Triaxial Helmholtz Coil Research Articles

Fast Error Calibration for Three-Axis SQUID Magnetometers Based on Full-Space Rotational and Frequency-Controllable Magnetic Field

In order to overcome the limitations of the traditional error calibration method for three-axis superconducting quantum interference device (SQUID) magnetometers, this article presents a fast error calibration method for three-axis SQUID magnetometers. In the proposed method, a full-space rotational and frequency-controllable magnetic field with constant total field intensity can be generated by a triaxial Helmholtz coil. Meanwhile, the nonorthogonal error, zero offset error, and proportional coefficient error of the three-axis SQUID magnetometers, which measure the relative value rather than the absolute value, can be accurately solved by an error modeling and ellipsoid fitting theory. Compared with the traditional scalar calibration method, this method replaces the rotation of Dewar and three-axis SQUID magnetometers with a rotating magnetic field, thus avoiding the interference and influence of motion. Compared with the traditional vector calibration method, this method does not need to ensure the alignment between the three-axis SQUID magnetometers and triaxial Helmholtz coil. Moreover, the interference of low-frequency magnetic field can be suppressed by shortening the period of rotating magnetic field. Simulation and experiments prove the effectiveness of this method. After calibration by the proposed method, the root-mean-square error is reduced to 0.414 from 138.411 nT in the electromagnetic shielding room. Repetitive and comparative experiments with the traditional method in field also prove the superiority and stability of the proposed method.

Design of A Three-axis Helmholtz Coil for Magnetic Sensor Calibration

Accurate measurement of magnetic sensor components is always an important issue in magnetic field applications, but there are unavoidable errors in the sensor system that need to be corrected before use. The common scalar correction method is difficult to effectively correct the sensor component because it requires a uniform and stable background magnetic field and depends on the magnetic field modulus. Therefore, a set of triaxial Helmholtz coils that can be used for sensor vector correction is designed to generate a controlled standard magnetic field. The design index of the coils, the size of the uniform zone, and the relationship between the magnetic field and the current were analyzed to provide a basis for the effective calibration of the sensor components. The measurement results show that the size of the uniform zone and the accuracy of the magnetic field of the coils designed in this paper meet the design requirements. Meanwhile, by using the coils in the calibration of the sensor array and the positioning of the magnetic target, the sensor error is reduced by three orders of magnitude, and the positioning accuracy of the magnetic target reaches 0.1 m with good practical effect.

The Geomagnetic Field (GMF) Is Required for Lima Bean Photosynthesis and Reactive Oxygen Species Production.

Plants evolved in the presence of the Earth's magnetic field (or geomagnetic field, GMF). Variations in MF intensity and inclination are perceived by plants as an abiotic stress condition with responses at the genomic and metabolic level, with changes in growth and developmental processes. The reduction of GMF to near null magnetic field (NNMF) values by the use of a triaxial Helmholtz coils system was used to evaluate the requirement of the GMF for Lima bean (Phaseolus lunatus L.) photosynthesis and reactive oxygen species (ROS) production. The leaf area, stomatal density, chloroplast ultrastructure and some biochemical parameters including leaf carbohydrate, total carbon, protein content and δ13C were affected by NNMF conditions, as were the chlorophyll and carotenoid levels. RubisCO activity and content were also reduced in NNMF. The GMF was required for the reaction center's efficiency and for the reduction of quinones. NNMF conditions downregulated the expression of the MagR homologs PlIScA2 and PlcpIScA, implying a connection between magnetoreception and photosynthetic efficiency. Finally, we showed that the GMF induced a higher expression of genes involved in ROS production, with increased contents of both H2O2 and other peroxides. Our results show that, in Lima bean, the GMF is required for photosynthesis and that PlIScA2 and PlcpIScA may play a role in the modulation of MF-dependent responses of photosynthesis and plant oxidative stress.

Transcriptomics and Metabolomics of Reactive Oxygen Species Modulation in Near-Null Magnetic Field-Induced Arabidopsis thaliana.

The geomagnetic field (GMF) is a natural component of Earth's biosphere. GMF reduction to near-null values (NNMF) induces gene expression modulation that generates biomolecular, morphological, and developmental changes. Here, we evaluate the effect of NNMF on gene expression and reactive oxygen species (ROS) production in time-course experiments on Arabidopsis thaliana. Plants exposed to NNMF in a triaxial Helmholtz coils system were sampled from 10 min to 96 h to evaluate differentially expressed genes (DEGs) of oxidative stress responses by gene microarray. In 24-96 h developing stages, H2O2 and polyphenols were also analyzed from roots and shoots. A total of 194 DEGs involved in oxidative reactions were selected, many of which showed a fold change ≥±2 in at least one timing point. Heatmap clustering showed DEGs both between roots/shoots and among the different time points. NNMF induced a lower H2O2 than GMF, in agreement with the expression of ROS-related genes. Forty-four polyphenols were identified, the content of which progressively decreased during NNMF exposition time. The comparison between polyphenols content and DEGs showed overlapping patterns. These results indicate that GMF reduction induces metabolomic and transcriptomic modulation of ROS-scavenging enzymes and H2O2 production in A. thaliana, which is paralleled by the regulation of antioxidant polyphenols.

Modified tri-axial square Helmholtz coil for omnidirectional wireless power transfer

Modified tri-axial square Helmholtz coil for omnidirectional wireless power transfer

Error Calibration for Full Tensor Magnetic Gradiometer Probe Based on Coordinate Transformation Method

In order to calibrate the zero offset error and triaxial non-orthogonal error of full tensor magnetic gradiometer (FTMG) probe composed of superconducting quantum interference device (SQUID) magnetometers, we propose a new calibration method in this article. With the help of the triaxial Helmholtz coil, we can generate a magnetic field with known parameters. By establishing the objective functions containing the error parameters for the outputs of the SQUIDs and solving them with the least-squares fitting algorithm, the included angle between the SQUID sensor and the Helmholtz coil can be obtained, then all the required error parameters can be calculated by coordinate transformation method. Compared with the traditional method, this method does not need to rotate the SQUID magnetometers-based probe to collect the data set for calibration, thus avoiding the influence of motion induced noise on the calibration results. In order to verify the effectiveness of the proposed method, we adopted the widely used ellipsoid fitting method as a comparison method and conducted field comparison experiments. The results show that the proposed calibration method is better than the traditional ellipsoid fitting calibration method under the same experimental environment. The root mean square errors of five independent magnetic gradient tensor components are reduced to 0.39, 0.35, 0.41, 0.31 and 0.57 nT/m from 1630.55, 756.59, 3097.56, 1051.09 and 1245.64 nT/m by the proposed method.

Soft and Hard Iron Compensation for the Compasses of an Operational Towed Hydrophone Array without Sensor Motion by a Helmholtz Coil.

Usually, towed hydrophone arrays are instrumented with a set of compasses. Data from these sensors are utilized while beamforming the acoustic signal for target bearing estimation. However, elements of the hydrophone array mounted in the neighborhood of a compass can affect the Earth’s magnetic field detection. The effects depend upon the materials and magnetic environment present in the vicinity of the platform hosting the compass. If the disturbances are constant in time, they can be compensated for by means of a magnetic calibration procedure. This process is commonly known as soft and hard iron compensation. In this paper, a solution is presented for carrying out the magnetic calibration of a COTS (Commercial Off the Shelf) digital compass without sensor motion. This approach is particularly suited in applications where a physical rotation of the platform that hosts the sensor is unfeasible. In our case, the platform consists in an assembled and operational towed hydrophone array. A standard calibration process relies on physical rotation of the platform and thus on the use of the geomagnetic field as a reference during the compensation. As a variation on this approach, we generate an artificial reference magnetic field to simulate the impractical physical rotation. We obtain this by using a tri-axial Helmholtz coil, which enables programmability of the reference magnetic field and assures the required field uniformity. In our work, the simulated geomagnetic field is characterized in terms of its uncertainty. The analysis indicates that our method and experimental set-up represent a suitably accurate approach for the soft and hard iron compensation of the compasses equipped in the hydrophone array under test.

A comprehensive calibration method for non-orthogonal error and scale factor error of triaxial Helmholtz coil.

In order to calibrate the non-orthogonal error and scale factor error of triaxial Helmholtz coil, a comprehensive error calibration method is proposed in this paper. The comprehensive error model is established first, and then the method to generate a frequency-controllable spatial rotating magnetic field whose magnetic field intensity is constant based on triaxial Helmholtz coil is introduced. Based on the fact that the magnetic field intensity generated by the current through the coil is constant, the objective function is constructed and the error parameters are solved using the least-squares fitting method. Simulation experiments and field tests prove the effectiveness and feasibility of this method. The most obvious finding to emerge from this study is that the proposed method is not only suitable for the electromagnetic shielding room environment but also suitable for the field tests in the presence of a background geomagnetic field far away from urban electricity interference. The root mean square error value is reduced to 0.7 nT from 298.2 nT in the electromagnetic shielding room, and it is reduced to 0.8 nT from 299.0 nT in the wild. Compared to the two-step calibration method, the proposed method reduces the sampling time by controlling the frequency of the rotating magnetic field and reduces the influence of the changes of the background geomagnetic field on the experimental results. This method has better anti-interference ability. Because the modulus of the background geomagnetic field has no effect on this method, it gets rid of the dependence on large current or background geomagnetic field shielding devices. Comparative experiments and repetitive experiments verify the practicability and stability of this method.

A Novel Calibration Method for Magnetometer Array in Nonuniform Background Field

The measurement accuracy of the magnetometer system is closely related to the calibration effect. Available magnetometer calibration methods face the limitation on the assumption that the background magnetic field is uniform. The fact is that the experiment magnetic environment is inhomogeneous for the presence of human activities mainly. This problem could be partially addressed by an auxiliary large-scale triaxial Helmholtz coil to compensate the nonuniformity of magnetic field. This paper proposes a novel calibration method based on the tensor invariants in the nonuniform magnetic field without extra device. The inhomogeneity of background field implies a nonzero gradient field; a new correction model in the gradient field has been established. Calibration parameters are estimated to compensate the observed data using the concept of magnetic gradient tensor and the corresponding rotational tensor invariants, combined with the Levenberg Marquardt optimization. And after the calibration operation, the tensor invariants should be close to a constant. Numerical simulations have been designed and carried out, showing that the proposed algorithm had a good compensation performance with fast convergence, robustness in any gradient field. Field experiments with fluxgate magnetometer array were also conducted to verify this calibration procedure. The measured results are consistent with the simulation results. The root-mean-square (RMS) error is reduced from 616.239 to 1.608 nT/m, after calibration. In addition, the machining error of the frame, the time stability of the background field, the scale of gradient field, and robustness of this proposed method have been discussed.

Howland Current Source Applied to Magnetic Field Generation in a Tri-Axial Helmholtz Coil

This work describes the design and testing of a power Voltage-Controlled Current Source (VCCS) based on the Howland Current Source (HCS) topology. This source is part of a system that contains a three-axial Helmholtz coil and is used to generate a controlled magnetic field environment for aerospace applications. Initially, the paper presents the HCS theory and practical limitations on the premise that the system must be built using low-cost off-the-shelf components. The paper also carefully address on how to design and plan the VCCS matching physical and electrical parameters/limitations of a specific Helmholtz coil. All project details as well as the built VCCS electronics and its results are shown. These include linearity and a first order calibration test, stability and low-frequency error measurement, step response and a frequency limitation analysis. The built source is capable of sourcing up to ±1.5 A at ±25 V, maintaining its linearity and achieving an error smaller than 0.5% with a first order calibration. The final HCS prototype together with the Helmholtz coil allows an excellent capability regarding magnetic field generation for both open and closed-loop applications.

Estimation of Angular Deviations in Precise Magnetometers

Capabilities for calibrations of angular deviations of sensor triplets in precise magnetometers were evaluated in a 2.5 m, triaxial Helmholtz coil facility. The coil system is located in a magnetically quiet environment at SANSA Space Science in Hermanus, South Africa. The angular calibration results obtained from the “thin-shell” calibration procedure were compared with direct measurements on a nonmagnetic tilting/rotational platform. One-year expanded uncertainty of angular deviation calibrations is estimated as 6 × 10−2 degrees of arc; 3 × 10−4 degrees coil orthogonality is possible when doing a numerical recalibration and correction on a short-term basis. In addition, an approach for obtaining body-to-sensor angular calibrations is presented, allowing for speed-up of the calibrations and possibly increasing their accuracy and repeatability by avoiding alignment to the coils with a laser beam and leveling.

Bio-inspired magnetic helical microswimmers made of nickel-plated Spirulina with enhanced propulsion velocity

Bio-inspired magnetic helical microswimmers have attracted much attention for performing complex tasks at low Reynolds numbers. To fabricate such helical microswimmers with enhanced propulsion velocity in bulk, Spirulina were electroless plated with nickel coating. The morphology, coating composition and magnetic property of the as-prepared microswimmers were investigated in detail. The results showed that homogeneous and compact nickel coating was successfully deposited on the helical biotemplates with good surface quality. Furthermore, the locomotion behavior of the microswimmers under the rotating magnetic field generated by the triaxial Helmholtz coils was also studied, and the propulsion mechanism was analyzed. Different parameters affecting the propulsion velocities were optimized. The microswimmers can not only be propelled and steered flexibly in deionized water, but also reach a high forward velocity of more than 12 body lengths per second even under a relatively low field strength, indicating excellent swimming performance of these helical microswimmers.

Tri-axial square Helmholtz coil system at the Alibag Magnetic Observatory: upgraded to a magnetic sensor calibration facility

Abstract. A tri-axial square Helmholtz coil system for the study of palaeomagnetic studies, manufactured by GEOFYZIKA (former Czechoslovakia), was successfully commissioned at the Alibag Magnetic Observatory (IAGA code: ABG) in the year 1985. This system was used for a few years, after which the system encountered technical problems with the control unit. Rectification of the unit could not be undertaken, as the information document related to this system was not available, and as a result the system had been lying in an unused state for a long time, until 2015, when the system was recommissioned and upgraded to a test facility for calibrating the magnetometer sensors. We have upgraded the system with a constant current source and a data-logging unit. Both of these units have been designed and developed in the institute laboratory. Also, re-measurements of the existing system have been made thoroughly. The upgraded system is semi-automatic, enabling non-specialists to operate it after a brief period of instruction. This facility is now widely used at the parent institute and external institutions to calibrate magnetometers and it also serves as a national facility. Here the design of this system with the calibration results for the space-borne fluxgate magnetometers is presented.

A simple geomagnetic field compensation system for uniform magnetic field applications

In this paper a simple geomagnetic field compensation system for uniform magnetic field applications of low magnitude and frequency is presented. The compensation system is based on an array of Tri-axial Square Helmholtz (TSH) coils, an array of tri-axial Hall effect sensors and a microcontroller system in order to compensate the small variations of the ambient magnetic fields (magnitudes close to the geomagnetic field between 25 μT and 65 μT) on a volume of interest. The geomagnetic field experimentally obtained of 39.5 μT was compensated, achieving a uniform magnetic field of approximately zero. Finally, the proposed system emerges as a simple alternative for control and compensation of magnetic fields in several applications.

Magnitude and Orientation Error Correction of a Superimposed Spatial Universal Rotating Magnetic Vector

Based on the orthogonal superposition theorem of three alternating magnetic components, a universal uniform magnetic spin vector is superimposed using tri-axial Helmholtz coils, achieving successive digital control of the orientation, the rotational speed, and the magnetic flux density of the universal magnetic spin vector. For increasing the magnitude and orientation accuracy of the magnetic spin vector, this paper presents a mathematical model associated with the magnitude error and orientation error of the universal magnetic spin vector, along with a double error compensation method for the magnitude and orientation of the universal magnetic spin vector superimposed by three alternating magnetic components. The double error compensation method includes the current magnitude compensation by three different structural coefficients of tri-axial Helmholtz coils and the current phase compensation by two relative phase differences under linear polarization. The results have shown that the double compensation method can increase the magnitude and orientation accuracy of the rotating magnetic vector effectively, which would achieve an accurate posture adjustment and steering control on the capsule robots in curving environment.

Towards metal detection and identification for humanitarian demining using magnetic polarizability tensor spectroscopy

This paper presents an inversion procedure to estimate the location and magnetic polarizability tensor of metal targets from broadband electromagnetic induction (EMI) data. The solution of this inversion produces a spectral target signature, which may be used in identifying metal targets in landmines from harmless clutter. In this process, the response of the metal target is modelled with dipole moment and fitted to planar EMI data by solving a minimization least squares problem. A computer simulation platform has been developed using a modelled EMI sensor to produce synthetic data for inversion. The reconstructed tensor is compared with an assumed true solution estimated using a modelled tri-axial Helmholtz coil array. Using some test examples including a sphere which has a known analytical solution, results show the inversion routine produces accurate tensors to within 12% error of the true tensor. A good convergence rate is also demonstrated even when the target location is mis-estimated by a few centimeters. Having verified the inversion routine using finite element modelling, a swept frequency EMI experimental setup is used to compute tensors for a set of test samples representing examples of metallic landmine components and clutter for a broadband range of frequencies (kHz to tens of kHz). Results show the reconstructed spectral target signatures are very distinctive and hence potentially offer an efficient physical approach for landmine identification. The accuracy of the evaluated spectra is similarly verified using a uniform field forming sensor.

Parametric design of tri-axial nested Helmholtz coils.

This paper provides an optimal parametric design for tri-axial nested Helmholtz coils, which are used to generate a uniform magnetic field with controllable magnitude and direction. Circular and square coils, both with square cross section, are considered. Practical considerations such as wire selection, wire-wrapping efficiency, wire bending radius, choice of power supply, and inductance and time response are included. Using the equations provided, a designer can quickly create an optimal set of custom coils to generate a specified field magnitude in the uniform-field region while maintaining specified accessibility to the central workspace. An example case study is included.

Precise Calibration Method for Triaxial Magnetometers Not Requiring Earth’s Field Compensation

A calibration procedure for calibrations of triaxial magnetometers is presented. The procedure uses a triaxial Helmholtz coil system and an Overhauser scalar magnetometer and is performed in the Earth's field range. The triaxial coils are first calibrated with the Overhauser magnetometer, and subsequently, a triaxial magnetometer calibration is performed. As opposed to other calibration approaches, neither Earth's field nulling system nor movements of the magnetometer are needed. A real calibration test was carried out-the extended calibration uncertainty was better than 430 ppm in sensitivity and 0.06{\deg} in orthogonality.

Magnetic field uniformity of the practical tri-axial Helmholtz coils systems.

In this paper, effects of the assembly misalignments and the manufacturing mismatches on the magnetic field uniformity of a practical tri-axial Helmholtz coils system have been modeled mathematically. These undesired effects regularly occur in any practical tri-axial Helmholtz coils system. To confirm the mathematical calculations, a tri-axial Helmholtz coils system has been constructed and the uniformity of its magnetic field has been measured under different conditions. The experimental results are in good agreement with the mathematical analyses.

METODOLOGÍA DE DISEÑO E IMPLEMENTACIÓN DE UN SISTEMA PARA GENERACIÓN DE CAMPOS MAGNÉTICOS UNIFORMES CON BOBINAS HELMHOLTZ CUADRADA TRI-AXIAL

The design and implementation methodology of a system to generate low-magnitude and low-frequency uniform magnetic fields on a specific volume using a tri-axial square Helmholtz coil is presented. The designing procedure is based on theoretical concepts and simulations from simple mathematical expressions that relate the area, with uniform magnetic field, with the length of the coils. Also, the computational model is constructed and simulated using finite element software. It is observed that theoretical results are consistent with simulation model results and the magnetic field measurement tests. It is concluded that the design methodology allows establishing a simplified and repeatable procedure to obtain a uniform magnetic field in the volume of interest suitable for in-vitro or in-vivo studies.