Method for calibrating a sensor unit

Abstract

The invention relates to a method for calibrating a sensor unit for measuring magnetic fields. The sensor unit comprises a nitrogen-vacancy magnetometer, which has, as the sensor medium, a diamond crystal that has nitrogen-vacancy centers, and a magnetic field-generating device for generating a magnetic field in the region of the sensor medium. The method has the following steps: generating a specified static magnetic field in the region of the sensor medium by means of the magnetic field-generating device, measuring the respective vectorial magnetic field for at least three different orientations of the sensor medium by means of the magnetometer while the specified static magnetic field is being generated by the magnetic field-generating device, and ascertaining an internal vectorial magnetic field on the basis of the magnetic field strengths measured for each of the at least three different orientations and on the basis of the at least three different orientations. The invention relates to a sensor unit for measuring magnetic fields, to a computer program, and to a machine-readable storage medium.

Description

[0001]R.406737 - 1 - Description Title Method for calibrating a sensor unit The invention relates to a method for calibrating a sensor unit for measuring magnetic fields, a sensor unit for measuring magnetic fields, a computer program, and a machine-readable storage medium. State of the art Various sensor technologies are known for measuring very small magnetic field strengths. One of the most sensitive sensor types is SQUID magnetometers (Superconducting Quantum Interference Device), which are based on superconducting components and can resolve individual magnetic flux quanta or fields down to the range of a few femtotesla (fT). The disadvantage of SQUID sensors, however, is the need to cool them below the superconducting transition temperature, which for most superconducting materials is below 77 Kelvin.ie, below the temperature of liquid nitrogen. Quantum-based magnetic sensors are also known, for example, from DE 102018220234 A1 or DE 10 2018214617 A1. Nitrogen vacancy-based (NV-based) magnetometers can measure the vector magnetic field—the absolute amplitude and the spatial orientation. To do so, these devices require a predetermined static magnetic field, also called a bias magnetic field (offset field B0,which is typically generated with permanent magnets or coils) and very precise positioning of the components and the orientation of the lattice of the R.406737 - 2 - diamond with respect to this field. In addition, precise knowledge of the B0 itself and precise knowledge of the diamond's orientation with respect to B0 are required. These parameters are usually either unknown or known only to a limited extent and / or with insufficient accuracy. The reasons for these uncertainties include, among others, any type of assembly tolerances, the influence of the sensor housing and terminals on B0, the influence of magnetized parts of the sensor unit and soft magnetic materials on B0, tolerances in the assembly of the sensor unit components, the diamond process technology (growth and polishing affecting the final lattice orientation), strain of the diamond due to growth, polishing, temperature, or assembly,Temperature-related effects such as thermal drifts in the components, temperature influence on assembly tolerances, temperature changes in the magnetization of the B0-generating magnets, all tolerances related to optical pumping and optical detection, and tolerances in the electronics and microwave resonator. For these reasons, an initial calibration and subsequent recalibrations of the sensor unit may be necessary. US Pat. No. 8,494,799 B2 discloses a method for dynamically calibrating a compass of a portable device, for example, a smartphone. Disclosure of the Invention The object underlying the invention is to be seen inTo provide a concept for calibrating a sensor unit for measuring magnetic fields. This object is achieved by means of the respective subject matter of the independent claims. Advantageous embodiments of the invention are the subject matter of respective dependent subclaims. R.406737 - 3 - According to a first aspect, a method for calibrating a sensor unit for measuring magnetic fields is provided, wherein the sensor unit comprises a nitrogen vacancy center magnetometer, which has a diamond crystal having nitrogen vacancy centers as the sensor medium, and a magnetic field generating device for generating a magnetic field in the region of the sensor medium, wherein the method comprises the following steps: generating a predetermined static magnetic field in the region of the sensor medium by the magnetic field generating device,Measuring a vectorial magnetic field by the magnetometer for at least three different orientations of the sensor medium while the predetermined static magnetic field is generated by the magnetic field generating device; determining an internal vectorial magnetic field based on the vectorial magnetic fields measured for the at least three different orientations and based on the at least three different orientations. According to a second aspect, a sensor unit for measuring magnetic fields is provided, comprising: a nitrogen vacancy center magnetometer, which has a diamond crystal having nitrogen vacancy centers as the sensor medium, and a magnetic field generating device for generating a predetermined static magnetic field in the region of the sensor medium, wherein the sensor unit is configuredto carry out all steps of the method according to the first aspect. According to a third aspect, a computer program is provided which comprises instructions which, when executed by a computer, for example by the sensor unit according to the second aspect, cause the computer to carry out a method according to the first aspect. According to a fourth aspect, a machine-readable storage medium is provided on which the computer program according to the fourth aspect is stored. R.406737 - 4 - The invention is based on and includes the finding that the above object is achieved byby measuring a vectorial magnetic field for at least three different orientations using the nitrogen vacancy center magnetometer. Based on the respective measured vectorial magnetic fields and based on the three different orientations, an internal vectorial magnetic field is determined. Based on this internal vectorial magnetic field, the sensor unit can then be calibrated. Whenever only "magnetic field" is written in the description, it should always be understood that this refers to the vectorial magnetic field. A magnetic field, as defined in the description, is therefore a vectorial magnetic field. This means that a measurement of a magnetic field is a measurement of a vectorial magnetic field. The magnetometer therefore measures a vectorial magnetic field. A measurement of a magnetic field, as defined in the description, is therefore a measurement of a vectorial magnetic field.i.e., the vector magnetic field. The vector magnetic field is defined by the absolute value and the direction of the magnetic field. Measuring a magnetic field therefore includes measuring the absolute value and the direction of the magnetic field. The magnetometer always measures the total magnetic field consisting of the external magnetic field and the internal magnetic field. A user is usually only interested in the external magnetic field. If the internal magnetic field were known precisely, the external magnetic field could be easily calculated as follows: external magnetic field = measured magnetic field - internal magnetic field. The calibration procedure specifically involves rotating or shifting the magnetometer into three different orientations. When the magnetometer shifts, the internal magnetic field shifts with it.where the external magnetic field does not shift. This property (shift of the internal magnetic field along with the magnetometer) allows the calculation of the actual external magnetic field, provided that the external vectorial magnetic field has been measured in at least three known orientations. R.406737 - 5 - For each measurement in an orientation, all three components of the magnetic field are measured relative to a three-dimensional coordinate system. At least three measurements are performed for three different orientations of the magnetometer. Each measured magnetic field consists of the external magnetic field (if present) and the internal magnetic field of the magnetometer. Since three components of the magnetic field are thus determined for at least three orientations, at least nine equations can be formulated,This will be explained in more detail below. The internal magnetic field is generated by the sensor unit itself. The internal magnetic field is based on the static magnetic field generated by the magnetic field generating device and depends in particular on the intrinsic properties of the sensor unit, especially the properties of a sensor housing. The internal magnetic field is only approximately known, as the influence of the sensor housing, etc., is unknown. The goal of the method is to determine the precise internal field so that it can be subtracted from the external magnetic field measured by the magnetometer, ultimately allowing the pure external magnetic field to be measured. The concept described here therefore comprises a calibration procedure that enables the calibration of NV-based magnetometers. The method can be applied in magnetically shielded environments.But the main advantage is its applicability even in noisy and unshielded environments. This eliminates the need for technically complex and expensive shielding measures. R.406737 - 6 - The method requires, as a minimum, three vector magnetic field measurements, performed by the magnetometer in three different orientations. The method does not require any prior knowledge of the internal or intrinsic magnetic field, which can also be referred to as the offset field B0 or ​​bias magnetic field, the residual magnetization of the sensor unit components, the orientation of the diamond with respect to the bias field B0, or the ambient magnetic fields. Subsequent calibrations using the same method can also provide information about whether further recalibrations are necessary and how often they should be performed. The calibration procedure requires little or no additional hardware other than the sensor unit itself and is fast enoughto be performed daily or even hourly. Temperature dependence and / or other drifts or changes in the environment are automatically taken into account. A nitrogen vacancy magnetometer as described comprises a diamond crystal containing nitrogen vacancy centers as the sensor medium and is designed to detect a magnetic field strength at a measurement location by reading a spin resonance in the sensor medium that is dependent on the magnetic field strength. The magnetometer specifically reads multiple spin resonances using so-called ODMR and measures the strength of the magnetic field and its direction – vectorial magnetic field. ODMR stands for "Optically Detected Magnetic Resonance." A nitrogen vacancy magnetometer can also be referred to as an NV magnetometer, where "NV" stands for "nitrogen vacancy."When only the term "magnetometer" is used, the term "NV magnetometer" should always be used. The internal magnetic field can also be referred to as an intrinsic magnetic field, bias magnetic field, offset magnetic field, or B0. Internal or intrinsic refers to the sensor unit. R.406737 - 7 - The sensor unit comprises a magnetic field generating device for generating a predetermined, in particular substantially homogeneous, static magnetic field in the region of the sensor medium. The NV center in the diamond has four possible arrangements, each of which becomes visible in the fluorescence spectrum as a separate frequency split, allowing the magnetic field direction and strength to be extracted for each spatial direction. For example, the magnetic field generating device has a Helmholtz coil arrangement.At least the sensor medium of the magnetometer is arranged within the Helmholtz coil arrangement. To generate such a predetermined static magnetic field, a Helmholtz coil arrangement is used, in particular, within which at least the sensor medium or the sensor head of the NV magnetometer is located. Helmholtz coils can be used to generate a particularly homogeneous magnetic field. For example, the magnetic field generating device comprises one or more permanent magnets and / or one or more arrays of permanent magnets, for example Halbach arrays, Aubert arrays,and / or one or more arrangements of multiple permanent magnets. The sensor unit comprises, for example, at least one excitation light source for radiating light into the sensor medium of the magnetometer. The sensor unit comprises, for example, at least one microwave source for generating a resonant field in the sensor medium. The sensor unit comprises, for example, at least one photodetector for detecting resonance-dependent fluorescent light from the sensor medium. The diamond is designed, for example, as a thin diamond plate. R.406737 - 8 - Nitrogen vacancy center magnetometers offer very high sensitivity, but are also easy to implement in a compact design.This results in small sensor heads. Complex cooling, such as with SQUID sensors, is not necessary. Furthermore, NV defect centers inherently allow vectorial magnetic field measurements. This provides the technical advantage, for example, that a magnetic field can be efficiently measured by the sensor unit. Furthermore, the sensor unit can include, for example, a microwave resonator in the region of the sensor medium that is tuned to the spin resonance of the sensor medium. A microwave resonator can generate a homogeneous microwave field in the relevant areas of the sensor medium.While the microwave source can also be located remotely and fed into the microwave resonator via suitable connections. The sensor unit described here is based in particular on a quantum-based or optically pumped NV magnetometer. The magnetometers described here as examples use optically pumped and / or optically detected magnetic resonance (ODMR). This exploits the fact that under the influence of an external magnetic field, the energy levels of certain spin states of unpaired electrons split, the so-called Zeeman effect. The splitting of the energy levels results in altered transitions during relaxation from excited states,which can then be measured, for example, by optical and microwave excitation and detection of the resulting fluorescence radiation, or by observing optical properties such as light absorption. The measured optical parameters can then be used to determine the magnetic field strength and direction. Diamond NV magnetometers are based on the readout of magnetic resonances from specific defect centers in diamond, particularly nitrogen vacancies (NV), which occur as impurities in the carbon lattice of R.406737 - 9 - diamond and can also be deliberately introduced. If the NV center is optically excited in its normal state without an existing magnetic field, for example, by irradiating a pump laser beam with a suitable wavelength (in this case in the green wavelength range, e.g., at 532 nm for off-resonance excitation),The electrons are lifted from the triplet ground state to the excited triplet state and relax, emitting fluorescent light in the red wavelength range at, for example, 637 nm. Since the probability for non-spin-conserving transitions from the spin state is proportional to the spin quantum number m, s =±1 is larger, excitation pumping ensures that the NV centers are mostly in the spin state m s =0 hyperpolarized. Stimulation can be achieved with laser pulses and / or continuous wave lasers. Between the m s = 0 and m s=±1 spin states in the ground state, there is an energy difference corresponding to the frequency difference, which in this case is approximately 2.87 GHz. If, in addition to the optical excitation, microwave radiation is irradiated into the diamond, a dip in the red fluorescence occurs at this resonance frequency of 2.87 GHz (in the absence of the internal and external magnetic field), since the spin-polarized electrons are deflected by the microwave field from the m s = 0 in the m s =±1 ground state and from there by the pump light into the m s =±1 excited state. From there, however, mainly non-radiative transitions and weak infrared fluorescence transitions occur via the singlet state, while fluorescence in the red region disappears. If an external magnetic field is present, the so-called Zeeman effect leads to the splitting of the otherwise equal-energy m s=±1 triplet levels into energetically equidistant Zeeman levels. When the fluorescence intensity is plotted against the microwave frequency, two notches appear in the fluorescence spectrum, the frequency spacing of which is linearly proportional to the magnetic field strength of the external magnetic field. The magnetic field sensitivity is defined primarily by the minimum resolvable frequency shift and can reach up to 1 pT / √Hz. Since the NV center in single-crystal diamond has four possible arrangements in the crystal lattice, the presence of a directed magnetic field causes the NV centers present in the crystal to react with varying degrees to the external magnetic field depending on their position in the R.406737 - 10 - crystal. This results in four pairs of fluorescence minima appearing in the spectrum, from whose shape and relative positions both the magnitude of the magnetic field strength and the direction of the external magnetic field can be clearly determined.For example, the total of 24 microwave resonances can be measured to measure the vector magnetic field. The NV-center magnetometer offers a variety of advantages for this application. In addition to the aforementioned very high sensitivity, a wide measurement range (> 1 Tesla) can also be covered. The underlying Zeeman effect is linearly dependent on the existing magnetic field and, moreover, shows no degradation, since the measurement is based on quantum mechanical states. Furthermore, an NV-center magnetometer offers the possibility of determining external magnetic fields vectorially based on the various orientations present in the diamond lattice. Additionally or alternatively, the magnetic spin resonance in diamond can be read out electrically. This detects charge carriers that have been elevated into the conduction band of diamond by two-photon ionization of the NV centers.In one embodiment of the method, it is provided that for the measurements in the at least three different orientations, the sensor medium is arranged one after the other in at least three different predetermined holding positions of a calibration stand. This results in the technical advantage, for example, that the orientations can be easily determined. In one embodiment of the method, it is provided that the respective orientation is measured by at least one gyroscope. This results in the technical advantage, for example, that any orientations can be used without the need for a calibration stand to determine the orientations, so that, for example, such a stand can be dispensed with for calibration.In one embodiment of the method, a three-dimensional x,y,z laboratory coordinate system is used to determine the at least three orientations. The axes of a coordinate system as described herein are, for example, not aligned coplanarly. For example, a coordinate system as described herein is a Cartesian coordinate system. This provides the technical advantage that the orientations are determined in a comprehensible manner. In the following, an L-coordinate system refers to the three-dimensional x,y,z laboratory coordinate system. "L" stands for "laboratory." The reference system is therefore the laboratory, i.e., generally the environment of the sensor unit. In the following, a D-coordinate system refers to a three-dimensional x,y,z diamond coordinate system. "D" stands for "diamond." The reference system is therefore the diamond.In one embodiment of the method, it is provided that for the measurement in one of the at least three orientations, the sensor medium is rotated by a predetermined rotation angle, for example 45°, about the z-axis of the three-dimensional x,y,z laboratory coordinate system relative to another of the at least three orientations. In one embodiment of the method, it is provided that for the measurement in one of the at least three orientations, the sensor medium is rotated about any axis in the xy-plane of the x,y,z laboratory coordinate system, which is not parallel, but in particular perpendicular to the z-axis of the x,y,z laboratory coordinate system. R.406737 - 12 - This results in the technical advantage, for example, that one of the orientations can be easily determined. A measurement of a magnetic field strength by the NV magnetometer, which is not located in a magnetically shielded environment, includes information about: ^. ^^^^: internal / intrinsic magnetic field, which is generated, among other things, by the magnetic field generating device (e.g., generated by coils and / or permanent magnets), as well as the influence of the magnetized parts of the sensor unit and any magnetic field generated by the sensor unit itself, such as the field created by electrical currents within the sensor unit. ^ ^^^^ : Earth's external magnetic field, including the magnetic field anomaly due to the presence of soft magnetic materials. ^ ^^^^^^^^ : external magnetic field from nearby currents, magnets, etc. The concept allows the measurement and differentiation between the internal and external magnetic field. The distinction between internal and external magnetic fields is important for the calibration of the sensor unit, especially the NV magnetometer, and for the correct determination of the bias magnetic field. ^^^^essential. To perform the calibration procedure, only three measurements in non-coplanar orientations are required as a minimum, each after rotating the NV magnetometer by a known and defined angle. Increasing the number of measurements beyond the required minimum leads to a gradual improvement of the original calibration. Furthermore, it is particularly advantageous for the calibration procedure if the active surface of the sensor medium (the diamond) is in the same position for all three measurements, which can be ensured, for example, using a flat surface and a ruler. In the case of very inhomogeneous external R.406737 - 13 - magnetic fields that vary across the volume of the sensor medium, the calibration can be supported by a simple holder, such as a tripod, with defined connections and orientations, which serves as a calibration stand.As previously described, the minimal calibration protocol is based on three measurements, numbered 1, 2, and 3 below, with different orientations. When formulating corresponding equations relative to a diamond coordinate system (denoted by a superscript "D"), these rotations in the diamond coordinate system only affect the contribution of the external magnetic field. The first rotation can, for example, be 0°, meaning no rotation is performed for the first measurement. Therefore, the magnetic field vectors in the diamond coordinate system can be calculated as follows: A rotation of the sensor medium can be described as a rotation in the x, y, and z coordinates of the laboratory coordinate system (denoted by a superscript "L"). The rotation in the laboratory coordinate system "L" does not correspond to a rotation in the x, y, and z coordinates of the diamond coordinate system. In particular, ^ ^ ^ ^^^invariant to rotations in the D-coordinate system, while ^ ^ ^ ^^,^ = ^ ^ ^ ^^ is invariant under rotations in the L-coordinate system. This can be summarized as follows, using transformation matrices from the L-coordinate system to the D-coordinate system and vice versa: where ^ ^→^ is the transformation matrix from the D-coordinate system to the L-coordinate system, where the inverse transformation the unity condition ⋅ ^ ^→^ = 1 is fulfilled. R.406737 - 14 - Since the calibration rotations of the sensor medium in the L-coordinate system are assumed to be known, they can be represented as known rotation matrices that correspond to the rotation in the equation above. As an example, three non-coplanar rotations are chosen as follows. For the first measurement, it is assumed that for the measurement of the initial external field ^ ^ ^^^ no rotation (unit rotation) is required. The second measurement is performed after a rotation of ^ (for example, ^ = 45°) around the z-axis of the L-coordinate system. The third measurement must ensure the non-coplanarity condition and can be performed around any axis in the xy-plane of the L-coordinate system that is not parallel to the z-axis of the L-coordinate system, but, for example, perpendicular to the z-axis. For example, a rotation around an axis in the xy-plane by an amount of ^° (e.g., ^ = 20°). Accordingly, the above equations (1) to (3) can be rewritten as: where ^ ^ a rotation around the z-axis of the L-coordinate system and ^(^) a rotation around a vector in the xy-plane of the L-coordinate system by an angle of To simplify the calculations, for example, the L-coordinate system can be aligned with the position of the sensor medium after the first rotation and the axis of the second rotation can be chosen as the x-axis of the L-coordinate system, ie, since ^ ^ ^ ^^ is unknown, it can be assumed, for example, that ^ ^ ^ ^^ themselves as ^ ^ ^ ^^,^^^ If the "new" index is omitted, this results in: R.406737 - 15 - This system of 9 equations includes 9 variables: The intrinsic (constant) magnetic field components of the sensor ^ ^ ^ ^^^,^ , ^ ^ ^ ^^,^ u ^ ^ nd ^ ^^^^,^ . The external magnetic field components ^ ^ ^ ^^,^ , ^ ^ ^ ^^,^ , ^ ^ ^ ^^,^. The transformation angles of the transformation between the two coordinate systems ^, ^, and ^. The transformation between the two coordinate systems can be represented as three individual rotations around the three axes of the coordinate system: While the inverse transformation is given by the transpose: The use of one or more gyroscopes enables calibration of the sensor unit without the need for additional elements (such as a ruler or calibration stand). Furthermore, the use of one or more gyroscopes allows for an increase in the number of measurements required for calibration, resulting in higher calibration accuracy. Furthermore, active angular position determination enables additional real-time calibration checks and recalibrations required for specific applications. The method can therefore be applied anywhere and at any time, provided it is physically possible to rotate the sensor medium around multiple axes during the active calibration time.406737 - 16 - According to one embodiment, gyroscopic sensors, the gyroscopes (including, but not limited to, microelectromechanical systems (MEMS) gyroscopes or gyrometers) are used, which measure the angular variations during the rotations and movements of the sensor medium. These angular measurements, together with the measurements of the vector magnetic field itself by the magnetometer, can be used to construct the necessary orientation changes for the calibration process. The calibration process therefore comprises, for example, a rotation of the magnetometer and a continuous recording of its angular position and / or its three-dimensional orientation with the aid of one or more gyroscopic sensors, i.e., the gyroscopes.The rotations include at least three non-colinear or non-coplanar orientations as described above, but may additionally include, for example, a random rotation and roll and / or pitch and / or yaw of the magnetometer, which also provide sufficient information for calibration. The recording or measurement of the angular orientation of the NV magnetometer during calibration can, for example, be performed by a 3D gyroscope and / or by three independent 1-axis gyroscopes, whereby the specific implementation depends on the actual use, the required precision, the bandwidth, the costs, etc. The use of one or more gyroscopes described here has the following advantages in particular: The need for additional, external calibration equipment (such as a ruler or a calibration stand) can be avoided.Specific, predefined rotation requirements can be avoided, which facilitates the implementation of the procedure. On-the-fly calibration is possible, e.g., during commissioning of the sensor unit. R.406737 - 17 - Real-time verification of the sensor unit's calibration and recalibrations, as well as a check of whether recalibration is necessary and, if so, how often, can be enabled. The sensor unit is enabled to track its calibration status by introducing self-awareness of the calibration status. More than three measurements can be made possible for calibration, which leads to higher calibration accuracy. Continuous temporal tracking of the magnetometer alignment using gyroscopes enables the application of known methods for improving calibration, control, and prediction, such asKalman filtering is used to process the gyroscopic data, further improving the accuracy of the data used for magnetometer calibration. Rotations such as pitch, roll, and rotation allow for the acquisition of multiple data points at closely spaced positions at different times, which can reduce the influence of dynamic time-varying magnetic noise during calibration. Since the sampling rates of miniature gyroscopes can exceed 1000 Hz, a standard calibration of 3 seconds (about 1 second for each rotation axis) can enable over 3000 measurements. To ensure the overall accuracy of the calibration, the measurement error of the gyroscopes can be taken into account. The drift of commercially available (MEMS) gyroscopes, for example, is on the order of 60 mrad / h (3.5° / h).In addition, the point-to-point error at a sampling rate of 100 Hz to 1000 Hz is on the order of 40 µrad / s (0.002° / s). These point-to-point error values ​​enable particularly precise calibration. For example, when using a calibration stand, with a manufacturing tolerance of 50 µm on the calibration stand and a magnetometer package of approximately 10 cm, an angular error in the positioning of the sensor medium on the stand of approximately 0.0057° (~50 µm / 10 cm) is expected, which corresponds to a cumulative error of 2.87 s of measurements with a gyroscope (0.0057° / [0.002° / s]). During this time, a gyroscopic calibration performs at least 287 measurements at a sampling rate of 100 Hz (compared to a measurement with a calibration stand), which further reduces the error through statistical averaging in the calibration algorithm and Kalman filtering of the gyroscopic data.Thus, real-time calibration, real-time recalibration, continuous calibration, continuous calibration improvement, and self-awareness of the calibration status can be implemented for embodiments in which the NV magnetometer itself or the system implementing the NV magnetometer has a non-static position over time. In this case, methods of optimal control of dynamic systems can be used to incorporate the continuously acquired angular position and magnetic field data to improve the calibration. The method for calibrating the sensor unit is particularly suitable for detecting a change in the predetermined static magnetic field due to a temperature change of the magnetic field generating device. For example, it is assumed that the change in the magnetic field due to the temperature change is constant during at least three consecutive measurements.If the calibration procedure is performed multiple times, for example, at different times, a change in the internal magnetic field due to a change in temperature can be detected. The change in the internal magnetic field can then be taken into account in a subsequent determination of the external magnetic field, thus increasing the measurement accuracy. If permanent magnets are used to generate the predetermined static magnetic field, for example, the magnetization of the permanent magnets can change with temperature, leading to a change in the R.406737 - 19 - magnetization and thus to a change in the predetermined static magnetic field and thus the internal magnetic field.The general definition and equations for the measurements and reconstruction of the bias magnetic field are based on the above, but omit the simplifications related to only three measurement orientations and introduce a reconstruction procedure as follows: ^. ^^^^ : internal / own or intrinsic magnetic field (e.g., generated by Helmholtz coils and / or permanent magnets), as well as the influence of the magnetized parts of the sensor unit and any magnetic field generated by the sensor unit itself, e.g., the magnetic field resulting from electrical currents within the sensor unit. This magnetic field is invariant to rotations and translations from the perspective of the reference frame attached to the diamond or to the sensor unit itself (D-coordinate system). ^ ^^^: external magnetic field, consisting of the Earth's magnetic field, including the magnetic field anomaly due to the presence of soft magnetic materials, as well as contributions from the external magnetic field of nearby currents, magnets, etc. The equations describing the rotation of the sensor medium in the diamond coordinate system are: where the first equation (I.) refers to the initial orientation of the sensor medium at the beginning of the calibration procedure without any rotation, while the second equation (II.) additionally contains the general rotation matrix ^(^). This general rotation can be represented as successive rotations around the three principal axes: ^ ( ^ ) = ^^ ( ^ ) ∙ ^^ ( ^ ) ∙ ^^ ( ^ ) ,R.406737 - 20 - where the angles ^, ^, ^^^ ^ are measured by the one or more gyroscopes. For example, when calibrating using gyroscopes, multiple rotations are performed. In this case, the alignment or orientation of the sensor medium at each iteration j=1,2...n of the calibration with a total of n rotations or rotation steps can be represented as a matrix multiplication of the corresponding rotations. n can be three. ^(^ ^ ) = ^, where ^ is the identity matrix and where ^(^ ^ ) is the initial rotation according to step j=1. ^ ^ ^^ ^ ^ = ^ ^ ^^ ^ ^ ∙ ^ ^ ^^ ^ ^ ∙ ^ ^ ^^ ^ ^, ^ > 1, where ^ ^ ^^ ^ ^ the individual rotation in step ^ > 1 with respect to the current (last recorded) position. ^^^ ^ ^ = > 1, where ^^^ ^^ is the final orientation after the j>1 rotations, defined as applying the j-step rotation which returns to the previous position ^^^ ^^^ ^ was applied, which in turn is a result of the multiplication of j-1 rotation matrices. Since ^ is a vectorial 3D quantity, a magnetic field measurement at three different alignments or orientations contains 9 equations and 9 unknown variables, thus a well-determined system. If more than three measurements are performed, such as when recording the orientation of the sensor medium using gyroscopes, more than 9 equations result, so that the system is: is overdetermined and can be solved, for example, using the method of least squares as follows R.406737 - 21 - This overdetermination and least squares fitting (where, for example, p = 2) is statistically advantageous for error reduction compared to measuring only three different orientations. Solving the system of equations can be performed using other methods, for example: gradient method, machine learning methods, other optimization methods, linear and nonlinear optimization methods, etc. After applying one of the described calibrations, either with the help of a calibration stand and / or with the help of one or more gyroscopes, the values ​​of ^ ^ ^ ^^^ , ^ ^ ^ →^ , ^ ^→^ known. In this case, any additional measurement of the total magnetic field ^ ^ ^ ^^ , as measured in the diamond coordinate system, can be directly related to the external magnetic field in the laboratory coordinate system as follows: In the case where the measurement is made after the magnetometer has been rotated with respect to the laboratory coordinate system, which may be the case, for example, if the magnetometer was not returned to its original position after calibration but remained rotated with respect to the original position, which can be described by a known rotation matrix ^(^), the equation for ^ ^ ^ ^^ be defined as follows: ^ ^ ^^ = ^ ^ ^ ^ ^ ^ ^ ^ ^→^ ^ ( ) ^^^ − ^ ^^^^ ^The sensor unit is, for example, programmed to execute the computer program. R.406737 - 22 - The invention is explained in more detail below with reference to preferred exemplary embodiments. The figures show: Fig. 1 shows a flow diagram of a method for calibrating a sensor unit for measuring magnetic fields, Fig. 2 shows a sensor unit for measuring magnetic fields, Fig. 3 shows a machine-readable storage medium, Fig. 4 shows a perspective top view of a calibration stand, and Fig. 5 shows a top view of the calibration stand according to Fig. 4. Fig. 1 shows a flow diagram of a method for calibrating a sensor unit for measuring magnetic fields, wherein the sensor unit comprises a nitrogen vacancy center magnetometer, which has a diamond crystal having nitrogen vacancy centers as the sensor medium, and a magnetic field generating device for generating a magnetic field in the region of the sensor medium.According to a step 101, a predetermined static magnetic field is generated in the region of the sensor medium by the magnetic field generating device. In a step 103, a first magnetic field strength is measured by the magnetometer while the predetermined static magnetic field is generated by the magnetic field generating device. Here, the NV magnetometer, i.e. the sensor medium, is in a first orientation. Subsequently, the NV magnetometer is brought or displaced into a second orientation, which is different from the first orientation. According to a step 105, a second measurement of a second magnetic field strength is carried out by the NV magnetometer for the second orientation, while the predetermined static magnetic field is generated by the magnetic field generating device. R.406737 - 23 - Subsequently, the sensor medium, i.e. the NV magnetometer, is brought or displaced into a third orientation.which is different from the first orientation and different from the second orientation. According to a step 107, a third measurement of a third magnetic field strength is performed by the magnetometer for the third orientation while the predetermined static magnetic field is generated by the magnetic field generating device. According to a step 109, a magnetic field strength of an internal magnetic field is determined based on the measured first magnetic field strength, the measured second magnetic field strength, and the measured third magnetic field strength, as well as based on the three different orientations. Fig.2 shows a sensor unit 201 for measuring magnetic fields, comprising: a nitrogen vacancy center magnetometer 203, which has a diamond crystal 205 having nitrogen vacancy centers 207 as the sensor medium, and a magnetic field generating device 209 for generating a predetermined static magnetic field in the region of the sensor medium, wherein the sensor unit is configured to carry out all steps of the method according to the first aspect. The sensor unit 201 comprises a 3D gyroscope 211, which is configured to measure corresponding angles with respect to all three axes x, y, z of a three-dimensional x, y, z coordinate system. For example, instead of or in addition to the 3D gyroscope 211, the sensor unit 201 comprises a separate gyroscope for each axis, i.e., a single-channel gyroscope. Fig.3 shows a machine-readable storage medium 301 on which a computer program 303 is stored.The computer program 303 comprises instructions which, when executed by a computer, cause the computer to carry out a method according to the first aspect. Fig. 4 shows a calibration stand 401 in a perspective top view. R.406737 - 24 - The calibration stand 401 comprises a plurality of stop surfaces against which a sensor unit according to the second aspect can rest in different orientations. By way of example, such stop surfaces are provided with the reference numerals 403, 405, 407, 409, 411, 413, 415, 417, 419, 421, 423, 425. Fig. 5 shows a top view of the calibration stand 401. Three frames 501, 503, 505 are shown as a section, which rest against different stop surfaces. Thus, three orientations are defined in which the sensor unit can be successively displaced, so that a vector magnetic field can be measured in each of these orientations. Reference numeral 501 denotes a first orientation.Reference numeral 503 denotes a second orientation, and reference numeral 505 denotes a third orientation. The third orientation 505 is outside the plane of the paper. These stop surfaces 403 to 425 thus allow the sensor unit to be moved into different orientations or positions.

Claims

R.406737 - 25 - Claims 1. A method for calibrating a sensor unit (201) for measuring magnetic fields, wherein the sensor unit (201) comprises a nitrogen vacancy center magnetometer (203) having a diamond crystal (205) having nitrogen vacancy centers (207) as the sensor medium, and a magnetic field generating device (209) for generating a magnetic field in the region of the sensor medium, wherein the method comprises the following steps: generating (101) a predetermined static magnetic field in the region of the sensor medium by the magnetic field generating device (209), measuring (103, 105, 107) a vectorial magnetic field by the magnetometer (203) for at least three different orientations of the sensor medium while the predetermined static magnetic field is generated by the magnetic field generating device (209),Determining (109) an internal vectorial magnetic field based on the vectorial magnetic fields measured for the at least three different orientations and based on the at least three different orientations.

2. The method according to claim 1, wherein for the measurements in the at least three different orientations, the sensor medium is arranged successively in at least three different predetermined holding positions of a calibration stand (401).

3. The method according to claim 1 or 2, wherein the respective orientation is measured by at least one gyroscope (211).

4. The method according to one of the preceding claims, wherein a three-dimensional x, y, z laboratory coordinate system is used to determine the at least three orientations. R.406737 - 26 - 5. The method according to claim 4, wherein, for the measurement in one of the at least three orientations, the sensor medium is rotated by a predetermined rotation angle about the z-axis of the three-dimensional x,y,z laboratory coordinate system relative to another of the at least three orientations.

6. The method according to claim 4 or 5, wherein, for the measurement in one of the at least three orientations, the sensor medium is rotated about any axis in the xy-plane of the x,y,z laboratory coordinate system, which axis is not parallel, but in particular perpendicular to the z-axis of the x,y,z laboratory coordinate system. 7.A sensor unit (201) for measuring magnetic fields, comprising: a nitrogen vacancy center magnetometer (203) having a diamond crystal (205) having nitrogen vacancy centers (207) as the sensor medium, and a magnetic field generating device (209) for generating a predetermined static magnetic field in the region of the sensor medium, wherein the sensor unit (201) is configured to carry out all steps of the method according to one of the preceding claims.

8. The sensor unit (201) according to claim 7, comprising at least one gyroscope configured to measure the respective orientation.

9. A computer program (303) comprising instructions which, when the computer program (303) is executed by a computer, cause the computer to carry out a method according to one of claims 1 to 6.

10. A machine-readable storage medium (301) on which the computer program (303) according to claim 9 is stored.

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