SPECTROSCOPY OF A SAMPLE

TECHNICAL FIELD AND BACKGROUND

The present disclosure relates to a method and system for magnetic resonance spectroscopy.

Electron Spin resonance (ESR) and Nuclear Magnetic Resonance (NMR) spectroscopies are powerful tools to detect and characterize magnetic molecules by their electron or nuclear spin. For example, molecules in a sample of interest can be detected and characterized by detecting their magnetic or electronic resonance. Typically, a magnetic field is applied to the sample combined with a radio-frequency signal. A full resonance spectrum of the energy or frequency absorbed by the sample can be measured by varying the magnetic field and/or radiofrequency signal in time.

Unfortunately, in standard magnetic spectroscopy, the sensitivity of the detection (i.e. the minimum amount of molecule that is required for the measurement) is limited by the low energy of the spin transition to be detected. Typically a minimum of thousand molecules is required to perform NRM or ESR spectroscopy. Furthermore obtaining a full magnetic resonance spectrum requires a temporal sweep that takes a relatively long time. Furthermore, standard measurements require a strong magnetic field on large areas. This is e.g. provided by superconductor magnet, which makes ESR and NMR spectrometers quite expensive.

It is desired to address these or other problems in an improved method and system for measuring the magnetic resonance spectrum of a sample.

SUMMARY

One aspect of the present disclosure provides a method for measuring a magnetic resonance spectrum of a sample. The sample to be measured is provided in proximity to a sensor array. The sensor array comprises a plurality of magnetic resonance sensors distributed along a predetermined coordinate of the sensor array. A magnetic field gradient is applied over the sample. The direction of the gradient is such that the magnetic field varies over different regions of the sample as a function of a respective position of each sample region along the coordinate of the sensor array. Sensor signals of the magnetic resonance sensors are then recorded as a function of the coordinate to determine the magnetic resonance spectrum.

By applying a magnetic field gradient over the sample along a coordinate of the sensor array, different sensors can simultaneously measure the effect of different magnetic fields on the magnetic resonances in the sample. The simultaneous sensor signals can be distinguished along the coordinate and related to the magnetic field at that coordinate to reconstruct the magnetic spectrum. In this way an instantaneous magnetic spectrum can be obtained without having to sweep the magnetic field in time.

Another or further aspect of the present disclosure, provides a system for measuring a magnetic resonance spectrum of a sample. The system comprises a sensor array. The sensor array comprises a plurality of magnetic resonance sensors distributed along a predetermined coordinate of the sensor array. A sample cell may be configured to provide the sample to be measured in proximity to the sensor array, e.g. forming an interface with the sample or being suspended as particles throughout the sample. A magnet is configured to apply a magnetic field gradient over the sample such that magnetic field in use varies over different regions of the sample as a function of a respective position of each sample region along the coordinate of the sensor array. A measurement device is configured to record sensor signals of the magnetic resonance sensors as a function of the coordinate to determine the magnetic resonance spectrum. BRIEF DESCRIPTION OF DRAWINGS

These and other features, aspects, and advantages of the apparatus, systems and methods of the present disclosure will become better understood from the following description, appended claims, and accompanying drawing wherein:

FIG 1A schematically illustrates an embodiment of a system for measuring a magnetic resonance spectrum of a sample;

FIG IB schematically illustrates a close-up of sample regions interacting with respective sensors across a sensor interface;

FIG 2 schematically illustrates energy levels of a sensor NV (top) and corresponding sample region S (bottom);

FIGs 3A-3C schematically illustrate an embodiment for calculating the magnetic resonance spectrum M;

FIG 4A schematically illustrates an energy level diagram for a colour center;

FIG 4B illustrates an example of an average electron-spin state occupancy during a spin relaxation measurement;

FIGs 5A and 5B schematically illustrate embodiments for creating a magnetic field gradient;

FIG 6A and 6B schematically illustrate a cross-section and perspective view of one embodiment of a sample cell;

FIGs 7A-7C schematically illustrate an example for applying a second gradient to the sample itself;

FIGs 8A and 8B illustrate another embodiment with sensors embedded in the sample.

DESCRIPTION OF EMBODIMENTS

The invention is described more fully hereinafter with reference to the accompanying drawings, in which embodiments of the invention are shown. Embodiments may be described with reference to schematic and/or cross-section illustrations of possibly idealized embodiments and

intermediate structures of the invention. In the description and drawings, hke numbers refer to like elements throughout. Relative terms as well as derivatives thereof should be construed to refer to the orientation as then described or as shown in the drawing under discussion. These relative terms are for convenience of description and do not require that the system be constructed or operated in a particular orientation unless stated otherwise. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. The term "and/or" includes any and all combinations of one or more of the associated listed items. It will be understood that the terms "comprises" and/or "comprising" specify the presence of stated features but do not preclude the presence or addition of one or more other features. It will be further understood that when a particular step of a method is referred to as subsequent to another step, it can directly follow said other step or one or more intermediate steps may be carried out before carrying out the particular step, unless specified otherwise. Likewise it will be understood that when a connection between structures or components is described, this connection may be estabhshed directly or through

intermediate structures or components unless specified otherwise.

FIG 1A schematically illustrates an embodiment of a system 100 for measuring a magnetic resonance spectrum M of a sample lis. FIG IB schematically illustrates a close-up of sample regions S interacting with respective magnetic resonance sensors 12s across the sensor interface 12a.

In a preferred embodiment, the sample l is to be measured is brought in proximity to, e.g. contacted with, a sensor array 12. The sensor array 12 comprises a plurality of magnetic resonance sensors 12s

distributed along a predefined coordinate or direction X of the sensor array 12. A magnetic field gradient is applied over the sample l is such that the magnetic field B varies over different regions S of the sample l is as a function of a respective position of each sample region S along the

coordinate X. Sensor signals Lu of the magnetic resonance sensors 12s may thus be recorded as a function of the coordinate X to determine the magnetic resonance spectrum M.

In the embodiment shown, the sample l is to be measured is provided in contact with a sensor interface 12a. The sensor array 12 comprises a plurality of magnetic resonance sensors 12s distributed along at least one surface coordinate X of the sensor interface 12a. As described herein, the sensor interface 12a typically refers to a physical boundary, e.g. of a material forming the sensor array 12. For example, the system 100 as shown comprises a sensor array 12 with a sensor interface 12a forming a boundary between the sensors 12s and the sample regions S. In some embodiments, the sensors 12s are distributed inside a material forming the sensor array 12 at another side of the sensor interface 12a from the sample l is. In one embodiment, as shown, a sample cell 11 is configured to provide the sample l is to be measured in proximity, e.g. contact with the sensor interface 12 a.

In a further embodiment, a magnetic field gradient is apphed over the sample l is such that the magnetic field B varies over different regions S of the sample l is as a function of a respective position of each sample region S along the aforementioned surface coordinate X of the sensor interface 12a. For example, the system comprises one or more permanent magnets 13 to apply the magnetic field gradient over the sample l is. Alternatively, or in addition, one or more electromagnets can be used (not shown).

It will be appreciated that an energy (difference) AER, or equivalently the resonance frequency, associated with a magnetic resonance R of the sample l is at a specific value of the magnetic field B can be characteristic for a magnetic moment of constituents forming the sample l is. For example a nuclear magnetic moment or electron (para)magnetic moment of molecules/atoms in the sample may have an energy depending on the local magnitude (and direction) of the magnetic field. Typically a frequency of the magnetic resonance R of the sample l is varies proportional to an amplitude of the magnetic field B in the sample l is. For example, the resonance associated with an energy difference between up and down spin states may be proportional to a product of the magnetic field and a magnetic moment of the constituents, e.g. electron and/or nuclear spin.

In a preferred embodiment, as described herein, the sensors 12s are formed by Nitrogen-Vacancy colour centers, which will be denoted throughout the figures and description as "NV". However, it will be appreciated that the principles of the present disclosure are not limited to NV colour centers. For example, other types of colour centers or point defects may be used such as silicon-vacancy centers (Si-V) in Diamond or Carbon antisite -vacancy pairs (CsiVc) in Silicon Carbide. Besides colour centers also other types of microscopic structures may provide similar results. Accordingly the notation "NV", e.g. with reference to any particular sensor NV, its (relative) energies ENV, and magnetic field BNV thereat, may be exchanged to apply to any magnetic sensor. Furthermore, while one preferred embodiment comprises a solid array of sensors 12s, e.g. as formed by NV centers in a diamond lattice, also other embodiments can be envisaged, e.g. with a sample comprising embedded or suspended sensors as described below with reference to FIG 8.

Preferably, the magnetic sensors are relatively small and in close proximity to one another to measure an appreciable spectrum. For example, a cross-section size per sensor is preferably less than hundred micrometer, less than one micrometer, less than ten nanometer, or even less. Also a spacing between the sensors is preferably less than hundred micrometer, less than one micrometer, less than ten nanometer, or even less, e.g. no spacing there between. In a preferred embodiment, the magnetic sensors thus have microscopic dimensions. For example, the microscopic magnetic sensors may have a cross-section size between one and hundred nanometer, e.g. less than one nanometer for a typical Nitrogen-Vacancy colour center. A measurement range or volume of the microscopic magnetic sensors may be provided by their size and/or extend somewhat around the sensor cross- section e.g. between one and ten nanometer around. A density of the microscopic sensors may vary. For example, a volume density up to 10 ¹⁸ microscopic sensors per cm ³ , or more. For example, a surface density up to 10 ¹ per cm ² , or more. For densities above 10 ⁹ or 10 ¹⁰ per cm ² it may be difficult to optically distinguish ensembles of sensors, but still more sensors may provide more signal. It will be appreciated that the smaller the size and/or range of the magnetic sensors, the more different field strengths can be measured per unit of length or volume and the more sensors can be packed into a given volume.

Alternatively to microscopic structures such as NV centers, also other types sensor devices can be envisaged. In principle, any type of sensor which can output a recordable signal as a function of a magnetic resonance in a nearby sample region can be used. For example, the sensor signal may depend on a local coupling of the sensor with its respective nearby sample region. For example, the magnetic resonance sensors may comprise transducers producing electrical signals as a function of a magnetic resonance in the nearby sample region. For example, measurement of the sensor signals may comprises recording electrical signals from an array of sensors, e.g. wherein the surface coordinate of the sensor interface extends along at least one measurement direction aligned with a projection of the surface coordinate. Examples of such sensors may e.g. include a SQUID array (superconducting quantum interference device) with a magnetic field gradient applied over the array. Other sensors may include an array of GMR (Giant MagnetoResistance) sensors or an array of Hall effect probes. In one embodiment, each respective sensor 12s of the sensor array 12 is configured to provide a sensor signal Lu as a function of a coupling C between a volume S of the sample and the sensors. In the embodiment shown the sensor signal Lu is provided as a function of the coupling C across the sensor interface 12a. For example, such coupling C may depend on an energy matching between a magnetic resonance of a respective sensor 12s and a magnetic resonance of a respective sample region S of the sample l is at the coordinate X. Typically, a strength of the coupling C or hkehhood of interaction between the sensor 12s and the sample region S may depend on an energy ΔΕκ or frequency of the magnetic resonance of the sample region S matching the energy of the magnetic resonance of the sensor 12s.

In a preferred embodiment, sensor signals Lu of the magnetic resonance sensors 12s are recorded as a function of the coordinate X to determine the magnetic resonance spectrum M. For example, the system comprises a measurement device 16 configured to record the sensor signals Lu. For example, the signals are recorded on a storage medium of a controller 17, operatively connected to the measurement device 16.

In one embodiment, the sensor signals Lu comprise light, wherein the magnetic resonance sensors 12s comprise transducers producing the light as a function of a magnetic resonance in the nearby sample region S. In another or further embodiment, an amount of light or chance for emitting light depends on the local coupling C of the sensor 12s with its respective nearby sample region S. For example, the magnetic resonance sensors 12s exhibit a luminescence that is dependent on nearby magnetic resonances.

In one embodiment, the sensor signals Lu comprise light emitted by the sensors, e.g. a photoluminescent signal emitted by the sensors 12s. In the embodiment shown, the system comprises a light source 14 for sending light pulses Li to the sensor array 12. For example, the light pulses Li may trigger initialization and/or readout of the magnetic resonance sensors 12s. In one embodiment, the magnetic resonance sensors 12s are prepared in an initial state by a first light pulse Li, allowed some time to interact with the sample region S, and triggered by a second light pulse to emit a

photoluminescent signal Lu that is indicative of the interaction. In some embodiments a controller 17 is configured to control the light source 14, e.g. to use predefined timing of the hght pulses Li and/our readout of signals Lu. For example, signals from the measurement device 16 are gated to measure the signal Lu at a specific time interval, e.g. following the second pulse Li.

In a preferred embodiment, measurement of the sensor signals Lu comprises imaging light emitted from the sensor interface 12a. In the embodiment shown, the measurement device 16 comprises an array of light sensors to image hght signals Lu from the magnetic resonance sensors 12s. In some embodiments, the system comprises a projection system 15 for imaging light signals Lu from the magnetic resonance sensors 12s. Typically the projection system 15 comprises a system of lenses and/or mirrors to project an image of a light pattern emitted by the magnetic resonance sensors 12s onto an array of light sensitive pixels 16. For example, the projection system 15 comprises a microscope. Optionally, the projection system 15 comprises a filter to filter out the light pulses Li of the light source 14 while passing the luminescent light signals Lu of the magnetic resonance sensors 12s.

Advantageously, the projection system 15 may be configured to map the coordinate X of the sensor array onto different sensor element arranged along a corresponding coordinate X' of the measurement device 16, e.g. pixels of a light sensitive chip or camera. In one embodiment, the measurement device 16 comprises a pixel array with light sensitive pixels extending along at least one measurement direction aligned with a

projection of the coordinate X. In some embodiments, the measurement device 16 comprises a two-dimensional array of measurement pixels wherein one direction is aligned with the projection of the coordinate X, e.g. along the surface of the interface 12a, and another direction Y (not shown here) is aligned with some other variation, e.g. in the sample l is as will be discussed later with reference to FIGs 6 and 7.

As described herein, the sample l is is distinct from the sensor array 12. In one embodiment, the sample l is is held against the sensor interface 12a or the sample l is, e.g. by sample cell 11. For example a wall of the sample cell forms the sensor interface 12a. In some embodiments, the sample l is is fluid, e.g. hquid or gaseous. In other or further embodiments, the sample l is is flowed past the sensor interface 12a. Alternatively, the sample l is may be applied to a surface of the sensor interface 12a. In some embodiments, solid samples may be used, e.g. pushed against the sensor interface 12 a.

In the embodiment shown, the light Li is injected from a side of the sensor array 12, e.g. traversing a block of material while exciting the magnetic resonance sensors 12s, e.g. at the sensor interface 12a. For example, the light Li may bounce one or more times between the interfaces 12a, 12b, e.g. under a condition of partial or total internal reflection. Also other ways for pumping the magnetic resonance sensors 12s van be envisaged, e.g. from top or bottom, optionally combined with dichroic mirrors or light filters to pass only the resulting luminescent light Lu to a detector.

FIG 2 schematically illustrates energy levels of the sensor, in this case NV (top), and sample region S (bottom).

In one embodiment, the variation of the magnetic field B in the sample l is causes a corresponding variation of resonance energies ΔΕΕΙ, ΔΕΗ2, ΔΕΗ.Ι.3 associated with one or more magnetic resonances Ri,R2,R:3 in the sample l is as a function of the respective position of each sample region S along the coordinate X, e.g. the surface coordinate of the sensor interface 12a or other predefined coordinate of the sensor array and/or sample. Accordingly, it may occur that a respective sample region S within range of a respective sensor NV at a specific coordinate X2 matches in energy with a corresponding magnetic resonance NV0-1 of the respective sensor NV across the sensor interface 12a. This resonance can e.g. be detected when energy can be transferred between the sensor NV and the sample region S. For example, when the sensor NV is predominantly initiahzed in the m _s =0 state, the sensor may couple to one of the energy matching resonances in the sample region S to facihtate switching to the m _s =-l (or +1) state.

In one embodiment, positions XI, X2, X3 along the coordinate X are associated with respective values Bl, B2, B3 proportional to an amplitude of the magnetic field B at those positions. In another or further embodiment, respective amphtudes of the magnetic field B or values proportional thereto can be stored in a lookup-table or parametrized in a function for each measurement position along the coordinate X. In this way, resonances measured along the coordinate X can be related to specific values of the magnetic field B.

In some embodiments, an energy ΔΕΝΥ of the magnetic resonance NVo-i of the sensor NV is dependent on any magnetic field BNV which may permeate the sensor interface 12a. For example, an energy ΔΕΝΥ of the magnetic resonance NVo-i of the sensor NV decreases proportional to an amplitude of the magnetic field BNV at the sensor NV. It will be appreciated that when the energy difference ΔΕΝΥ of the magnetic resonance sensors NV decreases with increasing magnetic fields B while the energy differences AER increases, this may effectively cause a scaling of the expected

correspondence between the coordinate X and the magnetic field B. In this way the amplitude of the magnetic field required to measure a particular resonance can be decreased. FIGs 3A-3C schematically illustrate an embodiment for

calculating the magnetic resonance spectrum M. FIG 3A schematically shows an amplitude or strength of the magnetic field B by grayscale as a function of the coordinates X,Y. FIG 3B schematically shows an amplitude of the measured signals Lu by grayscale as a function of the coordinates X,Y. FIG 3C schematically shows an amplitude of the measured signals Lu as a function of the amplitude of the magnetic field B.

In one embodiment, the magnetic resonance spectrum M of the sample is calculated based on the sensor signals Lu as a function of the surface coordinate X. For example, an amplitude or strength of the magnetic field B varies as a function of the surface coordinate X. In one embodiment, amplitudes B1,B2,B3 of the magnetic field can be determined as a function of one or more coordinates X,Y. For example, the correspondence between the magnetic field and the coordinates can be determined by measurement, e.g. even using the sensors themselves. For example, the correspondence can be determined using a calibration sample with one or more known

resonances. In some embodiments, the correspondence is determined by calculation, e.g. simulation of the magnetic field.

In one embodiment, amplitudes M1,M2 ,M3 of the magnetic resonance spectrum M are calculated based on amplitudes L1,L2,L3 of the measured sensor signals Lu for different positions X1,X2,X3 along the surface coordinate X based on corresponding values B1,B2,B3 of the magnetic field B at those positions. For example, a magnetic resonance R2 of the sample l is is detected by its energy AER2 matching the energy AENV of the sensor NV for a specific value B2 of the magnetic field B resulting in a corresponding sensor signal L2 at a specific surface coordinate X2 associated with that specific value B2 of the magnetic field B. For example, the measurement may provide nuclear magnetic resonance NMR spectrum and/or electron paramagnetic resonance EPR spectrum. FIG 4A schematically illustrates an energy level diagram for a colour center, e.g. the Nitrogen-Vacancy colour center NV.

Energy levels indicated with the letter "G" refer to the colour center in the electronic ground state. Energy levels indicated with the letter "E" refer to the colour center in the electronic excited state. The numbers "3" in ³ G and ³ E and "1" in ^] G and ^X E represent the number of allowable spin states "m _s ", i.e. spin multiplicity. This may range from -S to S for a total of 2S+1 possible states. For example, in a triplet state where S = 1, m _s can be -1, 0, or 1. The energy difference AENV between the m _s =0 and m _s =±l states typically corresponds to the microwave region. Accordingly this may couple to magnetic resonances in the sample region S having a matching energy ΔΕκ depending on the magnetic field B. The coupling may thus affect the relative population of those levels, thereby affecting the luminescence intensity L. This is one of the mechanisms by which magnetic resonances in the sample region S can be detected.

Transitions between the (electronic) ground triplet state ³ G and (electronic) excited triplet state ³ E may be effected by absorption of photons, in the present case by excitation with a first light beam Li. Decay of the electronic excited state ³ E can produce a photon which is measured as luminescence Luj or Lu2. Alternatively, the excited state may decay also to the excited singlet state Έ via non-radiative transitions No or Ni, depending on the spin-state m _s . The excited singlet state ^J E may decay to the ground singlet state 'G via non-radiative decay path N3. The singlet decay may also producing luminescence L3, but at another, relatively high, wavelength (low energy). The ground singlet state ^X G may non-radiatively convert back to the ground triplet state ³ G.

Preferably, a hkehhood of a radiative versus non-radiative decay depends on the electron-spin m _s of the colour center. For example, in the case of the Nitrogen-Vacancy colour center, a likelihood of radiative decay Lui for an electron-spin m _s =0 is higher than radiative decay Lu2 for an electron-spin m _s =±l. Conversely, the hkelihood of non-radiative decay No for electron-spin ms=0 is lower than non-radiative decay Ni an electron-spin depends on the likehhood of the radiative decay, which is higher when the colour center is in the ms=0 state. Also, due to the different decay paths, the colour center is more likely to be in the m _s =0 state after excitation, which is one way to initiahze the colour center to a known state.

FIG 4B illustrates an example of an average electron-spin state occupancy during different steps of some of the methods as described herein. In a quantum system the spin state is measured in one of discrete

eigenstates. The present diagram may thus illustrate the chance of measuring one or the other state, e.g. determined by repeated

measurements and/or measuring an ensemble of colour centers.

The average occupancy of the electron-spin may start at an equilibrium value m _s ="s _e ", e.g. determined according to a Boltzmann distribution depending on the energy of the different states. In one

embodiment, the initial state m _s =so is set by the first light beam Li (pump) coinciding colour center. This may cause a transition of the colour center to an electronic excited state ³ E, which -after decay- predominantly leaves the colour center in one of specific spin states, e.g. m _s =0. This initiahzed spin state m _s =so may evolve according to a progression which may be influenced by the presence of a nearby resonance of the sample region S during a time period "At". After this time, the spin-state may have progressed to a state m _s =Sp. The progressed spin state "s _p " may be read out using a second light beam Li (probe) which is directed to coincide with the colour center. This may produce luminescence light Lu. The amount of luminescence Lu may be a function of the electron-spin (m _s ) which may be dependent on the progression of the electron-spin m _s ="s _p ", which may be dependent on the resonance energy ΔΕκ of the sample region S, which may be dependent on the magnetic field B.

In one embodiment, a relaxation time T ₁ of the magnetic resonance sensors NV is measured. For example, the relaxation time Ti of a respective sensor NV is dependent on a coupling between the sensor and a respective sample region S. In some embodiments, the relaxation time Ti decreases for increased coupling C when the energy ΔΕκ. of the sample region S matches an energy AEN of the sensor NV

In one embodiment, the sensors NV are given a predefined time At to couple or interact with a resonance of a respective sample regions S under the influence of the specific magnetic field B dependent on the position of the sample region S and sensor along the surface coordinate X. For example, the magnetic resonance sensors NV are pumped by a first light beam Li from an equilibrium state s _e to an initial state so, wherein the sensors decay back to equilibrium state s _e according to a relaxation time Ti .

In some embodiments (not shown), an additional magnetic field is produced e.g. by an antenna. For example, the antenna can produce the additional magnetic field at a modulation frequency matching an energy difference between electron-spin states m _s of the colour center for

manipulating a progression of the electron-spin by facihtating a transition between the electron-spin states. For example, the measured luminescence is enhanced or suppressed depending on whether the modulation frequency of the electron beam matches the energy difference between the electron- spin states m _s . For example the spin can be configured to be sensitive to a particular external resonance. Alternatively, or in addition, the magnetic field modulation can also be used to manipulate the spin of the sample. In other or further embodiments (not shown), the state of the electron-spin m _s is manipulated after initialization to obtain a quantum superposition of at least two electron-spin states m _a =0; m _s =±l. For example, a probability of measuring a specific electron-spin state is dependent on a relative phase of wave functions in the quantum superposition. Accordingly, a progression of the relative phase may be dependent on a relative energy of the electron- spin states and/or the relative energy of the electron-spin states is

dependent on the magnetic field B. In one embodiment, a probability of measuring a specific electron-spin state is dependent on a coherence of wave functions in the quantum superposition. For example, a coherence of the quantum superposition is dependent on the magnetic field B.

In one embodiment, a first radiofrequency field "RF 1" (not shown) is added to coherently manipulate the spin of the NV center, e.g. creating a quantum superposition. Then it is not the Ti of the NV center, but its T2 which can be more sensitive. In some embodiment all the frequencies could be sent at the same time, e.g. one signal RF1 with several frequencies, or several RF1 with one frequencies. In another or further embodiment, a second radiofrequency field "RF2" (not shown) is added. For example, RF2 may match the resonance of the sample (and not the NV center), e.g. the signal RF2 may have only one frequency. In some cases these two

radiofrequency signals are synchronized, to make the NV center sensitive to the region of the sample that are affected by RF2. In this case, in regions where the condition of RF2 matches, the coupling C may be higher thus locally affecting the signal Lu. This is DEER for double electron- electron resonance.

FIG 5A schematically illustrates one embodiment wherein a magnet 14 is placed at one side of the sample l is to provide a decreasing magnetic field B there through as a function of the surface coordinate X.

FIG 5B schematically illustrates another embodiment wherein the sample l is is placed in the magnetic field B provided by an

arrangement of magnets 14.

In a preferred embodiment, an amplitude of the magnetic field varies monotonically over the sample lis. This allows a relatively

straightforward correspondence between the surface coordinate X and the magnetic field amplitude. In another or further embodiment, the amplitude of the magnetic field varies linearly, or according to another known function, over the sample l is. This may further simplify mapping the magnetic field amplitudes to the corresponding coordinate X.

In one embodiment, a direction of the magnetic field B is aligned with a direction of the magnetic resonance sensors NV, e.g. an orientation of a crystal lattice with point defects forming the magnetic resonance sensors NV. For example, a direction of the electron spin of the colour center is aligned with the direction of the magnetic field. It will be noted that the direction of the magnetic (vector) field may be different than the direction of the magnetic (amplitude) gradient.

FIG 6A and 6B schematically illustrate a cross-section and perspective view of one embodiment of a sample cell 11.

In one embodiment, the sample cell 11 comprises a sample chamber for holding a sample l is to be measured. Preferably, a wall of the sample chamber is formed by a sensor array 12 with a sensor interface. The sensor array 12 comprises a plurality of magnetic resonance sensors NV distributed along at least one surface coordinate X of the sensor interface. Typically, the sample cell 11 is configured to provide the sample l is in contact with the sensor interface 12a.

In some embodiments, a separate or integrated magnet 13 is configured to apply a magnetic field gradient over the sample l is such that the magnetic field in use varies over different regions of the sample l is as a function of a respective position of each sample region along the surface coordinate X of the sensor interface.

In one embodiment, the sample l is contacts the sensor interface over an extended two dimensional surface. Preferably, the sample cell or flow channel is flattened in a direction transverse to the sensor interface. As described herein, the magnetic field B is varied along a first dimension X. In some embodiments, signals of the magnetic resonance sensors NV are integrated over points along a second direction where the magnetic field B is constant.

In other or further embodiments, the sample l is itself is varied along a second dimension Y, preferably transverse to the first dimension X. In one embodiment, the sample cell 11 comprise one or more flow channels F1,F2 to flow the sample l is over the sensor interface of the sensor array 12. For example, the sample lis flows in a direction Y transverse to the surface coordinate X along the magnetic field gradient. In another or further embodiment, magnetic resonances of a sample l is in a flow channel F3 are measured both along the flow direction Y and the direction X of the magnetic gradient. For example, a chemical and/or biological reaction is measured along the flow direction Y.

In one embodiment, two or more flow channels F1,F2 with reaction components come together in a combined flow channel F3 to produce reaction products. In another or further embodiment, the sample lis to be measured comprises the reaction products in the combined channel F3. It will be appreciated that this allows the progression of a reaction to be measured by instantaneous measurement of magnetic resonance spectra at different positions Y along the reaction channel F3. In some embodiments, a flow rate in the channel F3 is adapted to control the resolution of different reaction stages along the flow coordinate Y. For example by increasing the flow rate, different stages of the reaction may be further apart along the dimension Y of the flow.

In one embodiment, e.g. as illustrated in FIG 6B or otherwise, the sample l is is held in sample cell formed between a magnet 13 and the sensor array 12. In another or further embodiment, the magnet 13 has a variable degree of magnetization along the surface coordinate X. This may provide a relatively compact arrangement. It can even be envisaged to apply light sensors (not shown) directly to the sensor array 12 for an even further comp actific ation .

FIGs 7A-7C schematically illustrates another example for varying the sample along the second dimension. In one embodiment, a chemical or biological gradient G is formed onto the sensor interface 12a in one direction Y transverse to the surface coordinate X which will be along the magnetic field gradient. For example, a plasma gradient is applied to the surface of the material forming the sensor interface 12a. For example a first step 701 comprises implanting surface defects; a second step comprises annealing to form colour centers NV, and a third step comprises creating a chemical gradient e.g. using gradient plasma treatment.

FIGs 8A and 8B schematically illustrate an alternative embodiment similar to FIGs 1A and IB, but without the physical sensor interface separating the (solid) array of sensors from the sample. Instead, in the embodiment shown, the plurality of magnetic resonance sensors 12s are distributed throughout the sample along a sample coordinate X. The magnetic field B varies over different regions S of the sample l is as a function of a respective position of each sample region S along the sample coordinate X. The sensor signals Lu of the magnetic resonance sensors 12s are thus recorded as a function of the sample coordinate to determine the magnetic resonance spectrum M.

In one embodiment, the sample coordinate may a surface coordinate along a surface of a (relatively thin) sample cell 11 holding the sample l is. While the sensors 12s are distributed through the sample l is to measure respective regions S thereof, the sample l is is distinguished from the sensors, e.g. comprising a liquid or biological sample. For example, the sensors 12s may comprise magnetically sensitive particles such as nanocrystals with NV centers embedded throughout the sample l is. In some embodiments, the sample l is may comprise a suspension with NV nanocrystals.

While the present systems and methods have been described in particular detail with reference to specific exemplary embodiments thereof, it should also be appreciated that numerous modifications and alternative embodiments may be devised by those having ordinary skill in the art without departing from the scope of the present disclosure. For example, embodiments wherein devices or systems are disclosed to be arranged and/or constructed for performing a specified method or function inherently disclose the method or function as such and/or in combination with other disclosed embodiments of methods or systems. Furthermore, embodiments of methods are considered to inherently disclose their implementation in respective hardware, where possible, in combination with other disclosed embodiments of methods or systems. Furthermore, methods that can be embodied as program instructions, e.g. on a non-transient computer- readable storage medium, are considered inherently disclosed as such embodiment.

Finally, the above-discussion is intended to be merely illustrative of the present systems and/or methods and should not be construed as limiting the appended claims to any particular embodiment or group of embodiments. The specification and drawings are accordingly to be regarded in an illustrative manner and are not intended to limit the scope of the appended claims. In interpreting the appended claims, it should be understood that the word "comprising" does not exclude the presence of other elements or acts than those listed in a given claim; the word "a" or "an" preceding an element does not exclude the presence of a plurality of such elements; any reference signs in the claims do not limit their scope; several "means" may be represented by the same or different item(s) or implemented structure or function; any of the disclosed devices or portions thereof may be combined together or separated into further portions unless specifically stated otherwise. The mere fact that certain measures are recited in mutually different claims does not indicate that a combination of these measures cannot be used to advantage. In particular, all working combinations of the claims are considered inherently disclosed.