Magnetic field nulling

Abstract

An apparatus for nulling a magnetic field within a nulling region in an external ambient magnetic field. Separate magnetic field generating elements 102 are located at separate respective locations surrounding the nulling region for generating respective nulling magnetic fields extending into the nulling region. Magnetic field sensing elements 103 are positioned at separate locations within the nulling region for sensing values of the magnetic field there. A feedback control unit 150 controls the values of the respective nulling magnetic fields generated by each of the magnetic field generating elements in response to values of the magnetic field sensed by the magnetic field sensing elements. This is done by driving the magnetic field generating elements with electric currents that reduce the magnetic field values detected by magnetic field sensing elements to values not exceeding a pre-set threshold value corresponding to a pre-set nulling of the magnetic field within the nulling region.

Description

[0001] MAGNETIC FIELD NULLING

[0002] Field of the Invention

[0003] The present invention relates to methods and apparatus for magnetic field nulling and particularly, although not exclusively, to methods and apparatus for magnetic field nulling in applications of Magnetoencephalography (MEG).

[0004] Background

[0005] Magnetoencephalography (MEG) is a well-established medical technique for mapping brain electrical activity by recording magnetic fields that this activity generates. The magnetic fields generated by a brain are very weak and an environment in which there is effectively no (or negligible) ambient magnetic field environment is necessary to make them detectable. The magnetic field detecting sensors used in MEG are often based on superconducting quantum interference devices (SQUID). These devices require liquid helium cooling which is very costly. An alternative sensor technology is optically pumped magnetometers (OPM) that do not need cooling thereby reducing cost of the MEG apparatus.

[0006] An environment in which there is effectively no (or negligible) ambient magnetic field (e.g., for MEG applications) is usually delivered using large and very costly magnetically shielded rooms (MSR). These rooms typically comprise walls, floors and ceilings formed from a magnetically shielding material. Additionally, MSRs may be equipped with additional systems to cancel any remaining magnetic fields present within the MSR which may arise from limitations of the MSR or from equipment within it. The cost of MSRs is so significant that few institutions can afford MEG devices.

[0007] For MEG measurements, the patient must come to an MSR because the MEG device cannot be moved together with MSR to the patient. Inside the MSR, preferably only non-magnetic objects should be used to reduce additional ambient magnetic fields within the MSR. In addition, and MSR has very limited space and no windows. That limits possibility of bringing tools that can be used to interact with the patient, which is important for checking brain response. The static nature of the MSR prevents one from investigating patients in different environments, for example outside a building or in different environment bringing with it psychical comfort. This is particularly significant if an MSR environment is not comfortable for patients with claustrophobia or is scary for children.

[0008] Long-time patient monitoring, for example during sleep is very difficult within an MSR. In addition, an MSR prevents one from combining MEG measurements with other concurrent measurements requiring large devices for other techniques. For example, if one can remove the need for an MSR, this permits a concurrent measurement of MEG and low field MRL

[0009] In addition, within an MSR one cannot avoid certain time varying magnetic field sources such as a patient’s beating heart or power lines supplying power to MEG equipment within the MSR (e.g., a 8545725

[0010] 2 computer or the like). Where MSR itself needs additional compensation of such remaining internal magnetic fields, that may be delivered using Helmholtz coils or bi-planar coils placed inside the MSR.

[0011] The present invention has been devised in light of the above considerations.

[0012] Summary of the Invention

[0013] A magnetic field nulling system commonly comprises magnetic field sensors and magnetic field cancellation coils working in tandem. The magnetic field cancellation coils typically employ high-precision amplifiers, filters and current sources for providing excitation / drive currents into the magnetic field nulling coils to which the coils respond by generating magnetic fields configured to cancel an ambient magnetic field in a designated nulling region of space. The inventors have realised that a magnetic field nulling system most preferably produces a suitably low level of electronic noise. This is highly desirable for effective nulling. However, the inventors have also realised that there is a compromise between, on the one hand, achieving suitably low electronic noise levels and, on the other hand, providing alternating (AC) excitation / drive currents to the magnetic field nulling coils that alternate at a suitable frequency, or frequencies within a bandwidth of frequencies. This is because the provision of higher-frequency excitation / drive currents produces a higher electronic noise figure than the provision of relatively lower- frequency excitation / drive currents.

[0014] In view of this realisation, the invention flows from a realisation that it is common for a magnetic field to be nulled to comprise a predominantly static (or slowly-varying) field component, being the dominant component, combined with a subsidiary (lower amplitude) but more quickly time-varying field component. Typically, the static field component is mostly due to the Earth’s magnetic field, which may change slowly due to geomagnetic or space-weather influences, and the more rapidly time-varying field component is due to electrical devices in or around the nulling region that are powered from an alternating current (AC) mains electrical power supply. The inventors have realised that, just as an ambient magnetic field may be decomposed into a “slowly-varying” component and a “quickly-varying” component, so too can the excitation / drive currents, for driving the magnetic field nulling coils, be similarly decomposed into “slowly- varying” and “quickly-varying” components, respectively configured for use in nulling the “slowly-varying” and “quickly-varying” magnetic fields. The “quickly-varying” excitation / drive currents, likely to contain relatively more current noise, may then be supplied to drive magnetic field nulling coils configured to produce relatively less magnetic noise in response to a given excitation / drive current. The “slowly- varying” excitation / drive currents, likely to contain relatively less noise, may then be supplied to drive magnetic field nulling coils that are not so configured to produce relatively less magnetic noise in response to a given excitation / drive current. Here, a reference to “a given excitation / drive current” refers to a common reference current or, put in other words, that the differently-configured magnetic field nulling coils respond differently to the same input current in terms of their respective magnetic noise figure. A magnetic field nulling coil configured to produce relatively less magnetic noise may, for example, comprise a winding having fewer turns than are present in a magnetic field nulling coil that is not so configured to produce relatively less magnetic noise. 8545725

[0015] 3

[0016] The control of a magnetically low noise environment by a feedback loop of magnetic sensors, electronic amplification and field cancelling coils may be implemented. The invention provides a technique for improving the performance of such a system.

[0017] In a first aspect, the invention may provide an apparatus for nulling a magnetic field within a nulling region in an ambient magnetic field comprising: a plurality of separate magnetic field generating elements placed at separate respective locations surrounding the nulling region for generating respective nulling magnetic fields extending into the nulling region; a plurality of magnetic field sensing elements placed at a plurality of respective separate locations within the nulling region for sensing respective values of the magnetic field within the nulling region; a feedback control unit for controlling the values of the respective nulling magnetic fields generated by each of the plurality of magnetic field generating elements in response to values of the magnetic field sensed by the plurality of magnetic field sensing elements by driving the magnetic field generating elements with respective electric currents that reduce the magnetic field values detected by respective magnetic field sensing elements to values not exceeding a pre-set threshold value corresponding to a pre-set nulling of the magnetic field within the nulling region; wherein one or more of said magnetic field generating elements each comprises a first electromagnetic coil comprising a winding of one or more turns and a second electromagnetic coil comprising a winding of more turns than are present in the first electromagnetic coil; and, wherein the feedback control unit is configured to drive the first electromagnetic coil with alternating electric currents having a first frequency, and to drive the second electromagnetic coil with alternating electric currents having a second frequency that is lower than the first frequency.

[0018] In this way, the invention implements the idea of achieving cancellation (or ‘nulling’) of a magnetic field within a volume of space by using magnetic field generating elements each comprising a pair of (i.e., first and second) electromagnetic coils in which the electromagnetic coils of a given pair are subject to separate respective alternating excitation / drive currents of differing frequencies (i.e., different drive channels), one of relatively lower frequency and one of relatively higher frequency, to generate a corresponding pair of separate respective component nulling magnetic fields. By combining the separate component nulling magnetic fields of a pair of coils, a magnetic field generating element may provide a contribution to an overall magnetic nulling field able to account for “slowly-varying” and “quickly-varying” components of an ambient magnetic field, with less magnetic noise present.

[0019] It is to be understood that references herein to a first electromagnetic coil and a second electromagnetic coil of a magnetic field generating element, is not limited to two electromagnetic coils and includes a reference to at least two (i.e., two, or three or more) electromagnetic coils of a magnetic field generating element. For example, the one or more magnetic field generating elements may each comprise three or more electromagnetic coils each being driven by a respective one of three or more separate alternating excitation / drive currents in which the frequency of any one of the respective separate alternating excitation / drive currents differs from the frequencies of each one of the other respective separate 8545725

[0020] 4 alternating excitation / drive currents (i.e., different drive channels). The frequencies collectively spanned by the separate three or more alternating excitation / drive currents may include a relatively lowest frequency value and a relatively highest frequency value (i.e., relative to the other frequencies included amongst the three or more drive signal frequencies). One or more relatively intermediate frequencies thereby may also be present having respective intermediate frequency values in between the relatively lowest frequency value and the relatively highest frequency value.

[0021] The three or more electromagnetic coils may each comprise a respective winding of a number of turns (i.e., total number) in which the number of turns of a winding of any one of the three or more electromagnetic coils differs from the number of turns of a winding of any one of the other electromagnetic coils amongst the three or more electromagnetic coils. The value of the total number of turns of windings of individual electromagnetic coils amongst the three or more electromagnetic coils may include a relatively lowest value (i.e., lowest total number of turns) and a relatively highest value (i.e., highest total number of turns). One or more relatively intermediate values (i.e., intermediate total number of turns) may thereby also be present having respective intermediate values in between the relatively lowest value and the relatively highest value. The feedback control unit may be configured to drive the electromagnetic coil comprising a winding of the relatively highest total number of turns with alternating electric drive currents having the relatively lowest frequency value. The feedback control unit may be configured to drive the electromagnetic coil comprising a winding of the relatively lowest total number of turns with alternating electric drive currents having the relatively highest frequency value. The feedback control unit may be configured to drive the electromagnetic coil comprising a winding of a relatively intermediate total number of turns with alternating electric drive currents having a relatively intermediate frequency value. In general, the feedback control unit may be configured to drive the three or more electromagnetic coils such that a (or any) winding of fewer turns than are present in each of one or more other electromagnetic coils of the three or more electromagnetic coils, is driven by alternating electric drive currents of a higher frequency than the frequency of the alternating electric drive currents with which feedback control unit drives each of the one or more other electromagnetic coils. Put in other words, the fewer the number of turns (in total) a given coil has, as amongst the plurality of separate coils of a magnetic field generating element, then the greater may be the frequency of the drive current used to drive that coil.

[0022] A reference herein to a coil comprising a winding “...of...” a number of turns may include a reference to a total number of turns, whether the number is a particular value or a relative quantity (e.g., “more” / “fewer” etc.).

[0023] The feedback control unit may be configured for delivering separately alternating electric currents respectively to the first and second electromagnetic coils of a given magnetic field generating element. The feedback control unit may comprise a first power control unit for delivering a first alternating electric current having the first frequency to the first electromagnetic coil of a given magnetic field generating element, and a separate second power control unit for delivering a second alternating electric current having the second frequency to the second electromagnetic coil of the given magnetic field generating 8545725

[0024] 5 element. The amplitude of the second alternating electric current may exceed the amplitude of the first alternating electric current by a factor of between about 500 and about 5000, or by a factor of between about 500 and about 2000, or by a factor of between about 500 and about 1000, such as about 750. For example, the amplitude of the second alternating electric current may be between about 20mA and about 80mA (e.g., about 40mA), and the amplitude of the first alternating electric current may be between about 20 / zA and about 80 / zA (e.g., about 55 / zA). A benefit is providing a first and second electromagnetic coils of a given magnetic field generating element is that each can be driven by a suitably chosen drive current, in which both the frequency and the amplitude of the AC drive current delivered to the respective one of the first and second coils is best suited for the purpose of the coil in question, being respectively configured for use in nulling either the “slowly-varying” or “quickly-varying” ambient magnetic fields using suitably “quickly-varying” or more “slowly-varying” drive currents of with relatively smaller or larger drive current amplitudes, respectively, as appropriate.

[0025] The first and second power control units may be separately optimized for resolution and bandwidth, with the overall system providing superior performance. The separate electromagnetic coils may thereby provide the low-frequency and high-frequency components of a cancelling / nulling magnetic field optimised or improved in terms of reducing magnetic noise produced. The separate coils used may have different numbers of turns to match the requirements of the individual electronic systems.

[0026] The first and second electromagnetic coils may each comprise electrically conductive coils adapted for conducting the electric drive currents. Coil structures or designs (e.g., solenoids, flat spiral coils, etc.) such as would be readily available and apparent to the skilled person, may be used or adapted for this purpose. The first and second electromagnetic coils of a given magnetic field generating element may be co-located (or at least immediately adjacent to each other, e.g., spaced apart by not more than the greatest dimension of the smaller of the coils) in a space surrounding the nulling region so that the component nulling magnetic field generated by the electromagnetic coil each extend into the nulling region from substantially the same location. For example, the turns first and second electromagnetic coils of a given magnetic field generating element may comprise one common winding comprising both the turns in the second electromagnetic coil and the one or more turns in the first electromagnetic coil. The turns in the second electromagnetic coil may be preceded by, or succeeded by, the one or more turns in the first electromagnetic coil of the common winding. The first electromagnetic coil and the second electromagnetic coil may be connected to a common electrical ground terminal. Accordingly, the windings of the first and second electromagnetic coils may share one or more turns in common. The feedback control unit maybe configured to drive the shared turns with a shared alternating electric current comprising a superposition of the alternating electric currents having the first frequency and the second frequency.

[0027] The first power control unit may be connected electrically to the common winding at a location thereon between successive turns of the common winding such that first electromagnetic coil comprises at least the terminal (i.e. , final, last or ultimate) turn of the common winding. The number of turns in the first electromagnetic coil may comprise not more than one turn. For example, when a common winding is 8545725

[0028] 6 used, the first electromagnetic coil may comprise only the terminal, final, last or ultimate turn of the common winding. In other examples, the number of turns in the first electromagnetic coil may comprise not more than two turns, or not more than three turns, or not more than four turns or not more than five turns, as appropriate for the circumstances at hand.

[0029] The number of turns in the second electromagnetic coil may exceed the number of turns in the first electromagnetic coil by a factor of between 50 and 150, such as a factor of between, 80 and 100 (e.g., about 90). For example, if the first electromagnetic coil comprises only one turn, then the second electromagnetic coil may comprise to 50 to 150 turns, or 80 to 100 turns (e.g., about 90 turns).

[0030] The first frequency may exceed the second frequency by a factor of between 50 and 150, or between 70 and 100, such as about 80. The first power control unit and the second power control unit may be configured accordingly.

[0031] In some examples, the first frequency may not exceed about 10 kHz, or may not exceed about 5kHz, or may not exceed about 2.5kHz. In some examples, the second frequency may not exceed about 100Hz, or may not exceed about 75Hz, or may not exceed about 50Hz, or may not exceed about 30Hz. The inventors have found that applying these frequency limits provides good results in terms of lower magnetic noise and improved magnetic nulling.

[0032] The plurality of magnetic field generating elements may be arranged at their separate respective locations in a first array shaped according to a three-dimensional reference surface surrounding the nulling region. The plurality of magnetic field sensing elements may be arranged at their separate respective locations defining a second array shaped according to a three-dimensional reference surface. The second array may be configured to be substantially concentric with the first array. The inventors have found that this concentricity improves nulling performance. The plurality of magnetic field generating elements may be arranged at their separate respective locations substantially equidistant from the centre of the nulling region thereby defining a substantially spherical array surrounding the nulling region.

[0033] The plurality of magnetic field sensing elements may be arranged at their separate respective locations substantially equidistant from the centre of the nulling region thereby defining a substantially spherical array within the nulling region. The inventors have found that this concentricity improves nulling performance. The size of a diameter of the array of magnetic field sensing elements may be at least 30% of the size of a diameter of the array of magnetic field generating elements. The inventors have found that this concentricity improves nulling performance. The separate respective locations in the first array and or the second array may be defined according to a respective regular lattice.

[0034] The plurality of magnetic field generating elements may comprise at least 10, or at least 50, or at least 200 separate magnetic field generating elements. 8545725

[0035] 7

[0036] The pre-set threshold value corresponding to a pre-set nulling of the magnetic field within the nulling region may be not greater than 5x109Tesla, or not greater than 5x1010Tesla. The inventors have found that a threshold value such as this provides good nulling performance.

[0037] In a second aspect, the invention may provide a method for nulling a magnetic field within a nulling region in an ambient magnetic field comprising: providing a plurality of separate magnetic field generating elements placed at separate respective locations surrounding the nulling region for generating respective nulling magnetic fields extending into the nulling region; providing a plurality of magnetic field sensing elements placed at a plurality of respective separate locations within the nulling region for sensing respective values of the magnetic field within the nulling region; controlling the values of the respective nulling magnetic fields generated by each of the plurality of magnetic field generating elements in response to values of the magnetic field sensed by the plurality of magnetic field sensing elements by driving the magnetic field generating elements with respective electric currents that reduce the magnetic field values detected by respective magnetic field sensing elements to values not exceeding a pre-set threshold value corresponding to a pre-set nulling of the magnetic field within the nulling region; wherein one or more of said magnetic field generating elements each comprises a first electromagnetic coil comprising a winding of one or more turns and a second electromagnetic coil comprising a winding of more turns than are present in the first electromagnetic coil; and, wherein said driving comprises driving the first electromagnetic coil with alternating electric currents having a first frequency and driving the second electromagnetic coil with alternating electric currents having a second frequency that is lower than the first frequency.

[0038] In the method, the first frequency my exceed the second frequency by a factor of between 50 and 150. In the method, first frequency may be such that it does not exceed about 10 kHz. In the method, second frequency may be such that it does not exceed about 100Hz.

[0039] The method may include providing magnetic field generating elements comprising electrically conductive coils, and conducting the electric currents thought respective such coils. The windings of the first and second electromagnetic coils may share one or more turns in common. The method may comprise driving the shared turns with a shared alternating electric current comprising a superposition of the alternating electric currents having the first frequency and the second frequency.

[0040] The method may include providing the plurality of magnetic field generating elements as arranged at the separate respective locations in a first array shaped according to a three-dimensional reference surface surrounding the nulling region. The method may include providing the plurality of magnetic field sensing elements as arranged at their separate respective locations defining a second array shaped according to a three-dimensional reference surface. The method may include providing the second array as substantially concentric with the first array. In the method, the separate respective locations in the first 8545725

[0041] 8 array may be defined according to a regular lattice. In the method, the separate respective locations in the second array may be defined according to a regular lattice.

[0042] The method may include providing the plurality of magnetic field generating elements as arranged at their separate respective locations substantially equidistant from the centre of the nulling region thereby defining a substantially spherical array surrounding the nulling region.

[0043] The method may include providing the plurality of magnetic field sensing elements as arranged at their separate respective locations substantially equidistant from the centre of the nulling region thereby defining a substantially spherical array within the nulling region.

[0044] In the method, the size of a diameter of the array of magnetic field sensing elements may be at least 30% of the size of a diameter of the array of magnetic field generating elements.

[0045] The method may include providing the plurality of magnetic field generating elements to comprise at least 10 separate magnetic field generating elements. The method may include providing the plurality of magnetic field generating elements to comprise at least 50 separate magnetic field generating elements.

[0046] The method may include providing the plurality of magnetic field generating elements to comprise at least 200 separate magnetic field generating elements.

[0047] In the method, the threshold value may be not greater than 5x10-9Tesla, or not greater than 5x10-10Tesla.

[0048] The invention includes the combination of the aspects and preferred features described except where such a combination is clearly impermissible or expressly avoided.

[0049] Summary of the Figures

[0050] Embodiments and experiments illustrating the principles of the invention will now be discussed with reference to the accompanying figures in which:

[0051] Figure 1a and Figure 1b show elements of a magnetic field nulling apparatus and a cross-sectional view of thereof, respectively.

[0052] Figure 2 shows a magnetic field strength spatial plot representing an ambient external magnetic field and e nulling region generated by a magnetic field nulling apparatus.

[0053] Figure 3 shows schematically the elements of a magnetic field nulling apparatus. 8545725

[0054] 9

[0055] Figure 4 shows schematically a process for controlling the elements of a magnetic field nulling apparatus.

[0056] Figure 5 shows schematically a magnetic field generating element of a magnetic field nulling apparatus.

[0057] Figure 6 shows schematically a magnetic field generating element of a magnetic field nulling apparatus.

[0058] Figure 7 shows schematically a magnetic field generating element of a magnetic field nulling apparatus.

[0059] Detailed Description of the Invention

[0060] Aspects and embodiments of the present invention will now be discussed with reference to the accompanying figures. Further aspects and embodiments will be apparent to those skilled in the art. All documents mentioned in this text are incorporated herein by reference.

[0061] Figure 1 a shows an example if the invention in the form of an apparatus for use in nulling a magnetic field within a nulling region in an external ambient magnetic field. Figure 1 b shows the apparatus in crosssection. The apparatus comprises a plurality of separate magnetic field generating coil elements 8 each comprising a circular loop of mutually common diameter and each being placed at separate respective location upon a first notional spherical shell reference surface surrounding the nulling region for generating respective nulling magnetic fields extending into the nulling region. Each one of the magnetic field generating coil elements 8 comprises an electrical current input terminal (not shown) and a current output terminal (not shown) for the inputting and outputting, respectively, of a drive current to the coil in question.

[0062] A plurality of magnetic field sensing elements 6, for example OPM sensors, are placed at a plurality of respective separate locations within the nulling region for sensing respective values of the magnetic field within the nulling region. The magnetic field sensing elements are also placed at separate respective locations upon a second notional spherical shell reference surface surrounding the nulling region. The first and second spherical shell reference surfaces are concentric, with the diameter of the first reference spherical shell surface being about 2.5 times the diameter of the second reference spherical shell surface.

[0063] A patient’s head 2 is placed within the nulling region within the spherical shell array of the plurality of magnetic field sensing elements 6 so as to coincide with the centres of the first and second reference spherical shells. 8545725

[0064] 10

[0065] A feedback control unit (not shown, see item 10 Figure 2) is arranged to control the values of the respective nulling magnetic fields generated by each of the plurality of magnetic field generating elements 8 in response to values of the magnetic field sensed by the plurality of magnetic field sensing elements 6 by driving the magnetic field generating elements with respective electric currents that reduce the magnetic field values detected by respective magnetic field sensing elements to values not exceeding a pre-set threshold value corresponding to a pre-set nulling of the magnetic field within the nulling region.

[0066] Each magnetic field generating coil 8 is configured to face in a direction towards the centre or centroid of the array of magnetic field generating elements. In other words, each coil “faces” in a direction perpendicular to the plane containing a diameter of the coil. The direction in which each coil “faces” is a direction parallel to the winding axis of the coil (i.e. , the axis about which the windings wind, such as the coil’s symmetry axis). In this way, the direction in which a coil “faces” defines the orientation with which the magnetic field produced through the centre of that coil is parallel when driven by a current. The direction of that magnetic field is controlled by controlling the direction a given current flow direction through the coil.

[0067] Each coil 8 of the array of magnetic field generating elements is electrically separate and electrically isolated from any other coil of the array of magnetic field generating elements and each coil is driven independently of any of the other coils. Neighbouring coils in the array of magnetic field generating elements are arranged such that no coils of the array overlaps with any other neighbouring coil of the array. In other examples, neighbouring may at least partially overlap.

[0068] The patient 2 is shown wearing a MEG sensor cap 4, in this case OPM sensors are covering the patient’s head. The magnetic field sensors 6 are distributed around MEG sensor cap 4 at a safe distance. The patient’s brain magnetic field cannot be seen by magnetic field sensors 6. The magnetic field sensors 6 and the coils 8 each form a spherical lattice with an opening at its base for admitting the patient’s head 2.

[0069] It is to be noted that the invention is flexible in the sense that it does not need to use a lattice array coverage of magnetic field generating elements that cover the while of the spherical shell reference surface shape, and different notional reference surface shapes can be used. For example, the notional reference surface may be a spheroid or cylindrical shape. Because cancelling / nulling is achieved by electronic control of currents in the magnetic field generating elements 8, a variety of positioning of the magnetic field generating elements problem can be used. This gives flexibility in shaping array of the magnetic field generating elements.

[0070] Figure 2 shows an apparatus for nulling a magnetic field within a nulling region in an external ambient magnetic field comprising a plurality of separate magnetic field generating elements 8 placed at separate respective locations surrounding the nulling region for generating respective nulling magnetic fields extending into the nulling region. A plurality of magnetic field sensing elements 6 are placed at a plurality of respective separate locations within the nulling region for sensing respective values of the magnetic field within the nulling region. A feedback control unit 10 is configured for controlling the values of the 8545725

[0071] 11 respective nulling magnetic fields generated by each of the plurality of magnetic field generating elements in response to values of the magnetic field sensed by the plurality of magnetic field sensing elements. The feed-back control unit is arranged to drive the magnetic field generating elements 8 with respective electric currents that reduce the magnetic field values detected by respective magnetic field sensing elements 6 to values not exceeding a pre-set threshold value corresponding to a pre-set nulling of the magnetic field within the nulling region.

[0072] The feed-back control unit is arranged to calculate the appropriate driving currents. A minimisation of magnetic field readings in sensors 6 is obtained to achieve the required nulling of the magnetic field inside a targeted nulling volume. A magnetic field reading on a sensor 6 is the sum of all magnetic fields from all of the magnetic field generating elements 8 and the external ambient field combined. Each sensor and coil position is fixed, and the only variable that is changing is the drive current that has a proportional dependence to detected the magnetic field. The contribution of each magnetic field generating elements 8 (e.g., coil) to all sensors 6 can be calibrated. When the magnetic field is cancelled then so too is the feedback value of the magnetic field sensed by the sensors for the volume being surrounded by these sensors. There is a proportional dependence between drive current, I, delivered to a given magnetic field generating coil, and the magnetic field generated by the coil in response to that drive current. The following equations describe the spatial distribution of a magnetic field generated by a circular coil comprising a winding having N turns and driven by a drive current I, the field being expressed in cylindrical coordinates:

[0073] Details can be found in the following article:

[0074] [1] “Closed-form expressions for the magnetic fields of rectangular and circular finite-length solenoids and current loops”: by S. Hampton; R. A. Lane; R. M. Hedlof; R. E. Phillips; C. A. Ordonez: AIP Advances 10, 065320 (2020)

[0075] Here: p = a radial distance from the axis of the cylindrical coordinate system. z = the distance along the axis of the cylindrical coordinate system. a = radius of the turn of a coil. p0= permeability of free space.

[0076] K(k) = an elliptic integral of the 1st kind. 8545725

[0077] 12

[0078] E(k) = an elliptic integral of the 2nd kind.

[0079] Of course, the coil may comprise turns that are other than circular in shape, such as rectangular, and reference [1] provides the analytical form for the magnetic field generated by such a coil when driven by a drive current I. Other shapes for the turns of a coil may be employed, of course, as would be readily apparent to the person skilled in the art. What is notable about the expression for the magnetic field generated by the coil, whether circular, rectangular or other shape, is that the magnitude of the magnetic field is proportional to the magnitude of the drive current I. This current noise, A / , present drive current, will generate a corresponding magnetic field noise, ABpand ABZ, in the resulting magnetic field.

[0080] This magnetic field noise will influence the ability to achieve and maintain a desired degree of magnetic field nulling in a target nulling region. For example, one way in which the magnetic field noise may influence field nulling performance is to consider a process by which the apparatus of Fig. 2, for nulling a magnetic field, may be implemented. Such a process is described in detail in the following reference, the content and disclosures of which are incorporated herein by reference in their entirety:

[0081] [2] W02023 / 079081 A1 (Shimadzu Corporation)

[0082] In reference [2] a process is described by which, in an example of the invention, the apparatus for nulling a magnetic field may be implemented. The feedback control unit 10 may be arranged to determine a set of a plurality of optimal respective electric currents, I, with which to drive the corresponding plurality of magnetic field generating elements by applying an orthogonal projection algorithm. The feedback control unit 10 may be configured to generate a set of basis vectors for use in controlling the values of the respective nulling magnetic fields generated by each of the plurality of magnetic field generating elements 8, by applying the optimal respective electric currents, I. The feedback control unit 10 may be configured to use the set of basis vectors in calculating respective optimal electric currents with which to drive magnetic field generating elements of the apparatus. The set of basis vectors may be based on a plurality of measured values of a magnetic field generated within the nulling region individually by each of the plurality of magnetic field generating elements 8 (e.g., in isolation and as measured by the plurality of magnetic field sensing elements) when driven by a pre-set calibration electric current. The orthogonal projection algorithm may be arranged to generate an orthogonal basis set based on the plurality of measured values of a magnetic field generated within the nulling region individually by each of the plurality of magnetic field generating elements 8 when driven by a pre-set calibration electric current.

[0083] In other words, when calibrating the apparatus to create a set of basis vectors, each coil in turn is driven by an electric current alone while all other coils receive no drive current at all. The magnetic field generated by the lone coil is sensed by each of the magnetic field sensing elements 6 at their respective fixed locations within the nulling region. These measured field values are calibration values and define a basis vector for the lone coil in question. They are input from the respective magnetic field sensing elements 6 to the control unit 10 which stores them. The control unit is configured to repeat this process separately for each magnetic field generating coil 8 of the array of coils whereby each coil 8 takes the role of being the lone coil driven by an electric current. For each coil 8, the control unit 10 constructs a basis vector containing calibration magnetic field values for all n sensors 6. For a first coil it will be: 8545725

[0084] 13

[0085] [B11(By,, , Bz„ Bx,n, By,n,

[0086] The array of m coils results in an array of these basis vectors constructed using the respective basis vectors for all m coils:

[0087] Each measurement of a magnetic field with all sensors subsequently operating in the active cancellation cycle can be written as a pseudo-vector type construct:

[0088] [Sx-^Sy! ,Sz1

[0089] Making:

[0090] SX1, Sy, , Sz, , Sx2, Sy2, Sz2... = V^, V3, V4, VS, V6...

[0091] The equation for orthogonal projection can be applied as follows:

[0092] The terms <z7are terms containing the current for the jth coil. The control unit is configured to vary the value of the currents applied to each coil by varying the values of <z7in order to reduce the value of the magnetic field that would be measured by the magnetic field sensing elements collectively (e.g., as averaged amongst them) or individually to not exceed some desired pre-set threshold value corresponding to an appropriate level of field cancellation / nulling. To achieve cancelation the control unit 10 is configured to calculate the ‘negative’ values of currents with which each magnetic field generating coil must be driven by solving the following optimisation equation (note the negative sign appearing in the right-hand-side of this equation):

[0093] In general, only a few iterations (typically, only one iteration) are necessary to get the best current solution for external magnetic field nulling / cancelling. The orthogonal basis for the orthogonal projection method is created in the calibration process. The orthogonal basis need only be created once and may subsequently be used by the control unit for all active cancellation / nulling using sensor data received from the magnetic field sensor array during active cancelling / nulling operations. This is very fast and simple process. Because of that any field distortions coming from differences between them, imprecisions, are removed. Figure 3 summarises this process as comprising the steps of:

[0094] Step 16: Outputting, by the control unit 10, individual drive currents to magnetic field generating coils 8 in turn whilst no other coil receives a drive current. 8545725

[0095] 14

[0096] Step 18: Measure, by the magnetic field sensor array 6, the magnetic field within the nulling region.

[0097] Step 20: Calculating, by the control unit 10, individual drive currents to apply to coils 8 by solving the optimisation equation and driving the coils with drive currents calculates accordingly.

[0098] The feedback control unit 10 may be configured to continuously monitor (e.g., in uninterrupted fashion for a given duration of time, or intermittently) the magnetic field values provided by the magnetic field sensing elements 6 within the nulling volume and to continuously control (e.g., adjust) the respective electric currents supplied to the correcting magnetic field generating element 8. In this way, the feedback control 10 may implement an active field nulling over an extended period of time in which the electric currents required to appropriately reduce the magnetic field values detected by respective magnetic field sensing elements 6 are non-fixed and changeable (i.e. , subject to change when feedback control deems this necessary). The feedback control unit 10 may be arranged to apply the continuous control (e.g., adjustment) of the respective electric currents by calculating adjustments to the electric currents using the orthogonal projection algorithm as based on orthogonal basis set, and by adjusting the electric currents accordingly.

[0099] In this way, an external magnetic field (e.g., a geomagnetic field) may be nulled or cancelled. An external gradient magnetic field may be nulled or cancelled, or an external time varying magnetic field may be nulled or cancelled.

[0100] A 3D visualisation of a similar coil array nulling action is shown in Figure 3 (generated by calculation / simulation) according to embodiments of the invention. The surface height in Figure 3 represents magnetic flux density. A coil array with 252 coils was used with a diameter of 1 m in Figure 3. A 50pT uniform field was cancelled inside the coil to negligible values. The vector of the magnetic field was parallel to the Y axis. The cross-section through the middle of the coil array, containing the x-y plane at z=0, was taken in Figure 3. A nulled region 34 is clearly seen. A ‘dent’ 36, being one of several dents along the periphery of the nulled region, corresponds to the location on the surface where a magnetic field generating coil is located. This shows how large the nulled region is with the respect to the diameter of the coil array. The ambient external magnetic field 30 is shown by the surface part with 50pT undisturbed field strength. A dip 32 of the field either side of the coil array aligned along the y-axis is a response of cancelling the action of the uniform field which is also directed along the positive y-axis.

[0101] However, as noted above, the magnitude of the magnetic field generated that contributes to the overall nulling effect within the nulling region, is proportional to the magnitude of the drive current I. A current noise, A / , present drive current, will generate a corresponding magnetic field noise, ABpand BZ, in the resulting magnetic field contributed to the overall nulling field by each magnetic field generating coil 8. Moreover, in example of the invention using the calibration process described above, the presence of magnetic field noise, ABpand ABZ, will also influence the calculation of the orthogonal basis that is created in the calibration process and the orthogonal projection method described herein. 8545725

[0102] 15

[0103] Figure 5 and Figure 6 each illustrate a separate respective example of a magnetic field generating element 8 of a magnetic field nulling apparatus according to an example of the invention, together with associated drive current supply parts (42, 44) of the feedback control unit 10 connected to the magnetic field generating element 8 for supplying two drive currents, and I2, to it. This magnetic field generating element is used by the apparatus, along with a plurality of other such magnetic field generating elements, for nulling a magnetic field within a nulling region in an ambient magnetic field comprising as described above. The magnetic field generating element 8 shown in Figure 5, or Figure 6, is one of a plurality of separate such magnetic field generating elements placed at separate respective locations surrounding the nulling region for generating respective nulling magnetic fields extending into the nulling region, as shown in Figure 1 .

[0104] A plurality of the magnetic field sensing elements 6 are also placed at a plurality of respective separate locations within the nulling region for sensing respective values of the magnetic field within the nulling region, as described above, and such as shown in Figure 1 . The feedback control unit 10 controls the values of the respective nulling magnetic fields generated by each of the plurality of magnetic field generating elements 8 in response to values of the magnetic field sensed by the plurality of magnetic field sensing elements by driving the magnetic field generating elements 8 with respective electric drive currents, and I2, that reduce the magnetic field values detected by respective magnetic field sensing elements 6 to values not exceeding a pre-set threshold value. The threshold value may correspond to a pre-set nulling of the magnetic field within the nulling region. For example, the pre-set threshold value may be not greater than 5x109Tesla, or not greater than 5x1010Tesla, such as shown in Figure 4.

[0105] Each of the magnetic field generating elements 8 each comprises a first electromagnetic coil (54, 64) comprising a winding of one single turn, and a second electromagnetic coil 56, comprising a winding of 90-times more turns than are present in the first electromagnetic coil. For example, the second coil comprises a winding of ninety (90) turns in total.

[0106] The feedback control unit 10 comprises a first power control unit 44 comprising a current source including a 16-bit digital-to-analogue converter unit (DAC) 50 for receiving a first digital drive current control signal for input to a first analogue amplifier unit 52 to output a first analogue drive current , Iltinto the first electromagnetic coil (54, 64). The first analogue drive current, Iltis an alternating (AC) electric current having an amplitude of about 54 / zA and a frequency of 2.4 kHz. The first power control unit 44 produces a noise current density of about 240pA / ^Hz.

[0107] The feedback control unit 10 also comprises a second power control unit 42 comprising a current source including a 16-bit digital-to-analogue converter unit (DAC) 46 for receiving a second digital drive current control signal with which to control a second analogue amplifier unit 48 to output a second analogue drive current, I2, into the second electromagnetic coil 56. The second analogue drive current is an alternating (AC) electric current having an amplitude of about 40mA which is about 740 times greater than the amplitude of the first AC drive current, and a frequency of about 30Hz which is about 80 times smaller ( -80) than the value of the frequency of the first AC drive current. The second power control unit 42 8545725

[0108] 16 produces a noise current density of about 96pA / ^Hz. This is about 2.5 times lower than the noise current density produced by the first power control unit.

[0109] As noted above, the magnetic flux density B spatial distribution generated by a circular coil comprising a winding having N turns and driven by a drive current I, is expressed in cylindrical coordinates as follows:

[0110] The field flux density is directly proportional to the drive current I and the number of turns in the coil, N. Thus, a current noise A / produces a magnetic noise AB a N I.

[0111] Thus, because the number or turns on the first electromagnetic coil (54, 64) is ninety times less than the number or turns on the second electromagnetic coil 56, this reduces magnitude of the magnetic field generated by the first current flowing through the first electromagnetic coil, relative to the magnitude of the magnetic field generated by the second current flowing through the second electromagnetic coil, by a factor of 90. Consequently, the equivalent current noise density for magnetic noise is:

[0112] 240 / 90pA / ^Hz = 2.7pA / ^Hz.

[0113] The current noise density for magnetic noise for each turn of the N = 90 turns in the second electromagnetic coil individually is:

[0114] 96 / 90pA / ^Hz = 1 ,07pAA / Hz.

[0115] However, the cumulative noise of the N = 90 turns of the second electromagnetic coil in full is:

[0116] 90x96 / 90pA / Hz = 96pA / Hz.

[0117] The combined noise figure for the first and second electromagnetic coils is given by the square-root of the sum of the squared values of the individual current noise density values, giving the equivalent current noise density for magnetic noise in the two could combined is as follows:

[0118] ^(962+ 2.72) = 96.04pAA / Hz

[0119] By contrast to this, if the magnetic field generating element 8 of the magnetic field nulling apparatus had been provided with only the second coil 56, with the first coil omitted as shown in Figure 7, and the first and second power control units, 44, 42, had been configured to drive the second coil with a drive current comprising a combination (superposition) of the first drive current and the second drive current, the result would be that the equivalent current noise density for magnetic noise in second coil 56 (with the first coil absent) would be as follows:

[0120] ^(962+ [90x2.7]2) = 258.5pAA / Hz

[0121] Thus, an arrangement in which both the first current and the second current were driven as one through one 90-turn coil has the effect of dramatically increasing the magnetic noise AB a N I. 8545725

[0122] 17

[0123] Consequently, the first and second electromagnetic coils of a given magnetic field generating element according to the invention are, by contrast, each driven by a suitably chosen drive current, in which both the frequency and the amplitude of the AC drive current delivered to the respective one of the first and second coils is best suited for the purpose of the coil in question. The first coil (54, 64) is used for nulling lower-magnitude “quickly-varying” ambient magnetic field variations, and is driven by a lower-amplitude and higher-frequency first analogue drive current, Iltfor this purpose. By contrast, the second coil is used for nulling larger-magnitude “slowly-varying” ambient magnetic field variations, and is driven by a larger- amplitude and lower-frequency second analogue drive current, I2, current for this purpose.

[0124] The first and second electromagnetic coils each comprise electrically conductive coils adapted for conducting the electric drive currents. The coil structures or designs may be solenoids, flat spiral coils, or similar designs. The first and second electromagnetic coils are co-located in a space surrounding the nulling region so that the component nulling magnetic fields generated by the two electromagnetic coils each extend into the nulling region from substantially the same location. The first electromagnetic coil and the second electromagnetic coil in each of the examples shown in Figure 5 and Figure 6 are connected to a common electrical ground terminal.

[0125] For example, as shown in Figure 6, the turns first and second electromagnetic coils of a given magnetic field generating element may comprise one common winding (64, 56) comprising both the turns in the second electromagnetic coil 56 and the one turn in the first electromagnetic coil 64. The first ninety turns 56 in the second electromagnetic coil are succeeded by the one turn 64 in the first electromagnetic coil of a common winding having ninety-one turns. Accordingly, the windings of the first and second electromagnetic coils share one shared turn 64 in common. The feedback control unit is configured to drive the shared turn 64 with a shared alternating electric current comprising a superposition of the alternating electric currents having the first frequency and the second frequency. The first power control 44 unit is connected electrically to the common winding (64, 56) by a tapped connection 62 at a location between successive turns of the common winding such that first electromagnetic coil comprises the terminal (i.e. , final) turn of the common winding.

[0126] The plurality of magnetic field generating elements 8 are arranged at their separate respective locations in a first array shaped according to a three-dimensional spherical reference surface surrounding the nulling region, as shown in Figure 1. The plurality of magnetic field sensing elements 6 are arranged at their separate respective locations defining a second array shaped according to a three-dimensional spherical reference surface, also shown in Figure 1 . The second array is substantially concentric with the first array. The inventors have found that this concentricity improves nulling performance. The plurality of magnetic field generating elements 8 are arranged at their separate respective locations substantially equidistant from the centre of the nulling region thereby defining a substantially spherical array surrounding the nulling region.

[0127] The plurality of magnetic field sensing elements are also arranged at their separate respective locations substantially equidistant from the centre of the nulling region thereby defining a substantially spherical 8545725

[0128] 18 array within the nulling region. The inventors have found that this concentricity improves nulling performance. The size of a diameter of the array of magnetic field sensing elements may be at least 30% of the size of a diameter of the array of magnetic field generating elements. The inventors have found that this concentricity improves nulling performance. The separate respective locations in the first array and or the second array may be defined according to a respective regular lattice. The plurality of magnetic field generating elements may comprise at least 10, or at least 50, or at least 200 separate magnetic field generating elements.

[0129] The features disclosed in the foregoing description, or in the following claims, or in the accompanying drawings, expressed in their specific forms or in terms of a means for performing the disclosed function, or a method or process for obtaining the disclosed results, as appropriate, may, separately, or in any combination of such features, be utilised for realising the invention in diverse forms thereof.

[0130] While the invention has been described in conjunction with the exemplary embodiments described above, many equivalent modifications and variations will be apparent to those skilled in the art when given this disclosure. Accordingly, the exemplary embodiments of the invention set forth above are considered to be illustrative and not limiting. Various changes to the described embodiments may be made without departing from the spirit and scope of the invention.

[0131] For the avoidance of any doubt, any theoretical explanations provided herein are provided for the purposes of improving the understanding of a reader. The inventors do not wish to be bound by any of these theoretical explanations.

[0132] Any section headings used herein are for organizational purposes only and are not to be construed as limiting the subject matter described.

[0133] Throughout this specification, including the claims which follow, unless the context requires otherwise, the word “comprise” and “include”, and variations such as “comprises”, “comprising”, and “including” will be understood to imply the inclusion of a stated integer or step or group of integers or steps but not the exclusion of any other integer or step or group of integers or steps.

[0134] It must be noted that, as used in the specification and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Ranges may be expressed herein as from “about” one particular value, and / or to “about” another particular value. When such a range is expressed, another embodiment includes from the one particular value and / or to the other particular value. Similarly, when values are expressed as approximations, by the use of the antecedent “about,” it will be understood that the particular value forms another embodiment. The term “about” in relation to a numerical value is optional and means for example + / - 10%. 8545725

[0135] 19

[0136] References

[0137] A number of publications are cited above in order to more fully describe and disclose the invention and the state of the art to which the invention pertains. Full citations for these references are provided below. The entirety of each of these references is incorporated herein.

[0138] [1] “Closed-form expressions for the magnetic fields of rectangular and circular finite-length solenoids and current loops"', by S. Hampton; R. A. Lane; R. M. Hedlof; R. E. Phillips; C. A. Ordonez: AIP Advances 10, 065320 (2020)

[0139] [2] W02023 / 079081 A1 (Shimadzu Corporation)

Claims

854572520Claims:1 . An apparatus for nulling a magnetic field within a nulling region in an ambient magnetic field comprising: a plurality of separate magnetic field generating elements placed at separate respective locations surrounding the nulling region for generating respective nulling magnetic fields extending into the nulling region; a plurality of magnetic field sensing elements placed at a plurality of respective separate locations within the nulling region for sensing respective values of the magnetic field within the nulling region; a feedback control unit for controlling the values of the respective nulling magnetic fields generated by each of the plurality of magnetic field generating elements in response to values of the magnetic field sensed by the plurality of magnetic field sensing elements by driving the magnetic field generating elements with respective electric currents that reduce the magnetic field values detected by respective magnetic field sensing elements to values not exceeding a pre-set threshold value corresponding to a pre-set nulling of the magnetic field within the nulling region; wherein one or more of said magnetic field generating elements each comprises a first electromagnetic coil comprising a winding of one or more turns and a second electromagnetic coil comprising a winding of more turns than are present in the first electromagnetic coil; and, wherein the feedback control unit is configured to drive the first electromagnetic coil with alternating electric currents having a first frequency, and to drive the second electromagnetic coil with alternating electric currents having a second frequency that is lower than the first frequency.

2. An apparatus according to any preceding claim wherein the first frequency exceeds the second frequency by a factor of between 50 and 150.

3. An apparatus according to any preceding claim wherein the first frequency does not exceed about 10 kHz.

4. An apparatus according to any preceding claim wherein the second frequency does not exceed about 100Hz.

5. An apparatus according to any preceding claim wherein the number of turns in the second electromagnetic coil exceeds the number of turns in the first electromagnetic coil by a factor of between 50 and 150.

6. An apparatus according to any preceding claim wherein the number of turns in the first electromagnetic coil comprises not more than one turn.

7. An apparatus according to any preceding claim wherein the windings of the first and second electromagnetic coils share one or more turns in common and wherein the feedback control unit is configured to drive the shared turns with a shared alternating electric current comprising a854572521 superposition of said alternating electric currents having said first frequency and said second frequency.

8. An apparatus according to any preceding claim wherein the plurality of magnetic field generating elements are arranged at said separate respective locations in a first array shaped according to a three-dimensional reference surface surrounding the nulling region.

9. An apparatus according to any preceding claim wherein the plurality of magnetic field sensing elements are arranged at said separate respective locations defining a second array shaped according to a three-dimensional reference surface.

10. An apparatus according to claim 8 and claim 9 wherein the second array is configured to be substantially concentric with the first array.11 . An apparatus according to any of claims 8 to 10 wherein said separate respective locations in the first array are defined according to a regular lattice.

12. An apparatus according to any of claims 8 to 11 wherein said separate respective locations in the second array are defined according to a regular lattice.

13. An apparatus according to any preceding claim wherein the plurality of magnetic field generating elements are arranged at said separate respective locations substantially equidistant from the centre of the nulling region thereby defining a substantially spherical array surrounding the nulling region.

14. An apparatus according to any preceding claim wherein the plurality of magnetic field sensing elements are arranged at said separate respective locations substantially equidistant from the centre of the nulling region thereby defining a substantially spherical array within the nulling region.

15. An apparatus according to any preceding claim wherein the size of a diameter of the array of magnetic field sensing elements is at least 30% of the size of a diameter of the array of magnetic field generating elements.

16. An apparatus according to any preceding claim wherein the plurality of magnetic field generating elements comprises at least 10, or at least 50, or at least 200 separate magnetic field generating elements.

17. An apparatus according to any preceding claim wherein the threshold value is not greater than 5x10-9Tesla.

18. An apparatus according to any preceding claim wherein the threshold value is not greater than 5x10_10Tesla.85457252219. A method for nulling a magnetic field within a nulling region in an ambient magnetic field comprising: providing a plurality of separate magnetic field generating elements placed at separate respective locations surrounding the nulling region for generating respective nulling magnetic fields extending into the nulling region; providing a plurality of magnetic field sensing elements placed at a plurality of respective separate locations within the nulling region for sensing respective values of the magnetic field within the nulling region; controlling the values of the respective nulling magnetic fields generated by each of the plurality of magnetic field generating elements in response to values of the magnetic field sensed by the plurality of magnetic field sensing elements by driving the magnetic field generating elements with respective electric currents that reduce the magnetic field values detected by respective magnetic field sensing elements to values not exceeding a pre-set threshold value corresponding to a pre-set nulling of the magnetic field within the nulling region; wherein one or more of said magnetic field generating elements each comprises a first electromagnetic coil comprising a winding of one or more turns and a second electromagnetic coil comprising a winding of more turns than are present in the first electromagnetic coil; and, wherein said driving comprises driving the first electromagnetic coil with alternating electric currents having a first frequency and driving the second electromagnetic coil with alternating electric currents having a second frequency that is lower than the first frequency.

20. A method according to claim 19 wherein the first frequency exceeds the second frequency by a factor of between 50 and 150.

21. A method according to claim 19 or claim 20 wherein the first frequency does not exceed about 10 kHz.

22. A method according to any of claims 19 to 21 wherein the second frequency does not exceed about 100Hz.

23. A method according to any of claims 19 to 22 wherein the windings of the first and second electromagnetic coils share one or more turns in common and the method comprises driving the shared turns with a shared alternating electric current comprising a superposition of said alternating electric currents having said first frequency and said second frequency.

24. A method according to any of claims 19 to 23 including providing the plurality of magnetic field generating elements as arranged at said separate respective locations in a first array shaped according to a three-dimensional reference surface surrounding the nulling region.85457252325. A method according to any of claims 19 to 24 including providing the plurality of magnetic field sensing elements as arranged at said separate respective locations defining a second array shaped according to a three-dimensional reference surface.

26. A method according to claim 24 and claim 25 including providing the second array as substantially concentric with the first array.

27. A method according to any of claims 19 to 26 wherein said separate respective locations in the first array are defined according to a regular lattice.

28. A method according to any of claims 19 to 27 wherein said separate respective locations in the second array are defined according to a regular lattice.

29. A method according to any of claims 19 to 28 including providing the plurality of magnetic field generating elements as arranged at said separate respective locations substantially equidistant from the centre of the nulling region thereby defining a substantially spherical array surrounding the nulling region.

30. A method according to any of claims 19 to 29 including providing the plurality of magnetic field sensing elements as arranged at said separate respective locations substantially equidistant from the centre of the nulling region thereby defining a substantially spherical array within the nulling region.31 . A method according to any of claims 19 to 30 wherein the size of a diameter of the array of magnetic field sensing elements is at least 30% of the size of a diameter of the array of magnetic field generating elements.

32. A method according to any of claims 19 to 31 including providing the plurality of magnetic field generating elements to comprise at least 10 separate magnetic field generating elements.

33. A method according to any of claims 19 to 32 including providing the plurality of magnetic field generating elements to comprise at least 50 separate magnetic field generating elements.

34. A method according to any of claims 19 to 33 including providing the plurality of magnetic field generating elements to comprise at least 200 separate magnetic field generating elements.

35. A method according to any of claims 19 to 34 wherein the threshold value is not greater than 5x10-9Tesla.

36. A method according to any of claims 19 to 35 wherein the threshold value is not greater than 5x1010Tesla.

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