Method for calibrating a sensor system with at least three sensors, in particular magnetic field sensors

Abstract

The invention relates to a method for calibrating a sensor system (1) comprising at least three sensors (2, 3, 4), comprising the following steps • Detection of a first frequency spectrum (5) by a first sensor (2); • Detection of a second frequency spectrum (6) by a second sensor (3); • Detection of a third frequency spectrum (7) by a third sensor (4); • Comparing the first, second and third frequency spectrums (5, 6, 7), whereby a first frequency interval (I1) in which the first and second frequency spectrums (5, 6) and / or the first and third frequency spectrums (5, 7) and / or the second and third frequency spectrums (6, 7) exhibit at least a largely identical, non-zero signal pattern can be identified; Providing a first mapping rule for the first frequency interval (8) such that the frequency spectra (5, 6, 7) which are at least largely identical in the first frequency interval (I1) are combined with each other, in particular subtracted from each other.

Description

[0001] The present invention relates to a method for calibrating a sensor system with at least three sensors, in particular magnetic field sensors, and to the sensor system for carrying out the method. Background of the invention

[0002] To detect a magnetic field, gradiometers—systems of two or more magnetic field sensors—are often used to measure an external magnetic field at at least two different locations. Finite differences are then calculated from the signals to approximate the underlying field gradients. A direct determination of the magnetic field gradient, for example, using sensors based on the Casimir effect, is described in the publication Javor et al. (2021). Analysis of a Casimir-driven parametric amplifier with resilience to Casimir pull-in for MEMS single-point magnetic gradiometry. Microsystems & Nanoengineering, 7(1), 73. With some gradiometer types, the signal is physically subtracted, for example, with gradiometers based on superconducting quantum interference devices (SQUIDs), see Uzunbajakau et al. (2005). Optimization of a third-order gradiometer for operation in unshielded environments.IEEE transactions on applied superconductivity, 15(3), 3879-3885). Other gradiometers rely on computer-aided or electronics-aided subtraction of the sensor signals (such as a photodiode signal in the setup by Masuyama et al. 2021).

[0003] These approaches have in common that the signals from the sensors used are processed together regardless of their spectral noise characteristics. If the intrinsic (device-based) or extrinsic noise characteristics differ significantly, the desired increase in the signal-to-noise ratio through the difference calculation of the two signals fails. Disclosure of the invention

[0004] The invention relates to a method for calibrating a sensor system comprising at least three sensors, in particular synchronized sensors, especially magnetic field sensors. For this purpose, a first frequency spectrum is recorded by a first magnetic field sensor, a second frequency spectrum by a second magnetic field sensor, and a third frequency spectrum by a third magnetic field sensor, each in the same or at least overlapping frequency ranges, either without or with a known signal. The first, second, and third frequency spectrums are then compared. At least one first frequency interval can be determined in which the first, second, and / or third frequency spectrums are identical or largely identical, i.e., exhibit an identical or nearly identical signal profile that is not zero.The frequency spectra, which are at least largely identical in the first frequency interval, are combined, in particular subtracted, thus providing a first mapping rule for the first frequency interval. Applying this first mapping rule in a measurement results in an improved signal-to-noise ratio for the first frequency interval.

[0005] When comparing the first, second, and third frequency spectra, a second frequency interval can be identified in which at least two of the three frequency spectra are largely identical. Analogous to the provision of the first mapping rule, a second mapping rule is provided for the second frequency interval, such that the first and third, or the second and third, or the first and second frequency spectra are subtracted from each other. A general mapping rule is then provided, taking into account both the first and second mapping rules. This can then be applied in a subsequent measurement.

[0006] It is understood that when comparing the first, second, and third frequency spectra, further frequency intervals can be identified in which identical or nearly identical signal waveforms are present. Mapping rules can also be established for these frequency intervals—as described above—and these are then taken into account when providing the general mapping rule. Likewise, the sensor system can include additional sensors that acquire further frequency spectra, which are then included in the comparison of the frequency spectra. In this way, the general mapping rule is derived as a combination of several mapping rules.

[0007] The sensor system can be considered a gradiometer comprising at least three magnetic field sensors. Essentially, a gradiometer acquires signals from different sensors and subtracts them from one another, thus disregarding any potentially present homogeneous interference magnetic field. This approach takes advantage of the fact that the (to be acquired) useful signal is a local signal that decays rapidly with increasing distance from the sensors of the sensor system, while ambient noise originating at a distance decays only slowly with distance. Therefore, the useful signal is strongest at the sensor closest to the signal source. Using the gradiometer, the magnetic ambient noise, which limits the sensitivity of highly sensitive magnetic sensors, can thus be at least approximately canceled out.

[0008] However, if sensors with different intrinsic and / or extrinsic noise characteristics are combined in the gradiometer, the effects caused by external or internal interfering magnetic fields may not cancel each other out, but rather accumulate in the spectrum. The method and sensor system according to the invention make it possible to combine magnetic field sensors with different intrinsic and / or extrinsic noise characteristics in a single sensor system without having to accept these negative effects.

[0009] In one embodiment of the invention, the method is carried out in a shielded environment. This makes it possible to take device-related, intrinsic noise into account when compiling the general imaging sequence. If the sensor system includes sensors that differ in their intrinsic noise, then, within a specific frequency interval, only the frequency spectra of those sensors exhibiting at least largely identical signal characteristics are combined. By providing and applying the corresponding imaging sequence, an almost noise-free measurement is enabled.

[0010] In one embodiment of the invention, the method is carried out in an unshielded environment. This allows both the intrinsic sensor noise of the sensor system and external noise to be taken into account. If sensors with differing sensitivities in certain frequency ranges are combined in the sensor system, it is possible that certain sensors in the system will detect an external interference signal present in a frequency interval in which these sensors are particularly sensitive, while other sensors will not detect this interference signal. In this case, only the frequency spectra of those sensors that detect this interference signal are combined within this frequency interval. By providing and applying the appropriate mapping rules, this interference signal can then be efficiently suppressed during a measurement.

[0011] In one embodiment of the invention, the method is performed in the presence of a known signal. This makes it possible to analyze the behavior of the respective sensors of the sensor system in the frequency interval in which the signal is present and to optimize the imaging rule for this frequency interval. For example, scaling effects—such as when the signal intensities of two frequency spectra in the frequency interval in which the signal is present are in a fixed ratio to each other—can be identified and incorporated into the respective imaging rule. In this way, the signal-to-noise ratio can be further optimized.

[0012] In one embodiment of the invention, at least one of the sensors is an NV magnetometer. The NV magnetometer has a particularly high sensitivity and is also capable of detecting the direction of a magnetic field. Alternatively or additionally, at least one of the sensors can also be a fluxgate magnetometer or a SQUID.

[0013] In one embodiment of the invention, at least one of the sensors has a transfer function that differs from the transfer function of at least one of the other sensors. In this case, sensors that react differently to the incoming signals are combined. Such a sensor system, comprising sensors with different transfer functions, is particularly versatile and flexible in its application. In particular, the sensors used can be sensitive in different frequency ranges, so that the sensor system as a whole is sensitive over a very wide frequency range.

[0014] In one embodiment of the invention, at least two of the sensors are arranged at the same or nearly the same first position. The sensor system can be oriented such that the source of the useful signal is located closer to the first position than at a second position where a third of the at least three sensors is located. Thus, the actual intensity of both the useful signal and the external interference magnetic field is the same for these at least two sensors. If the sensors arranged at the first position are different sensor types and / or sensors with different transfer functions, the sensor system can, for example, cover a very large frequency range.

[0015] The invention also includes the sensor system for carrying out the method. The sensor system comprises a control device configured to evaluate measured values ​​acquired by the at least three sensors and to compare the resulting frequency spectra. The control device is further configured to generate imaging instructions from this data in the manner described above and to apply them during a measurement, so that an optimal signal-to-noise ratio can be achieved.

[0016] The sensor system comprises at least three sensors, in particular synchronized sensors, especially magnetic field sensors, at least two of which are arranged to detect a signal at the first position. The third sensor is arranged to detect a signal at the second position. The sensor system can be oriented such that the signal at the first position is closer than the signal at the second position. Brief description of the drawings Fig. Figure 1 shows a flowchart of the procedure; Fig. Figure 2 shows an exemplary schematic structure of a sensor system according to an embodiment of the invention; Fig. Figure 2 shows exemplary frequency spectra of individual sensors of the sensor system. Embodiments of the invention

[0017] Fig. Figure 1 shows the process of the inventive method for calibrating a sensor system 1 according to the invention. The sensor system 1 comprises at least three sensors 2, 3, 4. In a first, second, and third step E1, E2, E3, a first, a second, and a third frequency spectrum 5, 6, 7 are acquired by the first, second, and third sensors, respectively. The sensor system 1 can include further sensors whose frequency spectra are also acquired. These steps are preferably carried out simultaneously. In further steps V1, Vi, ..., Vn, the acquired frequency spectra are compared with one another. If further frequency spectra were acquired in the preceding steps, these are also included in the comparison. In this way, a first frequency interval I1 can be identified in which the at least three frequency spectra 5, 6, 7 exhibit a signal profile that is at least largely identical and non-zero.Similarly, further frequency intervals, different from the first frequency interval I1, can be identified in which at least largely identical, non-zero signal waveforms are present. In further steps B1, B2, ...Bi, ...Bn, a first, a second, and further mapping rules are provided for the first frequency interval I1 and for the further frequency intervals identified in steps V1 to Vn by combining the at least largely identical frequency spectra, in particular by subtracting them from each other. In a final step V, a general mapping rule is compiled taking into account the first, the second, and any further mapping rules, which can then serve as the basis for a measurement.

[0018] Fig. Figure 2 shows a schematic setup of a sensor system 1 according to the invention. The sensor system 1 is configured as a first-order gradiometer and comprises three magnetic field sensors 2, 3, and 4. The signal from the first and second magnetic field sensors 2 and 3 is recorded at the same, or nearly the same, first position. The signal from the third magnetic field sensor 4 is recorded at a second position that differs from the first position. The first and second positions are spatially closer to the source of the useful signal than the third position.

[0019] Fig. Figure 3 shows an example spectrum recorded by the three magnetic field sensors 2, 3, and 4. The x-axis represents the frequency in Hz, and the y-axis represents the magnitude of the Fourier transform of the signal intensity, typically measured in the time domain. Only the one-dimensional case will be considered in the following discussion. Furthermore, phase differences between the sensors will initially be neglected.

[0020] The in Fig.The spectrum shown in Figure 3 was acquired without a useful signal. The Fourier spectrum of sensor 1 and sensor 3 is more similar to the Fourier spectrum of sensor 1 and sensor 2 with respect to the metric (F(x1), F(x3)) → ∥abs(F(x1)) - abs(F(x3)) ∥2 on a first frequency interval I1 (here [0 Hz, 50 Hz]) with respect to the metric (F(x1), F(x3)) ∥2. Here, F is the Fourier transform of the signal acquired in the time domain, abs is the absolute value of the complex-valued Fourier transform, and ||.||2 is the L2 norm on the real functions. The norm ||.||2 already expresses the expectation value of the signal differences. Subtracting the absolute values ​​of the Fourier transforms in the first frequency interval I1 thus represents a first mapping rule with which the interference signals appearing in the spectrum of the first and third sensors in the first frequency interval I1 can be eliminated.

[0021] If the respective Fourier transforms are in a fixed ratio to each other (e.g., F(x1) is always 80% of F(x3)), this can also be determined by comparing the Fourier spectra and taken into account when formulating the first mapping rule. In this case, these frequency transforms can be scaled up accordingly before subtraction, and the first mapping rule can be further optimized in this way.

[0022] On a second frequency interval I2, the situation is such that the Fourier spectrum of sensor 2 is more similar to that of sensor 3 than is the case for sensor 1 and sensor 3. By subtracting the absolute values ​​of the Fourier transforms, a second mapping rule can be formulated in which the interference signals appearing in the spectrum of the second and third sensors in the second frequency interval I2 are suppressed.

[0023] By combining the first and second mapping rules, a general mapping rule for mappings such as the following can be calculated: (x1,x2,x3)→F−1(F(x1)χ(l1)−F(x3)χ(l1)+F(x2)χ(l3)−F(x3)χ(l2)), where F -1 the inverse Fourier transform, I i the respective frequency interval and χ(I j ) display the indicator function on the specified frequency interval.

[0024] If the phases of the magnetic field sensors differ from each other or from a known signal (e.g., known from a calibration), the average phase of each sensor can be determined (analogous to the magnitude of the transfer function) and subtracted from that of the other. If the phase and magnitude differences between the sensors are not constant, the sensor pair with the lowest expected intrinsic noise can be selected for each frequency, e.g., by selecting them using `argmin`. xi, xj ∈ {x1, x2, x3} Var(x i | f , x j | f where x i | f the temporal signal of x i restricted to the frequency interval f (e.g. by filtering).

Claims

[1] Method for calibrating a sensor system (1) comprising at least three sensors (2, 3, 4) comprising the following steps • Detection of a first frequency spectrum (5) by a first sensor (2); • Detection of a second frequency spectrum (6) by a second sensor (3); • Detection of a third frequency spectrum (7) by a third sensor (4); • Comparing the first, second and third frequency spectrums (5, 6, 7), whereby a first frequency interval (I1) in which the first and second frequency spectrums (5, 6) and / or the first and third frequency spectrums (5, 7) and / or the second and third frequency spectrums (6, 7) exhibit at least a largely identical, non-zero signal pattern can be identified; • Providing a first mapping rule for the first frequency interval (8) such that the frequency spectra (5, 6, 7) which are at least largely identical in the first frequency interval (I1) are combined with each other, in particular subtracted from each other. [2] Method according to claim 1, wherein in the • By comparing the first, second, and third frequency spectrums (5, 6, 7), a second frequency interval (I2), different from the first frequency interval (I1), can be identified in which the first and third frequency spectrums (5, 7) and / or the second and third frequency spectrums (6, 7) and / or the first and second frequency spectrums (5, 6) exhibit a signal pattern that is at least largely identical and not zero; and • Providing a second mapping rule for the second frequency interval (I2) such that the frequency spectra (5, 6, 7) which are at least largely identical in the second frequency interval (I2) are combined with each other, in particular subtracted from each other; • Providing a general mapping rule by combining the first and second mapping rules. [3] Method according to claim 1 or 2, wherein the method is carried out in a shielded environment. [4] Method according to one of the preceding claims, wherein the method is carried out in an unshielded environment so that an intrinsic sensor noise of the sensor system (1) and an external noise can be taken into account. [5] Method according to any of the preceding claims, wherein the method is carried out with a known useful signal. [6] Method according to any of the preceding claims, wherein at least one of the sensors (2, 3, 4) is an NV magnetometer. [7] Method according to any of the preceding claims, wherein at least one of the sensors (2, 3, 4) has a transfer function which differs from the transfer function of at least one of the other sensors (2, 3, 4). [8] Method according to one of the preceding claims, wherein the first and the second sensor are arranged at a first position. [9] Method according to claim 8, wherein the third sensor is arranged at a second position, the second position being further away from the signal source than the first position. [10] Sensor system (1) for carrying out the method according to one of the preceding claims.

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