WO2006061618A1

WO2006061618A1 - Planar magnet arrangement for nuclear magnetic resonance

Info

Publication number: WO2006061618A1
Application number: PCT/GB2005/004711
Authority: WO
Inventors: Peter Simon Aptaker; Peter John Mcdonald
Original assignee: University Of Surrey
Priority date: 2004-12-08
Filing date: 2005-12-08
Publication date: 2006-06-15
Also published as: GB0426957D0

Abstract

An NMR apparatus (300) has a magnet arrangement (301) comprising three permanent magnets (302, 303, 304). The magnets (302, 303, 304) are arranged along a line with the central magnet (303) having its S pole facing upwards and the two other magnets (302, 304) having their N poles facing upwards to generate a magnetic field Bo. Two probe coils (306, 307) are positioned over the magnets (302, 303, 304). The centre of each of the coils (306, 307) is between a respective adjacent pair of the magnets (302, 303, 304), substantially equidistant from the centre of the pole at the top of each magnet (302, 303, 304) of the pair. The probe coils (306, 307) are connected to an electrical power source (not shown) in opposing directions such that when a current is passed though them by the power source, they generate a magnetic field B, that has opposing directions at the centre of each coil (306, 307) creating effective N and S poles offset from the poles of the magnets (302, 303, 304) of the magnet arrangement (301). The magnets (302, 303, 304) of the magnet arrangement (301) and probe coils (306, 307) are arranged such that the magnetic fields Bo, B1, they generate vary in strength only with height above the magnet arrangement (301) and vary in direction sinusoidally along the line of the magnet arrangement (301) orthogonal to one another in a sample volume, facilitating NMR measurement.

Description

PLANAR MAGNET ARRANGEMENT FOR NUCLEAR MAGNETIC RESONANCE

Field of the Invention

This invention relates to an apparatus and method for Nuclear

Magnetic Resonance (NMR). A particular, but not exclusive, application of the invention is depth resolved NMR spectroscopy in a substantially planar sample volume using an one sided NMR apparatus.

Background to the Invention

NMR makes use of the fact that atomic nuclei tend to align themselves with a magnetic field. More specifically, atomic nuclei in a magnetic field B₀ precess about the magnetic field B₀ at a defined frequency, known as the Larmor frequency ω, which is directly proportional to the strength of the magnetic field B₀.

Most NMR applications target hydrogen nuclei, for which the Larmor frequency ω tends to be in the radio spectrum for magnetic fields B₀ of typical strength. In the presence of a radio frequency (RF) pulse having a frequency approximately the same as the Larmor frequency ω and a component of magnetic field B₁ pointing in a different direction to the magnetic field B₀, hydrogen nuclei experience a torque that causes them to change their angle relative to the magnetic field B₀ away from equilibrium. After the RF pulse, the hydrogen nuclei precess about the magnetic field B₀ and revert to equilibrium unless acted on by further RF pulses. The way in which these changes occur is indicative of various properties of the molecular environment of the hydrogen nuclei and the microstructural properties of material in which they are situated. For example, immediately after application of a single RF pulse, the hydrogen nuclei precess in phase and it takes a period, known as the spin-spin relaxation time T₂, for this phase coherence to be lost. Similarly, after a longer period, known as the spin- lattice relaxation time T₁, the hydrogen nuclei return to thermal equilibrium. These periods and other similar characteristics can be measured by detecting RF signals emanating from the hydrogen nuclei in response to one or more RF pulses applied to them.

Overriding difficulties in virtually all NMR applications are the generation of a suitable magnetic field B₀ and suitable RF pulses. In order to resolve hydrogen nuclei in a sample material, the magnetic field B₀ is usually arranged to vary in strength across a sample, e.g. to have a gradient, and is hence usually referred to as a "gradient magnetic field". This variation in magnetic field strength means that hydrogen nuclei in different parts of the sample have different Larmor frequency ω indicative of their position. Moreover, if desired, they can be selectively addressed by RF pulses of an appropriate frequency. At the same time, the magnetic field Bi of the RF pulse must apply the same torque to all the hydrogen nuclei in the selectively addressed part of the sample. This means, in particular, that the orientation of the magnetic field B₁ of the RF pulse to the gradient magnetic field B₀ must be constant over the part of the sample being addressed. In order to achieve this, the magnetic fields B₀ and B-i are usually arranged to have constant direction throughout the sample. In particular, the gradient magnetic field B₀ is typically generated by creating a homogeneous magnetic field using one or more suitably arranged strong permanent magnets or current loops and applying a gradient to the field using separate so-called gradient magnets or current loops. For example, one of the most widely recognised applications of NMR is imaging, i.e. Magnetic Resonance Imaging (MRI), for medical use. A typical medical MRI scanner comprises one or more large superconducting coils that generate a large magnetic field that is largely homogeneous in a cylinder coaxial with and at the centre of the coil(s). This cylinder is the region of an MRI scanner in which a patient is positioned during medical imaging. A gradient can be applied to the magnetic field using suitably positioned supplementary coils. Indeed, in a typical medical MRI scanner, supplementary coils allow a gradient to be selectively applied in any direction across the cylinder of homogeneous magnetic field. This allows hydrogen nuclei in slices of the cylinder that have any orientation, or larger volumes, to be selectively addressed by appropriate RF pulses.

However, the present invention is particularly concerned with one sided NMR, which is a class of NMR applications that use NMR to analyse samples external to and on one side of an NMR apparatus. In other words, the sample site is generally accessible through a polar angle of substantially 360° and an angle of substantially 180° azimuthally with respect to the NMR apparatus. This allows NMR to be performed on large objects that would not fit in a conventional medical MRI scanner or on samples in situ. However, generation of a homogeneous magnetic field B₀ on one side of an NMR apparatus is particularly difficult. US 6208142 describes a one-sided medical MRI scanner. The scanner has coils arranged in the conventional way to generate a cylinder of homogeneous magnetic field. However, so-called shim coils are added to shift the cylinder axially out from the centre of the coils. The arrangement is not perfect; a cylinder of magnetic field, referred to as a sweet spot, having a direction parallel to the axis of the coils and a small gradient in that direction is created, but the cylinder is relatively small and the gradient means that only slices normal to the magnetic field direction can be resolved. This apparatus is also still of comparable size to a conventional MRI scanner and could not be used out of the laboratory, e.g. as a mobile apparatus.

US 6489872 describes a permanent magnet for an NMR apparatus in the shape of a hollow cylinder and having its direction of magnetisation along the main axis of the cylinder. This magnet generates a magnetic field with an area of relative homogeneity, again referred to as a sweet spot, coaxial with the main axis of the cylinder and spaced away from one of its ends. The sweet spot is therefore in a similar position to that generated by the apparatus described in US 6208142, but in this case the magnetic field at the sweet spot is homogeneous in both direction and strength. This allows hydrogen nuclei throughout the whole sweet spot to be addressed together to yield a single NMR signal. Alternatively, extra coils can be used to selectively generate a gradient in the magnetic field at the sweet spot and address hydrogen nuclei in different parts of the sweet spot as desired.

One problem with all these existing one-sided NMR apparatus is that they lack planar resolution. More specifically, to resolve atomic nuclei in thin slices of a sample, the magnetic field must have a large gradient, but there is a limit to the gradient that can be induced in the field at the sweet spot of these NMR apparatus without loss of directional homogeneity.

All of the magnet arrangements discussed above have circular symmetry. However, it is possible to generate a magnetic field with an area of relative homogeneity using linearly arranged magnets that has reasonable planar resolution. For example, a typical so-called NMR-MOUSE^® comprises two magnets arranged side by side in a plane, one with its N pole facing up and one with its S pole facing up. Between the magnets is a small coil oriented to generate a magnetic field in a direction that is normal to the plane. So, in a small volume above the plane and between the magnets, the magnetic field generated by the magnets is roughly horizontal in direction and the magnetic filed generated by the coil is roughly vertical in direction. Nuclear magnetic resonance measurements can therefore be extracted from this volume. The paper "3D imaging with a single sided sensor: an open tomography", J Perlo et al, Journal of Magnetic Resonance 166 (2004) pp 228-235, seeks to improve the NMR-MOUSE^® by adding two coils between the poles of the permanent magnet for generating a variable gradient in the magnetic field in the volume to assist NMR imaging. However, the volume from which NMR measurements can be extracted still remains fairly small. One type of NMR apparatus that has excellent planar resolution uses a so-called GARfield magnet, as described, for example, in the paper "A Novel High Gradient Permanent Magnet for Imaging Planar Thin Films", P.M. Glover et al, Journal of Magnetic Resonance, 139, 90 (1999). The GARfield magnet comprises two permanent magnets arranged so that the north (N) pole of one magnet is on one side of a sample site and the south (S) pole of the other magnet is on the other side of the sample site. Lines of flux between the magnets therefore extend from one side of the sample site to the other, very roughly horizontally when the apparatus is oriented for use. Between each of the poles and the sample site is a steel pole piece shaped to follow a contour of constant magnetic scalar potential. The pole pieces cause the strength of the magnetic field at the sample site to be constant (although the direction varies) in any plane of the sample site that is horizontal in use and to have a gradient in the vertical direction. However, a problem with the GARfield magnet is that the sample site is between the pole pieces. The GARfield magnet is not therefore suitable for use in a one sided NMR apparatus and it cannot be used to analyse large samples or samples in situ.

The present invention seeks to overcome these problems.

Summary of the Invention

According to a first aspect of the present invention, there is provided a nuclear magnetic resonance apparatus comprising: a substantially planar magnet arrangement comprising a plurality of magnets arranged substantially along a line with their magnetic dipoles oriented substantially perpendicular to and around an axis, which axis is parallel to the plane of the magnet arrangement and orthogonal to the line along which the magnets are arranged, and varying in direction periodically along the line in order to generate a gradient magnetic field that has substantially constant strength parallel to the plane of the magnet arrangement in a sample volume; and a complementary probe comprising a plurality of coils also arranged substantially along the line with their magnetic dipoles oriented substantially perpendicular to and around the axis and varying in direction periodically along the line in order to generate an excitation magnetic field that also has substantially constant strength parallel to the plane of the magnet arrangement in the sample volume, wherein the variation in the direction of the magnetic dipoles of the magnets has substantially the same period but is offset from the variation in the direction of the magnetic dipoles of the coils so that the gradient magnetic field is substantially orthogonal to the excitation magnetic field throughout the sample volume.

Also, according to a second aspect of the present invention, there is provided a method of nuclear magnetic resonance comprising: generating a gradient magnetic field using a substantially planar magnet arrangement comprising a plurality of magnets arranged substantially along a line with their magnetic dipoles oriented substantially perpendicular to and around an axis, which axis is parallel to the plane of the magnet arrangement and orthogonal to the line along which the magnets are arranged, and varying in direction periodically along the line so that the generated gradient magnetic field has substantially constant strength parallel to the plane of the magnet arrangement in a sample volume; and generating an excitation magnetic field using a complementary probe comprising a plurality of coils also arranged substantially along the line with their magnetic dipoles oriented substantially perpendicular to and around the axis and varying in direction periodically along the line so that the generated excitation magnetic field also has substantially constant strength parallel to the plane of the magnet arrangement in the sample volume, wherein the variation in the direction of the magnetic dipoles of the magnets has substantially the same period but is offset from the variation in the direction of the magnetic dipoles of the coils so that the gradient magnetic field is substantially orthogonal to the excitation magnetic field throughout the sample volume. Like the GARfield magnet, this magnet arrangement may provide a magnetic field that varies in strength in a single direction (normal to the plane of the magnet arrangement), but that has large variation in direction. The variation in directional homogeneity does not preclude nuclear magnet resonance measurement, as the complementary coil generates an excitation magnetic field (e.g. RF pulses) that, whilst also having large variation in direction, is perpendicular to the gradient magnetic field throughout the sample volume and has a strength gradient in the same direction. This allows NMR measurements to be performed over a sample volume that is relatively large with excellent planar resolution. The magnet arrangement may take a variety of precise forms. For example, the magnets might have different strengths and groups of adjacent magnets might have their magnetic dipoles oriented in the same direction. However, it is preferred that the magnetic dipoles of the magnets are each oriented one to the next by an equal angle. This angle might be say 45°, 90° or 180°. It is particularly preferred that the magnetic dipoles of adjacent magnets are oriented alternately between opposing directions orthogonal to the plane of the magnet arrangement. In this example, the magnetic dipoles are also typically all equal in strength.

The magnet arrangement is usually adapted maximise the sample volume. In particular, the magnets are spaced apart from one another along the line along which they are arranged. For example, the magnets may be spaced apart from one another by around a half of their width parallel to the line along which they are arranged. Similarly, the magnets may be longer in a direction perpendicular to the line along which they are arranged than parallel to the line. The magnets at each end of the magnet arrangement may also be wider parallel to the line along which they are arranged, stronger and/or thicker orthogonal to the plane of the magnet arrangement, than (the) other magnet(s) of the arrangement. Nonetheless, the magnet arrangement typically defines a surface and the sample volume is spaced away from the surface.

The magnets themselves are usually each permanent magnets. For example, the permanent magnets may each comprise a rare earth permanent magnet material. However, where the magnetic dipoles of adjacent magnets are oriented alternately between opposing directions orthogonal to the plane of the magnet arrangement, the magnets may each comprise: a permanent magnet block; and a pole piece of highly permeable magnetic material contoured substantially to follow a surface of constant magnetic scalar potential which is a Fourier exponential solution of the magnetic Laplace equation in air in Cartesian coordinates utilising only one fundamental trigonometric harmonic in the direction of the line of magnets and which is constant in a direction parallel to the plane of the magnet arrangement and orthogonal to the line along which the magnets are arranged.

The magnet arrangement may have any number of magnets. However, the applicants have identified that three magnets are sufficient to provide a substantial sample volume that is not overwhelmed by edge effects. At the same time, minimising the number of magnets makes the magnet arrangement simpler and cheaper to implement. In particular, it can help to minimise the weight of an NMR apparatus, which can make the apparatus more portable. It is therefore particularly preferred that the magnet arrangement comprises only the three magnets for generating the magnetic field. In the preferred embodiment, the magnet arrangement may have a backing plate of magnetically permeable material covering the back of the magnets, opposite to the sample volume, for containing the magnetic field generated at the back of the magnets.

The complementary probe typically comprises a number of coils equal to a number of half periods of variation in the direction of the magnetic dipoles of the magnets. More specifically, the complementary probe may have one less coil than the total number of magnets of the arrangement, e.g. only two coils. The coils are usually positioned substantially between the surface formed by the magnet arrangement and the sample volume. Similarly, the coils are usually substantially planar and parallel to the plane of the magnet arrangement. The apparatus may also have an electrically conductive but non-ferromagnetic shielding plate between the coils and the magnets. The coils may also be adapted to vary the size of the sample volume. In particular, a period of variation in direction of the magnetic dipoles of the coils can be reduced at each end of the complementary probe. This truncates the sample volume along the line along which the magnets are arranged. On the other hand, the coils may have windings spaced to provide a substantially sinusiodally varying current density along a/the line along which the magnets are arranged. This can increase the size of the sample volume in a direction orthogonal to the plane of the magnet arrangement. Likewise, each of the magnets and coils usually transects approximately the same area parallel to the plane of the magnet arrangement proximal to the sample volume. This also increases the size of the sample volume and is considered to be new by itself.

According to a third aspect of the present invention, there is therefore provided a nuclear magnetic resonance apparatus comprising: a magnet arrangement comprising a plurality of magnets for generating a magnetic field in a sample volume on one side of the magnets; and a complementary probe comprising one or more coils between the magnets and the sample volume for generating an excitation magnetic field in the sample volume, wherein the surface area transected by each of the magnets and the coils in the direction of the sample volume is approximately the same. Other features of the apparatus can include: a modulation coil positioned around each of the magnets to modulate the magnetic field produced by the magnets; and/or the magnet arrangement and the complementary probe being mounted in a housing such that they can be moved together in relation to the housing parallel to the main directions of magnetisation of the magnets to change the elevation of the sample volume with respect to the housing. The modulation coils are particularly useful for Continuous Wave nuclear magnetic resonance, as they allow audio frequency modulation of the gradient magnetic field generated by the magnet arrangement. The moveable mounting is useful for adjusting the height of the magnet arrangement and probe in relation to a sample fixed relative to the housing. According to a fourth aspect of the present invention, there is provided a substantially planar nuclear magnetic resonance apparatus having a magnetic field that is substantially constant in strength parallel to the plane of the apparatus and varies in direction by around 180° or more throughout a sample volume. Indeed, the magnetic field may vary in direction through 360° throughout the sample volume and preferably varies substantially sinusiodally in direction.

Finally, according to a fifth aspect of the present invention, there is provided a magnet arrangement for a nuclear magnetic resonance apparatus comprising three or more magnets arranged substantially in a line with their main directions of magnetisation oriented around and substantially orthogonal to an axis perpendicular to the line so as to generate a magnetic field that varies in strength only substantially perpendicular to a plane defined by the axis and the line throughout a sample volume.

Preferred embodiments of the invention are now described, by way of example only, with reference to the accompanying drawings. Brief Description of the Drawings

Figure 1 is a schematic illustration of an infinite sinusoidal current sheet on which the invention is based; and

Figures 2a to 2e are schematic illustrations of permanent magnet arrangements suitable for implementing the invention;

Figure 3 is a schematic illustration of a first embodiment of an NMR apparatus according to the invention; Figure 4 is a cross-sectional view of the NMR apparatus of figure 3 showing lines of magnetic flux for the magnetic fields generated by the apparatus;

Figure 5 is a plan view of the NMR apparatus of figure 3;

Figure 6 is a plan view of an alternate embodiment of a probe coil for the NMR apparatus of figure 3;

Figure 7 is a schematic graphical illustration of magnetic field strength for the magnetic fields generated by the apparatus of figure 3;

Figure 8 is a schematic graphical illustration of magnetic field strength for the magnetic fields generated by a modified version of the apparatus of figure 3;

Figure 9 is a photograph of an implementation of the apparatus of figure 3 mounted in a housing;

Figure 10 is an illustration of a version of the NMR apparatus of figure 3 modified for Continuous Wave NMR; Figure 11 is an illustration of a line of constant magnetic scalar potential of a magnetic field generated by a magnet arrangement upon which another embodiment of the invention is based; and

Figure 12 is an illustration of the embodiment of the invention based the line of constant magnetic scalar potential of figure 11.

Detailed Description of the Preferred Embodiments

Infinite Sinusoidal Current Sheet The invention can be best understood by considering an infinite planar current sheet 100 in a Cartesian coordinate system, as shown in figure 1. The current flows parallel to the x axis (which is referred to as depth in this document), but varies in magnitude and direction sinusiodally along the z axis (which is referred to as width in this document). Such a current sheet 100 generates a magnetic field (not shown), which is defined by

Laplace's equations. More specifically, the solution to Laplace's equations for the current sheet 100 gives a magnetic scalar potential φ(z, y) = a sin(fe) exp(-όy) ( 1 )

where a is a constant depending on, inter alia, the magnitude of the current and b is a variable equal to 2π divided by the period of variation of the current (which is identical to 2π divided by the period of variation in the magnetic field generated by the current sheet 100). This gives, in turn, magnetic field components B₂ , B_y , along the z axis and the y axis (which is

referred to as height in this document) respectively, of B₂ = ^- = ab cosibz) exp(-όy) (2) dz and

B = -Ψ- = -ab sin(δz) exp(-by) (3)

Sy

The magnetic field does not have a component along the x axis. From equations (2) and (3), it can be appreciated that the modulus (or strength) of the magnetic field is a function only of distance along the y axis, e.g. away from the plane of the current sheet 100, or

B\ = abexp(-by) (4)

In other words, the strength of the magnetic field is constant in any plane parallel to the plane of the current sheet 100, but decreases exponentially in strength along the z axis away from the current sheet 100.

Of course, this is not so for the direction of the magnetic field which varies sinusoidally through 360° perpendicular to the direction of the current, e.g. perpendicular to the x axis or in a plane defined by the y and z axes, as a function of distance along the z axis.

Permanent Magnet Approximation of Current Sheet 100

It is not possible to replicate exactly the infinite current sheet 100 in a real apparatus. Rather, the invention typically has a magnet arrangement comprising a plurality of magnets arranged to approximate the current sheet 100. In some embodiments, the magnets might be current loops, e.g. electromagnetic windings and in particular superconducting electromagnetic windings. However, in the embodiments described below, the invention is implemented using permanent magnet blocks. These might be blocks of ferrite, bonded or sintered rare earth magnetic material. In particular, the rare earth magnetic material can be Neodymium Iron Boron (NdFeB) or Samarium Cobalt (SmCo(1 :5) or SmCo(2:17)).

A permanent magnet block is roughly equivalent to a loop of current running around the direction of magnetisation of the magnet block in an anticlockwise direction when viewed from the north (N) pole at the perimeter of the magnet block. When several such magnet blocks are placed in a line, next to one another, with their directions of magnetisation at particular orientations, their effective current loops can approximate the current sheet 100 illustrated in figure 1.

Five embodiments of such magnet arrangements are illustrated with reference to figures 2a to 2e. For initial purposes, the magnet arrangements 200, 210, 220, 230, 240 of figures 2a to 2e are considered to comprise an infinite number of permanent magnet blocks 201 , 202, 211 , 221 , 231 , 241 arranged side by side along the z axis, e.g. along the width of the arrangements 200, 210, 220, 230, 240, and to have infinite dimensions along the x axis, e.g. infinite depth. The magnets 201 , 202, 211 , 221 , 231 , 241 can therefore be considered each to form an infinite plane defined by the x and z axes. For example, referring to figure 2a, in a first embodiment of the invention, a magnet arrangement 200 has a plurality magnet blocks 201 , 202 having a higher or lower strength of magnetisation and spacer blocks 203 of magnetically impermeable material, such as aluminium. All the blocks 201 , 202, 203 have equal width and are arranged periodically along the width of the arrangement 200, in a sequence comprising: 1) a higher strength magnet block 201 oriented with a South (S) pole lowest and a North (N) pole highest (e.g. at the bottom and top of the magnet arrangement 200 respectively as seen in the drawing); 2) a lower strength magnetic block 202 oriented in the same direction; 3) a spacer block 203; 4) a lower strength magnetic block 202 oriented in the opposing direction; 5) a higher strength magnetic block 201 oriented in the opposing direction; 6) another lower strength magnetic block 202 oriented in the opposing direction; 7) a spacer block 203; and 8) another lower strength magnetic block 202 oriented in the same direction. The sequence then repeats. Referring to figure 2b, in a second embodiment of the invention, a magnet arrangement 210 comprises a plurality of permanent magnet blocks 211 of equal width arranged side by side along the width of the arrangement 210. Adjacent magnet blocks 211 are oriented so that their directions of magnetisation are rotated with respect to one another by increments of 45° around the x axis (e.g. around an axis parallel to a plane defined by the magnet arrangement 210 and orthogonal to the width of the magnet arrangement 210). In this embodiment, the angle of orientation progresses anti-clockwise from left to right along the width of the magnet arrangement 210 as seen in the drawing, but this direction is arbitrary and clockwise rotation would be equivalent.

Referring to figure 2c, in another embodiment of the invention, a magnet arrangement 220 again comprises a plurality of permanent magnet blocks 221 of equal width arranged side by side along the width of the arrangement 220. Adjacent magnet blocks 221 are oriented so that their directions of magnetisation are rotated with respect to one another by increments of 90° around the x axis. Again, in this embodiment, the angle of orientation progresses anti-clockwise from left to right along the width of the magnet arrangement 210 as seen in the drawing, but this direction is arbitrary and clockwise rotation would be equivalent. Referring to figure 2d, in another embodiment of the invention, a magnet arrangement 230 again comprises a plurality of permanent magnet blocks 231 of equal width arranged side by side along the width of the arrangement 230. Adjacent magnet blocks 231 are oriented so that their directions of magnetisation are coaxial and rotated with respect to one another by increments of 180° around the x axis. In other words, the directions of magnetisation of adjacent pairs of magnet blocks 231 alternately face toward and away from one another along the width of the magnet arrangement 230.

Referring to figure 2e, in another embodiment of the invention, a magnet arrangement 240 again comprises a plurality of permanent magnet blocks 241 of equal width arranged side by side along the width of the arrangement 240. The magnet blocks 241 are oriented so that adjacent magnet blocks 241 have their directions of magnetisation parallel, side by side and rotated with respect to one another by increments of 180°around the x axis. In other words, the directions of magnetisation of the magnet blocks 241 alternately face up and down (along the y axis) as seen in the drawing.

Each of the magnet arrangements 200, 210, 220, 230, 240 illustrated in figures 2a to 2e generates a magnetic field similar to the magnetic field generated by the current sheet 100 illustrated in figure 1. However, the magnet blocks 201 , 202, 211 , 221 , 231 , 241 each have finite width. The current loops to which they are equivalent likewise therefore have a finite width and an equivalent current sheet made up from these equivalent current loops does not therefore have a current varies exactly sinusiodally along the z axis. This means that the magnet arrangements 200, 210, 220, 230, 240 only approximate the magnetic field generated by the current sheet 100 shown in figure 1 and given by equations (2) and (3).

More specifically, assuming they have odd symmetry about the origin of the z axis, the magnet arrangements 200, 210, 220, 230, 240 can be considered as equivalent to a current sheet having a current density K along the y axis of the general form

From this, it can be shown that, instead of having the "pure" form given in equations (2) and (3), the magnetic field generated by the magnet arrangements 200, 210, 220, 230, 240 includes a number of Fourier harmonics. For example, for the magnet arrangement 240 illustrated in figure 2e, the Fourier harmonics can be given by a Fourier series of the form

cos(fe) + cos(3fe) + cos(5fe).... (6)

The presence of higher order harmonics, e.g. such as those in the series given by equation (6), has a number of results. For example, close to the magnet blocks 201 , 202, 211 , 221 , 231 , 241 along the y axis, e.g. just above the magnet blocks 201 , 202, 211 , 221 , 231 , 241 , the magnetic field is slightly squarer than the functions given by equations (2) and (3). Similarly, the strength of the magnetic field fluctuates slightly along the z axis very close to the magnets 201 , 202, 211 , 221 , 231 , 241. The magnet arrangement 200 illustrated in figure 2a provides a good approximation, but is the most difficult to build due to the need to include magnets of different strengths. In the magnet arrangements 210, 220 illustrated in figures 2b and 2c, the magnetic field is augmented on one side of the arrangement 210, 220 (the upper surface 212, 222 in figures 2b and 2c) and reduced to zero or near zero on the opposing side of the arrangement (the lower surface 213, 223 in figures 2b and 2c). This can be a useful feature, as it avoids the need to use a backing plate or such like to shield the magnetic field away from the active side of an apparatus. The magnet arrangements 230, 240 illustrated in figures 2d and 2e give the worst approximations, but the magnetic fields generated by the magnet arrangements 230, 240 illustrated in figures 2d and 2e still approximate that of the current sheet 100 sufficiently accurately to have magnetic field strength independent of z at distances over say around half the width of the magnet blocks 201 , 202, 211 , 221 , 231 , 241. In addition, when a backing plate is provided on one side of the magnet arrangement 240 illustrated in figure 2e (e.g. the lower surface 243 in figure 2e) it confines the magnetic field, effectively preventing the magnetic field extending beyond the backing plate, and the magnetic field on the opposing side (e.g. the upper surface 242 in figure 2e) is augmented. So, the first embodiment of the NMR apparatus 300 according to the invention described below is based on this last magnet arrangement 240.

Truncation

In reality, the magnet arrangements 200, 210, 220, 230, 240 of the invention are not infinite in the x-z plane, but are truncated and therefore have finite size. This inevitably has an effect on the magnetic field generated by the magnet arrangements 200, 210, 220, 230, 240. For example, the magnetic fields generated by truncated versions of the magnet arrangements 200, 210, 220, 230, 240 deviate from the field generated by their equivalent infinite current sheet (as discussed above) toward the edges of the magnet arrangements 200, 210, 220, 230, 240, e.g. at each end of the width of the magnet arrangements 200, 210, 220, 230, 240 and at each end of the depth of the magnet arrangements 200, 210, 220, 230, 240. This means that close to the edges of the magnet arrangements 200, 210, 220, 230, 240 say within around half the period with which the direction of magnetisation of the magnet blocks 201 , 202, 211 , 221 , 231 , 241 varies, from the edges, the magnetic field strength becomes dependent on x and z (as well as y). Nonetheless, this still means that the magnetic field varies in strength only as a function of y over a majority the x-z plane directly above the magnets 201 , 202, 211 , 221 , 231, 241.

Similarly, the magnetic fields generated by the magnet arrangements 200, 210, 220, 230, 240 again deviate from the magnetic field generated by their equivalent infinite current sheet at large distances away from the magnets along the y axis. In other words, the magnetic field strength becomes dependent on x and z at large y. However, this effect is only noticeable at fairly large distances along the y axis, e.g. at several times the period with which the direction of magnetisation of the magnet blocks 201 , 202, 211 , 221 , 231, 241 varies.

NMR Apparatus Referring to figure 3, a first embodiment of an NMR apparatus 300 of the invention has a magnet arrangement 301 comprising three permanent magnets 302, 303, 304. The magnets 302, 303, 304 are arranged in a similar way to the magnets blocks 241 of the magnet arrangement 240 illustrated in figure 2e. In other words, the magnets 302, 303, 304 are next to one another in a line, with their directions of magnetisation parallel to one another and side by side. The directions of magnetisation of adjacent magnets 302, 303, 304 face in opposite directions. More specifically, the central magnet 303, e.g. the magnet 303 in between the two other magnets 302, 304, has its direction of magnetisation facing in the opposite direction to the other two magnets 302, 304. Using the normal convention that lines of magnetic flux flow from a North (N) pole to a South (S) pole, the central magnet 303 has a S pole at the top as seen in figure 3 and the two other magnets have a N pole at the top as seen in figure 3. Three magnets 302, 303, 304 are sufficient to generate a magnetic field B₀ that varies in strength only along the y axis over a significant volume. However, the use of only three magnets keeps the size and weight of the apparatus relatively small, so that the NMR apparatus 300 can be portable.

The magnets 302, 303, 304 are mounted on a backing plate 305. This is made from a magnetically permeable material, which in this embodiment is steel. The backing plate 305 substantially contains the magnetic field B₀ generated by the poles of the magnets 302, 303, 304 with which it is in contact. This has two effects. Firstly, it shields the space on the side of the backing plate 305 opposite to the magnets 302, 303, 304, e.g. the back or bottom of the apparatus 300, from the magnetic field B₀. It also reinforces the magnetic field B₀ generated at the poles of the magnets 302, 303, 304 not in contact with the backing plate 305, e.g. at the front or top of the apparatus 300. It will be appreciated by those skilled in the art that the backing plate 305 is not necessary. The magnet arrangement 301 of the NMR apparatus 300 would be effective without it. Furthermore, other magnet arrangements, such as those illustrated in figures 2b and 2c are largely self shielding, i.e. they do not generate a significant magnetic field at the side of the magnet arrangement 301 with which the backing plate 305 is in contact. The magnet arrangement 301 is arranged to limit some of the effects of its truncation from an infinite plane to some degree. In particular, in this embodiment, each of the magnets 302, 303, 304 comprises a rectangular block of permanently magnetic material that is deeper than it is wide or high. In other words, the rectangular blocks have their largest dimension in a plane formed by the magnets (the x-z plane) and perpendicular to the line formed by the magnets 302, 303, 304 (i.e. along the x axis). This means that the influence of the edges of the magnets 302, 303, 304 on either side of the line formed by the magnets 302, 303, 304 are comparatively less than for an arrangement 301 in which each of the magnets 302, 303, 304 comprises a rectangular block of permanently magnetic material with their largest dimension parallel to the line formed by the magnets 302, 303, 304 (i.e. along the z axis). In order to achieve a similar effect, shims or air gaps can be provided across the width of the magnets 302, 303, 304 toward their ends on either side of the line.

Recalling equations (5) and (6), the applicants have also recognised that the contribution of some of the higher order Fourier harmonics to the magnetic field generated by the magnets 302, 303, 304 can be limited to some degree. In particular, by spacing the magnets 302, 303, 304 apart from one another along the width of the magnet arrangement 301 , one or more of the Fourier harmonics can be minimised. In this embodiment, the magnets 302, 303, 304 are spaced apart by around half their width. In other words, the magnets 302, 303, 304 are spaced apart from one another by one sixth of the period of variation in direction of the magnetisation of the magnets 302, 303, 304 (which can be thought of a 60° over a 360° period).

Furthermore, the magnets 302, 304 at the ends of the line formed by the magnets 302, 303, 304 can be adapted to lessen the deviation of the magnetic field from the magnetic field generated by the equivalent infinite current sheet close to the ends of the line. For example, in this embodiment, the magnets 302, 304 at the end of the line formed by the magnets 302, 303, 304 (i.e. along the z-axis) are wider in the direction of the line than the magnet 303 in the middle. In other embodiment, the magnets 302, 304 at the end of the line are stronger. In yet another embodiment, the magnets 302, 304 at the end of the line are thicker in the direction of the height of the magnet arrangement 301.

As described in the introduction, in order to make NMR measurements, it is usually required to provide both a static/gradient magnetic field B₀, as provided by the magnets 302, 303, 304, and an excitation magnetic field B₁ of a radio frequency (RF) pulse, which can be produced by inductive coils. These coils are often referred to as a probe or probes. Referring again to figure 3, in this embodiment of the invention, two such probe coils 306, 307 are positioned over the poles of the magnets 302, 303, 304 not in contact with the backing plate 305, e.g. toward the top of the apparatus 300. The probe coils 306, 307 are co-planar and their plane is parallel to the top surfaces of the magnets 302, 303, 304. The centre of the each of the coils 306, 307 is between a pair of adjacent magnets 302, 303, 304, substantially equidistant from the centre of the pole at the top of each magnet 302, 303, 304 of the pair. In other words, the coils have substantially the same pitch along the line formed by the magnets 302, 303, 304 (the z direction) as the magnets 302, 303, 304 themselves.

The probe coils 306, 307 are connected to an electrical power source (not shown) in opposing directions. This means that, when a current is passed though them from the power source, the components of the magnetic field B₁ they each generate at their centre are in opposing directions. This is equivalent to two imaginary permanent magnets arranged with their directions of magnetisation parallel to one another, side by side and in opposing directions, e.g. the same as the permanent magnets 241 of the magnet arrangement 240 illustrated in figure 2e and the magnet arrangement 301 of the NMR apparatus 300 illustrated in figure 3. So, like the magnet arrangement 301 of the NMR apparatus, the probe coils 306, 307 generate a magnetic field B₁ that approximates the magnetic field generated by the current sheet 100 illustrated in figure 1. In other words, the magnetic field B₁ generated by the probe coils 306, 307 varies in strength only along the y axis, subject to the limits of the approximation near to the coils and the effects of truncation (as discussed above with reference to figures 2a to 2e). It can be recalled from equations (2) and (3), that the direction of the magnetic field generated by the current sheet 100 varies as a cosine function dependent on z. The directions of the magnetic fields B₀, B₁ generated by the magnet arrangement 301 and probe coils 306, 307 of the NMR apparatus 300 also therefore vary in this way, subject to their approximation and the effects of truncation. Furthermore, the magnets 302, 303, 304 of the magnet arrangement 301 are spaced apart from one another by the same distance as the probe coils 306, 307 and the magnets 302, 303, 304 and probe coils 306, 307 are offset in the direction of the z axis by half their width in that direction. This means that the cosine function of the magnetic field B₀ generated by the magnets 302, 303, 304 is 90° out of phase with the cosine function of the magnetic field B₁ generated by the coils 306, 307.

This is illustrated in figure 4, which is a cross sectional view of the NMR apparatus 300 illustrated in figure 3. The magnetic field B₀ generated by the magnets 302, 303, 304 of the magnet arrangement is illustrated by lines of magnetic flux which are solid in the drawing. The magnetic field B₁ generated by the probe coils 306, 307 is illustrated by lines of magnetic flux which are dashed in the drawing. As illustrated, the phase difference between the cosine functions results in the lines of flux being perpendicular to one another. Of course, this is again subject to the limits of the approximated magnetic fields B₀, B₁ and the effects of truncation discussed above. Nonetheless, the magnetic fields B₀, B₁ are perpendicular to one another over substantially the same volume that the magnetic field strength of both of the fields B₀, B₁ remains dependent substantially only on y.

Probe Coils Referring to figure 5, the probe coils 306, 307 of the NMR apparatus 300 are illustrated as single rectangular windings. This is merely illustrative. In most implementations of the invention, each coil 306, 307 actually comprises multiple concentric windings, for example substantially evenly spaced form one another. However, referring to figure 6, in another embodiment, the probe coils 306, 307 each comprise a sinusoidal coil 600. The sinusoidal coil 600 has windings 601 that are spaced apart from one another to generate a magnetic field B₁ that varies sinusiodally along the line formed by the magnets 302, 303, 304, e.g. the z axis. The spacing of the windings can be calculated using a stream function technique. So, the sinusoidal coil 600 can more closely approximate the magnetic field generated by the current sheet 100 illustrated in figure 1. In particular, the magnetic field generated by the sinusoidal coil 600 is less square and more sinusoidal very close to the surface of the coil 600. Conveniently, the sinusoidal coil 600 can be fabricated on a Printed Circuit Board (PCB). It will be understood by those skilled in the art that the magnetic resonance measurement made by the apparatus 300 will relate to an entire surface or shell (defined by the frequency of the RF pulse) at which the magnetic field B₀ generated by the magnets 302, 303, 304 has a given strength and the magnetic field B₁ generated by the coils 306, 307 intersects the magnetic field B₀ generated by the magnets 302, 303, 304 substantially perpendicularly. Referring to figures 7 and 8, this means that if the region of the magnetic field B₀ generated by the magnets 302, 303, 304 whose strength depends only on y is substantially the same as the region of the magnetic field B₁ whose strength depends only on y, the measurement will include a component from the edges of the fields B₀, B₁ outside a desired planar sample volume 700 in figure 7. This is not a problem when the sample 701 has a finite size that fits within the sample volume 700, as the component of the measurement from the edges of the fields B₀, B₁ is null. However, when a larger sample 801 is analysed, as illustrated in figure 8, the component of the measurement from the edges of the fields B₀, B₁ would contain a component from the sample outside of the desired planar sample volume 700. So, referring to figure 8, the width of the coils 306, 307 along the line formed by the magnets 302, 303, 304 can be reduced to reduce the region of the magnetic field B₁ generated by the coils 306, 307 whose strength depends only on y. The sample volume is then effectively bounded by end regions 802 in which edge effects begin to influence the magnetic field B₁ generated by the coils 306, 307.

Housing

Referring to figure 9, the NMR apparatus 300 is mounted in a housing 900. The housing 900 has a moveable platform 901 on which the apparatus 300 is secured. The platform 901 can move within the housing 900, up and down as illustrated in the drawing. This has the effect of moving the apparatus 300 parallel to the main directions of magnetisation of the magnets 302, 303, 304 to change the elevation of the sample volume with respect to the housing 900 and is useful for extending the volume of a sample that can be analysed and also for scanning through the sample volume in the y direction while using a single frequency (e.g. equal to the Larmour frequency ω). Modulation Coils

Referring to figure 10, in an alternative embodiment NMR apparatus 300, modulation coils 1000, 1001, 1002 are provided around the magnets 302, 303, 304. These coils 1000, 1001 , 1002 extend around the edges of the magnets 302, 303, 304 and comprise windings for carrying a current. When a current is passed through the coils the strength of the magnetic field generated by the respective magnets 302, 303, 304 is modulated by superposition of the magnetic field generated by the coils 1000, 1001 , 1002. This is useful, for example, in the alternative NMR techniques discussed below.

Alternative NMR Techniques

The invention has been described above in relation to conventional pulsed Fourier NMR. However, it is not limited to pulsed NMR and other NMR techniques can be used. In particular, the NMR apparatus 300 can be adapted for use with Continuous Wave (CW) NMR imaging in one dimension. This technique is described, e.g., in the paper "Continuous wave MRI of heterogeneous materials" A.J. Fagan et al, Journal of Magnetic Resonance 163 (2003) pp 318-324.

To perform CW NMR, the electrical power source connected to the probe coils 306, 307 causes the probe coils 306, 307 to emit a RF signal at a lower power than the RF pulses used in pulsed NMR, but of longer (so-called continuous) duration. The power supply therefore requires smaller peak power, which means it can be smaller and lighter. Consequently, the NMR apparatus 300 can be more portable. In addition to the continuous low power RF signal, CW NMR requires the gradient magnetic field generated by the magnets 302, 303, 304 to be modulated by an audio frequency field to produce a signal which is the first derivative of the required response. This can be achieved using the modulation coils 1000, 1001 , 1002 described above. More specifically, the modulation coils 1000, 1001, 1002 are connected to another electrical power source (not shown). The modulation coil 1001 associated with the magnet 303 having its S pole facing upwards is connected to the power source in one direction (illustrated by anti-clockwise arrow 1004 in figure 10) and the modulation coils 1000, 1002 associated with the magnets 302, 304 having their N poles facing upwards are connected to the power source in the opposite direction (illustrated by clockwise arrows 1003, 1005 in figure 10). This means that an alternating current (usually at an audio frequency, e.g. around 10 Hz to 1 kHz) applied to the modulation coils 1000, 1001 , 1002 by the electrical power source is 180° out of phase in adjacent modulation coils and that the main directions in which the modulation coils 1000, 1001 , 1002 modulate the main direction of magnetisation of adjacent magnets 302, 303, 304 therefore oppose one another. In other embodiments, white noise (or stochastic) excitation can be used, as described, e.g., in the paper "Selective Saturation with Low-Power Pulses" H. Nilgens et al; Journal of Magnetic Resonance, Series A 105 (1993) pp 108-112. In particular, a "Hadamard" pulse sequence with selective saturation might be used, as described, e.g., in "Hadamard NMR imaging with slice selection", H. Nilgens et al, Magnetic Resonance Imaging 14 (1996) pp 857-861. Again, this generally requires significantly less RF power, hence allowing the use of more portable power sources and, in particular, amplifiers.

Alternative Magnet Arrangement

In an alternate magnet arrangement 1200, illustrated in figures 11 and 12, pole pieces are used to modify the generated magnetic field B₀. Using equations (3) and (4), where there is a distance w between a number of opposing magnetic poles, the lines of constant magnetic scalar potential of the generated magnetic field can be described by

_{= ±} sin-¹ (sin(6w/2)exp(^)) b

This function is illustrated in figure 11. By truncating the lines of equipotential over a profile commensurate with the orientation of the surface of the magnetic poles 302, 303, 304, i.e. along the line A-A in figure 11 , the profile of three pole pieces 1201 , 1202, 1203 can be derived. These pole pieces 1201 , 1202, 1203 are fabricated from steel, so that they contain the magnetic field generated by the magnets 302, 303, 304 and effectively re- profile the poles. This improves the approximation of the magnetic field B₀ generated by the magnets 302, 303, 304 to that of the current sheet 100 illustrated in figure 1.

The described embodiments of the invention are only examples of how the invention may be implemented. Modifications, variations and changes to the described embodiments will occur to those having appropriate skills and knowledge. These modifications, variations and changes may be made without departure from the spirit and scope of the invention defined in the claims and its equivalents.

Claims

1. A nuclear magnetic resonance apparatus comprising: a substantially planar magnet arrangement comprising a plurality of magnets arranged substantially along a line with their magnetic dipoles oriented substantially perpendicular to and around an axis, which axis is parallel to the plane of the magnet arrangement and orthogonal to the line along which the magnets are arranged, and varying in direction periodically along the line in order to generate a gradient magnetic field that has substantially constant strength parallel to the plane of the magnet arrangement in a sample volume; and a complementary probe comprising a plurality of coils also arranged substantially along the line with their magnetic dipoles oriented substantially perpendicular to and around the axis and varying in direction periodically along the line in order to generate an excitation magnetic field that also has substantially constant strength parallel to the plane of the magnet arrangement in the sample volume, wherein the variation in the direction of the magnetic dipoles of the magnets has substantially the same period but is offset from the variation in the direction of the magnetic dipoles of the coils so that the gradient magnetic field is substantially orthogonal to the excitation magnetic field throughout the sample volume.

2. The apparatus of claim 1 , wherein the magnetic dipoles of the magnets are each oriented one to the next by an equal angle.

3. The apparatus of claim 1 or claim 2, wherein the magnetic dipoles of adjacent magnets are oriented alternately between opposing directions orthogonal to the plane of the magnet arrangement.

4. The apparatus of any one of the preceding claims, wherein the magnets are spaced apart from one another along the line along which they are arranged.

5. The apparatus of claim 4, wherein the magnets are spaced apart from one another by around a half of their width parallel to the line along which they are arranged.

6. The apparatus of any one of the preceding claims, wherein the magnets are longer in a direction perpendicular to the line along which they are arranged than parallel to the line.

7. The apparatus of any one of the preceding claims, wherein the magnets at each end of the magnet arrangement are wider parallel to the line along which they are arranged than (the) other magnet(s) of the arrangement.

8. The apparatus of any one of the preceding claims, wherein the magnets at each end of the magnet arrangement are thicker orthogonal to the plane of the magnet arrangement than (the) other magnet(s) of the arrangement.

9. The apparatus of any one of the preceding claims, wherein the magnetic dipoles of the magnets are all equal in strength.

10. The apparatus of any one of claims 1 to 7, wherein the magnets at each end of the magnet arrangement are stronger than (the) other magnet(s) of the arrangement.

11. The apparatus of any one of the preceding claims, wherein the magnet arrangement defines a surface and the sample volume is spaced away from the surface.

12. The apparatus of any one of the preceding claims, wherein the magnets are each permanent magnets.

13. The apparatus of claim 13, wherein the permanent magnets each comprise a rare earth permanent magnet material.

14. The apparatus of any one of the preceding claims, wherein the magnetic dipoles of adjacent magnets are oriented alternately between opposing directions orthogonal to the plane of the magnet arrangement and the magnets each comprise: a permanent magnet block; and a pole piece of highly permeable magnetic material contoured substantially to follow a surface of constant magnetic scalar potential which is a Fourier exponential solution of the magnetic Laplace equation in air in Cartesian coordinates utilising only one fundamental trigonometric harmonic in the direction of the line of magnets and which is constant in a direction parallel to the plane of the magnet arrangement and orthogonal to the line along which the magnets are arranged.

15. The apparatus of any one of the preceding claims, wherein the magnet arrangement comprises only three magnets for generating the gradient magnetic field.

16. The apparatus of any one of the preceding claims, wherein the magnet arrangement has a backing plate of magnetically permeable material covering the back of the magnets, opposite to the sample volume, for containing the magnetic field generated at the back of the magnets.

17. The apparatus of any one of the preceding claims, wherein the complementary probe comprises a number of coils equal to the number of half periods of the variation in the direction of magnetic dipoles of the magnets.

18. The apparatus of any one of the preceding claims, wherein the coils are positioned substantially between a/the surface formed by the magnet arrangement and the sample volume.

19. The apparatus of any one of the preceding claims, wherein the coils are substantially planar and parallel to the plane of the magnet arrangement.

20. The apparatus of any one of the preceding claims, wherein the period of variation in direction of the magnetic dipoles of the coils is reduced at each end of the complementary probe to truncate the sample volume.

21. The apparatus of any one of the preceding claims, wherein each of the magnets and coils transects approximately the same area parallel to the plane of the magnet arrangement proximal to the sample volume.

22. A nuclear magnetic resonance apparatus comprising: a magnet arrangement comprising a plurality of magnets for generating a magnetic field in a sample volume on one side of the magnets; and a complementary probe comprising one or more coils between the magnets and the sample volume for generating an excitation magnetic field in the sample volume, wherein the surface area transected by each of the magnets and the coils in the direction of the sample volume is approximately the same.

23. The apparatus of any one of the preceding claims, wherein the coils have windings spaced to provide a substantially sinusiodally varying current density along a/the line along which the magnets are arranged.

24. The apparatus of any one of the preceding claims, comprising an electrically conductive but non-ferromagnetic shielding plate between the coils and the magnets.

25. The apparatus of any one of the preceding claims, comprising a modulation coil positioned around each of the magnets to modulate the magnetic field produced by the magnets.

26. The apparatus of any one of the preceding claims, wherein the magnet arrangement and the complementary probe are mounted in a housing such that they can be moved together in relation to the housing parallel to the main directions of magnetisation of the magnets to change the elevation of the sample volume with respect to the housing.

27. A substantially planar nuclear magnetic resonance apparatus having a magnetic field that is substantially constant in strength parallel to the plane of the apparatus and varies in direction by around 180° or more throughout a sample volume.

28. The apparatus of claim 27, wherein the magnetic field varies in direction through 360° throughout the sample volume.

29. The apparatus of claim 27 or claim 28, wherein the magnetic field varies substantially sinusiodally in direction.

30. A magnet arrangement for a nuclear magnetic resonance apparatus comprising three or more magnets arranged substantially in a line with their main directions of magnetisation oriented around and substantially orthogonal to an axis perpendicular to the line so as to generate a magnetic field that varies in strength only substantially perpendicular to a plane defined by the axis and the line throughout a sample volume.

31. A method of nuclear magnetic resonance comprising: generating a gradient magnetic field using a substantially planar magnet arrangement comprising a plurality of magnets arranged substantially along a line with their magnetic dipoles oriented substantially perpendicular to and around an axis, which axis is parallel to the plane of the magnet arrangement and orthogonal to the line along which the magnets are arranged, and varying in direction periodically along the line so that the generated gradient magnetic field has substantially constant strength parallel to the plane of the magnet arrangement in a sample volume; and generating an excitation magnetic field using a complementary probe comprising a plurality of coils also arranged substantially along the line with their magnetic dipoles oriented substantially perpendicular to and around the axis varying in direction periodically along the line so that the generated excitation magnetic field also has substantially constant strength parallel to the plane of the magnet arrangement in the sample volume, wherein the variation in the direction of the magnetic dipoles of the magnets has substantially the same period but is offset from the variation in the direction of the magnetic dipoles of the coils so that the gradient magnetic field is substantially orthogonal to the excitation magnetic field throughout the sample volume.

32. The method of claim 31 , wherein the magnetic dipoles of the magnets are each oriented one to the next by an equal angle.

33. The method of any one of claims 31 to 32, wherein the magnetic dipoles of adjacent magnets are oriented alternately between opposing directions orthogonal to the plane of the magnet arrangement.

34. The method of any one of claims 31 to 33, wherein the magnets are spaced apart from one another along the line along which they are arranged.

35. The method of claim 34, wherein the magnets are spaced apart from one another by around a half of their width parallel to the line along which they are arranged.

36. The method of any one of claims 31 to 35, wherein the magnets are longer in a direction perpendicular to the line along which they are arranged than parallel to the line.

37. The method of any one of claims 31 to 36, wherein the magnets at each end of the magnet arrangement are wider parallel to the line along which they are arranged than (the) other magnet(s) of the arrangement.

38. The method of any one of claims 31 to 37, wherein the magnets at each end of the magnet arrangement are thicker orthogonal to the plane of the magnet arrangement than (the) other magnet(s) of the arrangement.

39. The method of any one claims 31 to 38, wherein the magnetic dipoles of the magnets are all equal in strength.

40. The method of any one of claims 31 to 38, wherein the magnets at each end of the magnet arrangement are stronger than (the) other magnet(s) of the arrangement.

41. The method of any one of claims 31 to 40, wherein the magnet arrangement defines a surface and the sample volume is spaced away from the surface.

42. The method of any one of claims 31 to 41 , wherein the magnets are each permanent magnets.

43. The method of claim 42, wherein the permanent magnets each comprise a rare earth permanent magnet material.

44. The method of any one of claims 31 to 43, wherein the magnetic dipoles of adjacent magnets are oriented alternately between opposing directions orthogonal to the plane of the magnet arrangement and the magnets each comprise: a permanent magnet block; and a pole piece of highly permeable magnetic material contoured substantially to follow a surface of constant magnetic scalar potential which is a Fourier exponential solution of the magnetic Laplace equation in air in Cartesian coordinates utilising only one fundamental trigonometric harmonic in a direction parallel to the plane of the magnet arrangement and orthogonal to the line along which the magnets are arranged.

45. The method of any one of claims 31 to 44, wherein the magnet arrangement comprises only three magnets for generating the gradient magnetic field.

46. The method of any one of claims 31 to 45, wherein the magnet arrangement has a backing plate of magnetically permeable material covering the back of the magnets, opposite to the sample volume, for containing the magnetic field generated at the back of the magnets.

47. The method of any one of claims 31 to 46, wherein the complementary probe comprises a number of coils equal to the number of half periods of the variation in the direction of magnetic dipoles of the magnets.

48. The method of any one of claims 31 to 47, wherein the coils are positioned substantially between a/the surface formed by the magnet arrangement and the sample volume.

49. The method of any one of claims 31 to 48, wherein the coils are substantially planar and parallel to the plane of the magnet arrangement.

50. The method of any one of claims 31 to 49, wherein the period of variation in direction of the magnetic dipoles of the coils is reduced at each end of the complementary probe to truncate the sample volume.

51. The method of any one of claims 31 to 50, wherein each of the magnets and coils transects approximately the same area parallel to the plane of the magnet arrangement proximal to the sample volume.

52. A method of nuclear magnetic resonance spectroscopy comprising: generating a gradient magnetic field in a sample volume using a magnet arrangement comprising a plurality of magnets, the sample volume being on one side of the magnets; and generating an excitation magnetic field in the sample volume using a complementary probe comprising one or more coils between the magnets and the sample volume, wherein the surface area transected by each of the magnets and the coils in the direction of the sample volume is approximately the same.

53. The method of any one of claims 31 to 52, wherein the coils have windings spaced to provide a substantially sinusiodally varying current density along a/the line along which the magnets are arranged.

54. The method of any one of claims 31 to 53, wherein the complementary probe has an electrically conductive but non-ferromagnetic shielding plate between the coils and the magnets.

55. The method of any one of claims 31 to 54, wherein the magnet arrangement has a modulation coil positioned around each of the magnets to modulate the magnetic field produced by the magnets.

56. The method of any one of claims 31 to 55, wherein the magnet arrangement and the complementary probe are mounted in a housing such that they can be moved together in relation to the housing parallel to the main directions of magnetisation of the magnets to change the elevation of the sample volume with respect to the housing.

57. The method of any one of claims 31 to 56, wherein the excitation magnetic field generated by the coils is in the form of one or more radio frequency pulse(s).

58. A method of performing continuous wave nuclear magnetic resonance spectroscopy using the method of any one of claims 31 to 56.

59. A method of performing stochastic nuclear magnetic resonance spectroscopy using the method of any one of claims 31 to 56.

60. A method of nuclear magnetic resonance spectroscopy comprising generating, using a substantially planar apparatus, a gradient magnetic field that is substantially constant in strength parallel to the plane of the apparatus and varies in direction by around 180° or more throughout a sample volume.

61. The method of claim 60, wherein the magnetic field varies in direction through 360° throughout the sample volume.

62. The method of claim 60 or claim 61 , wherein the magnetic field varies substantially sinusiodally in direction.

63. A method of generating a magnetic field for nuclear magnetic resonance spectroscopy using a magnet arrangement having three or more magnets arranged substantially in a line with their main directions of magnetisation oriented around and substantially orthogonal to an axis perpendicular to the line so that the generated magnetic field varies in strength only substantially perpendicular to a plane defined by the axis and the line throughout a sample volume.

64. A nuclear magnetic resonance apparatus substantially as described with reference to the accompanying drawings.

65. A magnet arrangement for a nuclear magnetic resonance apparatus substantially as described with reference to the accompanying drawings.

66. A method of nuclear magnetic resonance spectroscopy substantially as described with reference to the accompanying drawings.

67. A method of generating a magnetic field for nuclear magnetic resonance spectroscopy substantially as described with reference to the accompanying drawings.