A precise and efficient way to calibrate 3D magnetometers is by utilizing triaxial coil systems. We describe the development and characterization of a 3D coil system that generates magnetic flux densities up to 2 mT in arbitrary field direction. Coil parameters, such as coil constants and the misalignment of its spacial axes are determined with nuclear magnetic resonance (NMR) techniques, ensuring traceability to SI standards. Besides the generation of a constant magnetic field inside a sphere of radius 1 cm in the center of the coil, the 3D coil system enables the realization of gradient and saddle field profiles, which allow a precise estimate of sensor positions in 3D. Fluxgate and Hall sensor measurements are carried out to characterize the quality of the generated magnetic fields. The homogeneity achieved the orthogonality, and the position and structure of the saddles are determined experimentally and compared to calculated values.

Magnetic field sensors with 3D sampling capabilities play an increasing role in modern industrial and consumer applications

Additionally, considerable efforts in the development of comprehensive calibration routines are undertaken in order to comply with high quality standards, e.g., ISO 26262 for the automotive industry. Nevertheless, complete traceability of vector magnetic field calibrations to metrological standards, specifically in regard to the directionality, is currently not always guaranteed. This gap needs to be closed accordingly.

At first, calibration routines have been developed for vector sensors in satellites measuring the Earth's magnetic field (EMF)

Therefore,

Here, we present a new 3D magnetic coil system, specifically developed for traceable calibrations of triaxial magnetic field sensors up to flux densities of 2 mT, which are within the measurement range of our nuclear magnetic resonance (NMR) calibration technique, and can be powered with standard current sources. Besides the generation of homogeneous magnetic fields, saddle and gradient field profiles can be generated as well, which additionally enables the determination of the precise position of the sensitive volume of a 3D sensor.

The paper is organized in the following way. Calculation and setup of the 3D coil system are described at first, followed by an experimental characterization of the coil properties. The NMR measurements are utilized to estimate coil constants and deviations from orthogonality of its three field axes. The quality of generated field profiles of homogeneous, gradient and saddle configuration within the center volume is probed by movable 3D fluxgate and Hall sensors mounted on a triaxial scanning unit. The experimental results are compared with initial calculations at the end of the paper.

Due to the three axes

The design represents a compromise between a sufficiently large area of field
homogeneity and an increasing grade of mechanical complexity, when more than one pair of coils per axis are interleaved in a 3D arrangement. Field homogeneity is rather poor for Helmholtz coils

To obtain the final coil layout, we introduced an optimization algorithm emulating genetic selection

3D compact coil system based on two split-pair coils with

Center points of winding packages (

The final parameters for

Calculated relative flux densities

Figure

As seen in Fig.

All characterization measurements are carried out within the Physikalisch-Technische Bundesanstalt (PTB)'s active EMF compensation

The coil constants

Coil constants obtained for each axis (

The uncertainty of the measurements is dominated by the uncertainty of the current. Furthermore, contributions from the positioning of the sample in the field center and the area of homogeneity need to be taken into account.

Manufacturing the coil body from one piece of material results in coil axes that are almost perpendicular to each other. Nevertheless, unavoidable deviations from ideal dimensions due to machining tolerances need to be estimated and included into correction terms in order to precisely generate magnetic field vectors with the 3D coil system. We use a scalar method to determine those deviations. Due to the compensation, EMF can be neglected.

To measure the angle between two coil axes, both coils are excited with similar currents,

Angle

Finally, we test the magnetic flux density distribution by performing sensor scans in a defined volume at the field center. The movement is done by means of three orthogonal translation stages (MT105-NM from Steinmeyer Mechatronik) made of non-magnetic material. Sensors with weight less than 2 kg can be moved

In general, the position of a magnetic field sensor can be determined with a 3D coil system by varying the currents in individual winding packages, leading to different distributions of the magnetic field. The simplest version is a gradient field with reversed currents in winding packages of one coil of a split pair in respect to its counterpart. In gradient configuration, a scalar magnetometer detects only a field minimum in the center, whereas a vector magnetometer detects

One needs to keep in mind that three individual sensors in a 3D magnetometer have finite dimensions and are not located at one identical point. Therefore, one needs a more complex magnetic field distribution than the simple gradient field in order to determine the exact position of each individual sensor. We introduce the saddle field as calculated from the 3D coil parameters and shown in Fig.

The cylindrical body of the fluxgate magnetometer was positioned concentrically in the opening of the 3D coil system measuring along the

Measurements of the flux densities along the

In our measurements we found a homogeneity better than

As already mentioned, a saddle field with quadratic change of the flux density in the coil center can be obtained by changing the current direction in the outer winding packages. The analytic expression along the

Magnetic flux density in the shape of a saddle can be resolved in the experimental data as seen in Fig.

Direct comparison of experimental and theoretical results for homogeneous

For each component (

Parameter

The saddle points of the individual coil axes are not necessarily at the same location, therefore, we used 3D Hall probe data with the exact known sensor positions, i.e., Eq. (

Deviation of the position of the saddle points in

If one assumes that the coil axes of the saddle fields have a similar misalignment of axes as in the homogeneous field configuration, the deviations of midpoints can be converted into an absolute coordinate system. Calibrations of unknown 3D magnetometers benefit from this capability. The position of individual sensor elements of the magnetometer can be determined relative to each other. We tested this option with the fluxgate magnetometer and found that the positions of the sensors were less than 0.2 mm apart.

We calculated, built and tested a compact 3D coil system based on double split coils that can be used to generate magnetic flux densities up to 2 mT, pointing in any arbitrary direction. During layout of the system, a genetic algorithm was used to optimize the coil parameters. We found that precise manufacturing is crucial to reach the desired specifications for the 3D coil system. We obtained a relative homogeneity

The 3D coil system is suitable for calibrations of vector magnetometers, but needs further in-depth characterization. So far, values of magnetic flux density vectors are traceable to SI standards. In a next step, the magnetic field vector should be linked to an orthogonal reference frame for traceability of sensor position and angularity. The homogeneity of individual axes of the 3D coil is approximately known. The position of individual sensor elements can be determined by means of an inhomogeneous current feed to the 3D coil system, specifically gradient and saddle field configurations.

The code generated during the current study is available from the corresponding author on reasonable request.

The data sets underlying the figures are available from the corresponding author on reasonable request.

MA initiated the project. NR conducted theoretical simulations of the coil layout, supervised the manufacturing of the coil frame and winded the coil, performed fluxgate and Hall probe measurements and analyzed the data. RK carried out NMR experiments and estimated coil constants. JL supervised the 3D coil design. All authors discussed the results. NR and FW drafted the manuscript with contributions from all authors.

The contact author has declared that none of the authors has any competing interests.

Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Nicolas Rott thanks PTB colleagues at department 5.5. Wissenschaftlicher Gerätebau, and Manfred Kitschke & Dennis Jortzick for technical support.

This open-access publication was funded by the Physikalisch-Technische Bundesanstalt (PTB).

This paper was edited by Klaus-Dieter Sommer and reviewed by two anonymous referees.