux density. The computer successively repeats these assigned magnetic field values during the second stage of the process, records the measurement results obtained for the magnetometer under calibration and calculates the systematic and random compo-

Table 2 Calibration of serial proton magnetometers G 856 (Geometrix) BS (␮T)

Serial number (year) 2777373 (2007)

20 30 40 50 60 70 80 90 100

2777384 (2007)

277381 (2004)

2777373 (2007)

ΔM

RSTD

|BM↑ − BM↓ |

ΔM

RSTD

|BM↑ − BM↓ |

ΔM

RSTD

|BM↑ − BM↓ |

ΔM

RSTD

|BM↑ − BM↓ |

5.6 −0.6 −0.5 −0.5 −0.6 −0.6 –0.7 −0.8 −0.9

0.5 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

1.6 1.6 1.6 1.7 1.7 1.8 1.8 1.8 1.9

4.3 −0.5 −0.3 −0.5 −0.6 −0.6 −0.7 −0.7 −0.7

0.5 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

−0.3 −0.4 −0.4 −0.4 −0.4 −0.4 –0.4 −0.4 −0.4

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

−0.4 −0.4 −0.3 −0.3 −0.3 −0.3 −0.3 −0.3 −0.2

0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1

1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1 1.1

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Table 3 Calibration of serial proton Overhauser magnetometers POS-1 (Ural State Technical University) BS (␮T)

Serial number (year) 112 (2007)

20 30 40 50 60 70 80 90 100

113 (2007)

116 (2007)

104 (2007)

ΔM

RSTD

|BM↑ − BM↓ |

ΔM

RSTD

|BM↑ − BM↓ |

ΔM

RSTD

|BM↑ − BM↓ |

ΔM

RSTD

|BM↑ − BM↓ |

−0.22 0.03 0.16 0.34 0.49 0.64 0.78 0.93 1.08

0.02 0.02 0.01 0.01 0.01 0.01 0.01 0.02 0.01

1.2 1.2 1.2 1.3 1.3 1.4 1.4 1.5 1.5

0.16 0.37 0.54 0.50 0.52 0.63 0.69 0.77 0.77

0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

−0.20 −0.03 0.14 0.30 0.40 0.49 0.60 0.69 0.77

0.06 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01

0.8 0.8 0.8 0.8 0.8 0.9 0.9 0.9 0.9

0.35 0.28 0.12, 0. 07 0.11 0.10 0.05 0.02 −0.05

0.05 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01

0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05

nents of the uncertainty, including those caused by the sensor magnetization and orientation. Tables 2–5 give some calibration results obtained for serial proton magnetometers G 856 and proton Overhauser magnetometer POS-1, as well as for cesium self-oscillated optical pumping (OP) magnetometers G 858 and Cs magnetometers used as the basis of the Scintrex Cs-2, Cs-3 magnetometer sensors. Some features of the operational principles and calibration of proton magnetometers demanded additional control. As is known regarding proton magnetometers, the periods of polarization and precession frequency control do not coincide. Some delay is present between them. This time is large enough that a high-speed magnetic field feedback system can remove the disturbance of the field from polarization. This effect is important in the one-volume calibration system. However, proton magnetometers can also be controlled by a second method, the application of the three-volume calibration system. In this case, the effect of polarization is absent in view of the remoteness of the stabilizer sensor: it is 30 m distant from the sensor of the magnetometer being calibrated.

Table 6 gives the data obtained when calibrating experimental potassium (Alexandrov et al., 1996) and He–Cs optical pumping magnetometers developed in Russia. The following symbols are used in the tables. BS Magnetic flux density reproduced by standard system. BM Magnetic flux density measured by the magnetometer being calibrated. BM↑ , BM↓ Magnetic flux densities measured by proton and He–Cs magnetometers at two optimum oppositely directed orientations of the sensor axis with respect to the magnetic flux density direction. ΔM Correction applied to the readings of the calibrated proton and He–Cs magnetometers: ΔM = BS − (BM↑ + BM↓ )/2 (Tables 2 and 3). BM (45◦ ), BM (α) MFD measured by self-oscillated optical pumping magnetometers at orientations of the sensor axis to the magnetic flux density direction of 45◦ and α.

Table 4 Cesium magnetometers G 858 (Geometrix) BS (␮T)

29268a 2007b

29393a

29272a

29273a

29265a

−1.0 1.0 2.6 4.0 5.5 7.6 10.2 14.1 17.7 0.6(20 ␮T) 0.3(50 ␮T) 6.2(100 ␮T) 0.01

−0.5 1.4 3.0 4.3 5.8 7.7 10.4 13.9 18.6 0.7(20 ␮T) 0.1(50 ␮T) 5.0(100 ␮T) 0.01

−1.3 1.1 2.6 3.5 5.8 6.2 8.2 10.8 14.9 0.1(20 ␮T) 0.7(50 ␮T) 4.5(100 ␮T) 0.01

Δ45 = [BS − BM ] (nT) (α = 45◦ ) 20 30 40 50 60 70 80 90 100 δ = |BM (45◦ ) − BM (α◦ )| (nT) α = (20–70◦ ), BS (␮T) RSTD (nT) a b

S/n. Year.

−0.8 1.4 3.2 4.7 6.5 8.8 11.8 16.0 21.0 0.8(20 ␮T) 0.2(50 ␮T) 4.3(100 ␮T) 0.01

−1.4 1.2 2.8 4.2 5.8 7.6 10.0 13.5 18.6 0.1(20 ␮T) 0.1(50 ␮T), 5.1(100 ␮T) 0.01

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Table 5 Magnetometers Scintrex cesium magnetometer sensor BS (␮T)

20 30 40 50 60 70 80 90 100 δ = |BM (45◦ ) − BM (α◦ )| (nT) α = (20–70◦ ), BS (␮T) a

CS-2, Model 757010, S/n 9909145a

CS-2 Model 759009, S/n 0309117a

CS-2, Model 759009, S/n 0309120a

CS-3 Model 762010 S/n 0311045a

2005b Δ45 = [BS − BM ] (nT) (α = 45◦ )

2007b

2005b

2007b

2007b

0.5 0.6 0.75 1.15 1.3 1.5 1.9 2.2 2.7 0.1(20 ␮T) 0.05(60 ␮T) 0.6(100 ␮T)

−0.3 −0.2 −0.1 −0.1 −0.1 −0.3 0.5 0.9 1.4 0.2(20 ␮T) 0.2(60 ␮T) 0.1(100 ␮T)

−0.3 −0.2 −0.1 0.3 0.6 1.0 1.7 2.4 3.5 0.3(20 ␮T) 0.3(60 ␮T) 0.5(100 ␮T)

−0.1 0.0 0.0 0.0 −0.15 −0.3 0.5 0.9 1.5 0.3(20 ␮T) 0.2(60 ␮T) 0.5(100 ␮T)

−0.1 −0.1 0.5 0.7 1.0 1.3 1.7 2.3 3.1 0.1 (20, 60, 100 ␮T)

S/n, Model. Year.

b

As can be seen in Tables 2 and 3, the magnetization of sensors (|BM↑ − BM↓ |/2) exceeds the random uncertainty by one or two orders of magnitude in some cases, which results in the dependence of magnetometer readings on the orientation of the sensor axes with respect to the magnetic flux density direction. Besides, in some magnetometers, the magnetization intensity also depends on the magnetic flux density value. The application of correction procedures from the results of calibration will allow us to reduce systematic uncertainty if repeated calibrations confirm the reproducibility of magnetometer data. Tables 4 and 5 give calibration results for cesium magnetometers. Cesium self-oscillated optical pumping magnetometers that have high sensitivity and fast reaction are used mainly to measure small increments in the scalar magnetic flux density. The Table 6 Self-oscillating potassium K-41 and He–Cs magnetometer BS (␮T)

Potassium K-41 magnetometer 2004a [BS − BM ] (α = 45◦ ) (nT)

He–Cs magnetometer MKCG-03 2005a BS − (BM↑ + BM↓ )/2 (nT)

10 20 30 40 50 60 70 80 90 100

– 0.03 0.20 0.36 0.42 0.40 0.20 0.33 0.20 –

−0.04 −0.03 0.01 0.02 0.03 0.03 0.04 0.05 0.05 0.10

RSTD (nT) a

Year.

|BM (45◦ ) − BM (α◦ )| <0.02 nT

|BM ↑ − BM ↓| = (0.1–0.15) nT

0.002 τ =1s

0.003 τ =5s

uncertainty of measurements in an absolute format is not usually analyzed or is estimated with much less accuracy than for proton magnetometers because of the known substantial dependence of MR frequency shifts on operational factors. As can be seen from Table 4, where the results of model G858 magnetometer calibrations are shown, the systematic uncertainty Δ45 and the orientation error depend on the magnetic flux density values. The systematic uncertainty grows from 0.5 to 1.4 nT at 20 ␮T to 15–21 nT at 100 ␮T, and the orientation error also increases from 0.1 to 6 nT when the axis of the sensor deviates to an angle of ±25◦ from the optimum angle of 45◦ . The uncertainty Δ45 was measured at the sensor axis orientation at the optimum angle of 45◦ to the magnetic flux density direction, the magnetometer reading error being 0.01 nT. The random uncertainty for Scintrex Cs-2 and Cs-3 magnetometer sensors was estimated using an external magnetometer processor with the reading error of 0.001 nT. Thus, the random standard deviation (RSTD) in the range 20–100 ␮T was within 0.001–0.002, 0.002–0.003 nT (Cs-2, Cs-3) and 0003–0.004 nT (Cs-3) at the measurement speeds of 1, 0.1 and 0.01 s, respectively. From the data of Table 5, it follows that the systematic and orientation errors in Scintrex sensor-base magnetometers are considerably reduced in comparison with earlier cesium magnetometers and approach those of proton devices. In the range 20–50 ␮T, the systematic uncertainty lies within 0.1–1.1 nT, and the orientation dependence is estimated to be within 0.1–0.3 nT, both increasing to 1.4–3.5 and 0.1–0.6 nT, respectively, in the range 60–100 ␮T. The uncertainty reproducibility estimate for one of the magnetometers calibrated at an interval of 2 years shows a change in the correction Δ45 of 0.1–0.3 nT and a change in the orientation of 0.3 nT for ±25◦ in the range 20–50 ␮T. The change in the correction Δ45 for the 2-year period was an increase of 1.2–2.0 nT in the range 60–100 ␮T.

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Table 6 shows the calibration data for the self-oscillating potassium K-41 magnetometer (State Optical Institute, Russia) (Alexandrov et al., 1996) and the He–Cs magnetometer MKCG03 (“Geologorazvedka” company, Russia). For the potassium K-41 self-oscillating magnetometer, the optimum angle between sensor axes and the magnetic flux density direction is 45◦ , the normal axis orientation for the He–Cs sensor being along the magnetic flux density. Therefore, the orientation error for the K-41 sensors was estimated at the deviation of the axis direction at the angle of ±20◦ from the optimum orientation, and for the He–Cs magnetometer it was estimated by measurements at the angles of 0◦ and 180◦ between the directions of the magnetic flux density and the sensor axes. The calibration results show a minimum systematic uncertainty for the He–Cs magnetometer of less than 0.05 nT in the range of 20–90 ␮T and a maximum of 0.1 nT at 100 ␮T. It also follows from the results obtained that a very small (less than 0.02 nT) record-breaking orientation error in the whole measurement range was achieved for the potassium K-41 magnetometer. 4. Conclusion The experimental accuracy of estimation of six models of serial geomagnetometers and experimental examples of quantum scalar geomagnetometers using the standard calibration system has been discussed. Results of metrological investigation in the whole Earth magnetic field range show that the measurement error and the RSTD can exceed the uncertainty of gyromagnetic ratios by hundreds of times for quantum magnetic

resonance magnetometers used in practice. An essential increase in accuracy is possible with the help of an adequate metrological approach to eliminating the affecting factors and determining corrections for uncompensated shifts of the magnetic resonance frequency. The results were obtained using a standard calibration system based on a helium–cesium magnetometer, a new type of three-axis coil with high field uniformity and extended working volume, and a potassium stabilizer of the magnetic field. The standard system allows reductions in the systematic uncertainty of magnetic flux density realization, as well as errors appropriate to calibration procedures of 0.01–0.04 nT with the random standard deviation of 0.001 nT in the range 20–100 ␮T. References Alexandrov, E.B., Balabas, M.V., Posgalev, A.S., Vershovskii, A.K., Yakobson, N.N., 1996. Laser Phys. 6 (N2), 244–251. Blinov, E.V., Ghitnikov, R.A., Kuleshov, P.P., 1982. Geofizicheskaya Apparatura N76, 9–12. Blinov, E.V., Kuleshov, P.P., 1987. Opt. Spectrosc. 62, 963–964. Blinov, E.V., Ghitnikov, R.A.P.P., Ilyina, E.A., Kuleshov, P.P., Shifrin, V.Ya., 1986. Izmeritelnaya Technika N11, 53–55 (Russian). Flowers, J.L., Petly, B.W., Richards, M.G., 1993. Metrology 30, 75–87. Mohr, P.J., Taylor, B.N., 2005. Rev. Modern Phys. 77, 1–107. Shifrin, V.Ya., Alexandrov, E.B., Chikvadze, T.I., Kalabin, V.N., Yakobson, N.N., Khorev, V.N., Park, P.G., 2000. Metrologia 37, 219–227. Shifrin, V.Ya., Park, P.G., Khorev, N.V., Choi, C.H., Kim, C.S., 1998. IEEE Trans. Instrum. Meas. 47, 638–643. Shifrin, V.Ya., Park, P.G., Kim, C.G., Khorev, V.N., Choi, C.H., 1997. IEEE Trans. Instrum. Meas. 46 (N2), 97–100.