Method for operating a temperature-compensated microwave-free NV magnetometer

Abstract

The present invention describes a method for determining compensated measured values ​​of at least two physical quantities using a sensor system. The sensor system comprises at least one sensor element (SE) with crystals containing color centers. Both the first and the second physical quantities act on the sensor element (SE). A computer system (RSYS) controls the method. First, the sensor element (SE) is irradiated with modulated pump radiation (LB). Program code and configuration parameters for carrying out a correction procedure are provided, these parameters being stored in a memory of the sensor system or the computer system (RSYS). The fluorescence radiation (FL) of the color centers, which is influenced by the physical quantities, is detected.Fluorescence parameters are determined from the time course of the intensity of the fluorescence radiation (FL) and the pump radiation (LB) and represented as vector components of a fluorescence vector (Fv). An initial measurement of the first physical quantity is obtained by mapping the fluorescence vectors onto a sensor state vector (Sz), for example, using a neural network model with configuration parameters determined by a training program. This ensures that the initial measurement depends only on the first physical quantity and not on the second, resulting in a compensated measurement. This compensated measurement is then output, stored, transmitted, or used further.

Description

On priorities

[0001] The German patent application submitted here takes the priorities of the German patent applications 1. DE 10 2024 105 872.2 of 29.02.2024 and 2. DE 10 2024 105 873.0 of 29.02.2024 and 3. DE 10 2024 118 484.1 of 01.07.2024. Field of invention

[0002] The invention is directed to a temperature-compensated microwave-free NV magnetometer and NV sensor system.

[0003] DE 10 2023 122 657 A1 describes a microwave-free magnetometer based on NV centers, which forms the basis of the technical teaching described here. The magnetometer of DE 10 2023 122 657 A1 exhibits a temperature drift in practice, which is intended to be improved with the technical teaching of the document presented here.

[0004] The technical teaching of the present document investigates the combined temperature- and magnetic-field-dependent behavior of high-NV-density microdiamonds in an all-optical, frequency-domain setup, exploiting the change in fluorescence lifetime. The technical teaching of the present document uses this frequency-domain data to train neural networks for predicting temperatures and magnetic flux densities of magnetic fields. For a magnetic field with a magnetic flux density B(t) of zero, the technical teaching of the present document demonstrates that the technical teaching of the present document is capable of determining temperatures ϑ(t) in the range from 0°C to 100°C with a standard deviation of 1.24°C.Furthermore, the technical teaching of the document presented here shows that the technical teaching of the document presented here is able to predict magnetic flux densities (B(t)) of applied magnetic fields with simultaneous variation of temperatures (ϑ(t)) ​​of the environment with a higher accuracy than with the approach of observing the fluorescence intensity (F. i (t)) at a single excitation frequency as pump radiation frequency (f pmp ) of the pump radiation (LB). General IntroductionAll-optical magnetic field measurement with NV centers

[0005] Negatively charged nitrogen vacancy (NV) centers in diamonds have sparked considerable interest in magnetic field measurement. Most systems manipulate spin states using microwave (MW) excitation to achieve high sensitivities and spatial resolutions. However, these systems have limitations related to microwave transmission, such as microwave interaction with the environment and the need for a galvanic connection. In contrast, all-optical systems rely exclusively on optical access to the measurement volume, enabling the development of a fiber-based sensor. Such sensors can incorporate non-magnetic and non-conductive probes and enable high insulation resistances. Furthermore, setups without microwave (MW) excitation are less complex and easier to implement in industrial applications.

[0006] All-optical setups can achieve high sensitivities for narrowband features, but they require stable bias fields with precise alignment. Our setup, however, exploits the fluorescence change caused by spin mixing for magnetic fields up to approximately 50 mT, enabling the detection of a wide range of magnetic fields without the need for bias fields. The result is a compact and universally applicable sensor head.

[0007] Recently, we published a purely optical setup in DE 0 2024 105 739.4 that utilizes the excited-state lifetime of optically pumped NV centers. This setup is based on measuring the fluorescence lifetime in the frequency domain, where the intensity of the excitation light is modulated at a sufficiently high frequency. With increasing frequency, the low-pass characteristic of the fluorescence lifetime leads to a reduction in amplitude and a phase shift between the excitation signal in the form of the time course of the pump radiation intensity (I pmp (t)) and the fluorescence signal in the form of the time course of the fluorescence radiation intensity (I fl (t)) from 0 ° to 90 °. The lifetime components in the excited state of the color centers - here, for example, the NV centers in diamond - react to magnetic fields, which is reflected in a general change in the frequency response of the fluorescence intensity (I fl(t)) depending on the pump radiation frequency (f pmp ). Our investigations revealed a high magnetic contrast of the fluorescence intensity (I fl (t)) at low excitation frequencies (pump radiation frequencies f pmp ) and a peak in the magnetic contrast of the phase shift (φ(B)) at an excitation frequency (pump radiation frequency (f pmp ) by f pmp =13 MHz. The measurement of the phase (φ) (fluorescence delay measurement value F φ (t)) at a fixed pump radiation frequency (f pmp ) as a function of the magnetic flux density B offers, compared to the measurement of the fluorescence intensity (I fl (t)) in the form of the fluorescence intensity measurement value F i(t) provides a high immunity to fluctuations in the optical path, depending on the magnetic flux density B. Such fluctuations, caused, for example, by movements in the optical fiber (optical waveguide), could be misinterpreted as magnetic field changes in an intensity-based setup. State of the art

[0008] For the purpose of clarity, the document presented here refers to the German patent applications DE 10 2024 105 739.4 and DE 10 2024 105 740.8, which were still unpublished at the time of filing this document. Task

[0009] The proposal is therefore based on the task of providing a solution for the provision of mobile quantum computers.

[0010] This problem is solved by the independent claim. Further embodiments are the subject of subclaims. Solution to the task

[0011] The document presented here describes a preferably computer- and / or machine-implemented method for determining measured values ​​of one or more physical quantities. Whenever color centers are mentioned in the following, paramagnetic centers are to be understood as an embodiment of the color centers. The method can typically be used as a method for temperature-compensated operation of a color-center-based magnetometer or color-center-based sensor, with the use of NV centers in diamond as the color center being particularly preferred. Paramagnetic centers are preferably used as the color centers.

[0012] The following characteristics represent the characteristics of the proposal. The characteristics and their sub-characteristics can be combined with each other and with other characteristics and sub-characteristics of this proposal and with characteristics of the description, as long as the result of this combination is meaningful. In the case of a combination, it is not necessary to include all sub-characteristics of a characteristic in a single characteristic.

[0013] The features are therefore merely preferred combinations of characteristics from various examples. The feature references can therefore be explicitly changed if appropriate. They simplify the reworking of the proposal. The claim arises from the applicable claims.

[0014] The proposed method for determining at least one compensated measured value of at least two physical quantities preferably comprises the steps: • Providing a sensor system with at least one or more sensor elements (SE), wherein the one or more sensor elements (SE) comprise one or more crystals and wherein one or more crystals of these crystals comprise one or more color centers and wherein the first physical quantity acts on the one or more sensor elements (SE) and wherein the second physical quantity acts on the one or more sensor elements (SE); • In particular, providing a computer system (RSYS) of the sensor system; • Pump radiation (LB), which shows a temporal progression of the pump radiation intensity (I pmp (t)) of the pump radiation (LB); • Irradiating the one or more sensor elements (SE) with a pump radiation (LB) with a pump radiation wavelength (λ pmp ), in particular by means of a pump radiation source (LD), wherein the temporal course of the pump radiation intensity (I pmp(t)) the pump radiation (LB) is modulated with a modulation signal, in particular with a transmission signal S5(t); • Providing program code for a computer and / or machine-implemented correction method, in particular in one or more memories (MEM) of the computer system (RSYS) of the sensor system; • Providing configuration parameters for carrying out the computer- and / or machine-implemented correction method, wherein in particular the provision takes place in one or more memories (MEM), in particular of the sensor system and / or computer system (RSYS); • detecting the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE), which depends in different ways on the at least two physical quantities, in particular by means of one or more photodetectors (PD) and / or one or more arrays of photodetectors (PD) and / or one or more electronic cameras; • Determination of at least two different fluorescence parameters (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) as vector components of an at least two-dimensional computer and / or machine-implemented fluorescence vector F v from the temporal progression (I fl (t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) in combination with the temporal course of the pump radiation intensity (I pmp (t)) the pump radiation (LB); • Determining a first measured value of the first physical quantity of the one or more sensor elements (SE) in the form of a first size parameter of a one- or multi-dimensional computer- and / or machine-implemented sensor state vector (S z ) - by imaging one or more fluorescence vectors (F v), whose respective vector components each comprise at least two fluorescence parameters and / or - by mapping one or more fluorescence frequency vectors (F fv ), whose respective vector components each contain at least two fluorescence parameters (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) and at least one pump radiation frequency (f pmp ) and / or - by imaging one or more fluorescence frequency microwave vectors (F fµv ), the respective vector components of which each contain at least two fluorescence parameters and at least one pump radiation frequency (f pmp ) and at least one microwave frequency (f µw ) include - , on the one- or multi-dimensional computer and / or machine-implemented sensor state vector (S z), wherein the mapping is carried out using provided configuration parameters and wherein the mapping is carried out by executing the program code for the computer- and / or machine-implemented correction method, in particular by a computer system (RSYS), and wherein the configuration parameters for carrying out the computer- and / or machine-implemented correction method have been determined by means of a previously executed computer- and / or machine-implemented training program, ◯ that the first measured value depends on the first physical quantity of the one or more sensor elements (SE) and ◯ that the first measured value does not depend or substantially does not depend on the second physical quantity of the one or more sensor elements (SE), ◯ so that the first measured value can be used as a compensated first measured value of the first physical quantity of the one or more sensor elements (SE); • Outputting and / or keeping ready and / or storing and / or transmitting and / or using the determined compensated first measured value of the first physical quantity of the one or more sensor elements (SE).

[0015] By capturing a measurement vector from several measurement values, this measurement vector (the fluorescence vector F v ) then to a vector of decoupled physical quantities (the sensor element state vector S z ). The document presented here refers to this measurement vector as fluorescence vector F v . A fluorescence vector F v in the sense of the document presented here typically includes at least one respective fluorescence intensity measurement value F i(t) and at least one respective fluorescence delay measurement value F φ (t). The following description is based on this two-dimensional basic structure of the fluorescence vector F v It is conceivable that the fluorescence vectors F v multidimensional with a dimensionality greater than 2. For example, it is conceivable to carry out the measurements with a pump radiation frequency f pmp modulated temporal intensity profile (I pmp (t)) of the pump radiation (LB) and for each pump radiation frequency (f pmp ) such a fluorescence vector F v as a sub-fluorescence vector of a total fluorescence vector as a higher-dimensional fluorescence vector F v to determine and use. The fluorescence vector F vTherefore, in the sense of the document presented here, preferably comprises several recorded fluorescence parameters, which preferably comprise measured values ​​recorded in different ways (fluorescence intensity measured value F i (t), fluorescence delay measurement value F φ (t)) of the intensity (I fl (t)) of the fluorescence radiation or its temporal course. These fluorescence parameters (fluorescence intensity measured value F i (t), fluorescence delay measurement value F φ (t)) preferably form the components of the fluorescence vector F v . For a first fluorescence parameter (fluorescence intensity measurement value F i (t)) of the fluorescence vector F v For example, it is preferably the intensity (I fl (t))of the fluorescence radiation (FL) in the form of fluorescence intensity measurements F i (t). For a second fluorescence parameter (fluorescence delay measurement value F φ (t)) of the fluorescence vector F vFor example, it is preferably the time delay (unit of measurement: time) and / or the phase shift (φ) (unit of measurement: angle) of the temporal course of the intensity (I fl (t)), ie the temporal intensity profile (I fl (t)) of the fluorescence radiation (FL) versus the time course (I pmp (t)) the intensity of the pump radiation (LB) in the form of fluorescence delay measurements F φ (t).

[0016] The problem identified during the development of the technical teaching of the document presented here is that the fluorescence parameters (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) of the fluorescence vectors F v within the fluorescence vectors F v are not independent of each other. Furthermore, it was found that the fluorescence parameters of the fluorescence vectors F vdepends on the values ​​of external physical quantities such as the one or more temperatures ϑ(t) of the one or more sensor elements (SE) and the magnetic flux density (B(t)) which flows through the one or more sensor elements (SE) with the crystals and the color centers contained therein.

[0017] The task of the method proposed here, preferably implemented by a computer and / or machine, is to generate from one or more of these computer and / or machine-implemented fluorescence vectors F v on the one hand to one or more computer and / or machine-implemented sensor element state vectors S z Each sensor element state vector S zin the sense of the document presented here, preferably one or more measured values ​​for one or more of these external physical quantities. These measured values ​​should then no longer be dependent on one another, even if these external physical quantities may not be dependent on one another. For example, a first physical quantity can be the one or more temperatures ϑ(t) of the one or more sensor elements (SE), and a second physical quantity can be the magnetic flux density (B(t)) of the magnetic field flowing through the one or more sensor elements (SE). Their two respective measured values ​​then preferably each form the respective computer- and / or machine-implemented sensor element state vector S z within the meaning of the document presented here.

[0018] Since, with suitable computer and / or machine-implemented mapping of the one or more fluorescence vectors F von the one hand to one or more sensor element state vectors S z on the other hand, the vector components of the sensor element state vector S z should be independent of each other, this leads to a compensation of parasitic effects. For example, if the one or more temperatures ϑ(t) of the one or more sensor elements (SE) are a second vector component of the sensor element state vector S zand the magnetic flux density B(t) of the magnetic field flowing through the one or more sensor elements (SE) is the first vector component, then in this example, this first vector component is a temperature-compensated measured value of the magnetic flux density B(t) of the magnetic field flowing through the one or more sensor elements (SE). This temperature-compensated measured value of the magnetic flux density B(t) of the magnetic field flowing through the one or more sensor elements (SE) then typically no longer depends, or at least depends to a significantly reduced extent, on the one or more temperatures ϑ(t) of the one or more sensor elements (SE).

[0019] According to the invention, it was recognized that the computer- and / or machine-implemented imaging of the one or more computer- and / or machine-implemented fluorescence vectors F von the one hand to one or more computer and / or machine-implemented sensor element state vectors S z a computer and / or machine-implemented neural network model is particularly suitable.

[0020] According to the invention, it was therefore recognized that a computer system (RSYS) of a sensor system that uses the proposed method and by means of a computer and / or machine-implemented method a detected computer and / or machine-implemented fluorescence vector F v to a computer and / or machine-implemented sensor element state vector S z by means of a computer- and / or machine-implemented multidimensional mapping function. The computer core (CPU) of the computer system (RSYS) of the sensor system preferably detects the fluorescence parameters of the fluorescence vector F using suitable detection means of the sensor system. vof the one or more sensor elements (SE) and stores the fluorescence vector F thus detected v typically in a memory (MEM) of the computer system (RSYS). The computer core (CPU) of the computer system (RSYS) then maps the detected fluorescence vector F by executing the program code of the computer- and / or machine-implemented method. v or the multiple detected computer- and / or machine-implemented fluorescence vectors F v to one or more computer and / or machine-implemented sensor element state vectors S z by means of said computer and / or machine-implemented multidimensional mapping function and stores the one or more sensor element state vectors S thus generated zin a memory (MEM) of the computer system (RSYS) or the sensor system, or outputs it, keeps it available for retrieval there, or otherwise uses it. The parameters of said computer- and / or machine-implemented multidimensional mapping function represent the conversion parameters of the proposed method. According to the invention, the document presented here proposes implementing the computer- and / or machine-implemented mapping function in the form of a computer- and / or machine-implemented neural network and / or a computer- and / or machine-implemented artificial intelligence method and preconfiguring it using predetermined configuration parameters.

[0021] According to the proposal, a first physical quantity of the physical quantities is preferably a flux density value of the magnetic flux density (B(t)) at the location(s) of the one or more sensor elements (SE). Preferably, the measured values ​​of this flux density value of the magnetic flux density (B) form flux density measured values ​​as the first parameter of an exemplary sensor element state vector S z .

[0022] According to the proposal, a second physical quantity of the physical quantities is preferably the one or more temperatures ϑ(t) of the one or more sensor elements (SE). The measured values ​​of these one or more temperatures ϑ(t) form temperature measured values ​​as second quantity parameters of the exemplary sensor element state vector S z .

[0023] According to the proposal, the determination of measured values ​​(fluorescence intensity measured value Fi (t), fluorescence delay measurement value F φ (t)) from the time course (I fl (t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) and the temporal course of the intensity (I pmp (t)) of the pump radiation (LB) in the proposed method, the determination of fluorescence intensity measured values ​​F i (t) and fluorescence delay measurements F φ (t) from the time course (I fl (t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) and the temporal course of the intensity (I pmp (t)) of the pump radiation (LB). Preferably, the computer core (CPU) of the computer system (RSYS) of the sensor system determines a fluorescence intensity measurement value F i (t) of the time course (I fl(t)) of the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) by means of a vector network analyzer (VNA) or a lock-in amplifier (LIA). Typically, a photodetector (PD) converts the temporal progression of the intensity value (I fl (t)) of the fluorescence radiation (FL) into a received signal (S0(t)), which may optionally be filtered and / or amplified to a filtered received signal (S1(t)), for example by one or more amplifiers (V), which may include, for example, transimpedance amplifiers (TIA) and / or RF amplifiers (RF-Amp=). The vector network analyzer (VNA) or the lock-in amplifier (LIA) then links this receiver output signal (S0) or the filtered receiver output signal (S1) with a reference signal, for example the transmission signal S5(t) used as a modulation signal, which preferably corresponds to the intensity curve (I pmp(t)) of the pump radiation (LB). Typically, the vector network analyzer (VNA) or the lock-in amplifier (LIA) determines a measure (fluorescence intensity measurement value F i (t)), how large the proportion of the signal curve of the intensity curve (I pmp (t)) of the pump radiation (LB) in the intensity curve (I fl (t)) of the fluorescence radiation (FL) or, respectively, in the signals derived from it (S0(t), S1(t)). Typically, the vector network analyzer (VNA) or the lock-in amplifier (LIA) provide this measure as an analog or digitized signal or as a measured value (fluorescence intensity measured value F i (t)). Preferably, the vector network analyzer (VNA) and / or the lock-in amplifier (LIA) also determine a delay and / or phase shift of the temporal intensity profile (I fl(t)) of the fluorescence radiation (FL) or the signals derived therefrom (S0(t), S1(t)) compared to the reference signal (e.g. the transmission signal S5(t) typically used as a modulation signal) as fluorescence delay measurement value F φ (t). Preferably, they generate a corresponding output signal F φ(t). If necessary, the computer core (CPU) preferably digitizes one or more analog output signals of the vector network analyzer (VNA) or the lock-in amplifier (LIA) before further processing, for example, using an analog-to-digital converter (ADC) of the sensor system (SSYS). The analog-to-digital converter (ADC) can in some cases also be a single-bit analog-to-digital converter (ADC). The bit width of the analog-to-digital converter (ADC) preferably depends on the measurement task of the sensor system (SSYS). The computer core (CPU) of the computer system (RSYS) of the sensor system (SSYS) stores these digitized output values ​​of the vector network analyzer (VNA) or the lock-in amplifier (LIA), preferably as fluorescence measurement values ​​of preferably multidimensional fluorescence vectors (F v (t)) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ(t)). The digitized output values ​​of the vector network analyzer (VNA) or the lock-in amplifier (LIA) can typically be one- or multi-dimensional. They can, for example, be amplitude (fluorescence intensity measurement value F i (t)) and phase (fluorescence delay measurement value F φ (t)). It can also be the values ​​of an I / Q demodulation. The temporal intensity profile (I pmp (t)) of the pump radiation (LB) sinusoidally with a pump radiation frequency f pmp . A pulse-modulated control in the form of a pulse-modulated time course of the pump radiation intensity (I pmp (t)) of the pump radiation (LB) is also possible, but typically less preferred, since the harmonics lead to a lower performance of the phase measurement or delay measurement (determination of the fluorescence delay measurement values ​​F φ (t)) in the vector network analyzer (VNA) or in the lock-in amplifier (LIA).

[0024] The document presented here therefore proposes that the determination of measured values ​​(fluorescence intensity measured value F i (t), fluorescence delay measurement value F φ (t)) from the time course of the intensity (I fl (t)) of the fluorescence radiation (FL) of the color centers (NV) (in particular the NV centers) of the one or more sensor elements (SE) and the temporal course of the intensity (I pmp (t)) of the pump radiation (LB) the pairwise and essentially time-synchronous determination of fluorescence intensity measured values ​​F i (t) and fluorescence delay measurements F φ (t) as vector components of the fluorescence vector F v of the one or more sensor elements (SE) from the temporal course of the intensity (I fl (t)) of the fluorescence radiation (FL) of the color centers (NV) (in particular NV centers) of the one or more sensor elements (SE) and the temporal course of the intensity (Ipmp (t)) of the pump radiation (LB).

[0025] Preferably, the computer core (CPU) of the computer system (RSYS) uses F v (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) in the memory (MEM) of the computer system (RSYS) to one or more sensor element state vectors S z a computer- and / or machine-implemented neural network model (NNM) or another computer- or machine-implemented method. Preferably, the computer core (CPU) of the computer system (RSYS) then uses the acquired fluorescence vectors F for the computer- and / or machine-implemented mapping. v (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) in the memory (MEM) of the computer system (RSYS) to one or more sensor element state vectors Sz Network parameters of the computer- and / or machine-implemented neural network model (NNM) as configuration parameters. Preferably, the network parameters (configuration parameters) of the computer- and / or machine-implemented network model (NNM) or the computer-implemented artificial intelligence method are then also stored in a memory (MEM) of the computer system (RSYS) of the sensor system (SSYS), so that the computer core (CPU) of the computer system (RSYS) of the sensor system (SSYS) can, when executing the computer- and / or machine-implemented mapping of the detected fluorescence vectors F v (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) in the memory (MEM) of the computer system (RSYS) to one or more sensor element state vectors S z can access these configuration parameters.

[0026] Preferably, the computer core (CPU) of the computer system (RSYS) of the sensor system (SSYS) executes the program code of the respective computer- and / or machine-implemented neural network model (NNM) or the computer- and / or machine-implemented method in order to calculate the values ​​of the detected fluorescence vectors F v (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) in the memory (MEM) of the computer system (RSYS) to one or more sensor element state vectors S z in the memory (MEM) of the computer system (RSYS) of the sensor system (SSYS). The network parameters of the neural network model (NNM) thus represent configuration parameters within the meaning of the document presented here.

[0027] Input parameters of the computer and / or machine-implemented neural network model (NNM) preferably represent the vector components (fluorescence intensity measurement value F i(t), fluorescence delay measurement value F φ (t)) one or more fluorescence vectors F v and, if applicable, other optional measured values ​​and signal values ​​from inside and / or outside the sensor system (SSYS).

[0028] Output parameters of the computer and / or machine-implemented neural network model (NNM) preferably represent the vector components (temperature values ​​ϑ(t), values ​​of the magnetic flux density B(t)) of one or more sensor element state vectors S z and, if applicable, further optional signal values ​​or control signal values ​​for use within and / or outside the sensor system (SSYS).

[0029] Preferably, as already mentioned, the determination of measured values ​​(fluorescence intensity measured value F i (t), fluorescence delay measurement value F φ (t)) from the time course (I fl(t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) and the temporal course of the intensity (I pmp (t)) of the pump radiation (LB) the determination of fluorescence vectors F v (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) from the time course of the intensity (I fl (t)) of the fluorescence radiation (FL) of the color centers (NV) (in particular the NV centers) of the one or more sensor elements (SE) and the temporal course of the intensity (I pmp (t)) of the pump radiation (LB). Preferably, the respective fluorescence vectors F v each preferably at least one respective fluorescence intensity measurement value F i (t) and preferably at least one respective fluorescence delay measurement value F φ (t).

[0030] Preferably, at least one first measured value (e.g. value of the magnetic flux density B(t)) of the at least one first physical quantity of the one or more sensor elements (SE) is determined in the form of one or more first quantity parameters from one or more measured values ​​using the configuration parameters by means of a computer- and / or machine-implemented method, which, for example, comprises the calculation of at least one magnetic flux density value for the magnetic flux density (B(t)) at the location(s) of the one or more sensor elements (SE) as part of a sensor element state vector S z and / or the calculation of at least one or more temperature values ​​for the one or more temperatures ϑ(t) of the one or more sensor elements (SE) as part of a sensor element state vector S z using the said computer and / or machine-implemented neural network model (NNM).

[0031] Preferably, in this second implementation option, the computer core (CPU) executes the program code of this exemplary computer- and / or machine-implemented neural network model (NNM) or of the exemplary computer- and / or machine-implemented method of artificial intelligence in the computer- and / or machine-implemented calculation of a sensor element state vector S z (e.g., ϑ(t), B(t)). The program code, the values ​​of the configuration parameters (here the network parameters) and the current values ​​of the fluorescence vector F v (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) are preferably stored for this purpose in one or more memories (MEM) of the computer system (RSYS) of the sensor system. Preferably, the computer core (CPU) of the computer system (RSYS) stores the calculated sensor element state vector S z(e.g. ϑ(t), B(t)) in a memory (MEM) of the computer system (RSYS) of the sensor system (SSYS) or outputs it in whole or in part or keeps it ready for output or otherwise uses it in whole or in part.

[0032] Preferably, the one or more sensor elements (SE) comprise a plurality of crystals held together by a preferably optically transparent carrier material. Preferably, the respective carrier material of the one or more sensor elements (SE) is sensitive to electromagnetic radiation with the pump radiation wavelength (λ pmp ) of the pump radiation (LB) is essentially transparent and for electromagnetic radiation with the fluorescence radiation wavelength (λ pmp) of the fluorescence radiation (FL) is also essentially transparent. The advantage of the method is that, when correctly implemented, a first determined measured value (e.g. B(t)) of the at least first physical quantity of the one or more sensor elements (SE) in the sensor element state vector (S z ) depends to a lesser extent on other physical quantities such as the one or more temperatures ϑ(t) of the one or more sensor elements (SE). First further development of the procedure

[0033] In a first development of the method, the temporal course of the intensity (I pmp (t)) of the pump radiation (LB) with a modulation signal, in particular with a preferably periodic transmission signal S5(t), with a pump radiation frequency (f pmp), modulated. This has the advantage that a method such as a vector network analyzer (VNA) and / or a lock-in amplifier (LIA) and / or a matched filter can be applied. Second development of the procedure

[0034] In a second development of the method, at least one at least three-dimensional computer and / or machine-implemented fluorescence frequency vector (F fv ) comprising at least one at least two computer- and / or machine-implemented fluorescence vectors (F v ) and at least the value of the pump radiation frequency (f pmp ). This has the advantage that when evaluating the computer and / or machine-implemented fluorescence frequency vector (F fv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp) the different temperature behavior of the temporal course of the intensity (I fl (t)) of the fluorescence radiation (FL) can be used for evaluation by the computer system (RSYS) of the sensor system (SSYS). Third further development of the procedure

[0035] In a second development of the method, a first measured value of the first physical quantity of the one or more sensor elements (SE) (e.g. the magnetic flux density B(t)) is determined in the form of a first size parameter of a one- or multi-dimensional computer- and / or machine-implemented sensor state vector (S z ) by imaging one or more fluorescence vectors (F v ), the respective vector components of which preferably each contain at least two fluorescence parameters (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ(t)) and / or by mapping one or more fluorescence frequency vectors (F fv ), whose respective vector components each contain at least two fluorescence parameters (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) and at least one respective value of the pump radiation frequency (f pmp ) to the one- or multi-dimensional computer and / or machine-implemented sensor state vector (S z ) (e.g., ϑ(t), B(t)). The mapping is preferably performed using provided configuration parameters. Specifically, the mapping is performed by executing the program code for the computer- and / or machine-implemented correction method, in particular by a computer system (RSYS).

[0036] This has the advantage that when evaluating the computer and / or machine-implemented fluorescence frequency vector (F fv) (e.g. fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp ) the different temperature behavior of the temporal course of the intensity (I fl (t)) of the fluorescence radiation (FL) at different pump radiation frequencies (f pmp ) can be used for evaluation by the computer system (RSYS) of the sensor system (SSYS). Fourth further development of the procedure

[0037] In a fourth development of the method, a second measured value of the second physical quantity of the one or more sensor elements (SE) (e.g. the temperature ϑ(t)) ​​is determined in the form of a second variable parameter of the one- or multi-dimensional computer- and / or machine-implemented sensor state vector (S z ) by means of a computer- and / or machine-implemented imaging of one or more fluorescence vectors (F v) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) and / or by means of a computer and / or machine-implemented mapping of the one or more fluorescence frequency vectors (F fv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp ), whose respective vector components each contain at least two fluorescence parameters (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) to the one- or multi-dimensional computer and / or machine-implemented sensor state vector (S z) (e.g. (ϑ(t), B(t)). The computer- and / or machine-implemented mapping is carried out using provided configuration parameters. Furthermore, the computer- and / or machine-implemented mapping is carried out by executing the program code for the computer- and / or machine-implemented correction method, in particular by a computer system (RSYS) of the sensor system (SSYS). Preferably, the computer- and / or machine-implemented configuration parameters for carrying out the computer- and / or machine-implemented correction method of the computer- and / or machine-implemented mapping have also been determined simultaneously by means of a previously executed computer- and / or machine-implemented training program for carrying out a determination method (200), 1. that the second measured value (ϑ(t)) ​​depends on the second physical quantity of the one or more sensor elements (SE) (one or more temperatures ϑ(t)) ​​and 2. that the second measured value (ϑ(t)) ​​does not depend or does not depend essentially on the first physical quantity of the one or more sensor elements (SE) (e.g. B(t)), 3. so that the second measured value (ϑ(t)) ​​can be used as a compensated second measured value (ϑ(t)) ​​of the second physical quantity of the one or more sensor elements (SE) (e.g. one or more temperatures ϑ(t)).

[0038] This is typically followed by outputting, in particular via an interface (IF) of the computer system (RSYS), and / or keeping ready, in particular in a memory (MEM) of the computer system (RSYS), and / or storing, in particular in a memory (MEM) of the computer system (RSYS), and / or transmitting, in particular via a data transmission link (DSTR) connected to the computer system (RSYS), in particular to a higher-level computer system (ÜRSYS), and / or using the determined compensated second measured value (ϑ(t)) ​​of the second physical quantity of the one or more sensor elements (SE) (e.g. the one or more temperatures ϑ(t)).

[0039] This further development offers the advantage that the second measured value, which is typically a temperature measurement value (ϑ(t)), is also made available and can be used by the higher-level system (e.g., ÜRSYS), of which the sensor system (SSYS) is typically a part. Preferably, the second measured value (ϑ(t)) ​​then no longer depends on the current value of the first physical quantity (e.g., B(t)). Thus, the two measured values ​​of the fluorescence vector F are v ((Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) then to two independent measured values ​​(ϑ(t), B8t)), the vector components of the sensor element state vector S z are mapped and are available for use. Typically, these measured values ​​(ϑ(t), B(t)) of the sensor state vector S z (t) decoupled from each other. Fifth further development of the procedure

[0040] In a fifth refinement of the proposed, typically computer- and / or machine-implemented method, the one or more sensor elements (SE) are irradiated with electromagnetic radiation in the microwave range (MS). This has the advantage that the method proposed here can utilize the Zemann effect for measurement. In this context, the document presented here refers, as examples, to the following prior art documents: Fa. Lockheed: US 9 551 763 B1, US 9 823 313 B2, US 9 910 104 B2, US 9 910 105 B2, US 10 168 393 B2, US 10 459 041 B2, US 10 520 558 B2, US 2016 / 0 146 904 A1, US 2016 / 0216341 A1, US 2016 / 0 356 863 A1, US 2017 / 0 023 487 A1, US 2017 / 0 212 180 A1, US 2017 / 0 212 181 A1, US 2017 / 0 212 182 A1, US 2017 / 0 212 187 A1, US 2018 / 0 196 111 A1, US 2018 / 0 275 207 A1, US 2018 / 0 275 212 A1, US 2018 / 0 275 223 A1, US 2018 / 0 275 224 A1, WO 2015 142 945 A1, WO 2016 118 791 A1, WO 2017 014 807 A1, WO 2017 127 081 A1, WO 2017 127 091 A1, WO 2017 127 095 A1, WO 2017 127 096 A1, WO 2018 174 905 A1, WO 2018 174 911 A1, WO 2018 174 915 A1, WO 2018 174 918 A1 Do. Bosch: DE 10 2014 219 550 A1, DE 10 2014 219 561 A1, EP 3 198 264 B1, DE 10 2014 219 547 A1, DE 10 2015 208 151 A1, DE 10 2016 205 980 A1, DE 10 2016 210 259 A1, FROM 10 2016 210 259 B4, FROM 10 2016 221 065 A1, FROM 10 2017 205 099 A1, FROM 10 2017 205 265 A1, FROM 10 2017 205 268 A1, OF 10 2017 206 279 A1, DE 10 2018 202 238 A1, DE 10 2018 202 588 A1, DE 10 2018 203 845 A1, DE 10 2018 208 055 A1, DE 10 2018 208 102 A1, DE 10 2018 214 617 A1, DE 10 2018 216 033 A1, DE 10 2018 219 750 A1, DE10 2018 220 027 A1, DE 10 2018 220 234 A1, DE 10 2019 203 928 A1, DE 10 2019 203 929 A1, DE 10 2019 203 930 A1, DE 10 2019 203 930 B4, DE 10 2019 205 217 A1, DE 10 2019 209 441 A1, DE 10 2019 211 694 A1, DE 10 2019 211 694 B4, DE 10 2019 212 587 A1, DE 10 2019 216 390 A1, DE 10 2019 219 052 A1, DE 10 2019 220 348 A1, DE 10 2019 220 353 A1, DE 102020201565 A1, DE 10 2020 201 739 A1, DE 10 2020 204 237 A1, DE 10 2020 204 571 A1, DE 10 2020 204 729 A1, DE 10 2020 204 732 A1, DE 10 2020 206 032 A1,DE 10 2020 206 218 A1, DE 10 2020 207 200 A1, DE 10 2020 211 864 A1, DE 10 2020 214 278 A1, DE 10 2021 202 535 A1, DE 102021203 128 A1, DE 10 2021 203 129 A1, DE 10 2021 212 841 A1, DE 10 2021 213 620 A1, DE 10 2022 201 690 A1, DE 10 2022 201 695 A1, DE 10 2022 201 697 A1, DE 10 2022 201 705 A1, DE 10 2022 201 707 A1, DE 10 2022 201 710 A1, DE 10 2022 202 033 A1, DE 10 2022 204 526 A1, DE 10 2022 205 540 A1, DE 10 2022 205 563 A1, DE 10 2022 205 569 A1, DE 10 2022 209 424 A1, DE 10 2022 209 426 A1, DE 10 2022 209 429 A1, DE 10 2022 209 430 A1, DE 10 2022 209 436 A1, FROM 10 2022 209 439 A1, FROM 10 2022 209 442 A1, FROM 10 2022 211 859 A1, QT: DE 10 2023 115 906.2, DE 10 2023 122 664.9, WO 2024 041 703 A1

[0041] The combination of the technical methods and devices of the above documents in combination with the methods and devices disclosed in the technical teaching of the document presented here and / or their features is part of the document presented here and its technical teaching. None of these prior art documents discloses sinusoidal control and temperature compensation. According to the invention, sinusoidal and monofrequency control is an essential prerequisite for the applicability of the method disclosed here and the technical teaching of the document presented here. Sixth further development of the procedure

[0042] In a sixth development of the proposed, typically computer and / or machine-implemented method, the electromagnetic radiation in the microwave range (MS) has a microwave frequency (f µw). In the context of the document presented here, this means that the microwave radiation (MS) is preferably monofrequency at this microwave frequency (f µw ). This has advantages, since the response of the NV centers between color centers in one or more sensor elements (SE) and their temporal course of intensity (I fl (t)) whose fluorescence radiation (FL) can be detected and measured more precisely. Seventh further development of the procedure

[0043] In a seventh development of the proposed, typically computer- and / or machine-implemented method, at least one at least four-dimensional computer- and / or machine-implemented fluorescence frequency microwave vector F is formed fµv (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp , microwave frequency f µw), The computer- and / or machine-implemented fluorescence frequency microwave vector F fµv (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp , microwave frequency f µw ) preferably comprises at least the at least one at least two-dimensional computer and / or machine-implemented fluorescence vector F v (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) and at least the value of the pump radiation frequency (f pmp ) and additionally at least the value of the microwave frequency (f µwThis enables the evaluation of a microwave frequency dependence of the fluorescence radiation (FL), in particular by a computer- and / or machine-implemented artificial intelligence method such as a computer- and / or machine-implemented neural network model (NNM), which is preferably executed by the computer core (CPU) of the computer system (RSYS) of the sensor system. Eighth development of the procedure

[0044] In an eighth development of the proposed, typically computer- and / or machine-implemented method, a first measured value (e.g. the magnetic flux density B(t)) of the first physical quantity of the one or more sensor elements (SE) is preferably determined in the form of a first quantity parameter of a one- or multi-dimensional computer- and / or machine-implemented sensor state vector (S z ) i. by imaging one or more fluorescence vectors Fv , whose respective vector components each contain at least two fluorescence parameters (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t) include, and / or ii. by mapping one or more fluorescence frequency vectors F fv (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp ), whose respective vector components each contain at least two fluorescence parameters (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) and a value of the pump radiation frequency (f pmp ) and / or iii. by imaging one or more fluorescence frequency microwave vectors F fµv (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp , microwave frequency f µw) or (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), microwave frequency f µw ), whose respective vector components each contain at least two fluorescence parameters (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) and preferably a value of the pump radiation frequency (f pmp ) and a value of the microwave frequency (f µw ). This mapping is preferably carried out by a computer- and / or machine-implemented artificial intelligence method, such as a computer- and / or machine-implemented neural network model (NNM), which the computer core (CPU) of the computer system (RSYS) of the sensor system preferably executes. The mapping is preferably carried out on the one- or multi-dimensional computer- and / or machine-implemented sensor state vector (S z) (e.g. ϑ(t), B(t)). This mapping is preferably carried out using provided configuration parameters. The configuration parameters typically serve, among other things, to configure and / or parameterize the respective computer- and / or machine-implemented artificial intelligence method, such as the said computer- and / or machine-implemented neural network model (NNM). This mapping is typically carried out by executing the program code for the computer- and / or machine-implemented correction method, in particular by a computer system (RSYS). This enables the separation of the measured values ​​of the various physical quantities, such as the magnetic flux density B(t) and the temperature ϑ(t).Other measured values ​​of other physical quantities such as mechanical stress, acceleration, pressure, concentrations and properties of analytes in the vicinity of the one or more sensor elements (SE), etc. are conceivable and can be additionally extracted by the computer- and / or machine-implemented artificial intelligence method or the computer- and / or machine-implemented neural network model (NNM) if the input vector of the computer- and / or machine-implemented artificial intelligence method or the computer- and / or machine-implemented neural network model (NNM) is designed accordingly. Ninth further development of the procedure

[0045] In a ninth development of the proposed, typically computer- and / or machine-implemented method, a second measured value (ϑ(t)) ​​of the second physical quantity of the one or more sensor elements (SE) is determined in the form of a second quantity parameter of the one- or multi-dimensional computer- and / or machine-implemented sensor state vector (S z ) i. during the imaging of the one or more fluorescence vectors F v (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), whose respective vector components each comprise at least two fluorescence parameters, and / or, ii. during the imaging of the one or more fluorescence frequency vectors F fv (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp), the respective vector components of which each contain at least two fluorescence parameters and at least one value of the pump radiation frequency (f pmp ) and / or iii. during the imaging of the one or more fluorescence frequency microwave vectors F fµv (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp , microwave frequency f µw ) or (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t) Microwave frequency f µw ), whose respective vector components each contain at least two fluorescence parameters (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t) and preferably at least one value of the pump radiation frequency (f pmp ) and at least one value of the microwave frequency (f µw ) include.

[0046] This mapping is preferably performed by a computer- and / or machine-implemented artificial intelligence method, such as a computer- and / or machine-implemented neural network model (NNM), which is preferably executed by the computer core (CPU) of the computer system (RSYS) of the sensor system (SSYS). The mapping is preferably performed on the one- or multi-dimensional computer- and / or machine-implemented sensor state vector (S z) (e.g. ϑ(t), B(t)). This mapping is preferably carried out using provided configuration parameters. The configuration parameters typically serve, among other things, to configure and / or parameterize the respective computer- and / or machine-implemented artificial intelligence method, such as the said computer- and / or machine-implemented neural network model (NNM). This mapping is typically carried out by executing the program code for the computer- and / or machine-implemented correction method, in particular by a computer system (RSYS). This enables the separation of the measured values ​​(ϑ(t), B(t)) of the various physical quantities, such as the magnetic flux density (B(t)) and the temperature (ϑ(t)).Other measurements of other physical quantities such as mechanical stress, acceleration, pressure, concentrations and properties of analytes in the vicinity of one or more sensor elements (SE), etc., are conceivable. (See comments above). Tenth further development of the procedure

[0047] In a tenth development of the proposed, typically computer- and / or machine-implemented method, the computer- and / or machine-implemented method is a computer- and / or machine-implemented neural network model (NNM) and / or a computer- and / or machine-implemented artificial intelligence method.

[0048] This enables the determination of the computer- and / or machine-implemented configuration parameters for carrying out the computer- and / or machine-implemented correction method of the computer- and / or machine-implemented image by means of a previously executed computer- and / or machine-implemented training program in the manner 1. that the first measured value (B(t)) depends on the first physical quantity (value of the magnetic flux density B(t)) of the one or more sensor elements (SE) and 2. that the first measured value (B(t)) does not depend or substantially does not depend on the second physical quantity of the one or more sensor elements (SE) (one or more temperatures ϑ(t)), 3. so that the first measured value (B(t)) can be used as a compensated first measured value of the first physical quantity (magnetic flux density B(t)) of the one or more sensor elements (SE), 4. that the second measured value (ϑ(t)) ​​depends on the second physical quantity (one or more temperatures ϑ(t)) ​​of the one or more sensor elements (SE) and 5. that the second measured value (ϑ(t)) ​​does not depend or substantially does not depend on the first physical quantity (magnetic flux density B(t)) of the one or more sensor elements (SE), 6. so that the second measured value (ϑ(t)) ​​can be used as a compensated second measured value of the second physical quantity (one or more temperatures ϑ(t)) ​​of the one or more sensor elements (SE). Eleventh further development of the procedure

[0049] In an eleventh development of the proposed, typically computer- and / or machine-implemented method, the computer- and / or machine-implemented neural network model (here also referred to as neural network) (NNM) comprises a computer- and / or machine-implemented fully connected neural network (FCNN). The following sections describe the advantages of such a network. Twelfth further development of the procedure

[0050] In a twelfth refinement of the proposed, typically computer- and / or machine-implemented method, the computer- and / or machine-implemented neural network model (here also referred to as a neural network) (NNM) comprises a computer- and / or machine-implemented recurrent neural network (RNN), in particular a long short-term memory (LSTM). The following sections discuss the advantages and disadvantages of such a network. Alternatively, the authors of this document are experimenting with an autoencoder and regression from the latent space values. Thirteenth further development of the procedure

[0051] In a thirteenth development of the proposed, typically computer- and / or machine-implemented method, the computer- and / or machine-implemented neural network model (here also referred to as neural network) (NNM) comprises a computer- and / or machine-implemented convolutional neural network (CNN). The following sections describe the advantages and disadvantages of such a network. Fourteenth further development of the procedure

[0052] In a fourteenth development of the proposed, typically computer- and / or machine-implemented method, the computer- and / or machine-implemented neural network model (NNM) for the computer- and / or machine-implemented mapping of one or more fluorescence vectors (F v ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ(t)) and / or the computer and / or machine-implemented mapping of one or more fluorescence frequency vectors (F fv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp ) and / or the computer- and / or machine-implemented imaging of one or more fluorescence frequency microwave vectors (F fµv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp , microwave frequency f µw ) or (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), microwave frequency f µw ) to one or more sensor element state vectors (S z ) (ϑ(t), B(t)), in particular for the regression of the one or more temperatures (ϑ(t)) ​​from the values ​​of the vector components of the fluorescence vector (F v) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) and / or the fluorescence frequency vector (F fv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp ) and / or the fluorescence frequency microwave vector (F fµv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp , microwave frequency f µw ) or (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), microwave frequency f µw), a computer- and / or machine-implemented fully connected neural network (FCNN) (NNM) with three hidden computer- and / or machine-implemented layers and a computer- and / or machine-implemented output layer with a single computer- and / or machine-implemented node and a computer- and / or machine-implemented linear activation function.

[0053] This structure has proven particularly advantageous in the experimental development of the technical teaching presented here. It cannot be ruled out that other structures with more or less hidden computer- and / or machine-implemented layers, other output layers, and other activation functions could also achieve good or perhaps even better results. Fifteenth further development of the procedure

[0054] In a fifteenth development of the proposed, typically computer- and / or machine-implemented method, the computer- and / or machine-implemented neural network (NNM) for the computer- and / or machine-implemented mapping of one or more fluorescence vectors (F v ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) and / or the computer and / or machine-implemented mapping of one or more fluorescence frequency vectors (F fv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp ) and / or the computer- and / or machine-implemented imaging of one or more fluorescence frequency microwave vectors (F fµv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp , microwave frequency fµw ) or (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), microwave frequency f µw ) to one or more sensor element state vectors (S z ) (ϑ(t), B(t)) comprises a computer- and / or machine-implemented fully connected neural network (FCNN) (NNM) with three hidden computer- and / or machine-implemented layers with 95, 65 and 35 computer- and / or machine-implemented nodes and computer- and / or machine-implemented ReLU activation functions, and a computer- and / or machine-implemented output layer with a single computer- and / or machine-implemented node and a computer- and / or machine-implemented linear activation function.

[0055] This structure has proven particularly advantageous in the experimental development of the technical teaching presented here. It cannot be ruled out that other structures with more or fewer hidden computer- and / or machine-implemented layers, with more or fewer computer- and / or machine-implemented nodes, and with different output layers and different activation functions could also achieve good or perhaps even better results. Sixteenth further development of the procedure

[0056] In a sixteenth development of the proposed, typically computer- and / or machine-implemented method, a first relevant physical quantity of the one or more sensor elements (SE) is the magnetic flux density (B(t)) of the magnetic field that flows through the one or more sensor elements (SE) and their color centers (e.g., NV centers). In this eighth development, at least one first measured value of the first physical quantity (B(t)) of the one or more sensor elements (SE) is a flux density measured value of the magnetic flux density (B(t)) of the magnetic field that flows through the one or more sensor elements (SE) and their color centers (e.g., NV centers).In this eighth development of the proposed, typically computer- and / or machine-implemented method, this first measured value (B(t)) preferably represents a first vector component of the sensor state vector S. z The computer core (CPU) can use this sensor state vector S z using the proposed computer and / or machine-implemented method from the fluorescence vector F v (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) or from the fluorescence frequency vector F fv (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp ) or from the fluorescence frequency microwave vector F fµv (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp , microwave frequency f µw) or (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), microwave frequency f µw ). The computer core (CPU) can use this sensor state vector S z or parts thereof in a memory (MEM) of the sensor system (SSYS). The computer core (CPU) can store this sensor state vector S z or parts thereof in a memory (MEM) of the sensor system (SSYS). The computer core (CPU) can use this sensor state vector S z or parts thereof via a data interface (IF) of the computer system (RSYS) of the sensor system (SSYS) to a higher-level system (ÜRSYS). The computer core (CPU) can process this sensor state vector S z or parts of it via a signaling system (e.g. IF, DSTR). The computer core (CPU) can output this sensor state vector S z or parts of it for other purposes of the respective application. Seventeenth further development of the procedure

[0057] In a seventeenth development of the proposed, typically computer- and / or machine-implemented method, a second relevant physical quantity of the one or more sensor elements (SE) is the one or more temperatures (ϑ(t)) ​​of the one or more sensor elements (SE), wherein at least one second measured value of the physical quantity (ϑ(t)) ​​of the one or more sensor elements (SE) is one or more temperature measured values ​​of one or more temperatures (ϑ(t)) ​​of the one or more sensor elements (SE) as the second component of the sensor state vector S z This second measured value (ϑ(t)) ​​preferably represents a second vector component of the sensor state vector S in this eighth development of the proposed, typically computer and / or machine-implemented method. z(ϑ(t), B(t)). The computer core (CPU) can use this sensor state vector S z (ϑ8t), B(t)) using the proposed computer and / or machine-implemented method from the fluorescence vector F v (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) or the fluorescence frequency vector F fv (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp ) or the fluorescence frequency microwave vector (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp , microwave frequency f µw ) or (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), microwave frequency f µw ). The computer core (CPU) can use this sensor state vector S z(ϑ(t), B(t)) or parts thereof in a memory (MEM) of the sensor system (SSYS). The computer core (CPU) can use this sensor state vector S z (ϑ(t), B(t)) or parts thereof in a memory (MEM) of the sensor system (SSYS). The computer core (CPU) can use this sensor state vector S z (ϑ(t), B(t)) or parts thereof are transmitted via a data interface (IF) of the computer system (RSYS) of the sensor system (SSYS) to a higher-level system (ÜRSYS). The computer core (CPU) can process this sensor state vector S z (ϑ(t), B(t)) or parts thereof via a signaling system (IF, DSTR). The computer core (CPU) can output this sensor state vector S z (ϑ(t), B(t)) or parts thereof for other purposes of the respective application. Eighteenth further development of the procedure

[0058] In an eighteenth refinement of the proposed, typically computer- and / or machine-implemented method, one or more of the crystals comprise diamond. Diamond as a crystal material for quantum sensors with color centers offers numerous advantages over conventional materials such as silicon. These advantages make diamond a promising option for advanced sensor technologies and could make a significant difference in a wide range of applications. One of the most outstanding advantages of diamond is its exceptional hardness and chemical stability. Diamond is the hardest known material and offers high resistance to physical wear and chemical reactions. This ensures a long lifetime and reliability of the quantum sensors, even in extreme environments.In comparison, silicon is far more susceptible to mechanical damage and chemical degradation, which limits its applications.

[0059] Another significant advantage of diamond is its ability to host color centers, particularly nitrogen vacancy (NV) centers and the other diamond color centers mentioned in this document. These color centers in diamond are remarkably stable and offer unique quantum properties that are crucial for sensing. NV centers can operate at room temperature and enable highly sensitive magnetic field sensing to capture values ​​of the magnetic flux density B(t), as well as temperature sensing to capture one or more temperatures ϑ(t) with exceptional precision. Silicon-based materials do not possess comparable stable color centers and are therefore limited in their ability to process and store quantum information.In addition, diamond exhibits excellent thermal conductivity, far exceeding that of silicon. This effectively prevents heat buildup and maintains sensor functionality under extreme temperature conditions. Diamond therefore offers significant advantages in areas where precise temperature control and measurement are critical.

[0060] Finally, diamond is distinguished by its biocompatible properties. This opens up applications in the medical field, such as diagnostics and imaging, where interaction with biological tissue plays a role. Silicon is less suitable in this regard, as it can potentially cause adverse reactions.

[0061] Diamond as a crystal material for quantum sensors with color centers offers a number of advantages, including exceptional hardness, stability, unique quantum properties, high thermal conductivity, and biocompatibility. These properties make diamond a superior choice compared to conventional materials such as silicon and underscore its potential for innovative applications in various high-tech fields. Nineteenth further development of the procedure

[0062] In a nineteenth development of the proposed, typically computer- and / or machine-implemented method, one or more color centers of the one or more crystals comprising diamond comprise a color center from the set of possible color centers (PbV center, GeV center, SiV center, NV center, ST1 center, TR1 center, TR12 center), with an NV center being preferred. These color centers are known at the time of writing this document. This list is presumably not complete.

[0063] The following color centers in diamond, which may be relevant for sensory analysis or application in the presented method, are listed here with references: NV Center (Nitrogen Vacancy Center), Reference: Doherty, MW, et al. “The nitrogen-vacancy color center in diamond.” Physics Reports 528.1 (2013): 1-45. SiV center (silicon vacancy center), Reference: Rogers, LJ, et al. “Electronic structure of the negatively charged silicon-vacancy center in diamond.” Physical Review B 89.23 (2014): 235101. GeV Center (Germanium Failure Center), Reference: Iwasaki, T., et al. "Germanium-vacancy single color centers in diamond." Scientific Reports 5 (2015): 12882. SnV Center (Tin Failure Center), Reference: Tchernij, SD, et al. "Single-photon-emitting optical centers in diamond fabricated upon Sn implantation." ACS Photonics 4.10 (2017): 2580-2586. PbV Center (Lead Failure Center), Reference: Trusheim, ME, et al. "Transform-limited photons from a coherent tin-vacancy spin in diamond." Physical Review Letters 124.2 (2020): 023602. NVN Center (Nitrogen Vacancy Center), Reference: Naydenov, B., et al. “Spectroscopy and imaging of nitrogen-vacancy centers in diamond.” Applied Physics Letters 95.18 (2009): 181109. CrV center (chromium vacancy center), Reference: Aharonovich, I., et al. “Chromium single-photon emitters in diamond fabricated by ion implantation.” Physical Review B 81.12 (2010): 121201. Nickel centers (nickel vacancy centers), Reference: Aharonovich, I., and Neu, E. “Diamond nanophotonics.” Advanced Optical Materials 2.10 (2014): 911-928. NE8 center (nitrogen single atom center), Reference: Davies, G., and Hamer, MF “Optical studies of the 1,945 eV vibronic band in diamond.” Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 348.1653 (1976): 285-298. H3 center (nitrogen vacancy center), Reference: Collins, AT, et al. “Spectroscopic studies of the H3 (2,463 eV) and H4 (2,498 eV) luminescence bands in diamond.” Journal of Physics: Condensed Matter 5.19 (1993): 2533. H4 center (nitrogen vacancy center), Reference: Collins, AT, et al. “Spectroscopic studies of the H3 (2,463 eV) and H4 (2,498 eV) luminescence bands in diamond.” Journal of Physics: Condensed Matter 5.19 (1993): 2533. N3 center (nitrogen vacancy center), Reference: Clark, CD, et al. “The nitrogen-vacancy-hydrogen complex in diamond.” Philosophical Magazine B 52.3 (1985): 397-405. V0 center (silicon vacancy center, neutral), Reference: Goss, JP, et al. “Tetrahedral vacancies in diamond.” Physical Review Letters 77.14 (1996): 3041–3044. Boron Vacancy Center, Reference: Vlasov, II, et al. “Molecular-sized fluorescent nanodiamonds.” Nature Nanotechnology 9.1 (2014): 54-58. Chromium Center, Reference: Aharonovich, I., et al. “Chromium single-photon emitters in diamond fabricated by ion implantation.” Physical Review B 81.12 (2010): 121201. Europium-Zentrum, Referenz: Gaebel, T., et al. „Stable single-photon source in the near infrared.“ New Journal of Physics 16.11 (2014): 113071. Titanium-Zentrum, Referenz: Iwasaki, T., et al. „Germanium-vacancy single color centers in diamond.“ Scientific Reports 5 (2015): 12882. Kalzium-Zentrum, Referenz: Zaitsev, A. M. „Optical properties of diamond: a data handbook.“ Springer Science & Business Media, 2013. Silizium-Zentrum, Referenz: Clark, C. D., et al. „Silicon defects in diamond.“ Physical Review B 51.23 (1995): 16681-16688. Tin-Vacancy-Zentrum (SnV), Referenz: Tchernij, S. D., et al. „Single-photon-emitting optical centers in diamond fabricated upon Sn implantation.“ ACS Photonics 4.10 (2017): 2580-2586. Chrom-Vacancy-Zentrum (CrV), Referenz: Aharonovich, I., et al. „Chromium single-photon emitters in diamond fabricated by ion implantation.“ Physical Review B 81.12 (2010): 121201. Neodymium center (Nd), Reference: Aharonovich, I., et al. “Diamond-based single-photon emitters.” Reports on Progress in Physics 74.7 (2011): 076501. Phosphorus Center (P), Reference: Goss, JP, et al. “Tetrahedral vacancies in diamond.” Physical Review Letters 77.14 (1996): 3041-3044. VO center (vanadium vacancy center), Reference: Lee, J., et al. “Vanadium spin qubits as telecom quantum emitters in silicon carbide.” Nature Communications 12.1 (2021): 5546. CoZ center (cobalt vacancy center), Reference: Gulka, M., et al. “Cobalt-related single-photon color center in diamond.” Physical Review B 99.12 (2019): 125202. NiV center (nickel vacancy center), Reference: Sternschulte, H., et al. “1.681-eV luminescence center in chemical-vapor-deposited homoepitaxial diamond films.” Physical Review B 50.19 (1994): 14554. FeV Center (Eisen-Fehstellen-Zentrum), Reference: Thiering, G., and Gali, A. “Ab initio calculation of spin-orbit coupling for an NV center in diamond exhibiting dynamic Jahn-Teller effect.” Physical Review B 96.8 (2017): 081115. MgV center (magnesium vacancy center), Reference: Kato, H., et al. “Observation of negative differential resistance in a single intrinsic SiC pin diode with Mg doping.” Applied Physics Letters 91.24 (2007): 242107. Further color centers in diamond that may be relevant for sensor technology or the application in the presented method can be found in the book Zaitsev, AM “Optical properties of diamond: a data handbook.” Springer Science & Business Media, 2013. Twentieth further development of the procedure

[0064] In a twentieth development of the proposed, typically computer- and / or machine-implemented method, one or more crystals of the crystals, preferably all crystals of the crystals, are smaller than 1 mm and / or smaller than 500 µm and / or smaller than 200 µm and / or smaller than 100 µm and / or smaller than 50 µm and / or smaller than 20 µm and / or smaller than 10 µm and / or smaller than 5 µm and / or smaller than 2 µm and / or smaller than 1 µm and / or smaller than 500 nm and / or smaller than 200 nm and / or smaller than 100 nm and / or smaller than 50 nm. This has the advantage that the crystals typically have a substantially isotropic distribution of the orientations of the crystals in a small space.As a result, the intensity of the fluorescence radiation (FL) of the respective color centers, in particular the NV centers, which typically depends on the proportion of the magnetic flux density parallel to the axis of the respective color center, in particular NV center, no longer shows such a spatial dependence, but is typically isotropic and no longer dependent on the orientation of the one or more sensor elements (SE) in space. Twenty-first further development of the procedure

[0065] In a twenty-first development of the proposed, typically computer- and / or machine-implemented method, the crystals form a plurality of crystals, and the distribution of the spatial orientation of the crystals is stochastically substantially uniformly distributed, such that the sensitivity of the one or more sensor elements (SE) to the magnetic flux density B(t) is substantially spatially isotropic. The advantages have already been described in the previous section on the twelfth development of the method. As described there, the distribution of the spatial orientation of the crystals is preferably stochastically substantially uniformly distributed, such that the sensitivity of the one or more sensor elements (SE) to the magnetic flux density B(t) is substantially spatially isotropic. This has the advantage that the assembly of such sensor elements in the application devices is significantly simpler and with better C pk-values ​​is possible. Twenty-second further development of the procedure

[0066] In a twenty-second development of the proposed, typically computer and / or machine-implemented method, the determination of measured values ​​from the time course (I fl (t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) and the temporal course of the intensity (I pmp (t)) of the pump radiation (LB) the determination of fluorescence vectors F v (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) from the time course (I fl (t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) and the temporal course of the intensity (I pmp(t)) of the pump radiation (LB) as a fluorescence delay measurement value. Preferably, in the fourteenth development of the method, the respective computer- or machine-implemented fluorescence vectors F v each a respective fluorescence intensity measurement value F i (t) and a respective fluorescence delay measurement value F φ (t) and, if necessary, other measured values. Twenty-third further development of the procedure

[0067] In a twenty-third development of the proposed, typically computer- and / or machine-implemented method, the temporal profile (Ipmp(t)) of the intensity of the pump radiation (LB) is preferably at least partially sinusoidal with a preferably single pump radiation frequency (f pmp) modulated. Pulse-modulated control is also possible, but less preferred, since the harmonics lead to lower performance of the phase measurement or delay measurement in the vector network analyzer (VNA) or the lock-in amplifier (LIA). Twenty-fourth further development of the procedure

[0068] In a twenty-fourth development of the proposed, typically computer- and / or machine-implemented method, the electromagnetic radiation with which the method additionally irradiates the one or more sensor elements (SE) is preferably microwave-free.

[0069] Microwave-free control of one or more sensor elements (SE) in quantum sensors using diamond with NV centers (nitrogen vacancy centers) as the crystal material, and thus the use in the method proposed here, offers numerous technical and practical advantages over conventional sensors and methods that use microwaves to control the NV centers. The term "microwave-free" refers to the use of alternative methods for manipulating and controlling the NV centers without the use of microwave radiation, which typically lies in the frequency range of 300 MHz to 300 GHz and the wavelength range of 1 mm to 1 m.

[0070] Key advantages of microwave-free control are the significant reduction in energy consumption and heat generation. Microwave-based systems require considerable energy to generate and maintain microwave radiation, resulting in increased energy consumption and significant heat generation. This heat can negatively impact the stability and accuracy of the sensors. In contrast, microwave-free systems use optical or electrical methods to control the color centers, preferably the NV centers, which consume less energy and generate minimal heat. This leads to greater stability and reliability of the sensor systems (SSYS), especially in energy-sensitive and thermally critical applications.

[0071] Another significant advantage lies in the miniaturization and integration of the sensor systems (SSYS). Microwave-based sensor systems (SSYS) require complex and bulky hardware to generate and control the microwave radiation, which complicates miniaturization and integration into compact devices. Microwave-free sensor systems (SSYS), on the other hand, require less space and can be more easily integrated into smaller and portable form factors. This opens up new application possibilities, particularly in medical technology, mobile devices, and wearable sensor systems (SSYS). Despite these disadvantages of microwave-based sensor systems (SSYS), the technical teaching of the present document also addresses these sensor systems (SSYS) because microwave-based sensor systems offer advantages in terms of linearity and sensitivity.

[0072] However, microwave-free control also offers advantages in terms of manufacturing costs and the complexity of production processes. Microwave components are expensive and require precise manufacturing and calibration. Eliminating these components reduces manufacturing costs and simplifies the production process, making the technology more economical and accessible.

[0073] Another key advantage is improved electromagnetic compatibility. Microwave radiation can be susceptible to interference and affect other electronic devices. Microwave-free sensor systems (SSYS) minimize this interference, resulting in more reliable and interference-free sensor performance. This is especially important in sensitive environments such as medical diagnostic devices or precise scientific experiments.

[0074] Microwave-free control of one or more sensor elements (SE) in quantum sensors with NV centers in diamond thus offers significant advantages over microwave-based sensor systems (SSYS). Reduction in energy consumption and heat generation, improved miniaturization and integration, lower manufacturing costs, and improved electromagnetic compatibility make this technology a superior choice for a wide range of applications and underscore its potential to significantly influence the future of quantum sensing. Twenty-fifth further development of the procedure

[0075] In a twenty-fifth development of the proposed, typically computer and / or machine-implemented method, the determination of measured values ​​from the time course (I fl(t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) and the temporal course of the intensity (I pmp (t)) the pump radiation (LB) by means of a vector network analyzer (VNA), which in particular the computer system (RSYS) controls and / or regulates, in particular via a data bus (DB) and in particular by executing a computer-implemented control program, the program code of which is stored, in particular, at least temporarily, in at least one memory (MEM) of the computer system (RSYS), and in particular the output signal of which the computer system (RSYS) digitizes, in particular by means of an analog-to-digital converter (ADC), which can in particular be part of the vector network analyzer (VNA).

[0076] The use of a vector network analyzer (VNA) to measure the photodetector signal, here the received signal (S0) of the photodetector (PD), and the fluorescence radiation of NV centers in one or more sensor elements (SE) offers numerous advantages over other measurement devices for analyzing the received signal (S0) of the photodetector (PD). These advantages extend to the areas of precision, versatility, and data processing, thereby significantly improving the performance and reliability of the sensor system executing the method proposed here. This ultimately also significantly improves the process performance of the computer- and / or machine-implemented method proposed here.

[0077] Preferably, the vector network analyzer (VNA) generates the transmit signal (S5). Preferably, but not necessarily, the vector network analyzer (VNA) includes the corresponding signal generator (SGEN).Fig. It is shown separately in Figure 19. The transmitted signal (S5) is preferably used as a modulation signal for the amplitude modulation of the intensity (I pmp (t)) of the pump radiation (LB) of the pump radiation source (LD). Other modulation types are conceivable, but not preferred based on current knowledge.

[0078] A particular advantage is that a vector network analyzer (VNA) or the signal generator (SGEN) typically operates with a single pump radiation frequency (f pmp ) the intensity (I pmp (t)) of the pump radiation (LB) of the pump radiation source (LD). The transmission signal (S5) generated by the vector network analyzer (VNA) or the signal generator (SGEN) is therefore typically sinusoidal and preferably monofrequency and intensity-modulated with a single pump radiation frequency (f pmp) and preferably has essentially no harmonics. The response of the color centers (preferably the NV centers) to different pump radiation frequencies (f pmp ) of the intensity (I pmp (t)) of the pump radiation (LB) is different, can be seen in the currently unpublished German patent applications DE 10 2024 105 739.4 and DE 10 2024 105 740.8. Their technical content is also the technical content of the priority-establishing German patent applications DE 10 2024 105 872.2 and DE 10 2024 105 873.0 of February 29, 2024, so that these do not conflict with the technical teaching of the document presented here in a way that would preclude patent protection.

[0079] A key advantage of the vector network analyzer (VNA) is its high precision and accuracy. VNAs are designed to analyze complex electrical and / or electro-optical networks and therefore provide extremely precise measurement of the amplitude and phase of signals. Since the optical signals for controlling the color centers (NV centers) are based on an electrical transmission signal (S5(t)), and the optical response of the color centers (NV centers) is measured in the form of the temporal intensity variation (I fl(t)) of the fluorescence radiation (FL) is converted by suitable means, for example one or more photodetectors (PD) into a preferably electrical receiver output signal (S0(t)), VNAs can be used to analyze color centers (preferably NV centers). This accuracy of the VNAs is crucial when it comes to measuring the subtle fluorescence radiation (FL) of NV centers and / or other color centers, which is often weak and overlaid by noise. The ability of a VNA to perform precise measurements makes it possible to characterize the properties of the NV centers or color centers with high accuracy and thus to improve the performance of the method for measuring the sensor element state vectors (S z ) (ϑ(t), B(t)) of one or more sensor elements (SE) and thus of the sensor system (SSYS).

[0080] Another significant advantage is the versatility of the VNA. VNAs can process a wide range of frequencies and signal types in addition to pure sine signals, making them particularly suitable for analyzing the fluorescence radiation (FL) of the color centers (preferably NV centers) of one or more sensor elements (SE). They can not only measure the signal strength of the intensity curve (I fl (t)) of the fluorescence radiation (FL) (fluorescence intensity measurement value F i (t)) but also phase shifts (fluorescence delay measurement value F φ(t)) and, moreover, analyze typical, but not necessarily, distortions that may occur during the interaction of the pump radiation (LB) and other physical quantities, such as the magnetic flux density (B(t)) and the temperature (ϑ(t)), with the NV centers or color centers. This comprehensive analysis capability enables deeper insight into the dynamics of the NV centers or color centers and contributes to improving the sensor accuracy of the respective sensor systems that use and / or implement the proposed method.

[0081] Furthermore, VNAs, when used as separate, commercially available devices, typically offer advanced data processing and analysis tools. With integrated signal processing functions, commercially available VNAs can effectively filter noise and interfering signals, thereby increasing the quality of the measurement data. This is particularly important for applications in quantum sensor systems, where precise and noise-free signals are required to perform accurate measurements. The vector network analyzer's (VNA) ability to perform complex mathematical analyses and signal processing using computer- and / or machine-implemented techniques contributes significantly to increasing measurement accuracy and reliability.

[0082] Thus, the use of a vector network analyzer (VNA) to measure the photodetector signal, i.e., the respective received signals (S0) of one or more photodetectors (PD), the fluorescence radiation (FL) of paramagnetic centers, particularly NV centers, in one or more sensor elements (SE) when applying the computer- and / or machine-implemented method described in this document offers significant advantages over other measurement devices. The high precision and accuracy, the versatility in signal processing, and the advanced data processing tools make vector network analyzers (VNA) a superior choice for the characterization and optimization of quantum sensor systems that apply the proposed computer- and / or machine-implemented method.These advantages underline the potential of the vector network analyzer (VNA) to significantly improve the performance and reliability of quantum sensor systems applying the proposed computer- and / or machine-implemented method. Twenty-sixth further development of the procedure

[0083] In a twenty-sixth development of the proposed, typically computer and / or machine-implemented method, the determination of measured values ​​(fluorescence intensity measured value F i (t), fluorescence delay measurement value F φ (t)) from the time course (I fl (t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) and the temporal course of the intensity (I pmp(t)) the pump radiation (LB) by means of a lock-in amplifier (LIA), which in particular the computer system (RSYS) controls and / or regulates, in particular via a data bus (DB) and in particular by executing a computer-implemented control program, the program code of which is in particular stored at least temporarily in at least one memory (MEM) of the computer system (RSYS), and in particular the output signal of which the computer system (RSYS) digitizes, in particular by means of an analog-to-digital converter (ADC), which can in particular be part of the lock-in amplifier (LIA).

[0084] The use of a lock-in amplifier (LIA) to measure the photodetector signal (S0(t)) of the fluorescence radiation (FL) from NV centers in one or more sensor elements (SE) offers numerous advantages over other measurement devices. These advantages include high sensitivity, effective noise suppression, and ease of use, which are crucial in quantum sensor systems implementing the proposed computer- and / or machine-implemented method.

[0085] A key advantage of the lock-in amplifier (LIA) is its exceptional sensitivity. Lock-in amplifiers (LIA) typically utilize phase-sensitive detection techniques to measure very small signals in the presence of strong noise. This is particularly relevant for measuring the weak fluorescence (FL) radiation of paramagnetic centers, particularly NV centers or color centers, of one or more sensor elements (SE), which is often overlaid by background noise or parasitic background radiation. By synchronizing with the pump radiation frequency (f pmp ) of the modulation signal (transmission signal S5(t)) of the temporal course of the intensity (I pmp (t)) of the pump radiation (LB), i.e. with the transmission signal (S5(t)), as reference frequency, the lock-in amplifier (LIA) can receive the useful signal, namely the receiver output signal (S0) of the photodetector (PD), which is the intensity signal of the intensity curve (I fl(t)) of the fluorescence radiation (FL) of the paramagnetic centers, i.e., the color centers, into the received signal (S0). The lock-in amplifier (LIA) achieves this even when the portion of the transmitted signal (S5) in the receiver output signal (S0) is significantly below the noise level. The price to be paid for this is longer integration times, which increase the dead time of the quantum sensor system. In comparison, vector network analyzers (VNAs), while precise, are less effective at measuring extremely low-amplitude signals in highly noisy environments.

[0086] Another advantage of the LIA is its ability to effectively suppress noise. LIAs can specifically filter out noise signals that do not occur at the reference frequency, resulting in a significant improvement in the signal-to-noise ratio. This enables more precise and reliable measurements of the fluorescence radiation (FL) from color centers and NV centers by determining fluorescence measurement vectors F v ((Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ(t)). VNAs also provide noise suppression, but often through extensive, typically computer- and / or machine-implemented signal processing and filtering, which can be more complex and time-consuming. Preferably, the CPU of the quantum sensor system's computing system (RSYS) performs this computer- and / or machine-implemented signal processing and filtering if the quantum sensor system implements the method proposed here with a vector network analyzer (VNA). Preferably, the CPU of the quantum sensor system's computing system (RSYS) performs this computer- and / or machine-implemented signal processing and filtering for further quality improvement, typically to a different extent and in a different manner, if the quantum sensor system implements the method proposed here with a lock-in amplifier (LIA).

[0087] The ease of use and cost-effectiveness of the LIA are further advantages. LIAs are generally easier to use and require less calibration and setup compared to VNAs. This makes them particularly attractive for laboratories and industrial applications that require fast and precise measurements without the need for expensive and complex equipment, especially when the quantum sensor system presented here is built as a discrete laboratory system and is intended to execute the computer- and / or machine-implemented method presented here.

[0088] However, there are also disadvantages to using lock-in amplifiers (LIAs) compared to vector network analyzers (VNAs). Lock-in amplifiers (LIAs) are specialized for measuring signals at a single or a few reference frequencies, which limits their application possibilities. Vector network analyzers (VNAs), on the other hand, offer broad frequency analysis and detailed network characterization, making them more versatile. This particularly applies to multifrequency signal responses of the intensity (I) versus time. fl (t)) of the fluorescence radiation (FL) upon monofrequency excitation by a single pump radiation frequency (f pmp ) modulated pump radiation intensity (I pmp(t)) of the pump radiation (LB) irradiating the color centers or NV centers of the one or more sensor elements (SE). In applications requiring comprehensive frequency analysis and characterization of complex networks, vector network analyzers (VNAs) are typically superior.

[0089] The lock-in amplifier (LIA) thus offers significant advantages in measuring the photodetector signal (S0) of the fluorescence radiation (FL) from NV centers in one or more sensor elements (SE), particularly due to its high sensitivity and effective noise suppression. While vector network analyzers (VNA) are more versatile in frequency analysis and enable detailed network characterizations, lock-in amplifiers (LIA) are often the better choice for specific applications in quantum sensor systems that execute the proposed computer- and / or machine-implemented method and where weak signal components in highly noisy environments in the receiver output signal (S0) of the photodetectors (PD) that affect the temporal course of the fluorescence radiation intensity (I fl (t)) of the fluorescence radiation (FL) of the color centers or NV centers of the one or more sensor elements (SE) must be measured. Twenty-seventh further development of the procedure

[0090] In a twenty-seventh development of the proposed, typically computer- and / or machine-implemented method, the dependence of the one or more flux density measured values ​​of one or more magnetic flux densities B(t) determined by the computer core (CPU) of the computer system (RSYS) of the sensor system by executing the proposed computer- and / or machine-implemented method on one or more temperatures ϑ(t) of the one or more sensor elements (SE) is preferably less than 50% and / or better less than 20% and / or better less than 10% and / or better less than 5% and / or better less than 2% and / or better less than 1% and / or better less than 0.50% and / or better less than 0.20% and / or better less than 0.10% of the temperature required for measurability by the one or more sensor elements (SE) orof the sensor system (SSYS) with the maximum magnitude flux density value of the magnetic flux density B(t) of the magnetic field flowing through the one or more sensor elements (SE) provided for one or more sensor elements (SE) (typically the specification value of the sensor system (SSYS) for the measuring range of the magnetic flux density B(t)), divided by the temperature difference Δϑ between the maximum intended temperature value ϑ. max of the one or more sensor elements (SE) or the sensor system (SSYS) with the one or more sensor elements (SE) minus the minimum intended temperature value ϑ min of the one or more sensor elements (SE) or the sensor system (SSYS) with the one or more sensor elements (SE) (typically the specification value of the sensor system (SSYS) for the permissible temperature range [ϑ max , ϑ min ]).

[0091] These low dependencies can be improved by increasing the amount of training data and the number of layers and nodes of the computer- and / or machine-implemented neural network (NNM) model used. Since this can involve considerable effort, the error or dependency should be limited to the necessary extent. Twenty-eighth further development of the procedure

[0092] In a twenty-eighth development of the proposed, typically computer- and / or machine-implemented method, in comparison to the nineteenth development, the respective magnetic flux density B(t) is replaced by the respective value of a first physical quantity and the respective temperature ϑ(t) is replaced by the value of a respective second physical quantity. In the twentieth development of the proposed, typically computer- and / or machine-implemented method, the dependence of the measured values ​​of the first physical quantity (e.g., B(t)) on the second corrected measured values ​​of the second physical quantity (e.g.,ϑ(t)) ​​of the one or more sensor elements (SE) is preferably less than 50% and / or better less than 20% and / or better less than 10% and / or better less than 5% and / or better less than 2% and / or better less than 1% and / or better less than 0.50% and / or better less than 0.20% and / or better less than 0.10% of the maximum value of the first physical quantity (e.g. B(t)) intended for measurability by the one or more sensor elements (SE) or the sensor system (SSYS) with the one or more sensor elements (SE), which is intended to be able to act on the one or more sensor elements (SE) or the sensor system (SSYS), divided by the value difference between the maximum intended value of the second physical quantity (e.g. ϑ. max) that is to act on the one or more sensor elements (SE) or the sensor system (SSYS), minus the minimum intended value of the second physical quantity (e.g. ϑ min ) which is intended to be able to act on one or more sensor elements (SE) or the sensor system (SSYS). Twenty-ninth further development of the procedure

[0093] In a twenty-ninth development of the proposed, typically computer and / or machine-implemented method, at least two different fluorescence parameters (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) for each determination as respective vector components of at least two at least two-dimensional computer and / or machine-implemented fluorescence vectors F v (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value Fφ (t)) from the respective time course (I fl (t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) in combination with the respective temporal course of the pump radiation intensity (I pmp (t)) of the pump radiation (LB). Preferably, the first determination of these at least two determinations of the first fluorescence vector F v1 (first fluorescence intensity measurement F i1 (t), first fluorescence delay measurement value F φ1 (t); the fluorescence vectors F v at a first pump radiation frequency (f pmp1 ) the pump radiation frequency (f pmp ) of the time course of the pump radiation intensity (I pmp (t)) of the pump radiation (LB). Furthermore, the second determination of these at least two determinations of the second fluorescence vector F v2 (second fluorescence intensity measurement value F i2(t), second fluorescence delay measurement value F φ2 (t)) of the fluorescence vectors F v at a second pump radiation frequency (f pmp2 ) the pump radiation frequency (f pmp ) of the time course of the pump radiation intensity (I pmp (t)) of the pump radiation (LB). Preferably, the first pump radiation frequency (f pmp1 ) and the second pump radiation frequency (f pmp2 ) differ from each other.

[0094] This principle can be applied to n pump radiation frequencies (f pmp1 to f pmpn ) with n as an integer greater than 1.

[0095] In this variant of the twenty-ninth development of the proposed, typically computer and / or machine-implemented method, at least n different fluorescence parameters (fluorescence intensity measurement value F i (t), fluorescence delay measurement value Fφ (t)) each determination as respective vector components of at least n at least two-dimensional computer and / or machine-implemented fluorescence frequency vectors F fvi (i-th fluorescence intensity measurement value F ii (t), i-th fluorescence delay measurement value F φi (t)) from the respective time course (I fl (t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) in combination with the respective temporal course of the pump radiation intensity (I pmp (t)) of the pump radiation (LB) and the respective value of the i-th pump radiation frequency (f pmpi ) with i as a positive integer greater than 0 and less than or equal to 1.

[0096] Preferably, the first determination of these at least n-fold determinations of the first fluorescence frequency vector F fv1 (first fluorescence intensity measurement F i1(t), first fluorescence delay measurement value F φ1 (t), first pump radiation frequency f pmp1 ) of the fluorescence frequency vectors F fv at a first pump radiation frequency (f pmp1 ) the pump radiation frequency (f pmp ) of the time course of the pump radiation intensity (I pmp (t)) of the pump radiation (LB).

[0097] Furthermore, the second determination of these at least two determinations of the second fluorescence frequency vector F fv2 (second fluorescence intensity measurement value F i2 (t), second fluorescence delay measurement value F φ2 (t), second pump radiation frequency f pmp2 ) of the fluorescence frequency vectors F fv at a second pump radiation frequency (f pmp2 ) the pump radiation frequency (f pmp ) of the time course of the pump radiation intensity (I pmp (t)) of the pump radiation (LB).

[0098] This will now be done for the still missing n-2 pump radiation frequencies (f pmp3 to f pmpn ) continued.

[0099] In this case, the i-th determination of these at least n-fold determinations of the i-th fluorescence frequency vector F is typically carried out once for the i-th pump radiation frequency. fvi (i-th fluorescence intensity measurement value F ii (t), i-th fluorescence delay measurement value F φi (t), i-th pump radiation frequency f pmpi ) of the fluorescence frequency vectors F fv at an i-th pump radiation frequency (f pmpi ) the pump radiation frequency (f pmp ) of the time course of the pump radiation intensity (I pmp (t)) of the pump radiation (LB). Here, i is a positive integer greater than 2 and less than or equal to n.

[0100] Preferably, the n pump radiation frequencies en(f pmp1 to f pmpn ) differ from each other.

[0101] The advantage is that the computer system (RSYS) of the sensor system can then use the different behavior of the intensity (Ifl(t)) of the fluorescence radiation to carry out the computer and / or machine-implemented compensation, for example of the temperature influence. Thirtieth further development of the procedure

[0102] In a thirtieth development of the proposed, typically computer and / or machine-implemented method, this principle can be applied to m additionally radiated microwave frequencies (fµ w1 to f µWn ) with m as an integer greater than 1.

[0103] In this variant of the twenty-ninth development of the proposed, typically computer- and / or machine-implemented method, at least n times m times determination of at least n times m different fluorescence parameters is carried out per determination as respective vector components of typically n times m at least three-dimensional computer- and / or machine-implemented fluorescence frequency microwave vectors F fµv (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp , microwave frequency f µw ) from the respective time course (I fl (t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) in combination with the respective temporal course of the pump radiation intensity (I pmp (t)) of the pump radiation (LB) and the respective i-th pump radiation frequency (fpmpi ) and a j-th microwave frequency (f µwj ). The i,j-th fluorescence frequency microwave vector F fµvi,j preferably comprises at least one i,j-th fluorescence intensity measurement value F ii,j (t) and an i,j-th fluorescence delay measurement value F φ¡,j (t) and an i-th pump radiation frequency f pmpi , and a j-th microwave frequency f µwj .

[0104] For the purpose of explanation, the method is divided here into pump radiation frequency measurement cycles embedded in microwave frequency cycles.

[0105] A microwave frequency measurement cycle then typically comprises n pump radiation frequency measurement cycles.

[0106] First, the first pump radiation frequency measurement cycle takes place.

[0107] In this case, the first determination of these at least n-fold determinations of the first fluorescence frequency microwave vector F fµv1,1the fluorescence frequency microwave vectors F fmv at a first pump radiation frequency (f pmp1 ) the pump radiation frequency (f pmp ) of the time course of the pump radiation intensity (I pmp (t)) of the pump radiation (LB) and at a first microwave frequency (f µw1 ).

[0108] Second, the second pump radiation frequency measurement cycle takes place.

[0109] Furthermore, the second first determination of these at least n-fold determinations of the second first fluorescence frequency microwave vector F fµv2,1 the fluorescence frequency microwave vectors F fmv at a second pump radiation frequency (f pmp2 ) the pump radiation frequency (f pmp ) of the time course of the pump radiation intensity (I pmp (t)) of the pump radiation (LB) and at the first microwave frequency (f µw1 ).

[0110] This will now be done for the still missing n-2 pump radiation frequencies (f pmp3 to f pmpn ) for the remaining pump radiation frequency measurement cycles.

[0111] Then, for example, the second microwave frequency measurement cycle begins.

[0112] First, the first pump radiation frequency measurement cycle takes place in the second microwave frequency measurement cycle.

[0113] Preferably, the first second determination of these at least n-fold determinations of the first second fluorescence frequency microwave vector F fµv1,2 the fluorescence frequency microwave vectors F fmv at a first pump radiation frequency (f pmp1 ) the pump radiation frequency (f pmp ) of the time course of the pump radiation intensity (I pmp (t)) of the pump radiation (LB) and at a second microwave frequency (f µw2 ).

[0114] Second, the second pump radiation frequency measurement cycle takes place in the second microwave frequency measurement cycle.

[0115] Furthermore, the second second determination of these at least n-fold determinations of the second second fluorescence frequency microwave vector F fµv2,2 the fluorescence frequency microwave vectors F fmv at a second pump radiation frequency (f pmp2 ) the pump radiation frequency (f pmp ) of the time course of the pump radiation intensity (I pmp (t)) of the pump radiation (LB) and at the second microwave frequency (f µw2 ).

[0116] This will now be done for the still missing n-2 pump radiation frequencies (f pmp3 to f pmpn ) for the remaining pump radiation frequency measurement cycles in the second microwave frequency measurement cycle.

[0117] These microwave frequency measurement cycles are continued until preferably all m microwave frequency measurement cycles for preferably all m microwave frequencies (f µw1 to f µwm ) were carried out. Then typically n times m fluorescence frequency microwave vectors (F fµv1,1 to F fµvn,m ) are typically determined in terms of value and can be used as a total input vector, in particular by the computer core (CPU) of the computer system (RSYS) of the sensor system (SYS) for the said computer-implemented and / or machine-implemented method of artificial intelligence, i.e. in particular for a computer-implemented and / or machine-implemented neural network model.

[0118] Preferably, the n pump radiation frequencies (f pmp1 to f pmpn ) differ from each other.

[0119] Preferably, the m microwave frequencies (f µw1 to f µwm) differ from each other.

[0120] The advantage is that the computer system (RSYS) of the sensor system (SSYS) can then calculate the different behavior of the intensity (I fl (t)) of the fluorescence radiation (FL) at different pump radiation frequencies (f pmp1 to f pmpn ) and / or at different microwave frequencies (f µw1 to f µwm ) to perform computer- and / or machine-implemented compensation, for example, of the temperature influence. A microwave frequency f µw of 0 Hz is also considered the microwave frequency. A non-irradiation of a microwave field is considered an example of irradiation of a microwave field with f µw =0Hz. Thirty-first further development of the procedure

[0121] In a thirty-first development of the proposed method, a second relevant physical quantity of the one or more sensor elements (SE) is one or more temperatures (ϑ(t)) ​​of the one or more sensor elements (SE). Preferably, at least one second measured value of the second physical quantity of the one or more sensor elements (SE) is one or more temperature measured values ​​of the one or more temperatures (ϑ(t)) ​​of the one or more sensor elements (SE). This has the advantage that the sensor system (SSYS) in the overall system can make the one or more temperature values ​​(ϑ(t)) ​​available for further uses. Thirty-second further development of the procedure

[0122] In a thirty-second refinement of the proposed process, one or more of the crystals comprise diamond. This has the advantage that diamond, due to its strong covalent bonds between the carbon atoms, exhibits a weak coupling between the color centers and the lattice. This allows the pump radiation (LB) to significantly lower the spin temperatures of one or more color centers. Thirty-third further development of the procedure

[0123] In a thirty-third development of the proposed method, one or more color centers (paramagnetic centers) of the one or more crystals comprising diamond comprise a color center from the set of possible color centers {PbV, GeV, SiV, NV, ST1, TR1, TR12}. However, an NV center is preferred as the color center. The NV center is particularly well researched. The document presented here refers in particular to the book Zaitsev, AM "Optical properties of diamond: a data handbook." Springer Science & Business Media, 2013, and the other color centers mentioned above and elsewhere in this document. Thirty-fourth further development of the procedure

[0124] In a thirty-fourth development of the proposed method, one or more of the crystals, preferably all of the crystals, have a diameter of less than 1 mm and / or better less than 500 µm and / or better less than 200 µm and / or better less than 100 µm and / or better less than 50 µm and / or better less than 20 µm and / or better less than 10 µm and / or better less than 5 µm and / or better less than 2 µm and / or better less than 1 µm and / or better less than 500 nm and / or better less than 200 nm and / or better less than 100 nm and / or better less than 50 nm. It is therefore particularly preferably dust. This has the advantage that the crystals typically have a substantially isotropic distribution of the orientations of the crystals in a small space.As a result, the intensity of the fluorescence radiation (FL) of the respective color centers, in particular the NV centers, which typically depends on the proportion of the magnetic flux density parallel to the axis of the respective color center, in particular NV center, no longer shows such a spatial dependence, but is typically isotropic and no longer dependent on the orientation of the one or more sensor elements (SE) in space. Thirty-fifth further development of the procedure

[0125] In a thirty-fifth development of the proposed method, the one or more sensor elements (SE) comprise such a plurality of crystals, which are preferably diamond crystals. In this case, the crystals form this plurality of crystals. The advantages have already been described in the previous section on the fourth development of the method. As described there, the distribution of the spatial orientation of the crystals is preferably stochastically substantially uniformly distributed, so that the sensitivity of the one or more sensor elements (SE) to the magnetic flux density B(t) is substantially spatially isotropic. This has the advantage that the assembly of one or more such sensor elements (SE) in the application devices is considerably simpler and with better C pk -values ​​is possible. Thirty-sixth further development of the procedure

[0126] In a thirty-sixth development of the proposed method, the method is designed for the simultaneous and preferably pairwise measurement of one or more magnetic flux densities (B(t)) and one or more preferably associated temperatures (ϑ(t)). A first relevant physical quantity of the one or more sensor elements (SE) is one or more flux density measured values ​​of one or more magnetic flux densities (B(t)) flowing through the one or more sensor elements (SE), and at least one measured value of the second physical quantity of the one or more sensor elements (SE) is one or more temperature measured values ​​of the one or more temperatures (ϑ(t)) ​​of the one or more sensor elements (SE).The acquisition of one or more flux density measurements of the magnetic flux density (B(t)) using one or more such sensor elements (SE) is an advantageous embodiment of the proposed method with a range of applications. Typically, the proposed method can be used in various magnetometers. Training procedures for the above procedures

[0127] The document presented here describes a computer- and / or machine-implemented determination method (training method) for determining one or more configuration parameters for use in a computer- and / or machine-implemented method as a thirty-seventh development of the proposed method as described above. Typically, training hardware with a training computer system (TRSYS) comprising a training computer core (TCPU) and a training memory (TMEM) executes the computer- and / or machine-implemented determination method (training method). The program code, the training data, and the determined configuration parameters (network parameters) are preferably located in a training memory (TMEM) of the training computer system (TRSYS).The training processor core (TCPU) typically executes this program code when executing the computer- and / or machine-implemented determination method (training method) for determining one or more configuration parameters. The proposed computer- and / or machine-implemented determination method (training method) for determining one or more configuration parameters preferably comprises the following steps: • Providing at least one or more sensor elements (SE) or one or more sensor elements (SE) whose behavior corresponds to that of the one or more sensor elements (SE) and which is encompassed hereinafter by the term “sensor element (SE)” in the sense of these claims; • Provision of a training computer system (TRSYS); • Providing a temperature control device (TV), in particular a temperature cabinet and / or one or more heating and / or cooling devices; • Providing a magnetic field generating device (ME), in particular at least one Helmholtz coil pair and / or one or more permanent magnets, for generating a magnetic field that flows through the at least one or more sensor elements (SE); • Irradiating the one or more sensor elements (SE) with a pump radiation (LB) with a pump radiation wavelength (λ pmp ), in particular by means of a pump radiation source (LD), in particular of the sensor system, wherein the temporal course of the intensity (I pmp (t)) the pump radiation (LB) is modulated with a modulation signal (transmission signal S5(t)); • Setting the magnetic field to a predetermined flux density value (B(t)), in particular by means of the magnetic field generating device (ME), which is controlled in particular by the training computer system (TRSYS), and flooding the one or more sensor elements (SE) with this magnetic field with magnetic flux densities (B(t)) of predetermined flux density values; • Tempering the one or more sensor elements (SE) to temperature values ​​(ϑ(t)), in particular by means of the tempering device (TV) and / or the said heating and / or cooling devices, which are controlled in particular by the training computer system (TRSYS) and / or in particular regulated on the basis of the one or more temperature measured values ​​of one or more training temperature sensors (TS); • Detecting the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE), in particular by means of at least one optical filter (DCM) which is designed for fluorescence radiation (FL) and / or electromagnetic radiation with the fluorescence radiation wavelength (λ fl ) of the fluorescence radiation (FL) is essentially transparent and which is permeable to pump radiation (LB) and / or electromagnetic radiation with the pump radiation wavelength (λ pmp) the pump radiation (LB) is substantially non-transparent, and in particular by means of at least one or more photodetectors (LD) which converts the received fluorescence radiation (FL) into one or more received signals (S0) and in particular by means of at least one analog-to-digital converter (ADC) which converts the received signal(s) (S0) into one or more digitized received signals (S3) and in particular makes the values ​​of the digitized received signal(s) (S3) available to the computer core (CPU) of the computer system (RSYS), in particular via a memory (MEM) of the sensor system; • Determination of measured values ​​in the form of one- or multi-dimensional fluorescence vectors (F v ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) and / or three- or multi-dimensional fluorescence frequency vectors (F fv ) (Fluorescence intensity measurement value F i(t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp ) and / or of three- or four- or multi-dimensional fluorescence frequency microwave vectors (F fµv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp , microwave frequency f µw ) or (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), microwave frequency f µw ) ◯ from the time course (I fl (t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) and the temporal course of the intensity (I pmp (t)) the pump radiation (LB), in particular by means of a vector network analyzer (VNA) or a lock-in amplifier (LlA) and / or ◯ from the time course (I fl(t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) and the temporal course of the intensity (I pmp (t)) of the pump radiation (LB) and one or more values ​​of the pump radiation frequency (f pmp ), in particular by means of a vector network analyzer (VNA) or a lock-in amplifier (LIA) and / or ◯ from the time course (I fl (t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) and the temporal course of the intensity (I pmp (t)) of the pump radiation (LB) and one or more values ​​of the microwave frequency (f µw ) and in particular one or more values ​​of the pump radiation frequency (f pmp ), in particular by means of a vector network analyzer (VNA) or a lock-in amplifier (LIA), ◯ wherein in particular the vector network analyzer (VNA) or the lock-in amplifier (LIA) in particular combine the digitized received signal (S3) or the received signal (S0) or a signal derived therefrom with the modulation signal (transmitted signal S5(t)) and in particular carry out a possible subsequent digitization of the combination result and in particular making the digitized combination result available to the training computer system (TRSYS); • Saving measured values ​​in the form of fluorescence vectors (F v ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) or in the form of the fluorescence frequency vectors (F fv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp ) or in the form of the fluorescence frequency microwave vectors (F fµv) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp , microwave frequency f µw ) or (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), microwave frequency f µw ) in particular in one or more memories (TMEM) as stored measured values ​​for later use as training data; • Determining an optimized set of configuration parameters for use in the sensor system by executing a computer- and / or machine-implemented artificial intelligence training method, in particular by the training computer system (TRSYS) and in particular by executing one or more computer- and / or machine-implemented machine learning algorithms for regression, in particular by the training computer system (TRSYS), wherein this computer- and / or machine-implemented artificial intelligence training method uses stored fluorescence vectors (F v ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) and / or stored fluorescence frequency vectors (F fv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp) and / or stored fluorescence frequency microwave vectors (F fµv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp , microwave frequency f µw ) or (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), microwave frequency f µw ) used as training data; • The typically following step can include, for example, the following sub-steps in various forms: ◯ Saving the optimized set of configuration parameters thus determined, in particular in a memory (TMEM) of the training computer system (TRSYS), and / or ◯ Keeping the optimized set of configuration parameters available, in particular in a memory (TMEM) of the training computer system (TRSYS), and / or ◯ Output of the optimized set of configuration parameters, in particular via an interface (TIF) of the training computer system (TRSYS), and / or ◯ Transferring the optimized set of configuration parameters, in particular via a data transmission link (TDSTR) connected to the training computer system (TRSYS), in particular to a higher-level training computer system (TÜRSYS), and / or to a computer system (RSYS) of a sensor system for use in one of the previously described methods for operating a sensor system (SSYS) and / or ◯ Storing the optimized set of configuration parameters, in particular via a data transmission link (TDSTR) connected to the training computer system (TRSYS), in particular in a memory of a computer system (RSYS) of a sensor system for use in one of the previously described methods for operating a sensor system (SSYS), and / or ◯ Using at least one determined configuration parameter, in particular by a computer system (RSYS) of a sensor system and ▪ in particular for computer and / or machine-implemented imaging of fluorescence vectors (F v ) each with a fluorescence intensity measurement value and with at least one fluorescence delay measurement value determined within the sensor system, and / or ▪ in particular for computer and / or machine-implemented imaging of fluorescence frequency vectors (F fv ) each with a fluorescence intensity measurement value F i (t) and each with at least one fluorescence delay measurement value F φ (t) determined within the sensor system (SSYS) and at least one value of the pump radiation frequency (f pmp ), and / or ▪ in particular for computer and / or machine-implemented imaging of fluorescence frequency microwave vectors (F fµv) each with a fluorescence intensity measurement value F i (t) and each with at least one fluorescence delay measurement value F φ (t) determined within the sensor system (SSYS), and preferably at least one value of the pump radiation frequency (f pmp ) and at least one value of the microwave frequency (f µw ), ◯ to one or more sensor element state vectors (S v ) (ϑ(t), B(t)), with in particular at least one respective flux density measurement value (B(t)) and at least one respective temperature measurement value (ϑ(t)).

[0128] The computer- and / or machine-implemented detection method (training method) proposed here has, among other advantages, that it is also able to compensate for more complex dependencies within a sensor system. First training of the investigative procedure (training procedure) and / or thirty-eighth training of the procedure

[0129] In a first development of the proposed computer- and / or machine-implemented investigation method and / or the thirty-eighth development of the proposed method, the training computer system (TRSYS) executes the computer- and / or machine-implemented training method (investigation method) of the artificial intelligence. In this first development of the proposed computer- and / or machine-implemented investigation method, the training computer system (TRSYS) preferably executes, in particular, a program code for executing the computer- and / or machine-implemented artificial intelligence training method, which program code is typically located at least temporarily in at least one memory (TMEM) of the training computer system (TRSYS). Second training of the investigative procedure (training procedure) and / or thirty-ninth training of the proposed procedure

[0130] In a second development of the proposed computer- and / or machine-implemented detection method and / or thirty-ninth development of the proposed method, the computer- and / or machine-implemented training method (detection method) of the artificial intelligence comprises a computer- and / or machine-implemented neural network model (NNM) (also referred to here as a neural network). This is capable of mapping the complex relationships in the sensor system (SSYS) and / or in the one or more sensor elements (SE), provided they are reversible. Third training of the investigative procedure (training procedure) and / or fortieth training of the proposed procedure

[0131] In a third development of the proposed computer- and / or machine-implemented determination method and / or the fortieth development of the proposed method, the training computer system (TRSYS) sets the predetermined flux density value of the magnetic field with the magnetic flux density (B(t)) of the predetermined flux density value for each measurement for the determination of one or more training data sets. Preferably, each training data set comprises a value of the set magnetic flux density B(t), a set temperature value ϑ(t), a fluorescence intensity value F i (t) and a fluorescence delay measurement value F φ (t). The sensor system to be compensated (SSYS) and / or a typical representative of the sensor systems to be compensated (SSYS) records the respective fluorescence intensity value F i (t) and the respective fluorescence delay measurement value F φ(t). This fluorescence intensity value F i (t) and this fluorescence delay measurement value F φ (t) form a fluorescence vector F v of the associated training data set. The value of the set magnetic flux density B(t) and the set temperature value ϑ(t) together form a sensor element state vector S z of the relevant test data set. Preferably, the proposed computer- and / or machine-implemented determination method determines for different sensor element state vectors S z corresponding fluorescence vectors F vand then combines these into respective training data sets. The proposed computer- and / or machine-implemented determination method, which the training computer core (TCPU) preferably executes, preferably stores the thus determined training data sets in a memory (TMEM) of the training computer system (TRSYS). The training computer system (TRSYS) and / or another training computer system (TRSYS) can then use the thus determined training data sets of the thus created training database in the memory (TMEM) of the training computer system (TRSYS) to generate (train) the configuration parameters for the above-described computer- and / or machine-implemented artificial intelligence methods and / or the above-described computer- and / or machine-implemented neural network models (e.g., neuromorphic computers). Fourth training of the investigative procedure (training procedure) and / or forty-first training of the proposed procedure

[0132] In a fourth refinement of the proposed computer- and / or machine-implemented determination method and / or the forty-first refinement of the proposed method, one or more magnetic field sensors, in particular one or more Hall sensors, determine one or more flux density measurements for the magnetic flux density B(t) of the magnetic field flowing through the one or more sensor elements (DE). This enables, firstly, a precise determination of the magnetic flux density B(t) for use in the training data sets and, secondly, the adjustment of the magnetic flux density value to a predetermined value.For this purpose, the training computer core (TCPU) of the training computer system (TRSYS) detects the actual value of the magnetic flux density by means of one or more magnetic field sensors, compares this with a target value of the magnetic flux density, for example by forming a difference, preferably by means of a computer and / or machine-implemented method and preferably adjusts the actual value of the magnetic flux density to the target value of the magnetic flux density depending on the comparison result, for example by means of a magnetic field generating device (ME), which is controlled for example via a data bus by the training computer core (TCPU) of the training computer system (TRSYS). Fifth training of the investigative procedure (training procedure) and / or forty-second training of the proposed procedure

[0133] In a fifth refinement of the proposed computer- and / or machine-implemented determination method and / or the forty-second refinement of the proposed method, the training computer system (TRSYS) uses the flux density measurement values ​​to adjust and / or control the one or more flux density measurement values ​​for the magnetic flux density B(t) of the magnetic field flowing through the one or more sensor elements (SE) to the predetermined flux density value. This allows training data sets to be generated at predetermined flux density values. Sixth training of the investigative procedure (training procedure) and / or forty-third training of the proposed procedure

[0134] In a sixth refinement of the proposed computer- and / or machine-implemented determination method and / or the third refinement of the proposed method, the training computer system (TRSYS) adjusts the magnetic flux density B(t) of the magnetic field flowing through the at least one or more sensor elements (SE) using the magnetic field generation device (ME). This allows training data sets to be generated at predetermined flux density values ​​of the magnetic flux density B(t). Seventh training of the investigative procedure (training procedure) and / or forty-fourth training of the proposed procedure

[0135] In a seventh refinement of the proposed computer- and / or machine-implemented determination method and / or the forty-fourth refinement of the proposed method, a temperature control device (TV) controls the temperature of the one or more sensor elements (SE) to temperature values ​​of one or more temperatures ϑ(t). This allows training data sets to be generated at predetermined temperature values. Eighth training of the investigative procedure (training procedure) and / or forty-fifth training of the proposed procedure

[0136] In an eighth development of the proposed computer- and / or machine-implemented determination method and / or the forty-fifth development of the proposed method, the training computer system (TRSYS) controls the temperature control device (TV), in particular via a data bus (TDB) and / or a temperature control line. This allows training data sets to be generated at predetermined temperature values. Ninth training of the investigative procedure (training procedure) and / or forty-sixth training of the proposed procedure

[0137] In a ninth development of the proposed computer- and / or machine-implemented determination method and / or the forty-sixth development of the proposed method, the determination of measured values ​​from the temporal progression (I fl(t)) at least for some measured values ​​at one or more temperatures ϑ(t) of the one or more sensor elements (SE) of 0°C + / - 3°C. This has the advantage that the one or more offset temperature values ​​would be zero in a linear approximation. Experimental work has shown that this is advantageous when the temperatures in the data sets are specified in °C. Tenth training of the investigative procedure (training procedure) and / or forty-seventh training of the proposed procedure

[0138] In a tenth development of the proposed computer and / or machine-implemented determination method and / or the forty-seventh development of the proposed method, the determination of measured values ​​from the temporal progression (I fl(t)) at least for some measured values ​​at one or more temperatures ϑ(t) of the one or more sensor elements (SE) different from 0°C + / - 3°C (outside the temperature range). This has the advantage that the one or more offset temperature values ​​would be zero in a linear approximation. Experimental work has shown that this is advantageous when the temperatures in the data sets are specified in °C. Eleventh training of the investigative procedure (training procedure) and / or forty-eighth training of the proposed procedure

[0139] In an eleventh development of the proposed computer- and / or machine-implemented detection method and / or in a forty-eighth development of the proposed computer- and / or machine-implemented method, a first fluorescence parameter of the fluorescence vector (F v ) (Fluorescence intensity measurement value Fi (t), fluorescence delay measurement value F φ (t)) or the fluorescence frequency vector (F fv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp ) or the fluorescence frequency microwave vector (F fµv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp , microwave frequency f µw ) or (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), microwave frequency f µw ) to the intensity I fl (t) of the fluorescence radiation (FL) in the form of fluorescence intensity measurements F i (t). This has the advantage that this fluorescence parameter essentially depends on the magnitude of the magnetic flux density B(t). Twelfth training of the investigative procedure (training procedure) and / or forty-ninth training of the proposed procedure

[0140] In a twelfth development of the proposed computer- and / or machine-implemented detection method and / or in a forty-ninth development of the proposed computer- and / or machine-implemented method, a second fluorescence parameter of the fluorescence vector (F v ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) or the fluorescence frequency vector (F fv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp ) or the fluorescence frequency microwave vector (F fµv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency fpmp , microwave frequency f µw ) or (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), microwave frequency f µw ) by the time delay (unit of measurement time) and / or phase shift φ (unit of measurement angle) of the temporal course of the intensity (I fl (t)) of the fluorescence radiation (FL) versus the time course of the intensity (I pmp (t)) of the pump radiation (LB) in the form of fluorescence delay measurements F φ (t). This has the advantage that this fluorescence parameter depends essentially differently on the magnitude of the magnetic flux density B(t), or better, essentially less. Thirteenth training of the investigative procedure (training procedure) and / or fiftieth training of the proposed procedure

[0141] In a thirteenth development of the proposed computer- and / or machine-implemented determination method and / or in a fiftieth development of the proposed computer- and / or machine-implemented method, the value of a third vector component of the fluorescence frequency vector (F fv ) by the value of the respective pump radiation frequency (f pmp ). If a fluorescence frequency vector (F fv ) Part of one of the fluorescence frequency microwave vector (F fµv ), the value of a third vector component of the fluorescence frequency microwave vector (F fµv ) preferably, but not necessarily, also by the value of the respective pump radiation frequency (f pmp ). This has the advantage that this information can be used to improve the discriminatory power of the computer and / or machine-implemented method for determining the sensor state vectors (Sz ) (ϑ(t), B(t)) to be further improved. Fourteenth training of the investigative procedure (training procedure) and / or fifty-first training of the proposed procedure

[0142] In a fourteenth development of the proposed computer- and / or machine-implemented detection method and / or in a fifty-first development of the proposed computer- and / or machine-implemented method, the fluorescence frequency microwave vector (F fµv ) a fluorescence frequency vector (F fv ) and a further value of a fourth vector component. At this value of the particular fourth vector component of the fluorescence frequency microwave vector (F fµv ) is typically the value of the respective microwave frequency (f µw). This has the advantage that this information can be used to improve the discriminatory power of the computer and / or machine-implemented method for determining the sensor state vectors (S z ) to further improve. Fifteenth training of the investigative procedure (training procedure) and / or fifty-second training of the proposed procedure

[0143] In a fifteenth development of the proposed computer- and / or machine-implemented determination method and / or in a fifty-second development of the proposed computer- and / or machine-implemented method In a thirteenth development of the proposed computer- and / or machine-implemented determination method, a first physical quantity of the physical quantities is a flux density value of the magnetic flux density (B(t)), in particular at the location of the one or more sensor elements (SE), wherein the measured values ​​of this flux density value of the magnetic flux density (B(t)) are flux density measured values ​​as first quantity parameters. Sixteenth training of the investigative procedure (training procedure) and / or fifty-third training of the proposed procedure

[0144] In a sixteenth development of the proposed computer- and / or machine-implemented determination method and / or in a fifty-third development of the proposed computer- and / or machine-implemented method, a second physical quantity of the physical quantities is one or more temperatures ϑ(t) of the one or more sensor elements (SE), wherein the measured values ​​of this one or more temperatures ϑ(t) are temperature measured values ​​as second quantity parameters. Seventeenth training of the investigative procedure (training procedure) and / or fifty-fourth training of the proposed procedure

[0145] In a seventeenth development of the proposed computer- and / or machine-implemented investigation method and / or in a fifty-fourth development of the proposed computer- and / or machine-implemented method, the determination of measured values ​​from the temporal progression (I fl (t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) and the temporal course of the intensity (I pmp (t)) of the pump radiation (LB) the determination of fluorescence intensity measurements and fluorescence delay measurements from the time course (I fl (t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) and the temporal course of the intensity (I pmp (t)) of the pump radiation (LB), in particular in the form of a computer- and / or machine-implemented fluorescence vector (F v) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) and / or in particular in the form of a computer- and / or machine-implemented fluorescence frequency vector (F fv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp ) and / or in particular in the form of a computer- and / or machine-implemented fluorescence frequency microwave vector (F fµv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp , microwave frequency f µw ) or (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), microwave frequency f µw ). Eighteenth training of the investigative procedure (training procedure) and / or fifty-fifth training of the proposed procedure

[0146] In an eighteenth development of the proposed computer- and / or machine-implemented investigation method and / or in a fifty-fifth development of the proposed computer- and / or machine-implemented method, the determination of measured values ​​from the temporal progression (I fl (t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) and the temporal course of the intensity (I pmp (t)) of the pump radiation (LB) the pairwise and essentially time-synchronous determination of fluorescence intensity measured values ​​and fluorescence delay measured values ​​from the time course (I fl (t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) and the temporal course of the intensity (I pmp(t)) of the pump radiation (LB), in particular in the form of a computer- and / or machine-implemented fluorescence vector (F v ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t)) and / or in particular in the form of a computer- and / or machine-implemented fluorescence frequency vector (F fv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp ) and / or in particular in the form of a computer- and / or machine-implemented fluorescence frequency microwave vector (F fµv ) (Fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), pump radiation frequency f pmp , microwave frequency f µw ) or (fluorescence intensity measurement value F i (t), fluorescence delay measurement value F φ (t), microwave frequency f µw ). Nineteenth training of the investigative procedure (training procedure) and / or fifty-sixth training of the proposed procedure

[0147] In a nineteenth development of the proposed computer- and / or machine-implemented detection method and / or in a fifty-sixth development of the proposed computer- and / or machine-implemented method, in particular the computer- and / or machine-implemented fluorescence frequency vector (F fv ), a value of the pump radiation frequency (f pmp ). If a fluorescence frequency vector (F fv ) Part of one of the fluorescence frequency microwave vector (F fµv ), such a fluorescence frequency microwave vector (F fµv ) also a value of the respective pump radiation frequency (f pmp). This has the advantage that this information can be used to improve the discriminatory power of the computer and / or machine-implemented method for determining the sensor state vectors (S z ) to further improve. Twentieth training of the investigative procedure (training procedure) and / or fifty-seventh training of the proposed procedure

[0148] In a twentieth development of the proposed computer- and / or machine-implemented investigation method and / or in a fifty-seventh development of the proposed computer- and / or machine-implemented method, the computer- and / or machine-implemented fluorescence frequency microwave vector (F v ), a value of the microwave frequency (f µw). This has the advantage that this information can be used to improve the discriminatory power of the computer and / or machine-implemented method for determining the sensor state vectors (S z ) to further improve. Twenty-first training of the investigative procedure (training procedure) and / or fifty-eighth training of the proposed procedure

[0149] In a twenty-first development of the proposed computer- and / or machine-implemented investigation procedure and / or in a fifty-eighth development of the proposed computer- and / or machine-implemented procedure, the temporal progression (I pmp t)) the intensity of the pump radiation (LB) is at least partially sinusoidal with a pump radiation frequency (f pmp ) modulated. This has the advantage that no harmonics are excited during the measurement, which could cause interference. Twenty-second training of the investigative procedure (training procedure) and / or fifty-ninth training of the proposed procedure

[0150] In a twenty-second development of the proposed computer- and / or machine-implemented detection method and / or in a fifty-ninth development of the proposed computer- and / or machine-implemented method, the electromagnetic radiation with which the method additionally irradiates the one or more sensor elements (SE) is microwave-free.

[0151] Microwave-free control of one or more sensor elements (SE) in quantum sensor systems (SSYS) that utilize diamond with NV centers (nitrogen vacancy centers) as the crystal material, and thus the use in the method proposed here, offers numerous technical and practical advantages over conventional sensors and methods that use microwaves to control the NV centers or color centers. The term "microwave-free" refers to the use of alternative methods for manipulating and controlling the NV centers without the use of microwave radiation, which typically lies in the frequency range of 300 MHz to 300 GHz and the wavelength range of 1 mm to 1 m.

[0152] A key advantage of microwave-free control is the significant reduction in energy consumption and heat generation. Microwave-based systems require considerable energy to generate and maintain microwave radiation, resulting in increased energy consumption and significant heat generation. This heat can negatively impact the stability and accuracy of the sensors. In contrast, microwave-free systems use optical or electrical methods to control the color centers or NV centers, which consume less energy and generate minimal heat. This leads to greater stability and reliability of the sensors, especially in energy-sensitive and thermally critical applications.

[0153] Another significant advantage lies in the miniaturization and integration of sensor systems (SSYS). Microwave-based sensor systems (SSYS) require complex and bulky hardware to generate and control the microwave radiation, making miniaturization and integration of the sensor systems (SSYS) into compact devices difficult. Microwave-free sensor systems (SSYS), on the other hand, require less space and can be more easily integrated into smaller and portable form factors. This opens up new application possibilities, particularly in medical technology, mobile devices, and wearable sensor systems (SSYS).

[0154] Additionally, microwave-free control offers advantages in terms of manufacturing costs and production process complexity. Microwave components are expensive and require precise manufacturing and calibration. Eliminating these components reduces manufacturing costs and simplifies the production process, making the technology more economical and accessible.

[0155] Another key advantage is improved electromagnetic compatibility. Microwave radiation can be susceptible to interference and affect other electronic devices. Microwave-free sensor systems (SSYS) minimize this interference, resulting in more reliable and interference-free sensor system performance. This is especially important in sensitive environments such as medical diagnostic devices or precise scientific experiments.

[0156] Microwave-free control of one or more sensor elements (SE) in quantum sensor systems (SSYS) with NV centers in diamond or other color centers thus offers significant advantages over microwave-based systems. Reduction in energy consumption and heat generation, improved miniaturization and integration, lower manufacturing costs, and improved electromagnetic compatibility make this technology a superior choice for a wide range of applications and underscore its potential to significantly influence the future of quantum sensing. Twenty-third training of the investigative procedure (training procedure) and / or sixtieth training of the proposed procedure

[0157] In a twenty-third development of the proposed computer- and / or machine-implemented investigation method and / or in a sixtieth development of the proposed computer- and / or machine-implemented method, the determination of measured values ​​from the temporal progression (I fl (t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) and the temporal course of the intensity (I pmp(t)) the pump radiation (LB) by means of a vector network analyzer (VNA), which in particular the computer system (RSYS) or the training computer system (TRSYS) controls and / or regulates, in particular via a data bus (DB) and in particular by executing a computer-implemented control program, the program code of which is stored, in particular, at least temporarily, in at least one memory (MEM) of the computer system (RSYS), and in particular the output signal of which the computer system (RSYS) or the training computer system (TRSYS) digitizes, in particular by means of an analog-to-digital converter (ADC), which can in particular be part of the vector network analyzer (VNA). Twenty-fourth training of the investigative procedure (training procedure) and / or sixty-first training of the proposed procedure

[0158] In a twenty-fourth development of the proposed computer- and / or machine-implemented investigation method and / or in a sixty-first development of the proposed computer- and / or machine-implemented method, the determination of measured values ​​from the temporal progression (I fl (t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) and the temporal course of the intensity (I pmp(t)) the pump radiation (LB) by means of a lock-in amplifier (LlA), which in particular the computer system (RSYS) or the training computer system (TRSYS) controls and / or regulates, in particular via a data bus (DB) and in particular by executing a computer-implemented control program, the program code of which is stored, in particular at least temporarily, in at least one memory (MEM) of the computer system (RSYS) or in a memory (TMEM) of the training computer system (TSYS), and in particular the output signal of which the computer system (RSYS) or the training computer system (TRSYS) digitizes, in particular by means of an analog-to-digital converter (ADC), which can in particular be part of the lock-in amplifier (LlA). Twenty-fifth training of the investigative procedure (training procedure) and / or sixty-second training of the proposed procedure

[0159] In a twenty-fifth development of the proposed computer- and / or machine-implemented determination method and / or in a sixty-second development of the proposed computer- and / or machine-implemented method, the dependence of the one or more flux density measured values ​​of the magnetic flux density B(t) on one or more temperatures ϑ(t) of the one or more sensor elements (SE) is preferably less than 50% and / or better less than 20% and / or better less than 10% and / or better less than 5% and / or better less than 2% and / or better less than 1% and / or better less than 0.50% and / or better less than 0.20% and / or better less than 0.10% of the value required for measurability by the one or more sensor elements (SE) orof the sensor system (SSYS) with the one or more sensor elements (SE), the maximum flux density value of the magnetic flux density of the magnetic field flowing through the one or more sensor elements (SE), divided by the temperature difference between the maximum intended temperature value of the one or more sensor elements (SE) or the sensor system (SSYS) with the one or more sensor elements (SE) minus the minimum intended temperature value of the one or more sensor elements (SE) or the sensor system (SSYS) with the one or more sensor elements (SE). Sixty-third further development of the proposed procedure

[0160] In a sixty-third development of the proposed computer- and / or machine-implemented method, the proposed computer- and / or machine-implemented method is characterized in that the computer system (RSYS) executes the computer- and / or machine-implemented artificial intelligence method, and in particular, that the computer system (RSYS) executes a program code for executing the computer- and / or machine-implemented artificial intelligence method, which program code is located at least temporarily in at least one memory (MEM) of the computer system (RSYS). This has the advantage that the sensor system can perform self-calibration using its computer system (RSYS). Sixty-fourth development of the proposed procedure

[0161] In a sixty-fourth development of the proposed computer- and / or machine-implemented method, the proposed computer- and / or machine-implemented method of artificial intelligence comprises a computer- and / or machine-implemented neural network model (NNM) (also referred to here as a neural network). This has the advantage that determining the conversion parameters does not necessarily require a complete understanding of all interrelationships. Sixty-fifth further development of the proposed procedure

[0162] In a sixty-fifth development of the proposed computer- and / or machine-implemented method, the proposed computer- and / or machine-implemented method is characterized in that the computer- and / or machine-implemented neural network model (NNM) (also referred to herein as a neural network) comprises a computer- and / or machine-implemented fully connected neural network (FCNN). The present document discusses the advantages of a fully connected neural network in more detail below. In preparing the present document, the inventors recognized that a computer- and / or machine-implemented fully connected neural network (FCNN) is particularly advantageous. Sixty-sixth development of the proposed procedure

[0163] In a sixty-sixth development of the proposed computer- and / or machine-implemented method, the proposed computer- and / or machine-implemented method is characterized in that the computer- and / or machine-implemented neural network model (NNM) (also referred to herein as a neural network) comprises a computer- and / or machine-implemented recurrent neural network (RNN), in particular a long short-term memory (LSTM). In preparing the document presented here, the inventors recognized that the use of a computer- and / or machine-implemented recurrent neural network (RNN) to determine the conversion parameters is possible, but, based on the inventors' experience, is less advantageous than the use of a fully connected neural network (FCNN). Sixty-seventh development of the proposed procedure

[0164] In a sixty-seventh development of the proposed computer- and / or machine-implemented method, the proposed computer- and / or machine-implemented method is characterized in that the computer- and / or machine-implemented neural network model (NNM) (also referred to herein as a neural network) comprises a computer- and / or machine-implemented convolutional neural network (CNN). During the preparation of the document presented here, the inventors recognized that the use of a computer- and / or machine-implemented convolutional neural network (CNN) to determine the conversion parameters is possible, but, based on the inventors' experience, is less advantageous than the use of a fully connected neural network (FCNN). Sixty-eighth development of the proposed procedure

[0165] In a sixty-eighth development of the proposed computer- and / or machine-implemented method, the proposed computer- and / or machine-implemented method is characterized in that the computer system (RSYS) adjusts the predetermined flux density value of the magnetic field with the magnetic flux density (B(t)) of the predetermined flux density value. This is particularly advantageous in order to preferably cover the entire possible range of flux density values ​​during calibration and, in particular, during self-calibration. Sixty-ninth further development of the proposed procedure

[0166] In a sixty-ninth development of the proposed computer- and / or machine-implemented method, the proposed computer- and / or machine-implemented method is characterized in that one or more magnetic field sensors, in particular one or more Hall sensors, determine one or more flux density measured values ​​for the magnetic flux density of the magnetic field flowing through the one or more sensor elements (SE). This is particularly advantageous in order to preferably cover the entire possible value range of the flux density values ​​during calibration, and in particular during self-calibration, and to check whether the relevant values ​​are actually set. Seventieth development of the proposed procedure

[0167] In a seventieth development of the proposed computer- and / or machine-implemented method, the proposed computer- and / or machine-implemented method is characterized in that the computer system (RSYS) uses the flux density measurement values ​​to adjust and / or control the one or more flux density measurement values ​​for the magnetic flux density B(t) of the magnetic field flowing through the one or more sensor elements (SE) to the predetermined flux density value. This is particularly advantageous in order to be able to cover the entire possible value range of the flux density values ​​during calibration and in particular during self-calibration, to check whether the relevant values ​​are actually set, and to be able to readjust the magnetic flux density B(t) at the location of the one or more sensor elements (SE) in the event of deviations using magnetic field generating devices (ME). Seventy-first development of the proposed procedure

[0168] In a seventy-first development of the proposed computer- and / or machine-implemented method, the proposed computer- and / or machine-implemented method is characterized in that the computer system (RSYS) adjusts the magnetic flux density B(t) of the magnetic field flowing through the at least one or more sensor elements (SE) by means of the magnetic field generating device (ME). This is particularly advantageous in order to be able to cover the entire possible range of flux density values ​​during calibration and in particular during self-calibration, to check whether the relevant values ​​are actually set, and, in the event of deviations, to be able to readjust the magnetic flux density B(t) at the location of the one or more sensor elements (SE) by means of magnetic field generating devices (ME). Seventy-second further development of the proposed procedure

[0169] In a seventy-second development of the proposed computer- and / or machine-implemented method, the proposed computer- and / or machine-implemented method is characterized in that a temperature control device (TV) controls the temperature of the one or more sensor elements (SE) to one or more temperature values ​​of one or more temperatures ϑ(t). This is particularly advantageous in order to preferably cover the entire possible range of temperature values ​​during calibration. Seventy-third further development of the proposed procedure

[0170] In a seventy-third development of the proposed computer- and / or machine-implemented method, the proposed computer- and / or machine-implemented method is characterized in that the computer system (RSYS) controls the temperature control device (TV), in particular via a data bus and / or a temperature control line. This has the advantage that the calibration can be carried out fully automatically. Seventy-fourth further development of the proposed procedure

[0171] In a seventy-fourth development of the proposed computer- and / or machine-implemented method, the proposed computer- and / or machine-implemented method is characterized in that the computer- and / or machine-implemented neural network model (NNM) for the regression of the one or more temperatures ϑ(t) from the measured values ​​comprises a computer- and / or machine-implemented fully connected neural network (FCNN) with three hidden computer- and / or machine-implemented layers and a computer- and / or machine-implemented output layer with a single computer- and / or machine-implemented node and a computer- and / or machine-implemented linear activation function.Regarding the advantages of using a computer- and / or machine-implemented fully connected neural network (FCNN), the present document refers to the later section "Description of a computer- and / or machine-implemented fully connected neural network (FCNN) in contrast to other neural networks." In developing the technical teaching of the present document, the inventors recognized that a computer- and / or machine-implemented fully connected neural network (FCNN) is particularly suitable for determining the conversion parameters. Seventy-fifth further development of the proposed procedure

[0172] In a seventy-fifth development of the proposed computer- and / or machine-implemented method, the proposed computer- and / or machine-implemented method is characterized in that the computer- and / or machine-implemented neural network model (NNM) for the regression of the one or more temperatures ϑ(t) from the measured values ​​comprises a computer- and / or machine-implemented fully connected neural network (FCNN) with three hidden computer- and / or machine-implemented layers with 95, 65 and 35 computer- and / or machine-implemented nodes and computer- and / or machine-implemented ReLU activation functions as well as a computer- and / or machine-implemented output layer with a single computer- and / or machine-implemented node and a computer- and / or machine-implemented linear activation function. Other details

[0173] The document presented here thus discloses a sensor system (SSYS) configured to carry out a method as described above. Such a sensor system has the advantage that it can generate one or more temperature-compensated measured values ​​of the one or more magnetic flux densities B(t) and one or more measured values ​​of the one or more temperatures ϑ(t) of the one or more sensor elements (SE), which are then available for use in other systems and / or in another method. The document presented here also reveals the possibility of a

[0174] Computer program product comprising program code for one or more computer- or machine-implemented method steps of the methods described above. Preferably, the program code of the computer program product is a) unencrypted or encrypted and b) wholly or partially i) is stored in a memory and / or ii) is stored in a storage medium and / or iii) kept on a computer system.

[0175] This typically serves the purpose of being executed or capable of being executed by a sensor system (SSYS) as described above and / or by device parts of a sensor system (SSYS) as described above and / or by a computer core (CPU) of a computer system RSYS of a sensor system (SSYS) as described above. This has the advantage that the hardware of a proposed sensor system (SSYS) can be improved at any time by means of an update with the program code of the computer program product.

[0176] The document presented here thus also discloses a storage medium or storage device containing program code and / or data for one or more computer- or machine-implemented method steps of the methods described above, and thus a computer program product or parts thereof. This has the advantage that the hardware of a proposed sensor system can be updated with high cybersecurity by directly electromechanically connecting such a memory and / or storage medium to the sensor system (SSYS).

[0177] The document presented here thus also discloses the use of a storage medium or memory containing program code and / or data for one or more computer- or machine-implemented method steps of one or more of the methods described above in a sensor system (SSYS) with one or more color centers in one or more sensor elements (SE). This has the advantage, for example, that the hardware of a proposed sensor system can be updated with high cybersecurity by directly electromechanically connecting such a memory and / or storage medium to the sensor system (SSYS).

[0178] The document presented here thus also discloses a memory, wherein the memory contains measurement data of a sensor system (SSYS) as described above, in particular one or more compensated first measured values ​​of the first physical quantity of the one or more sensor elements (SE). This has the advantage that the sensor system (SSYS) then requires no data connection and can be operated manually and thus reliably against detection.

[0179] The document presented here thus also discloses a data transmission path configured to transmit measurement data of a sensor system (SSYS) as described above, in particular one or more compensated first measured values ​​of the first physical quantity of the one or more sensor elements (SE). This has the advantage that the data transmission of the measurement data can take place directly.

[0180] The document presented here thus discloses a training system (TSYS) configured to execute a detection procedure as described above. Such a training system (TSYS) has the advantage of being able to generate one or more configuration parameters that are then available for use in the sensor systems (SSYS). The document presented here also reveals the possibility of a

[0181] Computer program product comprising program code for one or more computer- or machine-implemented method steps of the above-described investigation methods. Preferably, the program code of the computer program product is a) unencrypted or encrypted and b) completely or partially i) is stored in a memory and / or ii) is stored in a storage medium and / or iii) kept on a computer system.

[0182] This typically serves the purpose of being executed or capable of being executed by a training system (TSYS) as described above and / or by device parts of a training system (TSYS) as described above and / or by a training computer core (TCPU) of a training computer system (TRSYS) of a training system (TSYS) as described above. This has the advantage that the hardware of a proposed training system (TSYS) can be improved at any time by means of an update with the program code of the computer program product.

[0183] The document presented here thus also discloses a storage medium or storage device containing program code and / or data for one or more computer- or machine-implemented method steps of the aforementioned investigative methods, and thus a computer program product or parts thereof. This has the advantage that the hardware of a proposed training system (TSYS) can be updated with high cybersecurity by directly electromechanically connecting such a memory and / or storage medium to the training system (TSYS).

[0184] The document presented here thus also discloses the use of a storage medium or memory containing program code and / or data for one or more computer- or machine-implemented method steps of one or more of the aforementioned method and / or detection methods in a training system (TSYS) with one or more color centers in one or more sensor elements (SE). This has the advantage, for example, that the hardware of a proposed training system (TSYS) can be updated with high cybersecurity by directly electromechanically connecting such a memory and / or storage medium to the training system (TSYS).

[0185] The document presented here thus also discloses a memory, wherein the memory contains determined configuration parameters of a training system (TSYS) as described above, in particular one or more configuration parameters. This has the advantage that the training system (TSYS) then requires no data connection and can be operated manually, thus preventing detection.

[0186] The document presented here thus also discloses a data transmission path configured to transmit determined configuration parameters of a training system (TSYS) as described above, in particular one or more configuration parameters. This has the advantage that the data transmission of the configuration parameters can take place directly. Experimental PartTemperature Dependence in NV-Based Magnetometry

[0187] Temperature sensing of the temperature ϑ(t) using NV centers is an active research topic. It is typically based on detecting the zero-field splitting shift in optically detected magnetic resonance experiments. The method described here achieves high spatial resolutions, but there are limitations in the delivery of microwave radiation (MS) to the NV centers in the one or more sensor elements (SE).

[0188] Purely optical approaches for NV-based thermometry are also conceivable and are usually based on the change in the spectral shape. They are based on the observation of the shift of the zero-phonon line (ZPL) of the NV centers or a change in the intensity I fl(t) of the fluorescence radiation (FL) of the NV centers. The ratio of the ZPL of the NV centers to the total spectrum (i.e., the Debye-Waller factor) was also used in the development of the technical teaching of the present document. This ratiometric approach is a robust solution for temperature measurements of the temperature ϑ(t), since the total intensity I fl (t) of the fluorescence radiation (FL) can be influenced by many other factors. Sensitivities of 0.3 K / VHz have been reported for this approach using nanodiamonds with NV centers.

[0189] An increase in temperature ϑ(t) is accompanied by a general decrease in fluorescence intensity I fl (t) of the fluorescence radiation (FL). Time-resolved fluorescence spectroscopy has shown a reduction in the fluorescence lifetime with increasing temperature ϑ(t). The reduction in the fluorescence intensity I fl(t) of the fluorescence radiation (FL) with increasing temperature ϑ(t) is therefore not surprising, since the stationary observation is simply an average of the time-resolved phenomena over the intensity decay of the fluorescence intensity I fl (t) of the fluorescence radiation (FL) of the NV diamonds.

[0190] The technical teaching of this document examines, as an example, a sample of NV-rich diamond powder in a frequency domain fluorescence lifetime measurement (measurement of the fluorescence delay F φ (t)) at different temperatures ϑ(t) and different magnetic flux densities B8t) of the magnetic fields. Materials and MethodsFrequency domain measurements

[0191] In Fig. Figure 1 shows an example of the optical and electrical setup for measurements in the frequency domain. A collimated 520 nm laser diode (ams-OSRAM PLT5 520B) as the pump radiation source (LD) for pump radiation (LB) is supplied with energy by a laser driver (iC-Haus GmbH iC-HKB) (LDD) with an average optical output power of 12 mW. The input stage of the laser driver (LDD) is based on a comparator, which is responsible for switching the laser (pump radiation source (LD)) on and off during positive and negative half-waves of the input signal (transmission signal S5). The excitation light is guided through a dichroic mirror (DCM, Thorlabs DMPS567R) (DCM) and coupled into an optical waveguide (OFL) (fiber) with a 105 µm fiber core diameter. In developing the technical teaching of the document presented here,the end facet of the optical waveguide (LWL) (of the fiber) next to microdiamonds as crystals of the one or more sensor elements (SE), were placed in a glass cuvette. The microdiamonds preferably had a high density of color centers, in this case NV centers. This was done in this way during the development of the technical teaching presented here in order to initially measure without the influence of the adhesive or the carrier material of the one or more sensor elements (SE). In practice, this construction could possibly look different. The quantity of exemplary microdiamonds is preferably large enough to completely cover the end facet of the optical waveguide (LWL) (of the fiber). At this point, the document presented here refers to the document DE 10 2023 122 657 A1.The fluorescence radiation (FL) of the NV diamonds (crystals of the one or more sensor elements (SE)) is collected via the same optical fiber (FO), passed through a long-pass filter (LPF), and focused onto a photodiode (photodetector (PD)) (Thorlabs FELH600 & LA1951-AB). The photocurrent of the photodiode (photodetector (PD)) is amplified by a transimpedance amplifier (TIA) (12 kΩ, 75 MHz bandwidth) and passed to the vector network analyzer (VNA) via an RF amplifier (FR amp). The Vector Network Analyzer (VNA) samples the frequency of the output signal (transmit signal (S5)) at port one, which is connected to the laser driver (LDD), in a range of 1-100 MHz and records the response of the optical system (receiver output signal (S0)) in magnitude and phase at port two of the Vector Network Analyzer (VNA).During each sweep, the Vector Network Analyzer (VNA) records this response in the example presented here at 401 different frequencies (pump radiation frequencies (f. pmp ) of the modulation signal (transmission signal (S5) with which the intensity (I pmp (t)) of the pump radiation (LB) with an exemplary bandwidth of 1 kHz. For one observation, the average of five sweeps was recorded during the development of the technical teaching of the document presented here.

[0192] An electromagnet (magnetic field generating device (ME)), monitored by a Hall-effect sensor (HAL), is used to generate magnetic fields up to 80 mT. The electromagnet (magnetic field generating device (ME)), which contains the NV diamond sample (sensor element (SE)), is located in a climate chamber (temperature control device (TV)). Additionally, a PT100 temperature probe (training temperature sensors (TS)) monitors the ambient temperature inside the coil (magnetic field generating device (ME)). Regression with neural networks

[0193] In developing the technical teachings of the document presented here, the sensor system (SSYS) was operated at optical excitation powers for which no saturation behavior was expected. In this linear range, the temporal variation of the intensity (I fl (t)) of the fluorescence radiation (FL) as a convolution of the excitation signal (time course of the intensity (I pmp(t)) of the pump radiation (LB), i.e., the transmit signal (S5)) can be interpreted with the decay dynamics. According to a bi-exponential fluorescence decay, the corresponding transfer function can be written as the sum of two first-order low-pass filters. H(s)=a1s+1τ1+a2s+1τ2 with s = σ + jω and follows the Laplace transform of the sum of two exponential functions. The vector network analyzer (VNA) corrects the system response H(s) at B = 0 and the one or more defined temperatures ϑ(t) of the one or more sensor elements (SE), which result from all electrical and optical components necessary for the measurement, as well as the low-pass characteristic of the generation of the fluorescence radiation (FL) itself. The resulting measurement can be described by the ratio In the experiments to develop the technical teaching of this document, the vector network analyzer (VNA) was calibrated at 0°C.

[0194] In Fig. Figure 2 shows exemplary measurements at different temperatures ϑ(t) and different magnetic flux densities B(t) of the magnetic fields. We observe a high magnetic contrast of the magnitude of the intensity I fl (t) of the fluorescence radiation (FL) at low pump radiation frequencies f pmp and a high magnetic contrast of the phase φ (fluorescence radiation delay φ) around 13 MHz. With increasing temperature ϑ(t), the magnitude of the intensity I fl (t) of the fluorescence radiation (FL) in the entire range of excitation frequencies of the pump radiation frequencies f pmp In addition, the phase φ (fluorescence radiation delay φ) decreases with increasing temperature ϑ(t) at low frequencies of the pump radiation frequencies f pmp to.

[0195] In previous experiments to develop the technical teaching of the present document, only the magnetic flux density B(t) of the magnetic fields was varied, and the equation was adjusted to the measurements. With the additional variation of the temperature ϑ(t), these adjustments can no longer be applied satisfactorily. The present document therefore proposes using computer- and / or machine-implemented machine learning algorithms for the regression of these two variables. The following therefore investigates whether temperature-independent magnetometry can be implemented using the frequency-domain approach.

[0196] In a first step in developing the technical teaching presented here, the set temperature ϑ(t) in the climatic chamber was adjusted between 0°C and 100°C, with each ramp lasting one hour. Residence times of 10 minutes were added at the extremes. During 18 runs lasting 22 hours, 18,373 frequency responses were recorded at a magnetic flux density of the magnetic field of zero (0T). The elaboration used a neural network for the regression of the temperature ϑ(t) from the measured values. For this purpose, a fully connected neural network (FCNN) with three hidden layers with 95, 65, and 35 nodes and ReLU activation functions was implemented, as well as an output layer with a single node and a linear activation function. The observations are denoted by B and consist of the combination of magnitude |H r | and phase ∠H rat 401 different frequencies of the pump radiation frequencies f pmp Consequently, the input layer consists of 802 nodes. During development, the observations were divided into training, validation, and test sets in a ratio of 55%, 15%, and 30%, respectively. The observations were scaled per feature to fall within the interval [0, 1] by fitting a MinMaxScaler to the training data and applying it to all data. In developing the technical framework of this paper, TensorFlow was used to implement and train the neural network models (NNM). (Source: https: / / www.tensorflow.org / )

[0197] In the second step, the temperature ϑ(t) of the chamber (TV) was varied from 0°C to 80°C in 8 hours and back to 0°C in 4 hours. During this time, the magnetic flux density B(t) of the magnetic field was continuously adjusted in 25 steps from 0 mT to 30 mT and in 15 further steps to 80 mT. The number of discrete magnetic field steps was reduced at higher values ​​to limit the additional heating by the electromagnet to 20 K above the ambient temperature. 6494 frequency responses were recorded over a period of 16 hours. For the combined regression of temperature values ​​ϑ(t) and values ​​of the magnetic flux density B(t) of the magnetic fields from the measurements, an FCNN with the same architecture as in the previous case was used. Only the output layer was changed to two nodes with linear activation functions.The same split between training, validation, and test sets was used, and a MinMaxScaler was employed. (See also https: / / towardsdatascience.com / everything-you-need-to-know-about-min-max-normalization-in-python-b79592732b79). Results and DiscussionTemperature dependence

[0198] See also Fig. 3.

[0199] In a first step, the frequency responses of the pump radiation frequency f pmp at different temperatures ϑ(t) and a magnetic flux density B(t) of the magnetic field of zero (0T). An FCNN was trained for 800 epochs, after which the validation loss showed no significant improvement. The loss functions show no signs of overfitting (cf. Fig. 3c). Fig. Figure 3a shows the predictions of the FCNN on the test set. It shows a mean deviation from the linear relationship of 0.29°C and a standard deviation in Δ Tof 1.24°C. These results were consistent across multiple training runs with different randomly selected subsets for training and testing. No significant outliers were observed during the development of the technical teachings of the document presented here, demonstrating that the temperature ϑ(t) can be estimated at a magnetic flux density B8t) of the magnetic field of zero (0T), with 99% of the values ​​of Δ T within ±3.8°C. Temperature and magnetic field dependence

[0200] See also Fig. 4

[0201] In the second step, measurements were performed at slowly varying temperatures ϑ(t) while shifting the magnetic flux density B(t) of the applied magnetic field in discrete steps up to 76 mT. The Hall-effect magnetic field probe showed a temperature dependence of approximately -620 ppm / K, resulting in poor accuracy at high temperatures ϑ(t). To obtain more accurate magnetic field labels, the current values ​​of the electric currents of the electromagnet generating the magnetic field (magnetic field generating means (ME)) were used in the discrete steps. Therefore, the magnetic field in the electromagnet at T = 25°C was recorded with the Hall sensor as a function of the electric current in the electromagnet (ME). A linear fit was then used to calculate the magnetic field labels from the actual electric currents in the electromagnet (ME).

[0202] The same network structure, with the exception of two output nodes with linear activation functions, was used to simultaneously predict magnetic flux densities (B8t) of the magnetic fields and temperatures ϑ(t) from the observations. No overfitting was observed for more than 600 epochs, after which the validation loss no longer improved. Fig. 4a and Fig. Figure 4b shows the temperature predictions ϑ(t) and the differences in a linear relationship. Compared to the previous study, a higher variance was observed, with outliers up to ±22°C from the actual values. A mean deviation from the linear relationship of -0.15°C and a standard deviation in Δ Tof 3.63°C was observed. Additionally, the colors indicate the magnetic flux density B(t) of the magnetic fields associated with the observations. This allowed us to visualize possible clusters of magnetic fields that could lead to observations with higher prediction errors. Such clusters are not visible.

[0203] Fig. Figure 4c,d shows the same predictions regarding the magnetic flux densities B(t) of the magnetic fields. A mean deviation from a linear behavior of -0.13 mT with a standard deviation of 0.79 mT is found. Furthermore, 99% of the values ​​of Δ Bwithin ±3.27 mT, thus demonstrating the ability to predict magnetic flux densities B(t) of the magnetic fields independently of the one or more temperatures ϑ(t) of the one or more sensor elements (SE). A higher variance is observed at high magnetic flux densities B(t) of the magnetic fields. This could be a consequence of the smaller number of observations at these flux densities B(t). Colors were used to represent the temperatures ϑ(t) associated with the predictions and the underlying observations. A correlation between the error and specific temperature ranges is not apparent.

[0204] In an implementation where only the fluorescence intensity I fl (t) of the fluorescence radiation (FL) at a fixed excitation frequency (pump radiation frequency f pmp ), the error caused by different temperatures ϑ(t) can be estimated. In Fig. 5 is the fluorescence intensity I fl (t) of the fluorescence radiation (FL) at the lowest excitation frequency |H r (f = 1MHz)| (f=f pmp ) as a function of the magnetic flux density B(t) of the magnetic field in the temperature range investigated. A linear fit was applied to the data at 25°C in the range from 10 mT to 20 mT. The fit is then used to calculate the values ​​of the magnetic flux densities B(t) of the magnetic fields from the data at nominally 15.5 mT. The resulting values ​​of the magnetic flux densities B(t) of the magnetic fields would cover a range of 9 mT and have a standard deviation of 2.73 mT. The observation of the phase φ at a fixed excitation frequency (pump radiation frequency f pmp) would lead to similar values. In contrast, in the solution presented here, the predicted values ​​of the magnetic flux density B(t) of the magnetic fields at nominally 15.5 mT span a range of 0.37 mT for the recorded temperature range and show a standard deviation of 0.12 mT. conclusion

[0205] In this paper, the combined temperature and magnetic field dependent behavior of high NV density microdiamonds was investigated in an all-optical device operating in the frequency range of the pump radiation frequency f pmp based setup using the change in fluorescence lifetime (fluorescence radiation delay φ). It was shown that from these data, the applied magnetic flux densities B(t) of the magnetic fields can be predicted while varying the ambient temperature ϑ(t) with a higher accuracy than by solely observing the fluorescence intensity I fl(t) of the fluorescence radiation (FL) at a single excitation frequency (pump radiation frequency f pmp ).

[0206] Both studies also used recurrent neural networks, specifically LSTMs, for the regression tasks. However, no improvement in results compared to simple FCNNs was observed. Advantage

[0207] Such a sensor system has the advantage that the magnetic flux density values ​​B(t) of the sensor state vector S Z completely from the temperature measurement value ϑ(t) of the sensor state vector S Z are decoupled. This means that the flux density measured value B(t) of the respective sensor state vector S z is essentially decoupled from the value of the second physical quantity (ϑ(t)) ​​when applying the proposed method. Thus, the sensor system (SSSYS) can be considered temperature-compensated. List of characters Fig. Figure 1 shows a schematic representation of the optical and electrical setup for frequency domain measurements. Fig. Figure 2 shows example measurements at different temperatures and magnetic fields. Fig. Figure 3 shows (a) the overlay of the FCNN's predictions on the test set compared to the optimal linear relationship. (b) the differences of the predictions in (a) compared to the linear relationship. (c) the mean squared error on the training and validation sets during training of the FCNN. Fig. 4 shows the combined regression of temperatures and magnetic fields Fig. 5 shows the fluorescence intensity at excitation frequency f = 1MHz (pump radiation frequency f pmp ) as a function of the value of the magnetic flux density B(t) of the magnetic field and the temperature ϑ(t). Fig. 6 shows the sensor system. Fig. 7 Fig. Figure 7 illustrates the proposed procedure (100). Fig. 8 Fig. 8 largely corresponds to the Fig. 7, wherein a computer- and / or machine-implemented step of forming (136) a three-dimensional computer- and / or machine-implemented fluorescence frequency vector F fv is inserted. Fig. 9 Fig. 9 largely corresponds to the Fig. 8, wherein a computer- and / or machine-implemented step of irradiating (127) the one or more sensor elements (SE) with electromagnetic radiation in the microwave range is additionally inserted. Fig. 10 Fig. 10 largely corresponds to the Fig. 9, wherein additionally a computer and / or machine-implemented step of adjusting (186) the first microwave frequency (f µw1 ) of m intended microwave frequencies is inserted. Fig. 11 Fig. 11 largely corresponds to the Fig. 10, wherein a computer and / or machine-implemented step of querying (170) whether all n pump radiation frequencies have been set and measured has been additionally inserted. Fig. 12 Fig. 12 largely corresponds to the Fig. 11, wherein a computer and / or machine-implemented step of querying (180) whether all m microwave frequencies have been set and measured has been additionally inserted. Fig. 13 Fig. 13 shows an exemplary determination method (training method) (200) for determining one or more configuration parameters for use in the proposed method (100). Fig. 14 Fig. 14 largely corresponds to the Fig. 13, wherein a computer and / or machine-implemented step of forming (136) a three-dimensional fluorescence frequency vector F fv is inserted. Fig. 15 Fig. 15 largely corresponds to the Fig. 14, wherein a computer- and / or machine-implemented step of determining (140) a first measured value of the first physical quantity of the one or more sensor elements (SE) has been inserted. Fig. 16 Fig. 16 largely corresponds to the Fig. 15, wherein a computer- and / or machine-implemented step of irradiating (127) the one or more sensor elements (SE) with electromagnetic radiation in the microwave range is additionally inserted. Fig. 17 Fig. 17 largely corresponds to the Fig. 16, wherein additionally a computer and / or machine-implemented step of querying (170) whether all n pump radiation frequencies (f pmp1 to f pmpn ) were set and measured. Fig. 18 Fig. 18 largely corresponds to the Fig. 17, wherein additionally a computer and / or machine-implemented step of querying (180) whether all m microwave frequencies (f µw1 to f µwm ) were set and measured. Fig. 19 Fig. 19 shows a simplified and schematic representation of a proposed sensor system (SSYS) which is configured to carry out the proposed method (100). Fig. 20 Fig. 20 shows schematically and simplified the exemplary signal flow plan for a device of the Fig. 19. Fig. 21 Fig. 21 differs from the Fig. 20 in that the fluorescence vectors (F v (t)) with the value of the pump radiation frequency (f pmp ) to fluorescence frequency vectors (F fv(t) ) can be combined. Fig. 22 Fig. 22 largely corresponds to the Fig. 21. In addition, the microwave signal generator (µG) generates a microwave signal which is radiated into the one or more sensor elements (SE). Fig. 23 Fig. 23 corresponds to the Fig. 20, whereby the computer system (RSYS) additionally controls a microwave signal generator (µG). Fig. 24 Fig. Figure 24 illustrates an exemplary neural network model (NNM) for mapping a fluorescence frequency microwave vector (F fµv (t)) on sensor state vectors (S z (t)). Fig. 25: Fig. Figure 25 illustrates an example neural network model (NNM) for mapping a fluorescence frequency vector (F fv (t)) on sensor state vectors (S z (t)). Fig. 26 Fig. Figure 26 illustrates an exemplary neural network model (NNM) for mapping multiple fluorescence vectors (Fv(t1), Fv(tk)) to sensor state vectors (Sz(t)). Fig. Figure 27 shows a test system (TSYS) for determining the configuration parameters of a computer and / or machine-implemented neural network model (MMN) Description of the characters

[0208] The figures illustrate the proposal schematically and in a simplified manner. The disclosure of the document presented here is not limited to the figures and also includes other combinations. Figure 1

[0209] Fig. Figure 1 shows a schematic representation of the optical and electrical setup for frequency domain measurements of the frequency ranges of the pump radiation frequency f pmp The fiber tip with NV-rich diamond powder as an exemplary sensor element (SE) is located in an electromagnet (ME), which is monitored by a Hall-effect sensor and a PT100 temperature sensor.

[0210] In Fig. 1 is the optical and electrical setup for measurements in the frequency range of the pump radiation frequency f pmpA collimated 520 nm laser diode (ams-OSRAM PLT5 520B) serves as the pump radiation source (LD) for the pump radiation (LB) and is powered by a laser driver (iC-Haus GmbH iC-HKB) (LDD) with an average optical output power of 12 mW. The input stage of the laser driver (LDD) is based on a comparator, which is responsible for switching the laser (pump radiation source (LD)) on and off during positive and negative half-waves of the input signal. The excitation light (pump radiation LB) is guided by a dichroic mirror (DCM, Thorlabs DMPS567R) (DCM) and coupled into an optical fiber (OF) with a 105 µm core diameter fiber. The end facet of the optical waveguide (OW) (fiber) is placed in a glass cuvette next to microdiamonds as crystals of one or more sensor elements (SE), which preferably have a high density of color centers, here NV centers.The quantity of exemplary microdiamonds is preferably large enough to completely cover the end facet of the optical fiber (OF). At this point, the document presented here refers to document DE 10 2023 122 657 A1. The fluorescence radiation (FL) of the NV diamonds (crystals of the one or more sensor elements (SE)) is collected via the same optical fiber (OF) (same fiber), passed through a long-pass filter (LPF), and focused onto a photodiode (photodetector (PD)) (Thorlabs FELH600 & LA1951-AB). The electrical photocurrent of the photodiode (PD) is amplified by a transimpedance amplifier (TIA) and an RF amplifier (RF amp) (12 kΩ, 75 MHz bandwidth) and forwarded to the vector network analyzer (VNA).The Vector Network Analyzer (VNA) samples the frequency of the output signal (transmit signal (S5)) at port one, which is connected to the laser driver (LDD), in a range of 1-100 MHz and records the response (receiver output signal (S0)) in magnitude of intensity I. fl (t) of the fluorescence radiation (FL and phase φ at terminal two. During each sweep, the Vector Network Analyzer (VNA) records this response in the example presented here at 401 different frequencies (pump radiation frequencies (f pmp ) of the modulation signal (transmission signal (S5)) with which the intensity (I pmp (t)) modulated by the pump radiation (LB) with a bandwidth of 1 kHz. For one observation, the average of five sweeps is recorded.

[0211] An electromagnet (magnetic field generating device (ME)), monitored by a Hall-effect sensor, is used to generate magnetic fields up to 80 mT. The electromagnet (magnetic field generating device (ME)), which contains the NV diamond sample (sensor element (SE)), is located in a climate chamber (temperature control device (TV)). Additionally, the ambient temperature inside the coil (magnetic field generating device (ME)) was monitored with a PT100 temperature probe (training temperature sensors (TS)). Figure 2

[0212] Measurements of the magnitude |H r | and phase ∠H r depending on the excitation frequency f pmp at different temperaturesT (ϑ(t)) ​​and magnetic fields B.

[0213] In Fig. Figure 2 shows exemplary measurements at different temperatures and magnetic fields. We observe a high magnetic contrast of the magnitude of the intensity I fl(t) of the fluorescence radiation (FL) at low frequencies of the pump radiation frequency f pmp and a high magnetic contrast of the phase φ around 13 MHz. With increasing temperature ϑ(t), the magnitude of the intensity I fl (t) of the fluorescence radiation (FL) decreases over the entire range of excitation frequencies. In addition, the phase φ decreases with increasing temperature ϑ(t) at low frequencies of the pump radiation frequency f pmp to. Figure 3

[0214] (a) Superposition of the FCNN's predictions on the test set compared to the optimal linear relationship. (b) Differences of the predictions in (a) from the linear relationship. (c) Mean square error on training and validation sets during FCNN training. Figure 4

[0215] Fig. Figure 4 shows the combined regression of temperatures ϑ(t) and values ​​of the magnetic flux density B(t) of the magnetic fields. Fig. Figure 4(a) shows the temperature prediction ϑ(t) on the test set compared to the optimal linear relationship. The colors indicate the respective values ​​of the magnetic flux density B(t) of the observed magnetic field. Fig. Figure 4 (b) shows the differences of the predictions in (a) to the linear relationship. Fig. Figure 4 (c) shows predictions of the magnetic fields on the test set compared to the optimal linear relationship. The colors indicate the respective temperature of the observation. Fig. Figure 4 (d) shows differences between the predictions in (c) and the linear relationship. (e) Mean square error on training and validation sets during training of the FCNN.

[0216] In the second step, measurements were performed at slowly varying temperatures while shifting the applied magnetic field in discrete steps up to 76 mT. The Hall-effect magnetic field probe exhibited a temperature dependence of approximately -620 ppm / K, resulting in poor accuracy at high temperatures. To obtain more precise magnetic field markers, the electric currents applied to the electromagnet (ME) were used in the discrete steps. Therefore, the magnetic field in the electromagnet at T = 25°C was recorded with the Hall sensor as a function of the electric current in the electromagnet.

[0217] The same network structure, except for two output nodes with linear activation functions, was used to simultaneously predict the magnetic flux densities B(t) of the magnetic fields and the temperatures ϑ(t) from the observations. No overfitting was observed for more than 600 epochs, after which the validation loss no longer improved. Fig. Figures 4a and b show the temperature predictions ϑ(t) and the deviations from a linear relationship, respectively. Compared to the previous study, a higher variance was observed, with outliers up to ±22°C from the actual values. A mean deviation from the linear relationship of -0.15°C and a standard deviation in Δ Tof 3.63°C was observed. Additionally, the colors indicate the values ​​of the magnetic flux density B(t) of the magnetic fields associated with the observations. This allows visualization of possible clusters of magnetic fields that could lead to observations with higher errors in the predictions. However, no such clusters are visible.

[0218] Fig. 4c and Fig. 4d show the same predictions regarding the magnetic flux densities B(t) of the magnetic fields. A mean deviation from a linear behavior of -0.13 mT is found with a standard deviation of 0.79 mT. Furthermore, 99% of the values ​​of Δ Bwithin ±3.27 mT, thus demonstrating the ability to predict magnetic flux densities B(t) of magnetic fields independent of the sample temperature (temperature ϑ(t) of the sensor element (SE)). A higher variance is observed at high magnetic fields. This could be a consequence of the smaller number of observations at these magnetic flux densities. Colors were used to represent the temperatures ϑ(t) associated with the predictions and the underlying observations. Figure 5

[0219] Fig. 5 shows the fluorescence intensity at excitation frequency f = 1MHz (pump radiation frequency f pmp ) as a function of the magnetic flux density B(t) of the magnetic field and the temperature ϑ(t). The linear fit was applied to the data at 25 ° C in the range from 10 mT to 20 mT. In Fig. 5 is the fluorescence intensity at the lowest excitation frequency |H r(f = 1 MHz)| as a function of the magnetic flux density B(t) of the magnetic field in the investigated temperature range. A linear fit was applied to the data at 25°C in the range from 10 mT to 20 mT. The fit is then used to calculate the magnetic fields from the data at nominally 15.5 mT. The resulting magnetic field values ​​would span a range of 9 mT and have a standard deviation of 2.73 mT. Observing the phase at a fixed excitation frequency would lead to similar values. In contrast, in our solution, the predicted magnetic field at nominally 15.5 mT spans a range of 0.37 mT for the recorded temperature range and shows a standard deviation of 0.12 mT. Figure 6

[0220] Fig. 6 shows the sensor system. Figure 7

[0221] Fig. Figure 7 illustrates the proposed method (100). The proposed method (100) is preferably computer- and / or machine-implemented. Preferably, the program code and the configuration parameters of the method (100) are located at least temporarily in a memory (MEM) of the computer system (RSYS) of the sensor system (SSYS). Preferably, the computer core (CPU) of the computer system (RSYS) of the sensor system (SSYS) executes this program code and uses this configuration data when executing the proposed computer- and / or machine-implemented method (100). The method (100) begins, for example, with the provision (105) of a sensor system (SSYS) with at least one or more sensor elements (SE). This is followed, for example, by the provision (110) of a computer system (RSYS) of the sensor system (SSYS).This is followed, for example, by irradiating (115) the one or more sensor elements (SE) with a pump radiation (LB) having a pump radiation wavelength (. pmp), in particular by means of a pump radiation source (LD), wherein the temporal course of the intensity (I pmp (t)) of the pump radiation (LB) is modulated with a modulation signal, in particular with a transmission signal S5(t). This is followed, for example, by providing (120) program code for a computer- and / or machine-implemented correction method, in particular in one or more memories (MEM) of the computer system (RSYS) of the sensor system. The first pump radiation frequency (f pmp1 ) of n intended pump radiation frequencies (f pmp1 to f pmpn ) as the new pump radiation frequency (f pmp). This is followed by the provision (125) of configuration parameters for carrying out the computer- and / or machine-implemented correction method, wherein the provision takes place in particular in one or more memories (MEM), in particular of the sensor system and / or computer system (RSYS). Typically, this is followed by the detection (130) of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE), which depends in different ways on the at least two physical variables, in particular by means of one or more photodetectors (PD). This is followed by the determination (135) of at least two different fluorescence parameters as vector components of an at least two-dimensional computer- and / or machine-implemented fluorescence vector F v from the temporal progression (I fl(t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) in combination with the temporal course of the pump radiation intensity (I pmp (t)) of the pump radiation (LB). Then, the determination (140) of a first measured value of the first physical quantity of the one or more sensor elements (SE) takes place in the form of a first quantity parameter of a one- or multi-dimensional computer- and / or machine-implemented sensor state vector (S z ). This is followed by outputting (160) and / or keeping ready and / or storing and / or transmitting and / or using the determined compensated first measured value of the first physical quantity of the one or more sensor elements (SE). Figure 8

[0222] The Fig. 8 largely corresponds to the Fig. 7, wherein a computer- and / or machine-implemented step of forming (136) at least one at least three-dimensional computer- and / or machine-implemented fluorescence frequency vector F fv , which comprises at least one at least two computer and / or machine-implemented fluorescence vectors F v and at least the value of the pump radiation frequency (f pmp ) is inserted. Figure 9

[0223] The Fig. 9 largely corresponds to the Fig. 8, wherein additionally a computer- and / or machine-implemented step of irradiating (127) the one or more sensor elements (SE) with electromagnetic radiation in the microwave range and a computer- and / or machine-implemented step of determining (142) a second measured value of the second physical quantity of the one or more sensor elements (SE) in the form of a second quantity parameter of the one- or multi-dimensional computer- and / or machine-implemented sensor state vector (S z ) are inserted. A computer- and / or machine-implemented step of outputting (165) and / or keeping ready and / or storing and / or transmitting and / or using the determined compensated second measured value of the second physical quantity of the one or more sensor elements (SE) concludes the method of Fig. 9 off. Figure 10

[0224] The Fig. 10 largely corresponds to the Fig. 9, wherein additionally a computer and / or machine-implemented step of adjusting (186) the first microwave frequency (f µw1 ) of m intended microwave frequencies (f µw1 to f µwn ) as the new microwave frequency (f µw ) is inserted. Furthermore, a step of forming (137) at least one at least four-dimensional computer- and / or machine-implemented fluorescence frequency microwave vector F fµv which contains at least the at least one, at least two-dimensional computer- and / or machine-implemented fluorescence vector F v and which has at least the value of the pump radiation frequency (f pmp ) and which has at least the value of the microwave frequency (f µw ) includes. Figure 11

[0225] The Fig. 11 largely corresponds to the Fig. 10, wherein additionally a computer and / or machine-implemented step of querying (170) whether all n pump radiation frequencies (f pmp1 to f pmpn ) were set and measured.

[0226] Were all n pump radiation frequencies (f pmp1 to f pmpn ) and measured (branch “yes”), the procedure ends with Fig. 11.

[0227] If not all n pump radiation frequencies (f pmp1 to f pmpn ) are set and measured (branch “nine”), the computer and / or machine-implemented method (100) of the Fig. 11 the computer- and / or machine-implemented step of setting s(175) a further, different, i-th pump radiation frequency (f pmpi ) of n intended pump radiation frequencies (f pmp1 to f pmpn ) as the new pump radiation frequency (f pmp) and the computer- and / or machine-implemented method (100) starts again with the computer- and / or machine-implemented step of providing (125) configuration parameters for carrying out the computer- and / or machine-implemented correction method, wherein in particular the provision takes place in one or more memories (MEM), in particular of the sensor system and / or computer system (RSYS), followed by the computer- and / or machine-implemented step of irradiating (126) the one or more sensor elements (SE) with pump radiation (LB) of a pump radiation wavelength (λ pmp ), whose temporal intensity profile (I pmp (t)) with a pump radiation frequency (f pmp) is preferably sinusoidally modulated, preferably by means of a transmission signal S5(t). In this way, the computer- and / or machine-implemented, proposed method (100), when preferably carried out by the computer core (CPU) of the computer system (RSYS) of the sensor system (SSYS), determines for each of the n pump radiation frequencies (f pmp1 to f pmpn ) preferably a respective fluorescence frequency vector (F fv ), which the computer core (CPU) of the computer system (RSYS) of the sensor system (SSYS) then uses for the computer and / or machine-implemented determination of the sensor state vector (S z ) can be used. Figure 12

[0228] The Fig. 12 largely corresponds to the Fig. 11, wherein additionally a computer and / or machine-implemented step of querying (180) whether all m microwave frequencies (f µw1 to f µwm ) were set and measured.

[0229] Were not all m microwave frequencies (f µw1 to f µwm ) and measured (branch “no”), the computer and / or machine-implemented method (100) of the Fig. 12 the computer- and / or machine-implemented step of setting (183) a further, different, j-th microwave frequency (f µwj ) of m intended pump radiation frequencies (f µw1 to f µwm ) as the new microwave frequency (f µw In order to be able to start the measurement cycle of the different pump radiation frequencies from the beginning, the computer and / or machine-implemented method (100) of Fig. 12 prefers the additional step of computer- and / or machine-implemented setting (185) of the first pump radiation frequency (f pmp1 ) of n intended pump radiation frequencies (f pmp1 to f pmpn ) as the new pump radiation frequency (f pmp). This is followed again by the computer- and / or machine-implemented step of providing (125) configuration parameters for carrying out the computer- and / or machine-implemented correction method, wherein in particular the provision takes place in one or more memories (MEM), in particular of the sensor system and / or computer system (RSYS);

[0230] Were all m microwave frequencies (f µw1 to f µwm ) and measured (branch “no”), the computer and / or machine-implemented method (100) of the Fig. 12. Figure 13

[0231] Fig. 13 shows an exemplary computer- and / or machine-implemented determination method (training method) (200) for determining one or more computer- and / or machine-implemented configuration parameters for computer- and / or machine-implemented use in the proposed computer- and / or machine-implemented method (100).

[0232] The exemplary computer- and / or machine-implemented determination method (training method) (200) begins, for example, with the computer- and / or machine-implemented step of setting (185) the first pump radiation frequency (f pmp1 ) of n intended pump radiation frequencies (f pmp1 to f pmpn ) as the new pump radiation frequency (f pmp). In the example, the step of providing (105) a sensor system (SSYS) with at least one or more sensor elements (SE) follows. Additionally, in the example, the provision (205) of a training computer system (TRSYS) and the provision (210) of a temperature control device (TV), in particular a temperature cabinet and / or one or more heating and / or cooling devices, also take place.

[0233] In the example of Fig. 13, the exemplary computer- and / or machine-implemented determination method (training method) (200) comprises, for example, the computer- and / or machine-implemented step of irradiating (115) the one or more sensor elements (SE) with a pump radiation (LB) having a pump radiation wavelength (λ pmp ), in particular by means of a pump radiation source (LD), wherein the temporal course of the intensity (I pmp(t)) of the pump radiation (LB) is modulated with a modulation signal, in particular with a transmission signal S5(t).

[0234] In the example of Fig. 13, the exemplary computer- and / or machine-implemented determination method (training method) (200) comprises, for example, the exemplary computer- and / or machine-implemented step of setting (220) the magnetic field to a predetermined flux density value, in particular by means of the magnetic field generating device (ME), which is controlled in particular by the training computer system (TRSYS), and flooding the one or more sensor elements (SE) with this magnetic field with magnetic flux densities (B) of predetermined flux density values.

[0235] In the example of Fig. 13, the exemplary computer- and / or machine-implemented determination method (training method) (200) comprises, for example, the exemplary computer- and / or machine-implemented step of tempering (225) the one or more sensor elements (SE) to temperature values, in particular by means of the tempering device (TV), which is controlled in particular by the training computer system (TRSYS) and / or regulated in particular on the basis of the temperature measured values ​​of one or more training temperature sensors (TS).

[0236] In the example of Fig. 13, the exemplary computer- and / or machine-implemented determination method (training method) (200) comprises, for example, the exemplary computer- and / or machine-implemented step of detecting (130) the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE), which depends in different ways on the at least two physical variables, in particular by means of one or more photodetectors (PD).

[0237] In the example of Fig. 13, the exemplary computer- and / or machine-implemented determination method (training method) (200) comprises, for example, the exemplary computer- and / or machine-implemented step of determining (135) at least two different fluorescence parameters as vector components of an at least two-dimensional computer- and / or machine-implemented fluorescence vector F v from the temporal progression (I fl(t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) in combination with the temporal course of the pump radiation intensity (I pmp (t)) of the pump radiation (LB).

[0238] In the example of Fig. 13, the exemplary computer- and / or machine-implemented determination method (training method) (200) comprises, for example, the exemplary computer- and / or machine-implemented step of storing (230) determined measured values ​​in the form of the fluorescence vectors (F v ) or in the form of fluorescence frequency vectors (F fv ) or in the form of the fluorescence frequency microwave vectors (F fµv ) in particular in one or more memories (TMEM) as stored measured values ​​for later use as training data.

[0239] In the example of Fig. 13, the exemplary computer- and / or machine-implemented determination method (training method) (200) comprises, for example, the exemplary computer- and / or machine-implemented step of determining (235) an optimized set of configuration parameters for use in the sensor system by executing a computer- and / or machine-implemented artificial intelligence training method, in particular by the training computer system (TRSYS) and in particular by executing one or more computer- and / or machine-implemented machine learning algorithms for regression, in particular by the training computer system (TRSYS).

[0240] In the example of Fig. 13, the exemplary computer- and / or machine-implemented investigation method (training method) (200) comprises, for example, the exemplary computer- and / or machine-implemented steps a) storing (240) the optimized set of configuration parameters thus determined, in particular in a memory (TMEM) of the training computer system (TRSYS), and / or b) keeping (241) the optimized set of configuration parameters ready, in particular in a memory (TMEM) of the training computer system (TRSYS), and / or c) outputting (242) the optimized set of configuration parameters, in particular via an interface (TIF) of the training computer system (TRSYS), and / or d) transmitting (243) the optimized set of configuration parameters, in particular via a data transmission link (TDSTR) connected to the training computer system (TRSYS), in particular to a higher-level computer system (TÜRSYS), and / or to a computer system (RSYS) of a sensor system for use in a proposed method, and / or e) storing (244) the optimized set of configuration parameters, in particular via a data transmission link (TDSTR) connected to the training computer system (TRSYS), in particular in a memory of a computer system (RSYS) of a sensor system for use in a proposed method.

[0241] In the example of Fig. 13, the exemplary computer- and / or machine-implemented determination method (training method) (200) comprises, for example, the exemplary, typically final computer- and / or machine-implemented step of using (250) at least one determined configuration parameter, in particular by a computer system (RSYS) of a sensor system and in particular for computer- and / or machine-implemented imaging of fluorescence vectors (F v) each with a fluorescence intensity measurement value and each with at least one fluorescence delay measurement value, which were determined within the sensor system, and / or in particular for computer- and / or machine-implemented mapping of fluorescence frequency vectors (F fv ) each with a fluorescence intensity measurement value and with at least one fluorescence delay measurement value, which were determined within the sensor system, and at least one value of the pump radiation frequency (f pmp ), and / or in particular for computer- and / or machine-implemented imaging of fluorescence frequency microwave vectors (F fµv ) each having a fluorescence intensity measurement value and at least one fluorescence delay measurement value, which were determined within the sensor system, and at least one value of the pump radiation frequency (f pmp ) and at least one value of the microwave frequency (f µw) to one or more sensor element state vectors (S v ), with in particular at least one respective flux density measurement value of the magnetic flux density B(t) and at least one respective temperature measurement value of a temperature ϑ(t). Figure 14

[0242] The Fig. 14 largely corresponds to the Fig. 13, wherein a computer- and / or machine-implemented step of forming (136) at least one at least three-dimensional computer- and / or machine-implemented fluorescence frequency vector F fv , which comprises at least one at least two computer and / or machine-implemented fluorescence vectors F v and at least the value of the pump radiation frequency (f pmp ) is inserted. Figure 15

[0243] The Fig. 15 largely corresponds to the Fig. 14, wherein a computer- and / or machine-implemented step of forming (136) at least one at least three-dimensional computer- and / or machine-implemented fluorescence frequency vector F fv , which comprises at least one at least two computer and / or machine-implemented fluorescence vectors F v and at least the value of the pump radiation frequency (f pmp ) was inserted. Furthermore, a computer- and / or machine-implemented step of determining (140) a first measured value of the first physical quantity of the one or more sensor elements (SE) in the form of a first size parameter of a one- or multi-dimensional computer- and / or machine-implemented sensor state vector (S z ), inserted. Figure 16

[0244] The Fig. 16 largely corresponds to the Fig. 15, wherein additionally a computer- and / or machine-implemented step of irradiating (127) the one or more sensor elements (SE) with electromagnetic radiation in the microwave range and a computer- and / or machine-implemented step of determining (142) a second measured value of the second physical quantity of the one or more sensor elements (SE) in the form of a second quantity parameter of the one- or multi-dimensional computer- and / or machine-implemented sensor state vector (S z ) are inserted. Figure 17

[0245] The Fig. 17 largely corresponds to the Fig. 16, wherein additionally a computer and / or machine-implemented step of querying (170) whether all n pump radiation frequencies (f pmp1 to f pmpn ) were set and measured.

[0246] Were all n pump radiation frequencies (f pmp1 to f pmpn) and measured (branch “yes”), the procedure ends with Fig. 17.

[0247] If not all n pump radiation frequencies (f pmp1 to f pmpn ) are set and measured (branch “nine”), the computer and / or machine-implemented method (200) of the Fig. 17 the computer- and / or machine-implemented step of setting (175) a further, different, i-th pump radiation frequency (f pmpi ) of n intended pump radiation frequencies (f pmp1 to f pmpn ) as the new pump radiation frequency (f pmp) and the computer- and / or machine-implemented method (200) starts again with the computer- and / or machine-implemented step of setting (220) the magnetic field to a predetermined flux density value, in particular by means of the magnetic field generating device (ME), which is controlled in particular by the training computer system (TRSYS), and flooding the one or more sensor elements (SE) with this magnetic field with magnetic flux densities (B) of predetermined flux density values, and the computer- and / or machine-implemented step of tempering (225) the one or more sensor elements (SE) to temperature values, in particular by means of the tempering device (TV), which is controlled in particular by the training computer system (TRSYS) and / or regulated in particular on the basis of the temperature measurement value of one or more training temperature sensors (TS). Figure 18

[0248] The Fig. 18 largely corresponds to the Fig. 17, wherein additionally a computer and / or machine-implemented step of querying (180) whether all m microwave frequencies (f µw1 to f µwm ) were set and measured.

[0249] Were not all m microwave frequencies (f µw1 to f µwm ) and measured (branch “no”), the computer and / or machine-implemented method (200) of the Fig. 18 the computer- and / or machine-implemented step of setting (183) a further, different, j-th microwave frequency (f µwj ) of m intended pump radiation frequencies (f µw1 to f µwm ) as the new microwave frequency (f µw In order to be able to start the measurement cycle of the different pump radiation frequencies from the beginning, the computer and / or machine-implemented method (200) of Fig. 18 prefers the additional step of computer and / or machine-implemented setting (185) of the first pump radiation frequency (f pmp1 ) of n intended pump radiation frequencies (f pmp1 to f pmpn ) as the new pump radiation frequency (f pmp). The proposed method (200) begins the computer- and / or machine-implemented method (200) from the beginning with the computer- and / or machine-implemented step of setting (220) the magnetic field to a predetermined flux density value, in particular by means of the magnetic field generating device (ME), which is controlled in particular by the training computer system (TRSYS), and flooding the one or more sensor elements (SE) with this magnetic field with magnetic flux densities (B) of predetermined flux density values, and the computer- and / or machine-implemented step of tempering (225) the one or more sensor elements (SE) to temperature values, in particular by means of the tempering device (TV), which is controlled in particular by the training computer system (TRSYS) and / or regulated in particular based on one or more temperature measured values ​​of one or more temperatures ϑ(t) of one or more training temperature sensors (TS).

[0250] Were all m microwave frequencies (f µw1 to f µwm ) and measured (branch “no”), the computer and / or machine-implemented method (100) of the Fig. 18. Figure 19

[0251] Fig. 19 shows a simplified and schematic representation of a proposed sensor system (SSYS) which is configured to carry out the proposed method (100).

[0252] A signal generator (SGEN) preferably generates the transmission signal (S5(t)). Preferably, the transmission signal S5(t) is substantially sinusoidal. Preferably, the transmission signal (S5(t)) is monofrequency. Preferably, the temporal profile of the transmission signal (S5(t)) has a substantially sinusoidal shape. Preferably, the temporal profile of the transmission signal (S5(t)) has a substantially periodicity. Preferably, the temporal profile of the transmission signal (S5(t)) has a substantially pump radiation frequency (f pmp) as the frequency of its preferred sinusoidal modulation. The signal generator (SGEN) can be part of the vector network analyzer (VNA) and / or the lock-in amplifier (VMA).

[0253] Preferably, the pump radiation source (LD) converts the transmission signal (S5(t)) of the signal generator (SGEN) into a temporal progression of the intensity (I pmp (t)) of the pump radiation (LB) and emits this pump radiation (LB) into an optical system with optical functional components.

[0254] These optical functional elements can be, for example (but not only), optical functional elements from the following exemplary groups of optical functional elements: 1. Lenses, such as B. plano-convex lenses, plano-concave lenses, biconvex lenses, biconcave lenses, aspherical lenses etc. 2. Prisms, such as triangular prisms, Amici prisms, pentaprisms, wedge prisms, roof prisms, etc. 3. Mirrors, such as plane mirrors, concave mirrors, convex mirrors, parabolic mirrors, elliptical mirrors, dielectric mirrors, dichroic mirrors (DCM), MEMS mirrors, etc. 4. Filters such as color filters, polarizing filters, interference filters, neutral density filters, UV filters, long-pass filters, short-pass filters, band-pass filters, band-stop filters, photonic crystals, diffractive filters, etc. 5. Apertures, such as iris diaphragms, pinhole diaphragms, slit diaphragms, variable diaphragms, field diaphragms, 6. Diffraction gratings, such as reflection gratings, transmission gratings, phase gratings, holographic gratings, echelle gratings, photonic crystals, metamaterials, diffractive gratings, etc. 7. Optical fibers, such as optical fibers, optical waveguides, fiber optic bundles, waveguides, mono- and / or multimode fibers, etc. 8. Light sources (especially pump radiation sources (PD)), such as LEDs, laser diodes, halogen lamps, xenon lamps, arc lamps, etc. 9. Detectors (especially photodetectors (PD)) such as CCD sensors, CMOS sensors, SPADs, photodiodes, avalanche photodiodes, photomultipliers, etc. 10. Polarizers, such as dichroic polarizers, polarizing films, polarizing prisms, tungsten polarizers, Glan-Taylor prisms, etc. 11. Dispersive elements, such as spectral filters, monochromators, dispersive prisms, grating monochromators, achromatic double prisms, etc. 12. Optical correction elements, such as corrective lenses, field correctors, astigmatism correctors, color aberration correctors, field curvature correctors, etc. 13. Light beam control elements, such as beam splitters, beam combiners, beam deflectors, beam modulators, acousto-optical modulators, beam clamps, etc. 14. Image sensors, such as CMOS image sensors, CCD image sensors, infrared sensors, ultraviolet sensors, RGB sensors, etc. 15. Lighting elements such as collimators, diffusers, light guides, light distribution systems, light collectors, etc. 16. Optomechanical components, such as adjustment screws, brackets, guide rails, optical tables, positioning systems, etc. 17. Microlenses, such as single microlenses, microlens arrays, cylindrical microlenses, conical microlenses, spherical microlenses, gradient-index microlenses (GRIN lenses), etc. 18. Waveguides, such as plasmomic waveguide, dielectric waveguide, hollow fiber waveguide, stripline waveguide, ridge waveguide, etc. 19. Diffusers, such as microstructured diffusers, diffuser plates, lenticular diffusers, holographic diffusers, reflection diffusers etc. 20. Optical coatings, such as anti-reflective coatings, mirror coatings, protective coatings, polarization coatings, phase shift coatings, etc. 21. Micro-optical beam splitters, such as dichroic beam splitters, pole beam splitters, micro cube beam splitters, plate beam splitters, beam splitter arrays, etc.

[0255] This list is certainly not complete. Optical functional elements can belong to several groups of optical functional elements simultaneously. Further optical functional elements can be found, for example, in the books • Menzel, Erich, Werner Mirandé, and Ingolf Weingärtner. Fourier Optics and Holography. Springer-Verlag, 2013 • Haferkorn, Heinz. Optics: Physical and Technical Principles and Applications. John Wiley & Sons, 2003 • Hecht, Eugene. Optics. Walter de Gruyter GmbH & Co KG, 2023 • Saleh, Bahaa EA, and Malvin Carl Teich. Fundamentals of Photonics. John Wiley & Sons, 2008 • Hering, Ekbert, and Rolf Martin, eds. Photonics: Fundamentals, Technology, and Applications. Berlin, Heidelberg: Springer Berlin Heidelberg, 2006.

[0256] A unifying agent, here a dichroic mirror (DCM) phases in the example of the Fig. 19 the pump radiation into the optical path to the one or more sensor elements (SE) with the color centers (here preferably NV centers in a plurality of diamonds). On the way from this combining means - here the dichroic mirror (DCM) to the one or more sensor elements (SE), the pump radiation (LB) passes through, for example, an optical fiber (LWL) as an example of a first optical transmission path from the combining means (DCM) to the one or more sensor elements (SE). The pump radiation (LB) of the pump radiation wavelength (λ pmp) irradiates the one or more sensor elements (SE) and thus the crystals of the one or more sensor elements (SE) comprising the color centers (preferably NV centers in diamond). This excites the color centers (preferably the NV centers) to emit fluorescent radiation (FL). The one or more sensor elements (SE) typically and undesirably reflects back a portion of the pump radiation (LB) and re-emits a portion of the fluorescent radiation (FL), typically in the same direction. In the example of Fig. 19, the optical waveguide (LWL) transports a portion of the reflected pump radiation (LB) and a portion of the fluorescence radiation (FL) back toward one or more photodetectors (PD). Since the detection of the pump radiation (LB) by the one or more photodetectors (PD) is undesirable, a separating means, which here is, for example, the same as the combining means of the dichroic mirror (DCM), separates the fluorescence radiation (FL) from the pump radiation (LB) and allows the fluorescence radiation (FL) to pass toward the one or more photodetectors (PD9). The one or more photodetectors (PD) detect the temporal progression of the intensity I fl (t) of the fluorescence radiation (FL) and convert this temporal course of the intensity I fl(t) of the fluorescence radiation (FL) into a temporal profile of a receiver output signal (S0(t)). An amplifier (V), which may comprise, for example, a transimpedance amplifier (TIA) and / or an RF amplifier (RF amp), filters and / or amplifies the receiver output signal (S0(t)) to a filtered receiver output signal (S1(t)). A vector network analyzer (VNA) and / or a lock-in amplifier (LIA) analyze the temporal profile of the filtered receiver output signal (S1(t)) in relation to the temporal profile of the transmitted signal (S5(t)) or another signal that is related to the temporal profile of the intensity (I(t)) of the pump radiation (LB).Instead of a vector network analyzer (VNA) or a lock-in amplifier, another functionally equivalent device, such as an optimal filter or a matched filter, can be used. These are each temporally phase-synchronized with the transmitted signal (S5(t)) in order to evaluate the phase. The computer core (CPU) of the computer system (RSYS) of the sensor system (SSYS) controls the essential device components of the sensor system (SSYS) via a data bus (DB). The computer core (CPU) preferably executes computer- and / or machine-implemented methods, as described in the document presented here, at least temporarily using other device components of the sensor system (SSYS).The program code of these computer- and / or machine-implemented methods and the associated configuration parameters and data for carrying out these computer- and / or machine-implemented methods are preferably stored at least temporarily in one or more memories (MEM) of the computer system (RSYS) of the sensor system (SSYS). These memories can be volatile and / or non-volatile. The computer core (CPU) of the computer system (RSYS) of the sensor system (SSYS) preferably executes such program code when executing computer- and / or machine-implemented methods. The computer core (CPU) preferably communicates with one or more higher-level computer systems (ÜRSYS) via a data interface (IF) and an external data transmission link (DSTR). Figure 20

[0257] Fig. 20 shows schematically and simplified the exemplary signal flow plan for a device of the Fig. 19. The signal generator (SGEN) receives the value of a given pump radiation frequency (f pmp ) from a file in the memory (MEM) of the computer system (RSYS) of the sensor system (SSYS). The signal generator (SGEN) then preferably generates a sinusoidal transmission signal (S5(t)) that has this pump radiation frequency (f pmp ) as the frequency of the sinusoidal transmission signal (S5(t)). The transmission signal (S5(t)) can be provided with a DC offset. The pump radiation source converts the time profile of the transmission signal (S5(t)) into a time profile of the intensity (I pmp (t)) of the pump radiation (LB). The one or more sensor elements (SE) generate, depending on the temporal progression of the intensity (I pmp (t)) of the pump radiation (LB) reaching the one or more sensor elements (SE), a temporal progression of the total intensity (I g(t)) of the radiation towards the one or more photodetectors (PD). The temporal course of the total intensity (I g (t)) of the radiation in the direction of the one or more photodetectors (PD) comprises a reflected signal component of the temporal course of the intensity (I pmp (t)) of the pump radiation (LB) superimposed with the time course of the intensity (I fl (t)) of the fluorescence radiation (FL). A separating agent, here a dichroic mirror (DCM), separates the temporal progression of the intensity (I fl (t)) of the fluorescence radiation (FL) from the reflected signal component of the time course of the intensity (I pmp (t)) of the pump radiation (LB) and derives this temporal course of the intensity (I fl (t)) of the fluorescence radiation (FL) towards the one or more photodetectors (PD). The one or more photodetectors (PD) record the temporal variation of the intensity (Ifl (t)) of the fluorescence radiation (FL) that reaches them and convert this into the temporal profile of a receiver output signal (S0(t)). An amplifier (V), which may comprise a transimpedance amplifier (TIA) and / or an RF amplifier (RF amp), amplifies and / or filters the temporal profile of the receiver output signal (S0(t)) to an amplified receiver output signal (S1(t)). A vector network analyzer (VNA) and / or a lock-in amplifier (LIA) or a functionally equivalent device generates, depending on the temporal profile of the amplified receiver output signal (S1(t)) and thus depending on the temporal profile of the receiver output signal (S0(t)) and thus depending on the temporal profile of the intensity (I fl (t)) of the fluorescence radiation (FL) on the one hand and on the other hand as a function of the time course of the transmitted signal (S5(t)) and thus as a function of the time course of the intensity (I pmp(t)) of the pump radiation (LB) a fluorescence vector F v (t, which preferably has a fluorescence intensity value F i (t) and a fluorescence delay value F φ (t). In the example of Fig. 20, a computer and / or machine-implemented neural network model (NNM) evaluates the fluorescence vector (F v (t)) and generates from one or more fluorescence vectors (F v (t)) one or more measured values ​​of one or more temperatures (ϑ(t)) ​​and one or more measured values ​​of one or more magnetic flux densities (B(t)), which the computer system (RSYS) of the sensor system (SSYS) can store, keep available, reuse, signal, and / or output. The measured values ​​of the temperature (ϑ(t)) ​​and measured values ​​of the magnetic flux density (B(t)) then form the sensor state vector (S z(t)) which the computer system (RSYS) of the sensor system (SSYS) can store, keep available, reuse, signal and / or output.

[0258] Instead of a computer and / or machine-implemented neural network model (NNM), another computer and / or machine-implemented artificial intelligence method can be used to map one or more fluorescence vectors (F v (t)) on sensor state vectors (S z (t)) may be used. Figure 21

[0259] Fig. 21 differs from the Fig. 20 in that the fluorescence vectors (F v (t)) with the value of the pump radiation frequency (f pmp ) to the fluorescence frequency vectors (F fv (t)) and that the computer and / or machine-implemented neural network model (NNM) comprises one or more fluorescence frequency vectors (F fv(t)) and then from the one or more fluorescence frequency vectors (F fv (t)) generates the measured values ​​of the one or more temperatures (ϑ(t)) ​​and the measured values ​​of the one or more magnetic flux densities (B(t)), which the computer system (RSYS) of the sensor system (SSYS) can store, keep available, reuse, signal, and / or output. The measured values ​​of the one or more temperatures (ϑ(t)) ​​and the measured values ​​of the one or more magnetic flux densities (B(t)) then form the sensor state vector (S z (t)), which the computer system (RSYS) of the sensor system (SSYS) can store, keep available, reuse, signal and / or output. Preferably, the computer and / or machine-implemented neural network model (NNM) evaluates the following for the determination of a sensor state vector (S z (t)) several fluorescence frequency microwave vectors (F fµv (t)) with different values ​​of the pump radiation frequency (fpmp ) to improve the image.

[0260] Instead of a computer and / or machine-implemented neural network model (NNM), another computer and / or machine-implemented artificial intelligence method can be used to map one or more fluorescence frequency vectors (F fv (t)) on sensor state vectors (S z (t)) may be used. Figure 22

[0261] The Fig. 22 largely corresponds to the Fig. 21. In the Fig. 22, however, the microwave signal generator (µG) receives the value of a given microwave frequency (f µw ) from another file in the memory (MEM) of the computer system (RSYS) of the sensor system (SSYS). The microwave signal generator (µG) then generates, in addition to the radiations of Figure 22, preferably a microwave signal with the microwave frequency (f µw) and radiates this microwave signal by means of a microwave antenna or the like additionally into the one or more sensor elements (SE). The microwave signal of the microwave generator (µG) preferably has a temporal progression of intensity (I µw (t)) of the microwave radiation of the microwave signal. The one or more sensor elements (SE) generate, depending on the temporal progression of the intensity (I pmp (t)) of the pump radiation (LB) reaching the one or more sensor elements (SE), and additionally depending on the temporal progression of the intensity (I µw (t)) of the microwave radiation and its respective microwave frequency (f µw ) a respective temporal course of the total intensity (I g (t)) of the radiation towards the one or more photodetectors (PD).

[0262] Fig. 22 differs from the Fig. 21 additionally by the fact that the fluorescence vectors (F fv (t)) the Fig. 21 not only with the value of the pump radiation frequency (f pmp ) to fluorescence frequency vectors (F fv (t)) but also with the value of the microwave frequency (f µw ) to fluorescence frequency microwave vectors (F fµv (t)). Furthermore, the computer and / or machine-implemented neural network model (NNM) evaluates the fluorescence frequency microwave vector (F fµv (t)) and generates from one or more fluorescence frequency microwave vectors (F fµv(t)) the measured values ​​of the one or more temperatures (ϑ(t)) ​​and the measured values ​​of the one or more magnetic flux densities (B(t)), which the computer system (RSYS) of the sensor system (SSYS) can store, keep available, reuse, signal, and / or output. The measured values ​​of the one or more temperatures (ϑ(t)) ​​and the measured values ​​of the one or more magnetic flux densities (B(t)) then form the sensor state vector (S z (t)), which the computer system (RSYS) of the sensor system (SSYS) can store, keep available, reuse, signal and / or output. Preferably, the computer and / or machine-implemented neural network model (NNM) evaluates the following for the determination of a sensor state vector (S z (t)) several fluorescence frequency microwave vectors (F fµv (t)) with different values ​​of the pump radiation frequency (f pmp ) and / or different values ​​of the microwave frequency (f µw) to improve the image.

[0263] Instead of a computer and / or machine-implemented neural network model (NNM), another computer and / or machine-implemented artificial intelligence method can be used to represent one or more fluorescence frequency microwave vectors (F fµv (t)) on sensor state vectors (S z (t)) may be used. Figure 23

[0264] Fig. 23 corresponds to the Fig. 20, wherein the computer system (RSYS) additionally controls a microwave signal generator (µG) which generates a microwave signal of a microwave radiation (MS) with a microwave frequency (f µw ) is generated, which also radiates into the one or more sensor elements (SE) and the color centers contained therein. Therefore, the temporal progression of the intensity (I fl (t)) of the fluorescence radiation (FL) also depends on the temporal course of the intensity (I µw(t)) of this microwave radiation (MS) and its microwave frequency (f µw ) away. Figure 24

[0265] Fig. 24 illustrates an exemplary computer- and / or machine-implemented neural network model (NNM) as an example of a computer- and / or machine-implemented artificial intelligence method for mapping one or more fluorescence frequency microwave vectors (F fµv (t)) on sensor state vectors (S z (t)).

[0266] The fluorescence vectors (F v (t)) are multiplied by the value of the pump radiation frequency (f pmp ) and the microwave frequency (f µw ) to fluorescence frequency microwave vectors (F fµv (t)). The computer and / or machine-implemented neural network model (NNM) evaluates one or more fluorescence frequency microwave vectors (F fµv(t)) and generates from the one or more fluorescence frequency microwave vectors (F fµv (t)) one or more measured values ​​of one or more temperatures (ϑ(t)) ​​and one or more measured values ​​of one or more magnetic flux densities (B(t)), which the computer system (RSYS) of the sensor system (SSYS) can store, keep available, further use, signal and / or output. Figure 25

[0267] Fig. 25 illustrates an exemplary computer- and / or machine-implemented neural network model (NNM) as an example of a computer- and / or machine-implemented artificial intelligence method for mapping one or more fluorescence frequency vectors (F fv (t)) on sensor state vectors (S z (t)).

[0268] The fluorescence vectors (F v (t)) are multiplied by the value of the pump radiation frequency (f pmp ) to fluorescence frequency vectors (F fv(t)). The computer and / or machine-implemented neural network model (NNM) evaluates one or more fluorescence frequency vectors (F fv (t)) and generates from the one or more fluorescence frequency vectors (F fv (t)) one or more measured values ​​of one or more temperatures (ϑ(t)) ​​and one or more measured values ​​of one or more magnetic flux densities (B(t)), which the computer system (RSYS) of the sensor system (SSYS) can store, keep available, further use, signal and / or output. Figure 26

[0269] Fig. Figure 26 illustrates an exemplary computer- and / or machine-implemented neural network model (NNM) as an example of a computer- and / or machine-implemented artificial intelligence method for mapping multiple - here k - fluorescence vectors (F v (t1), F v (t k )) on sensor state vectors (S z(t)). The computer and / or machine-implemented neural network model (NNM) evaluates one or more fluorescence vectors (F v (t)) and generates from the one or more fluorescence vectors (F v (t)) one or more measured values ​​of one or more temperatures (ϑ(t)) ​​and one or more measured values ​​of one or more magnetic flux densities (B(t)), which the computer system (RSYS) of the sensor system (SSYS) can store, keep available, further use, signal and / or output. Figure 27

[0270] Fig. 27 shows a training system (TSYS).

[0271] Fig. 27 corresponds to the Fig. 23, wherein a training computer core (TCPU) of a training computer system (TRSYS) now controls a heating / cooling device (HZ) of a temperature control device (TZ) via a test data bus (TDB). The corresponding temperature sensors, which the training computer system (TRSYS) reads out in order to record one or more temperatures ϑ(t) of the one or more sensor elements (SE) and to readjust the one or more temperatures ϑ(t) of the one or more sensor elements (SE) by means of the one or more heating / cooling devices (HZ) in the event of deviations from a temperature setpoint, are not additionally shown for the sake of clarity.

[0272] The training computer core (TCPU) of the training computer system (TRSYS) also controls a magnetic field generation device (ME) via the test data bus (TDB). The corresponding magnetic field sensors, which the training computer system (TRSYS) reads out in order to detect the magnetic flux density B(t) at the location of the one or more sensor elements (SE) and to readjust the magnetic flux density B(t) at the location of the one or more sensor elements (SE) using the magnetic field generation device (ME) in the event of deviations from a flux density target value, are not shown for the sake of clarity. This enables the training computer core (TCPU) of the training computer system (TRSYS) to set the configuration parameters for the computer- and / or machine-implemented neural network model (NNM) orto determine the computer and / or machine-implemented artificial intelligence method by means of a computer and / or machine-implemented investigation procedure.

[0273] Preferably, the training computer core (TCPU) executes a program code, which is preferably stored at least temporarily in the training memory (TMEM) of the training computer system (TSYS), when it executes the computer- and / or machine-implemented determination method (200) for determining the configuration parameters for the sensor system (SSYS).

[0274] This test setup also allows the configuration parameters for sensor systems (SSYS) to be set according to the Fig. 19 determine. List of reference symbols ADC Analog-to-digital converter (ADC) of the sensor system; B magnetic flux density (also called magnetic field); CPU computer core (CPU) of the computer system (RSYS) of the sensor system; DB data bus (DB) of the computer system (RSYS) of the sensor system; DCM dichroic mirror (DCM); DSTR data transmission link; FL Fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE); f pmp Pump radiation frequency (f pmp ) of the modulation signal (transmission signal (S5(t)) of the intensity (I pmp (t)) the pump radiation (LB); F v computer- and / or machine-implemented fluorescence vector F v ; HAL Hall Effect Sensor (HAL); I fl (t) temporal course of the intensity (I fl (t)) the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) I pmp (t) temporal course of the intensity (I pmp (t)) the pump radiation (LB); (λ pmp ), pump radiation wavelength (λ pmp ) of the pump radiation (LB) LB pump radiation (LB); LD Pump radiation source (LD) for pump radiation (LB), whose intensity (I pmp (t)) is controlled by the modulation signal from which the transmission signal (S5(t)) is controlled; LDD Laser driver (LDD) of the pump radiation source (LD) for pump radiation (LB), LIA Lock-In Amplifier (LIA); LPF Longpass filter (LPF); LWL optical fiber (LWL); NV color centers (NV) (or paramagnetic centers) in the crystal(s) of the one or more sensor elements (SE); µG microwave signal generator (µG); ME magnetic field generating device (ME); MEM one or more memories (MEM) of the computer system (RSYS); MS Microwave radiation (MS); PD Photodetector (PD). The photodetector (PD) can be a plurality of photodetectors, for example, a CMOS CCD camera chip with evaluation electronics, which can be provided, for example, with imaging optics for imaging the fluorescence intensity image of one or more sensor elements (SE), for example, onto the said CMOS CCD camera chip and / or a plurality of photodetectors (PD). RSYS computer system; S0 Receiver output signal (S0) (also called receive signal); S1 filtered receive signal (S1) (also called filtered receiver output signal.) S5 transmit signal (S5(t)) (also called modulation signal); SE sensor element (SE). The sensor element (SE) preferably comprises one or more crystals (e.g., one or more diamond crystals), wherein one or more crystals of these one or more crystals comprise one or more paramagnetic centers (e.g., NV centers), which are also referred to as color centers in the document presented here, and are fully or partially embedded on at least one side in a carrier material (e.g., an optical adhesive such as NOA61) that is transparent to the fluorescence radiation of the paramagnetic centers and the pump radiation of the paramagnetic centers. SGEN signal generator (SGEN); S z computer and / or machine-implemented sensor state vector (S z ); SSYS Sensor System (SSYS); T temperature ϑ(t); ϑ(t) temperature ϑ(t), also denoted by T here; TCPU training computer core (TCPU) of the training computer system (TRSYS) of the training system; TIA Transimpedance Amplifier (TIA); TIF interface (TIF) of the training computer system (TRSYS); TMEM training memory (TMEM) of the training computer system (TRSYS); TRSYS training computer system (TRSYS) of the training system; TÜRSYS higher-level training computer system (TÜRSYS); TS training temperature sensors (TS), in particular for detecting a temperature ϑ(t); TV tempering device (TV); ÜRSYS higher-level computer system (ÜRSYS); VNA vector network analyzer; 100 Method (100) for determining at least one compensated measured value of at least two physical quantities; 105 Providing (105) a sensor system (SSYS) with at least one sensor element (SE); 110 Providing (110) a computer system (RSYS) of the sensor system (SSYS); 115 Irradiating (115) the one or more sensor elements (SE) with a pump radiation (LB) having a pump radiation wavelength (λ pmp ), in particular by means of a pump radiation source (LD), wherein the temporal course of the intensity (I pmp (t)) of the pump radiation (LB) is modulated with a modulation signal, in particular with a transmission signal S5(t) 120 Providing (120) program code for a computer- and / or machine-implemented correction method, in particular in one or more memories (MEM) of the computer system (RSYS) of the sensor system; 125 Providing (125) configuration parameters for carrying out the computer- and / or machine-implemented correction method, wherein in particular the provision takes place in one or more memories (MEM), in particular of the sensor system and / or computer system (RSYS); 126 Irradiating (126) the one or more sensor elements (SE) with pump radiation (LB) of a pump radiation wavelength (λ pmp ), whose temporal intensity profile (I pmp (t)) with a pump radiation frequency (f pmp ) is preferably sinusoidally modulated, preferably by means of a transmission signal S5(t). 127 Irradiating (127) the sensor element with electromagnetic radiation in the microwave range; 130 detecting (130) the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE), which depends in different ways on the at least two physical quantities, in particular by means of one or more photodetectors (PD); 135 Determining (135) at least two different fluorescence parameters as vector components of an at least two-dimensional computer- and / or machine-implemented fluorescence vector F v from the temporal progression (I fl(t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) in combination with the temporal course of the pump radiation intensity (I pmp (t)) the pump radiation (LB); 136 Formation (136) of at least one at least three-dimensional computer and / or machine-implemented fluorescence frequency vector F fv , which comprises at least one at least two computer and / or machine-implemented fluorescence vectors F v and at least the value of the pump radiation frequency (f pmp ) includes; 137 Formation (137) of at least one at least four-dimensional computer and / or machine-implemented fluorescence frequency microwave vector F fµv , which comprises at least one at least two-dimensional computer- and / or machine-implemented fluorescence vector F v and which has at least the value of the pump radiation frequency (f pmp) and which has at least the value of the microwave frequency (f µw ) includes; 140 Determining (140) a first measured value of the first physical quantity of the one or more sensor elements (SE) in the form of a first size parameter of a one- or multi-dimensional computer- and / or machine-implemented sensor state vector (S z ); 142 Determining (142) a second measured value of the second physical quantity of the one or more sensor elements (SE) in the form of a second size parameter of the one- or multi-dimensional computer- and / or machine-implemented sensor state vector (S z ) 160 Outputting (160) and / or keeping ready and / or storing and / or transmitting and / or using the determined compensated first measured value of the first physical quantity of the one or more sensor elements (SE); 165 Outputting (165) and / or keeping ready and / or storing and / or transmitting and / or using the determined compensated second measured value of the second physical quantity of the one or more sensor elements (SE). 170 Query (170) whether all n pump radiation frequencies (f pmp1 to f pmpn ) were adjusted and measured; 175 Setting (175) a further, different, i-th pump radiation frequency (f pmpi ) of n intended pump radiation frequencies (f pmp1 to f pmpn ) as the new pump radiation frequency (f pmp ); 180 Query (180) whether all m microwave frequencies (f µw1 to f µwm ) were adjusted and measured; 183 Setting (183) another, different, j-th microwave frequency (f µwj ) of m intended pump radiation frequencies (f µw1 to f µwm ) as the new microwave frequency (f µw ); 185 Setting (185) the first pump radiation frequency (f pmp1 ) of n intended pump radiation frequencies (f pmp1 to f pmpn ) as the new pump radiation frequency (f pmp ); 186 Setting (186) the first microwave frequency (f µw1 ) of m intended microwave frequencies (f µw1 to f µwn ) as the new microwave frequency (f µw ); 200 . Determination method (training method) (200) for determining one or more configuration parameters for use in the proposed method (100); 205 Providing (205) a training computer system (TRSYS); 210 Providing (210) one or more temperature control devices (TV), in particular a temperature cabinet and / or one or more heating or cooling devices as temperature control devices (TV); 215 Providing (215) a magnetic field generating device (ME), in particular at least one Helmholtz coil pair and / or one or more permanent magnets, for generating a magnetic field that flows through the at least one sensor element (SE); 220 Setting (220) the magnetic field to a predetermined flux density value, in particular by means of the magnetic field generating device (ME), which is controlled in particular by the training computer system (TRSYS), and flowing through the one or more sensor elements (SE) with this magnetic field with magnetic flux densities (B) of predetermined flux density values; 225 Tempering (225) the one or more sensor elements (SE) to one or more temperature values ​​of the one or more temperatures ϑ(t), in particular by means of one or more tempering devices (TV), which are controlled in particular by the training computer system (TRSYS) and / or in particular on the basis of the one or more temperature measured values ​​of the one or more temperatures ϑ(t) of one or more training temperature sensors (TS); 230 Saving (230) measured values ​​in the form of fluorescence vectors (F v ) or in the form of fluorescence frequency vectors (F fv ) or in the form of the fluorescence frequency microwave vectors (F fµv ) in particular in one or more memories (TMEM) as stored measured values ​​for later use as training data; 235 Determining (235) an optimized set of configuration parameters for use in the sensor system by executing a computer- and / or machine-implemented artificial intelligence training method, in particular by the training computer system (TRSYS) and in particular by executing one or more computer- and / or machine-implemented machine learning algorithms for regression, in particular by the training computer system (TRSYS); 240 storing (240) the optimized set of configuration parameters thus determined, in particular in a memory (TMEM) of the training computer system (TRSYS); 241 Keeping (241) the optimized set of configuration parameters available, in particular in a memory (TMEM) of the training computer system (TRSYS); 242 Outputting (242) the optimized set of configuration parameters, in particular via an interface (TIF) of the training computer system (TRSYS); 243 Transferring (243) the optimized set of configuration parameters, in particular via a data transmission link (TDSTR) connected to the training computer system (TRSYS), in particular to a higher-level computer system (TÜRSYS), and / or to a computer system (RSYS) of a sensor system for use in a proposed method; 244 Storing (244) the optimized set of configuration parameters, in particular via a data transmission link (TDSTR) connected to the training computer system (TRSYS), in particular in a memory of a computer system (RSYS) of a sensor system for use in a proposed method; 250 Using (250) at least one determined configuration parameter, in particular by a computer system (RSYS) of a sensor system and in particular for computer- and / or machine-implemented imaging of fluorescence vectors (F v) each with a fluorescence intensity measurement value and each with at least one fluorescence delay measurement value, which were determined within the sensor system, and / or in particular for computer- and / or machine-implemented mapping of fluorescence frequency vectors (F fv ) each with a fluorescence intensity measurement value and with at least one fluorescence delay measurement value, which were determined within the sensor system, and at least one value of the pump radiation frequency (f pmp ), and / or in particular for computer and / or machine-implemented imaging of fluorescence frequency microwave vectors (F fµv ) each having a fluorescence intensity measurement value and at least one fluorescence delay measurement value, which were determined within the sensor system, and at least one value of the pump radiation frequency (f pmp ) and at least one value of the microwave frequency (f µw) to one or more sensor element state vectors (S v ), with in particular at least one respective flux density measurement value of the magnetic flux density (B(t)) and at least one respective temperature measurement value of a temperature (ϑ(t)); GlossaryZPL table

[0275] The table is only an exemplary compilation of some possible paramagnetic centers (color centers). These can be used in their respective crystals as paramagnetic centers of the sensor element (20). The document presented here particularly recommends the use of NV centers in diamond as paramagnetic centers of the sensor element (20). The functionally equivalent use of other paramagnetic centers in other materials or other crystals as color centers is expressly possible. The pump radiation wavelengths λ pmp of the pump radiation 60 are also exemplary. Other pump radiation wavelengths λ pmpare usually possible if they are shorter than the wavelength of the ZPL (zero-phonon line) to be excited. Material of Crystal Sensor Element 20 Störstellenzentrum ZPL exemplary pump radiation wavelength (λ pmp ) Referenz Diamant NV-Zentrum 520nm, 532nm Diamant SiV-Zentrum 738 nm 685 nm / 2 / , / 3 / , / 4 / Diamant GeV-Zentrum 602 nm 532 nm / 4 / , / 5 / Diamant SnV-Zentrum 620 nm 532 nm / 4 / , / 6 / Diamant PbV-Zentrum 520 nm, 450 nm / 4 / , / 7 / 552 nm / 4 / , / 7 / 715 nm 532 nm / 7 / Diamant ST1-Zentrum 555 nm 532 nm / 15 / Diamant TR12-Zentrum 471 nm 410 nm / 16 / Silizium G-Zentrum 1278,38 nm 637 nm / 8 / Siliziumkarbid V SI -Center 862 nm(V1) 4H, 730 nm / 1 / , / 9 / , / 10 / 858,2 nm(V1') 4H 730 nm / 1 / , / 9 / , / 10 / 917 nm(V2) 4H, 730 nm / 1 / , / 9 / , / 10 / 865 nm(V1) 6H, 730 nm / 1 / , / 9 / , / 10 / <h2 style=";text-align:left;direction:ltr">887 nm(V2) 6H, <h2 style=";text-align:left;direction:ltr"> 730 nm / 1 / , / 9 / , / 10 / <h2 style=";text-align:left;direction:ltr"> 907 nm(V3) 6H <h2 style=";text-align:left;direction:ltr"> 730 nm / 1 / , / 9 / , / 10 / <h2 style=";text-align:left;direction:ltr"> Siliziumcarbide <h2 style=";text-align:left;direction:ltr"> DV-Zentrum <h2 style=";text-align:left;direction:ltr"> 1078-1132 nm 6H <h2 style=";text-align:left;direction:ltr"> 730 nm / 9 / <h2 style=";text-align:left;direction:ltr"> Siliziumcarbide V C V SI -Center <h2 style=";text-align:left;direction:ltr"> 1093-1140 nm 6H <h2 style=";text-align:left;direction:ltr"> 730 nm / 9 / <h2 style=";text-align:left;direction:ltr"> Siliziumcarbide <h2 style=";text-align:left;direction:ltr"> CAV-Zentrum <h2 style=";text-align:left;direction:ltr"> 648.7 nm 4H, 6H, 3C <h2 style=";text-align:left;direction:ltr"> 730 nm / 9 / <h2 style=";text-align:left;direction:ltr"> 651.8 nm 4H, 6H, 3C <h2 style=";text-align:left;direction:ltr"> 730 nm / 9 / <h2 style=";text-align:left;direction:ltr"> 665.1 nm 4H, 6H, 3C <h2 style=";text-align:left;direction:ltr"> 730 nm / 9 / <h2 style=";text-align:left;direction:ltr"> 668.5 nm 4H, 6H, 3C <h2 style=";text-align:left;direction:ltr"> 730 nm / 9 / <h2 style=";text-align:left;direction:ltr"> 671.7 nm 4H, 6H, 3C <h2 style=";text-align:left;direction:ltr"> 730 nm / 9 / <h2 style=";text-align:left;direction:ltr"> 673 nm 4H, 6H, 3C <h2 style=";text-align:left;direction:ltr"> 730 nm / 9 / <h2 style=";text-align:left;direction:ltr"> 675.2 nm 4H, 6H, 3C <h2 style=";text-align:left;direction:ltr"> 730 nm / 9 / <h2 style=";text-align:left;direction:ltr"> 676.5 nm 4H, 6H, 3C <h2 style=";text-align:left;direction:ltr"> 730 nm / 9 / <h2 style=";text-align:left;direction:ltr"> Siliziumcarbide N C V SI -Center <h2 style=";text-align:left;direction:ltr"> 1180 nm-1242 nm 6H <h2 style=";text-align:left;direction:ltr"> 730 nm / 9 / , / 13 / , / 14 /

[0276] In the document disclosed here, NV centers in diamond are particularly preferred. These were tested during the development of the technical teachings of this document. List of reference literature for the table above / 1 / Marina Radulaski, Matthias Widmann, Matthias Niethammer, Jingyuan Linda Zhang, Sang-Yun Lee, Torsten Rendler, Konstantinos G. Lagoudakis, Nguyen Tien Son, Erik Janzén, Takeshi Ohshima, Jörg Wrachtrup, Jelena Vučković, “Scalable Quantum Photonics with Single Color Centers in Silicon Carbide”, Nano Letters 17 (3), 1782-1786 (2017), DOI: 10.1021 / acs.nanolett.6b05102, arXiv:1612.02874 / 2 / C. Wang, C. Kurtsiefer, H. Weinfurter, and B. Burchard, “Single photon emission from SiV centers in diamond produced by ion implantation” J. Phys. B: At. Mol.Opt. Phys., 39(37), 2006 / 3 / Björn Tegetmeyer, “Luminescence properties of SiV centers in diamond diodes” Promotional Paper, University of Freiburg, 30.01.2018 / 4 / Carlo Bradac, Weibo Gao, Jacopo Forneris, Matt Trusheim, Igor Aharonovich, “Quantum Nanophotonics with Group IV Defects in Diamond,” DOI:10.1038 / s41467-020-14316-x, arXiv:1906.10992 / 5 / Rasmus Høy Jensen, Erika Janitz, Yannik Fontana, Yi He, Olivier Gobron, Ilya P. Radko, Mihir Bhaskar, Ruffin Evans, Cesar Daniel Rodriguez Rosenblueth, Lilian Childress, Alexander Huck, Ulrik Lund Andersen, “Cavity-Enhanced Photon Emission from a Single Germanium-Vacancy Center in a Diamond Membrane”, arXiv:1912.05247v3 [quant-ph] 25 May / 6 / Takayuki Iwasaki, Yoshiyuki Miyamoto, Takashi Taniguchi, Peter Siyushev, Mathias H. Metsch, Fedor Jelezko, Mutsuko Hatano, „Tin-Vacancy Quantum Emitters in Diamond“, Phys. Rev. Fr. Lett. 119 , 253601 ( 2017 ), doi: 10.1103 / PhysRevLett. / 7 / Matthew E. Trusheim, Noel H. Wan, Kevin C. Chen, Christopher J. Ciccarino, Ravishankar Sundararaman, Girish Malladi, Eric Bersin, Michael Walsh, Benjamin Lienhard, Hassaram Bakhru, Prineha Narang, Dirk Englund, „Lead-Related Quantum Emitters in Diamond“ Phys. Rev. B 99, 075430 (2019), DOI: 10.1103 / PhysRevB.99.075430, arXiv:1805.12202 [quant-ph] / 8 / M. Hollenbach, Y. Berencén, U. Kentsch, M. Helm, G. V. Astakhov „Engineering telecom single-photon emitters in silicon for scalable quantum photonics“ Opt. Express 28, 26111 (2020), DOI: 10.1364 / OE.397377, arXiv:2008.09425 [physics.app-ph] / 9 / Castelletto and Alberto Boretti, „Silicon carbide color centers for quantum applications“ 2020 J. Phys. Photonics2 022001 / 10 / V. Ivädy, J. Davidsson, N. T. Son, T. Ohshima, I. A. Abrikosov, A. Gali, „Identification of Si-vacancy related room-temperature qubits in 4H silicon carbide“, Phys. Rev.B, 2017, 96,161114 / 11 / J. Davidsson, V. Ivády, R. Armiento, N. T. Son, A. Gali, I. A. Abrikosov, „First principles predictions of magneto-optical data for semiconductor point defect identification: the case of divacancy defects in 4H-SiC“, New J. Phys., 2018, 20, 023035 / 12 / J. Davidsson, V. Ivädy, R. Armiento, T. Ohshima, N. T. Son, A. Gali, I. A. Abrikosov „Identification of divacancy and silicon vacancy qubits in 6H-SiC“, Appl. Phys. Lett. 2019, 114, 112107 / 13 / S. A. Zargaleh, S. Hameau, B. Eble, F. Margaillan, H. J. von Bardeleben, J. L. Cantin, W. Gao , „Nitrogen vacancy center in cubic silicon carbide: a promising qubit in the 1.5µm spectral range for photonic quantum networks“ Phys. Rev.B, 2018, 98, 165203 / 14 / S. A. Zargaleh et al „Evidence for near-infrared photoluminescence of nitrogen vacancy centers in 4H-SiC“ Phys. Rev.B, 2016, 94, 060102 / 15 / P. Balasubramanian, MH Metsch, Reddy, R. Prithvi, J. Lachlan, NB Manson, MW Doherty, F. Jelezko, “Discovery of ST1 centers in natural diamond” Nanophotonics, Vol. 8, No. 11, 2019, pages 1993-2002. https: / / doi.org / 10.1515 / nanoph-2019-0148 / 16 / J. Foglszinger, A. Denisenko, T. Kornher, M. Schreck, W. Knolle, B. Yavkin, R. Kolesov, J. Wrachtrup “ODMR on Single TR12 Centers in Diamond” arXiv:2104.04746v1 [physics.optics] Difference between lock-in amplifier (LIA) and vector network analyzer (VNA)

[0277] A vector network analyzer (VNA) and a lock-in amplifier are, in the sense of this document, two different instruments that can be used in the sensor technology presented here.

[0278] The vector network analyzer (VNA) is a measurement device generally used primarily for characterizing and analyzing electrical networks and components in radio-frequency and microwave applications. It enables precise measurement of the amplitude and phase of electrical signals—here, the AC drive signal in conjunction with the second amplifier output signal—over a wide frequency range and provides comprehensive information about the transmission characteristics of components such as filters, amplifiers, antennas, optical systems, fiber optics, paramagnetic centers, cables, and other device components involved in the signal path.

[0279] In contrast, a lock-in amplifier (LIA) is a specialized device typically used to detect and process weak signals in a high noise background, particularly using spread spectrum codes. It typically operates with a reference signal—here, the AC drive signal—synchronized with the signal under measurement, here, the second amplifier output signal. It can thus separate the wanted signal from unwanted noise. This enables the measurement of extremely low-amplitude signals that could not normally be reliably detected by conventional amplifiers.

[0280] While a vector network analyzer is widely applicable and provides detailed information about the signal path characteristics of the system presented here, a lock-in amplifier focuses on the precise detection and analysis of weak signals in highly noisy environments. The choice between these two devices therefore depends on the specific requirements of the measurement task as well as the desired accuracy and sensitivity of the measurement. Neural network model (neural network)

[0281] Definition of a computer- or machine-implemented neural network as defined in this document.

[0282] A computer-implemented and / or machine-implemented neural network is an artificial intelligence structure consisting of a multitude of interconnected computer-implemented and / or machine-implemented nodes (also referred to as neurons). This document also refers to a neural network as a neural network model. For the purposes of this document, a neural network is a computer- or machine-implemented neural network. Each of the computer-implemented and / or machine-implemented nodes of the computer-implemented and / or machine-implemented neural network is responsible for performing computer-implemented and / or machine-implemented calculations based on the input values ​​it receives from other nodes within the network.

[0283] The nodes are organized into several computer-implemented and / or machine-implemented layers, including at least one input layer, one or more hidden layers, and an output layer. The computer-implemented and / or machine-implemented input layer receives the raw data to be processed by the neural network. This data is passed to the nodes of the first computer-implemented and / or machine-implemented hidden layer. In the hidden layers, the nodes perform various computer-implemented and / or machine-implemented calculations and transformations on the input data to extract the underlying patterns or features. Finally, the last computer-implemented and / or machine-implemented layer passes the processed data to the computer-implemented and / or machine-implemented output layer, which provides the final results.

[0284] A key feature of a computer-implemented and / or machine-implemented neural network is its ability to learn. This is enabled by a computer-implemented and / or machine-implemented training algorithm that adjusts the weights of the connections between the nodes. The training process is typically performed using computer-implemented and / or machine-implemented algorithms such as gradient descent or backpropagation, which aim to minimize the error function.

[0285] A computer-implemented and / or machine-implemented neural network, as defined in this document, is a complex system of computer-implemented and / or machine-implemented nodes that are interconnected by computer-implemented and / or machine-implemented algorithms to perform complex pattern recognition and decision-making processes. Description of a computer- and / or machine-implemented fully connected neural network (FCNN) in contrast to other neural networks

[0286] A computer- and / or machine-implemented fully connected neural network (FCNN), as defined in this document, is a specific type of computer- and / or machine-implemented neural network characterized by its structure and connection pattern. In contrast to other types of computer- and / or machine-implemented neural networks, such as convolutional neural networks (CNNs) or recurrent neural networks (RNNs), an FCNN is characterized by the following features: Computer and / or machine-implemented node connections: In a computer and / or machine-implemented FCNN, each computer and / or machine-implemented node (neuron) in each layer is fully connected to every computer and / or machine-implemented node in the previous and subsequent layers. This means that the computer and / or machine-implemented inputs of each computer and / or machine-implemented node in a layer include the computer and / or machine-implemented outputs of all computer and / or machine-implemented nodes in the previous layer.

[0287] Computer and / or machine-implemented weight matrices: The connections between the computer and / or machine-implemented nodes of the different layers are described by computer and / or machine-implemented weight matrices. In an FCNN, each computer and / or machine-implemented weight matrix is ​​completely populated because every connection exists, in contrast to partially connected networks, where some connections are missing.

[0288] Computer and / or machine-implemented computations and algorithms: The computations in an FCNN involve applying computer- and / or machine-implemented linear transformations to the weight matrices, followed by computer- and / or machine-implemented nonlinear activation functions. These processes occur in each layer of the network. Computer- and / or machine-implemented learning algorithms such as gradient descent or backpropagation are used to adjust the computer- and / or machine-implemented weights and minimize the error function.

[0289] Application and flexibility: Computer- and / or machine-implemented FCNNs are versatile and can be used for a wide range of tasks, including classification, regression, and pattern recognition. They differ from other specialized neural network types such as CNNs, which are specifically optimized for processing images and visual data, or RNNs, which are designed for sequential data and temporal dependencies.

[0290] A computer- and / or machine-implemented fully connected neural network, as defined in this document, is characterized by its extensive connections between the computer- and / or machine-implemented nodes of each layer and the computer- and / or machine-implemented complete weight matrices, which distinguishes it from other specialized neural network types. This structure enables flexible applications, but often at the expense of higher computer- and / or machine-implemented computational complexity and larger computer- and / or machine-implemented memory requirements. However, this plays only a minor economic role here, since the neural network is used only during calibration. Description of a computer and / or machine-implemented Recurrent Neural Network (RNN) in contrast to other neural networks

[0291] A computer- and / or machine-implemented recurrent neural network (RNN), as defined in this document, is a specific type of computer- and / or machine-implemented neural network characterized by its ability to process sequential data and store state information over time. In contrast to other types of computer- and / or machine-implemented neural networks, such as fully connected neural networks (FCNNs) or convolutional neural networks (CNNs), an RNN, as defined in this document, is characterized by the following features: Computer- and / or machine-implemented recurrent connections: In a computer- and / or machine-implemented RNN, recurrent connections exist that allow information from previous points in time to be stored and applied to current calculations. Each computer- and / or machine-implemented node (neuron) in a layer is connected not only to the computer- and / or machine-implemented nodes of the previous and subsequent layers, but also to itself via a time delay, allowing the computer- and / or machine-implemented node to retain the state of previous points in time.

[0292] Computer and / or machine-implemented state information: Recurrent connections allow RNNs to maintain state information across a sequence of inputs. This allows contextual information to be incorporated into computations, which is particularly useful for tasks that require temporal dependencies or sequences, such as speech, text, or time series.

[0293] Computer- and / or machine-implemented computations and algorithms: The computations in an RNN involve the application of computer- and / or machine-implemented linear transformations through computer- and / or machine-implemented weight matrices, followed by computer- and / or machine-implemented nonlinear activation functions. Additionally, computer- and / or machine-implemented state information is incorporated through recurrent connections. Computer- and / or machine-implemented learning algorithms such as gradient descent or backpropagation through time (BPTT) are used to adapt the computer- and / or machine-implemented weights and minimize the error function.

[0294] Application and flexibility: Computer- and / or machine-implemented RNNs are particularly well-suited for tasks involving temporal sequences or contextual dependencies, such as natural language processing, machine translation, time series analysis, and music composition. They differ from other neural network types such as FCNNs, which lack mechanisms for storing state information over time, or CNNs, which are specifically optimized for processing spatial data such as images.

[0295] For the purposes of this document, a computer- and / or machine-implemented recurrent neural network is characterized by its recurrent connections and the ability to store and utilize state information over time. This structure enables the processing of sequential and time-dependent data, distinguishing it from other specialized neural network types. Description of a computer and / or machine-implemented Convolutional Neural Network (CNN) in contrast to other neural networks

[0296] A computer- and / or machine-implemented convolutional neural network (CNN), as defined in this document, is a specific type of computer- and / or machine-implemented neural network characterized by its particular architecture for processing visual and spatial data. In contrast to other types of computer- and / or machine-implemented neural networks, such as fully connected neural networks (FCNNs) or recurrent neural networks (RNNs), a CNN, as defined in this document, is characterized by the following features: Computer- and / or machine-implemented convolutional layers: A central feature of CNNs are the computer- and / or machine-implemented convolutional layers, in which computer- and / or machine-implemented filters (also called kernels) glide over the input data to generate computer- and / or machine-implemented feature maps. These computer- and / or machine-implemented convolutions allow the network to detect local features of the input data and learn hierarchical patterns.

[0297] Computer- and / or machine-implemented pooling layers: In addition to convolutional layers, CNNs typically contain computer- and / or machine-implemented pooling layers that reduce the dimension of feature maps by calculating local summaries of the data. Commonly used computer- and / or machine-implemented pooling methods are max pooling and average pooling. These layers help reduce the computational load and increase the robustness of the network to small shifts and distortions in the input data.

[0298] Computer- and / or machine-implemented hierarchical feature extraction: Through a sequence of computer- and / or machine-implemented convolutional and pooling layers, a CNN can transform complex and high-dimensional input data into increasingly abstract and meaningful features. This is particularly advantageous for tasks such as image recognition and classification, where it is important to identify spatial hierarchies and relationships in the data.

[0299] Computer and / or machine-implemented computations and algorithms: The computations in a CNN include the application of computer- and / or machine-implemented convolutional transforms, followed by computer- and / or machine-implemented nonlinear activation functions and computer- and / or machine-implemented pooling operations. Computer- and / or machine-implemented learning algorithms such as gradient descent or backpropagation are used to adjust the computer- and / or machine-implemented filter weights and network parameters and minimize the error function.

[0300] Application and flexibility: Computer- and / or machine-implemented CNNs are particularly well-suited for tasks involving spatial and visual data, such as image and video recognition, image segmentation, and object tracking. They differ from other neural network types such as FCNNs, which lack dedicated feature extraction and reduction mechanisms, or RNNs, which are designed to handle sequential data and temporal dependencies.

[0301] For the purposes of this document, a computer- and / or machine-implemented convolutional neural network is characterized by its specialized convolutional and pooling layers, as well as its capability for hierarchical feature extraction. This structure enables the efficient processing and analysis of visual and spatial data, distinguishing it from other specialized neural network types. Definition of the adjective “microwave-free”

[0302] For the purposes of this document, the term "microwave-free" describes the property of electromagnetic radiation being essentially free of wavelengths in the microwave range. Microwave-free radiation contains no or, for technical purposes, only negligible radiation components within the microwave range.

[0303] For the purposes of this document, the microwave range includes electromagnetic waves with wavelengths from approximately 1 millimeter (mm) to 1 meter (m), corresponding to frequencies from approximately 300 gigahertz (GHz) to 300 megahertz (MHz).

[0304] Accordingly, "microwave-free" means that the radiation in question does not contain any significant radiation components within this wavelength range of 1 mm to 1 m. This definition is used for the purposes of this document to ensure that no electromagnetic interference or effects occur in the microwave range. Definition of the term “sinusoidal”Definition

[0305] A sinusoidal signal, as defined in this document, is a periodic signal that can be described as a mathematical function of time and has the shape of a sine wave. Such a signal is described by the equation f(t) = A sin(ωt+ϕ), where A is the amplitude, ω is the angular frequency, and ϕ is the phase shift of the signal. Measurement method for determining sinusoidality

[0306] To determine the sinusoidal nature of a signal, the method of harmonic analysis is used. This method involves decomposing the signal into its harmonic components using a Fourier transform. A signal is considered sinusoidal if the fundamental component (the first harmonic component) dominates and the amplitudes of the higher harmonic components (second and subsequent) are negligible.

[0307] For the practical implementation of this measurement and analysis, reference is made to the standard DIN EN 61000-4-7, which describes detailed procedures for conducting harmonic analysis and evaluating the results. For the purposes of the technical teaching presented here, an analogous application of harmonic analysis is assumed. Concrete measurements

[0308] The Fourier transform was applied to measure a signal assumed to be sinusoidal. The signal exhibited a fundamental frequency ω with an amplitude A. The amplitudes of the higher harmonic components would then be, for example, as follows: harmonic component (2ω): 0.2 A harmonic component (3ω): 0.05 A harmonic component (4ωz): 0.01 A etc.

[0309] The measurement results would then confirm that the signal is primarily dominated by the fundamental frequency, while the higher harmonic components are negligible. Thus, the signal can be considered sinusoidal according to the specifications of the DIN EN 61000-4-7 standard. reference

[0310] The harmonic analysis and evaluation of the sinusoidal nature of the signal is proposed to be carried out in an analogous manner for the respective pump radiation frequency (f pmp ) according to the requirements of the standard: DIN EN 61000-4-7:2009-12; VDE 0847-4-7:2009-12: "Electromagnetic compatibility (EMC) - Part 4-7: Testing and measurement techniques - General guidance for harmonic, interharmonic and harmonic measurement of power systems and equipment connected to such systems." Other measurement techniques can be used analogously if they are similarly standardized. If one of these techniques concludes that a signal is sinusoidal, then this signal is considered sinusoidal within the meaning of this document. DIN EN 61000-4-7:2009-12; VDE 0847-4-7:2009-12 is therefore only one example of such a measurement technique. Definition of a monofrequency signal and determination of the property of monofrequency

[0311] A monofrequency signal is a periodic signal that consists exclusively of a single frequency component. It is a sinusoidal signal without any harmonic or other frequency components. The mathematical description of a monofrequency signal is f(t) = A sin(ωt + ϕ), where A is the amplitude, ω is the angular frequency, and ϕ is the phase shift of the signal. Measurement method for determining the monofrequency

[0312] To determine the monofrequency of a signal, the method of spectral analysis using Fourier transformation is used. This method allows the signal to be decomposed into its frequency components and the amplitudes of these components to be determined. A signal is considered monofrequency if only a single frequency component is present and the amplitudes of all other frequency components are negligibly small. This is the case if the squared amplitude of other frequencies that deviate from the fundamental frequency by more than + / - 10% in their frequency value amounts to less than 25%, preferably less than 10%, or better still, less than 5% of the squared amplitude of the frequencies that deviate from the fundamental frequency by less than + / - 10%, integrated over the frequency.

[0313] For the practical implementation of this measurement and analysis, reference is made to the aforementioned standard DIN EN 61000-4-7, which describes detailed procedures for performing the spectral analysis and evaluating the results. Definition of electromagnetic radiation in the microwave range and determination of the presence

[0314] For the purposes of this document, electromagnetic radiation in the microwave range refers to electromagnetic waves with frequencies in the range of approximately 300 MHz to 300 GHz. The wavelength of microwave radiation, for the purposes of this document, is in the range of 1 mm to 1 m. Measurement method for determining the presence of electromagnetic radiation in the microwave range

[0315] To determine the presence of electromagnetic radiation in the microwave range, for example, the method of spectral power density measurement using a spectrum analyzer is used. This method enables the acquisition and analysis of the electromagnetic spectrum, thereby determining the frequency and power density of the radiation. A spectrum analyzer detects and visualizes the frequency components of the electromagnetic radiation to determine whether the radiation falls within the microwave range.

[0316] For the practical implementation of this measurement and analysis, reference is made to the standard DIN EN IEC 55016-1-1:2020-09; VDE 0876-16-1-1:2020-09, "Requirements for equipment and methods of measuring radio disturbances and immunity - Part 1-1: Equipment and methods of measuring radio disturbances and immunity" - Measuring instruments (CISPR 16-1-1:2019); German version EN IEC 55016-1-1:2019, which describes detailed procedures for performing the power spectral density measurement and for evaluating the results. reference

[0317] The spectral power density measurement and assessment of the presence of electromagnetic radiation in the microwave range is carried out in accordance with the specifications of the standard: DIN EN 55016-1-1: “Equipment and methods for measuring radio frequency disturbances and disturbance field strengths - Part 1-1: Equipment and arrangements for measuring conducted and radiated disturbances. List of cited writings

[0318] If, in the context of the nationalization of a subsequent international application, the law of the respective legal system of the state in which the international application of the document presented here is nationalized allows disclosure by reference, the content of the following documents in combination with the technical teachings of the document presented here is an entire part of the disclosure presented here.

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Claims

[1] Method (100) for determining at least one compensated measured value of at least two physical quantities, ( Fig. 7) with the steps: Providing (105) a sensor system (SSYS) with at least one or more sensor elements (SE), - wherein the one or more sensor elements (SE) comprise one or more crystals and - wherein one or more crystals of these crystals comprise one or more color centers and - wherein the first physical quantity acts on the one or more sensor elements (SE) and - wherein the second physical quantity acts on the one or more sensor elements (SE); in particular providing (110) a computer system (RSYS) of the sensor system (SSYS); Providing pump radiation (LB) that provides a temporal progression of the pump radiation intensity (I pmp (t)) of the pump radiation (LB); Irradiating (115) the one or more sensor elements (SE) with a pump radiation (LB) having a pump radiation wavelength (λ pmp ), in particular by means of a pump radiation source (LD), - where the temporal course of the intensity (I pmp (t)) the pump radiation (LB) is modulated with a modulation signal, in particular with a transmission signal S5(t); Providing (120) program code for a computer- and / or machine-implemented correction method, in particular in one or more memories (MEM) of the computer system (RSYS) of the sensor system (SSYS); Providing (125) configuration parameters for carrying out the computer- and / or machine-implemented correction method, wherein in particular the provision takes place in one or more memories (MEM), in particular of the sensor system and / or computer system (RSYS) of the sensor system (SSYS); Detecting (130) the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE), which depends in different ways on the at least two physical quantities, in particular by means of one or more photodetectors (PD) and / or by means of one or more arrays of photodetectors, in particular by means of one or more CCD image sensors and / or by means of one or more electronic cameras; Determining (135) at least two different fluorescence parameters as vector components of an at least two-dimensional computer- and / or machine-implemented fluorescence vector (F v ) from the time course (I fl (t)) the intensity of the fluorescence radiation (FL) of the color centers (NV) of the one or more sensor elements (SE) in combination with the temporal course of the pump radiation intensity (I pmp (t)) the pump radiation (LB); Determining (140) a first measured value of the first physical quantity of the sensor element (SE) in the form of a first size parameter of a one- or multi-dimensional computer- and / or machine-implemented sensor state vector (S z ) - by imaging one or more fluorescence vectors (F v ), the respective vector components of which each comprise at least two fluorescence parameters, and / or - by mapping one or more fluorescence frequency vectors (F fv ), the respective vector components of which each contain at least two fluorescence parameters and at least one pump radiation frequency (f pmp ) and / or - by imaging one or more fluorescence frequency microwave vectors (F fµv ), the respective vector components of which each contain at least two fluorescence parameters and at least one pump radiation frequency (f pmp ) and at least one microwave frequency (f µw ) include - on the one- or multi-dimensional computer and / or machine-implemented sensor state vector (S z ), - where the mapping is done using provided configuration parameters and - wherein the mapping is carried out by executing the program code for the computer- and / or machine-implemented correction method, in particular by a computer system (RSYS), wherein the configuration parameters for carrying out the computer- and / or machine-implemented correction method have been determined by means of a previously executed computer- and / or machine-implemented training program (determination method), - that the first measured value depends on the first physical quantity of the one or more sensor elements (SE) and - that the first measured value does not depend or substantially does not depend on the second physical quantity of the one or more sensor elements (SE), - so that the first measured value can be used as a compensated first measured value of the first physical quantity of the one or more sensor elements (SE); Outputting (160) and / or keeping ready and / or storing and / or transmitting and / or using the determined compensated first measured value of the first physical quantity of the one or more sensor elements (SE). [2] Method according to claim 1, wherein the temporal course of the intensity (I pmp (t)) of the pump radiation (LB) with a modulation signal, in particular with a periodic transmission signal S5(t) with a pump radiation frequency (f pmp ), is modulated. [3] Method according to claim 2, ( Fig. 8) Formation (136) of at least one at least three-dimensional computer and / or machine-implemented fluorescence frequency vector (F fv ) comprising at least one at least two computer- and / or machine-implemented fluorescence vectors (F v ) and at least the value of the pump radiation frequency (f pmp ) includes; [4] Method according to claim 3, wherein the determination (140) of a first measured value of the first physical quantity of the one or more sensor elements (SE) in the form of a first quantity parameter of a one- or multi-dimensional computer- and / or machine-implemented sensor state vector (S z ) - by imaging one or more fluorescence vectors (F v ), the respective vector components of which each comprise at least two fluorescence parameters, and / or by mapping one or more fluorescence frequency vectors (F fv), the respective vector components of which each contain at least two fluorescence parameters and at least one respective value of the pump radiation frequency (f pmp ) to the one- or multi-dimensional computer and / or machine-implemented sensor state vector (S z ) is carried out, - where the mapping is done using provided configuration parameters and - wherein the mapping is carried out by executing the program code for the computer- and / or machine-implemented correction method, in particular by a computer system (RSYS). [5] Method according to one of claims 1 to 4, ( Fig. 9) Determining (142) a second measured value of the second physical quantity of the one or more sensor elements (SE) in the form of a second size parameter of the one- or multi-dimensional computer- and / or machine-implemented sensor state vector (S z ) - during the imaging of the one or more fluorescence vectors (F v ) and / or, - during the imaging of the one or more fluorescence frequency vectors (F fv ), - whose respective vector components each comprise at least two fluorescence parameters or - whose respective vector components each contain at least two fluorescence parameters and at least one value of the pump radiation frequency (f pmp ) include - on the one- or multi-dimensional computer and / or machine-implemented sensor state vector (S z ), - where the mapping is done using provided configuration parameters and - wherein the mapping is carried out by executing the program code for the computer- and / or machine-implemented correction method, in particular by a computer system (RSYS), wherein the configuration parameters for carrying out the computer- and / or machine-implemented correction method have also been determined at the same time by means of a previously executed computer- and / or machine-implemented training program, - that the second measured value depends on the second physical quantity of the one or more sensor elements (SE) and - that the second measured value does not depend or substantially does not depend on the first physical quantity of the one or more sensor elements (SE), - so that the second measured value can be used as a compensated second measured value of the second physical quantity of the one or more sensor elements (SE); Outputting (165) and / or keeping ready and / or storing and / or transmitting and / or using the determined compensated second measured value of the second physical quantity of the one or more sensor elements (SE). [6] Method according to one of claims 1 to 5, ( Fig. 10) with the step of irradiating (127) the one or more sensor elements (SE) with electromagnetic radiation in the microwave range. [7] Method according to claim 6, wherein the electromagnetic radiation in the microwave range has a microwave frequency (f µw ). [8] Method according to one of claims 2 to 7, ( Fig. 10) Formation (137) of at least one at least four-dimensional computer- and / or machine-implemented fluorescence frequency microwave vector (F fµv ), - which comprises at least one at least two-dimensional computer- and / or machine-implemented fluorescence vector (F v) and - which has at least the value of the pump radiation frequency (f pmp ) and - which has at least the value of the microwave frequency (f µw ) includes. [9] Method according to claim 8, wherein the determination (140) of a first measured value of the first physical quantity of the one or more sensor elements (SE) in the form of a first quantity parameter of a one- or multi-dimensional computer- and / or machine-implemented sensor state vector (S z ) - by imaging one or more fluorescence vectors (F v ), the respective vector components of which each comprise at least two fluorescence parameters, and / or by mapping one or more fluorescence frequency vectors (F fv ) and / or by imaging one or more fluorescence frequency microwave vectors (F fµv), the respective vector components of which each contain at least two fluorescence parameters and at least one respective value of the pump radiation frequency (f pmp ) and at least one value of the microwave frequency (f µw ) to the one- or multi-dimensional computer and / or machine-implemented sensor state vector (S z ) is carried out, - where the mapping is done using provided configuration parameters and - wherein the mapping is carried out by executing the program code for the computer- and / or machine-implemented correction method, in particular by a computer system (RSYS). [10] Method according to one of claims 7 to 9, wherein the determination (142) of a second measured value of the second physical quantity of the one or more sensor elements (SE) in the form of a second size parameter of the one- or multi-dimensional computer- and / or machine-implemented sensor state vector (Sz ) - during the imaging of the one or more fluorescence vectors (F v ) and / or - during the imaging of the one or more fluorescence frequency vectors (F fv ), and / or - during the imaging of the one or more fluorescence frequency microwave vectors (F rµv ), - whose respective vector components each comprise at least two fluorescence parameters or - whose respective vector components each contain at least two fluorescence parameters and at least one value of the pump radiation frequency (f pmp ) include or - whose respective vector components each contain at least two fluorescence parameters and at least one value of the pump radiation frequency (f pmp ) and at least one value of the microwave frequency (f µw ) include - on the one- or multi-dimensional computer and / or machine-implemented sensor state vector (S z ), - where the mapping is done using provided configuration parameters and - wherein the mapping is carried out by executing the program code for the computer- and / or machine-implemented correction method, in particular by a computer system (RSYS), [11] Sensor system (SSYS), wherein the sensor system (SSYS) is configured to carry out a method of claims 1 to 10. [12] Computer program product wherein the computer program product comprises program code for one or more computer- or machine-implemented method steps of a method of claims 1 to 10 and where the program code of the computer program product is a) unencrypted or encrypted and b) wholly or partly and at least temporarily - i) is stored in a memory (MEM) and / or - ii) is stored in a storage medium and / or - iii) is kept available on a computer system (RSYS), which are configured to enable the at least partial execution of the program code by a sensor system (SSYS) according to claim 11 and / or by device parts of a sensor system (SSYS) according to claim 11 and / or by a computer core (CPU) of a computer system (RSYS) of a sensor system (SSYS) according to claim 11. [13] Storage medium or memory (MEM), wherein the storage medium or memory (MEM) comprises a program code and / or data for one or more computer- or machine-implemented method steps of a method of claims 1 to 10. [14] Use of a storage medium or memory (MEM) comprising a program code and / or data for one or more computer- or machine-implemented method steps of a method of claims 1 to 10 in a sensor system (SSYS) having one or more color centers in one or more sensor elements (SE). [15] Memory (MEM), wherein the memory (MEM) comprises measurement data of a sensor system (SSYS) according to claim 11, in particular one or more compensated first measured values ​​of the first physical quantity of the sensor element (SE). [16] Data transmission path (DSTR), wherein the data transmission path is configured to transmit measurement data of a sensor system (SSYS) according to claim 11, in particular one or more compensated first measured values ​​of the first physical quantity of the one or more sensor elements (SE).

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