Pulse sequence and method for creating a radio-frequency magnetic field gradient with a spatially independent phase for NMR experiments

A composite RF pulse is created from a sequence of conventional homogeneous RF pulses and conventional gradient RF pulses and the composite pulse generates a gradient magnetic field with a spatially varying amplitude, but a spatially independent phase. In one embodiment of the invention, the pulse sequence consists of four conventional gradient RF pulses interspersed with two conventional homogeneous RF pulses. In another embodiment of the invention, a conventional gradient RF pulse is combined with a conventional homogeneous RF pulse and the pulse pair is repeated in order to generate an effective magnetic field with a spatially varying amplitude, but a spatially independent phase.

FIELD OF THE INVENTION 
This invention relates to nuclear magnetic resonance (NMR) spectroscopy 
and, in particular, to high resolution NMR experiments utilizing RF 
gradient pulses. 
BACKGROUND OF THE INVENTION 
All atomic nuclei of elements with an odd atomic mass or an odd atomic 
number possess a nuclear magnetic moment. Nuclear magnetic resonance is a 
phenomenon exhibited by this select group of atomic nuclei (termed "NMR 
active" nuclei), and is based upon the interaction of the nucleus with an 
applied, external magnetic field. The magnetic properties of a nucleus are 
conveniently discussed in terms of two quantities: the gyromagnetic ratio 
(.gamma.); and the nuclear spin (I). When an NMR active nucleus is placed 
in a magnetic field, its nuclear magnetic energy levels are split into 
(2I+1) non-degenerate energy levels, which are separated from each other 
by an energy difference that is directly proportional to the strength of 
the applied magnetic field. This splitting is called the "Zeeman" 
splitting and the energy difference is equal to hH.sub.o /2.pi. where h is 
Plank's constant and H.sub.0 is the strength of the applied magnetic 
field. The frequency corresponding to the energy of the Zeeman splitting 
(.omega.=.gamma.H.sub.0) is called the "Larmor frequency" and is 
proportional to the field strength of the magnetic field. Typical NMR 
active nuclei include .sup.1 H (protons), .sup.13 C, .sup.19 F, and 
.sup.31 P. For these four nuclei I=1/2, and each nucleus has two nuclear 
magnetic energy levels. 
When a bulk sample of material containing NMR active nuclei is placed 
within a magnetic field called the main static field, the nuclear spins 
distribute themselves amongst the nuclear magnetic energy levels in 
accordance with Boltzmann's statistics. This results in a population 
imbalance among the energy levels and a net nuclear magnetization. It is 
this net nuclear magnetization that is studied by NMR techniques. 
At equilibrium, the net nuclear magnetization of the aforementioned bulk 
sample is aligned parallel to the external magnetic field and is static 
(by convention, the direction of the main static field is taken to be the 
z-axis). A second magnetic field perpendicular to the main static magnetic 
field and rotating at, or near, the Larmor frequency can be applied to 
induce a coherent motion of the net nuclear magnetization. Since, at 
conventional main static magnetic field strengths, the Larmor frequency is 
in the megahertz frequency range, this second magnetic field is called a 
"radio frequency" or RF field. 
The effect of the RF field is to shift the nuclear magnetization direction 
so that it is no longer parallel to the main static field. This shift 
introduces a net coherent motion of the nuclear magnetization about the 
main static field direction called a "nutation". In order to conveniently 
deal with this nutation, a reference frame is used which rotates about the 
laboratory reference frame z-axis at the Larmor frequency and also has its 
z-axis parallel to the main static field direction. In this "rotating 
frame" the net nuclear magnetization, which is rotating in the stationary 
"laboratory" reference frame, is now static. 
Consequently, the effect of the RF field is to rotate the now static 
nuclear magnetization direction at an angle with respect to the main 
static field direction (z-axis). The new magnetization direction can be 
broken into a component which is parallel to the main field direction 
(z-axis direction) and a component which lies in the plane transverse to 
the main magnetization (x,y plane). The RF field is typically applied in 
pulses of varying length and amplitude and, by convention, an RF pulse of 
sufficient amplitude and length to rotate the nuclear magnetization in the 
rotating frame through an angle of 90.degree., or .pi./2 radians, and 
entirely into the x,y plane is called a ".pi./2 pulse". 
Because the net nuclear magnetization is rotating with respect to the 
laboratory frame, the component of the nuclear magnetization that is 
transverse to the main magnetic field or that lies in the x,y plane 
rotates about the external magnetic field at the Larmor frequency. This 
rotation can be detected with a receiver coil that is resonant at the 
Larmor frequency. The receiver coil is generally located so that it senses 
voltage changes along one axis (for example, the x-axis) where the 
rotating magnetization component appears as an oscillating voltage. 
Frequently, the "transmitter coil" employed for applying the RF field to 
the sample and the "receiver coil" employed for detecting the 
magnetization are one and the same coil. 
Although the main static field is applied to the overall material sample, 
the nuclear magnetic moment in each nucleus within the sample actually 
experiences an external magnetic field that is changed from the main 
static field value due to a screening from the surrounding electron cloud. 
This screening results in a slight shift in the Larmor frequency for that 
nucleus (called the "chemical shift" since the size and symmetry of the 
shielding effect is dependent on the chemical composition of the sample). 
In a typical NMR experiment, the sample is placed in the main static field 
and a .pi./2 pulse is applied to shift the net magnetization into the 
transverse plane (called transverse magnetization). After application of 
the pulse, the transverse magnetization, or "coherence", begins to precess 
about the x-axis, or evolve, due to the chemical shifts at a frequency 
which is proportional to the chemical shift field strength. In the 
rotating frame, the detector (which is stationary in the laboratory frame) 
appears to rotate at the Larmor frequency. Consequently, the detector 
senses an oscillation produced by an apparent magnetization rotation at a 
frequency which is proportional to the frequency difference between the 
Larmor frequency and the chemical shift frequency. 
Thus, the detected signal oscillates at the frequency shift difference. In 
addition to precessing at the Larmor frequency, in the absence of the 
applied RF field energy, the nuclear magnetization also undergoes two 
spontaneous processes: (1) the precessions of various individual nuclear 
spins which generate the net nuclear magnetization become dephased with 
respect to each other so that the magnetization within the transverse 
plane loses phase coherence (so-called "spin-spin relaxation") with an 
associated relaxation time, T.sub.2, and (2) the individual nuclear spins 
return to their equilibrium population of the nuclear magnetic energy 
levels (so-called "spin-lattice relaxation") with an associated relaxation 
time, T.sub.1. The latter process causes the received signal to decay to 
zero. The decaying, oscillating signal is called a free induction decay 
(FID). 
Many NMR experiments are designed such that the spin dynamics are uniform 
through the sample and, in these cases, the sample is placed in a uniform 
magnetic field. However, there are cases where it is advantageous to 
impose a spatial variation in the spin dynamics across the sample. Obvious 
examples of such cases include imaging experiments and diffusion 
experiments. The spin evolution may also be spatially modulated as a means 
of selecting a specific coherence pathway or multiple quantum spin state. 
Such a spatial variation may be introduced into an experiment by utilizing 
a magnetic field having a spatial variation (such as a linear gradient) to 
perform the experiment. Two magnetic fields are commonly employed in NMR 
experiments, B.sub.0 and B.sub.1 fields, which are fields that are 
oriented along the direction of the main static field and in the plane 
transverse to the main static field direction, respectively. 
B.sub.1 -gradients are commonly generated by a special RF coil which 
produces a magnetic field that has at least one component with a direction 
lying in the plane perpendicular to the main static field direction. When 
B.sub.1 -gradient magnetic fields are used in NMR spectroscopy 
experiments, the gradient magnetic field is often used in conjunction with 
a homogeneous RF magnetic field which is also generated by an RF coil. The 
homogeneous field and the gradient field can be generated either by two 
different RF coils or by a single coil which can alternately be driven in 
a gradient mode and a homogeneous mode. 
An example of the use of B.sub.1 -gradients in NMR spectroscopy has been 
described in detail in a paper entitled "The Selection of 
Coherence-Transfer Pathways by Inhomogeneous Z Pulses" by C. J. R. 
Counsell, M. H. Levitt and R. R. Ernst, Journal of Magnetic Resonance, 
v.64, pages 470-478, 1985. Another example of the use of B.sub.1 
-gradients in NMR spectroscopy has been described in detail in another 
paper entitled "The Equivalent of the DQF-COSY Experiment, with One 
Transient Per t.sub.1 Value, by Use of B.sub.1 Gradients", by J. Brondeau, 
D. Boudot, P. Mutzenhardt and D. Canet, Journal of Magnetic Resonance, v. 
100, pp. 611-618, 1992. B.sub.1 gradients have also been used for imaging 
by M. H. Werner and this approach is described in detail in a Ph.D. 
dissertation entitled, "NMR Imaging of Solids with Multiple-Pulse Line 
Narrowing and Radiofrequency Gradients" (M. H. Werner: Ph.D. Thesis, 
California Institute of Technology, Pasadena, Calif., 1993). 
Since the spin dynamics are relative to the homogeneous RF field whose 
phase may itself vary over the sample, it is understood that it is the 
uniformity of the relative phase difference between the gradient and the 
homogeneous RF fields which is important. To simplify this discussion, 
however, the homogeneous RF field is discussed as though it generated an 
ideal uniform field. 
An ideal field having a constant spatial field direction (or 
spatially-independent phase) can, in principle, be generated by means of 
an RF coil with proper geometry. However, practical requirements, such as 
RF efficiency, the frequency at which the coil is operated, and physical 
limitations on the size and placement of the gradient RF coil generally 
make it nearly impossible to generate an RF gradient magnetic field with a 
truly spatially independent phase. 
For many applications involving B.sub.1 -gradients, the spatial variation 
of the magnetic field should ideally be only a variation in magnitude of 
the field, with the direction of the field, or the phase, remaining 
constant over space. A spatial dependence of the phase causes signal 
reduction and artifacts in experiments where the B.sub.1 -gradient field 
is used in combination with a homogeneous RF field. 
Accordingly, it is an object of the present invention to provide a pulse 
sequence that converts an RF gradient field with a spatial variation in 
both amplitude and phase to an RF gradient field with a spatially 
dependent amplitude and a spatially independent phase. 
SUMMARY OF THE INVENTION 
The foregoing problems are overcome and the foregoing object is achieved in 
an illustrative embodiment of the invention in which a composite RF pulse 
is created from a sequence of homogeneous pulses and gradient pulses. The 
composite pulse generates a gradient magnetic field with a spatially 
varying amplitude, but a spatially independent phase. The creation of a 
B.sub.1 -gradient with a spatially independent phase allows for a simple 
and direct use of the B.sub.1 -gradient in a manner analogous to the use 
of a B.sub.0 gradient in many known experiments (such as multiple quantum 
filters, quadrature detection and imaging experiments). Additional 
advantages are that the gradient pulse is a simple sequence of RF pulses, 
switching times are short, the lock channel is not affected, there is no 
need for pre-emphasis, the lineshape is not distorted, no eddy currents 
are induced and the gradient is frequency-selective. 
In one embodiment of the invention, the pulse sequence consists of four 
conventional gradient RF pulses interspersed with two conventional 
homogeneous RF pulses. In another embodiment of the invention a 
conventional gradient RF pulse is combined with a conventional homogeneous 
RF pulse and the pulse pair is repeated in order to utilize the principle 
of second averaging to average the gradient pulse phase to zero.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
The RF magnetic field, B.sub.1 (r,t), generated in a conventional gradient 
RF coil can be described as: 
EQU B.sub.1 (r,t)=B.sub.1.sup.c (t)+B.sub.1.sup.g (r,t) (1) 
where B.sub.1.sup.c (t) is a spatially invariant contribution and 
B.sub.1.sup.g (r,t) is the gradient term, which varies over space. Each 
term on the right-hand side of the equation can be expressed in three 
orthogonal components with respect to the local frames of the spins: 
EQU B.sub.1 (r,t)=e.sub.x B.sub.x.sup.c (t)+e.sub.y B.sub.y.sup.c (t)+e.sub.z 
B.sub.z.sup.c (t)+e.sub.x B.sub.x.sup.g (r,t)+e.sub.y B.sub.y.sup.g 
(r,t)+e.sub.z B.sub.z.sup.g (r,t) (2) 
where the z-axis is chosen along the direction of the main magnetic field 
and the terms e.sub.x, e.sub.y, e.sub.z are unit vectors in the x, y and z 
directions of the laboratory frame. Since only the transverse terms of the 
RF magnetic field couple into the spin system, the z-components of the 
field will be neglected from here on. It is further assumed that the 
spatially invariant field is aligned along the x-axis; there is no loss in 
generality introduced with this choice of reference frame. The spatially 
dependent fields can be expressed in terms of gradients 
.differential.Bi/.differential..alpha. where i=x,y and .alpha.=u, v, z are 
the directions of the laboratory frame which is fixed with respect to the 
RF coil: 
##EQU1## 
The time dependence of the oscillating RF field can be expressed as 
cos(.omega.t+.phi.) where .omega. is the rotation frequency and .phi. is 
the phase angle of the RF field. The RF field can then be decomposed into 
a rotating component (arbitrarily referred to as clockwise, CW) and a 
counter-rotating component (counter-clockwise, CCW): 
##EQU2## 
Only those components that rotate in the same direction as the spins couple 
into the spin system. Therefore, one of the rotating components can be 
neglected, and, in the following discussion, only the counter clockwise 
(CCW) components will be preserved. 
If B.sub.1 is the strength of the RF field, then the resulting magnetic 
field can be expressed as: 
##EQU3## 
The total RF magnetic field generated by the gradient coil thus consists of 
a spatially invariant or homogeneous term and two orthogonal spatially 
dependent or gradient contributions. In order to simplify the equations, 
and, for convenience, the phase .phi. of the RF can be set to zero and the 
gradient terms of the x and y components can be written as G.sub.x and 
G.sub.y respectively, where 
##EQU4## 
Then the magnitude .vertline.B.vertline. and phase .xi. of the resultant 
RF magnetic field at location r and time t=0 are given by: 
##EQU5## 
From these equations, it is clear that, in general, both the magnitude and 
phase of the resultant magnetic field generated at a point by the RF field 
are spatial functions dependent on the location of the point within the RF 
coil. 
The present invention uses a combination of gradient RF pulses and 
homogeneous RF pulses to produce a combined field which retains only the 
spatial dependence in the magnitude of the magnetic field; the spatial 
dependence of the phase behavior of the magnetic field disappears. The 
spatially-independent phase behavior will be called a "pure" phase. In 
accordance with the principles of the invention, a homogeneous RF field is 
generated and combined with the conventional RF gradient field to 
selectively retain one component of the gradient field while averaging the 
orthogonal component substantially to zero. The generation of the 
homogeneous and gradient fields requires the use of either two coils, a 
conventional gradient RF coil and a conventional homogeneous RF coil, or a 
single coil which can be driven in either a gradient mode or a homogeneous 
mode by means of switching circuits. A suitable NMR probe is described in 
detail in U.S. Pat. No. 5,323,113 which is hereby incorporated by 
reference. 
In order to understand the combined effect of the gradient pulses and 
homogeneous pulses on the spin system, the interaction of the RF field 
with the spin system in a material can be described by an operator. It is 
common practice to express the operator in the coordinates of a frame 
rotating with the frequency of the RF irradiation around the z-axis. The 
Hamiltonian H.sub.h for an RF field with phase .theta. which is generated 
by a homogeneous coil or a coil operated in a homogeneous mode is given 
by: 
EQU H.sub.h =-.gamma.B.sub.1h {I.sub.x cos .theta.+I.sub.y sin .theta.}(9) 
where .gamma. is the gyromagnetic ratio of the material, B.sub.1h is the 
magnitude of the RF field and I.sub.x and I.sub.y are the spin angular 
momentum operators. 
By convention, an x-pulse is defined as an RF pulse with a phase .theta.=0 
and y, -x, and -y pulses are defined as RF pulses with phases .theta.=90, 
180 and 270 degrees, respectively. Using these definitions, the 
Hamiltonian H.sub.g for an RF field with phase .phi. and amplitude 
B.sub.1g which is generated by a gradient coil or a coil operated in a 
gradient mode is given by: 
##EQU6## 
where .gamma. is the gyromagnetic ratio and G.sub.x and G.sub.y are the 
gradient terms previously defined. 
In the multiple pulse cycles described below, the homogeneous RF field will 
define the symmetry of the experiment. Two pulse sequences will be 
discussed, one based on the refocussing properties of a conventional 
Carr-Purcell RF pulse sequence and another based on a mechanism called 
"second averaging". Both sequences can be conveniently analyzed using a 
technique called average Hamiltonian theory. 
The first inventive RF composite pulse comprises the six RF pulses as 
follows: 
EQU G.sub..phi. -.pi.).sub.x -G.sub..psi. -G.sub..psi. -.pi.).sub.x 
-G.sub..phi.(11) 
where G.sub..phi. and G.sub..psi. are gradient RF pulses with phases .phi. 
and .psi., respectively, and .pi.).sub.x and .pi.).sub.x are homogeneous 
RF pulses, with a rotation angle of .pi. radians and phases x and -x, 
respectively. An illustrative pulse cycle is diagrammed in FIG. 1 which 
illustrates the six pulse sequence of line (11). The pulses are 
illustrated as a function of time increasing to the right. The gradient 
pulses comprise pulses 100, 104, 106 and 110 and the homogeneous pulses 
comprise pulses 102 and 108. 
The averaged Hamiltonian for this pulse sequence, which is valid for small 
gradient evolution, is given by: 
##EQU7## 
This averaged Hamiltonian is equal to the Hamiltonian for an RF field with 
phase: 
##EQU8## 
and magnitude: 
##EQU9## 
As shown by equations (13) and (14), the phase of the resultant gradient 
field is no longer dependent on the location in the gradient coil, and the 
spatial dependence is entirely contained in the magnitude of the resultant 
field (in the terms G.sub.x and G.sub.y). Thus, this inventive sequence 
can be used in place of conventional gradient pulses in an NMR experiment 
to achieve a B.sub.1 gradient with a spatially-independent phase. 
A second illustrative approach used in accordance with the present 
invention to achieve a gradient RF field with a spatially independent 
phase, employs a phenomenon called "second averaging". The principle of 
second averaging is described in detail in a publication entitled 
"Quantitative Aspects of Coherent Averaging. Simple Treatment of Resonance 
Offset Processes in Multiple-Pulse NMR", A. Pines and J. Waugh, Journal of 
Magnetic Resonance, v. 8, pps. 354-365, 1972. 
According to the principles of second averaging, a rotation produced by a 
small gradient interaction can be time-averaged to zero by introducing a 
large interaction into the gradient sequence, which large interaction 
produces a rotation that is orthogonal to the rotation generated by the 
small interaction. The effect of the small rotation is equivalent to a 
perturbation on the large rotation so that the small interaction is 
time-averaged. By suitably selecting the large interaction, the small 
interaction can be averaged substantially to zero. For example, a pulse 
sequence which has a gradient term as the small interaction and a suitable 
large interaction is the pulse sequence: 
EQU (G.sub..phi. -.epsilon..sub.x).sub.n (15) 
in which G.sub..phi. is a gradient RF pulse with phase .phi. and 
.epsilon..sub.x is a homogeneous x-pulse with rotation angle .epsilon., 
and the sequence is repeated n times. A pulse sequence illustrating this 
new sequence is diagrammed in FIG. 2 where pulse 200 is the gradient pulse 
and pulse 202 is the homogeneous pulse. The averaged Hamiltonian for this 
sequence is: 
EQU &lt;H&gt;=-.gamma.B.sub.1g I.sub.x [(1+G.sub.x)cos .phi.-G.sub.y sin .phi.](16) 
The average Hamiltonian in equation (16) is equal to the Hamiltonian for an 
RF field with phase 0 and magnitude B.sub.1g .sqroot.(1+G.sub.x).sup.2 
cos.sup.2 .phi.+G.sub.y.sup.2 sin .sup.2 .phi.. Therefore, the phase of 
the resulting gradient field produced by this sequence is spatially 
independent, and all of the spatially-dependent terms are contained in the 
field magnitude. 
The principles of the present invention are illustrated below by three 
examples: a COSY experiment involving P/N type selection, an RF imaging 
experiment and a multiple quantum filtering experiment. A COSY experiment 
is a well-known two-dimensional homonuclear experiment that maps out the 
scalar coupling network between nuclear spins. Common problems encountered 
in this type of experiment include axial peaks, mirrored peaks and 
instrument artifacts. The axial peaks are generated by magnetization which 
did not evolve during the evolution period. The mirrored peaks cause the 
two dimensional spectrum to appear as a mirror image of itself (the two 
sets of peaks are called P-type and N-type) and occur since the experiment 
cannot distinguish the sense (clockwise or counterclockwise) of the 
magnetization rotation during the evolution period. These problems are 
conventionally dealt with by using one of three techniques. The first 
technique involves cycling the phases of the RF pulses in a predetermined 
way and coherently adding the results of several experiments. This adding 
process eliminates axial peaks and selects one set of resonances (P-type 
or N-type). The problem with phase cycling is that several scans, each 
with a different phase, must be conducted to generate a single data point 
and, if a single scan has a sufficient signal-to-noise ratio to generate 
acceptable data, phase cycling leads to inefficient use of spectrometer 
time. 
An alternative technique to phase cycling employs B.sub.0 gradients, to 
eliminate axial peaks and select P -or N-type resonances. This latter 
technique is described in detail in a paper entitled "Pulsed Field 
Gradients in NMR. An alternative to Phase Cycling" by P. Barker and R. 
Freeman, Journal of Magnetic Resonance, v. 64, pps. 334-338, 1985 and the 
RF pulse sequence for this experiment is depicted in FIG. 3. 
As shown in FIG. 3, the pulse sequence comprises two homogeneous 
##EQU10## 
pulses 300 and 302 separated by a time interval t.sub.1. B.sub.0 gradient 
pulses 304 mid 306 are applied both before and after the second 
homogeneous pulse 302 and an FID 308 is collected during the t.sub.2 time 
interval 310. 
The third technique uses B.sub.1 gradients generated by RF pulses to 
eliminate axial peaks and select P- or N-type resonances. For example, the 
evolution of a spin system under an inhomogeneous static field or B.sub.0 
gradient can be described as a rotation of the spins about the z-axis of 
the rotating frame where the angle of rotation is a function of position. 
As described in detail in a paper entitled "The Selection of 
Coherence-Transfer Pathways by Inhomogeneous Z Pulses" by C. J. R. 
Counsell, M. H. Levitt and R. R. Ernst, Journal of Magnetic Resonance, 
v.64, pages 470-478, 1985, it is known that a similar effect can be 
achieved with an RF gradient field by incorporating an RF gradient pulse 
in a composite pulse sequence such as: 
##EQU11## 
is a homogeneous .pi./2 pulse with phase .phi., .theta. represents an RF 
gradient pulse with phase .phi.+.pi./2 and which produces a rotation angle 
that is a function of the location of the spins in the gradient coil and 
##EQU12## 
is a homogeneous .pi./2 pulse with phase .phi.+.pi.. By sandwiching the 
gradient between two homogeneous .pi./2 pulses, this composite pulse 
sequence can also be viewed as switching the evolution plane of the spins 
due to the RF gradient from perpendicular to the applied RF field to 
perpendicular to the static magnetic field. 
To complete the analogy between B.sub.0 and B.sub.1 gradients, a planar 
variation of the RF field over the sample is required. Therefore, the 
phase of the RF gradient has to be independent of the spatial location in 
the coil. In the implementation of the composite pulse discussed in the 
Counsell et al. paper referenced above, the RF gradient pulse was 
generated with a normal RF coil by exploiting the residual inhomogeneity 
of the coil to produce the required gradient. However, in accordance with 
the invention, a dual coil configuration can be used in which the gradient 
strength is optimized by suitably designing the geometry of the gradient 
coil. In a two coil configuration, however, the phases of the homogeneous 
and gradient fields cannot be assumed to be identical. 
More particularly, spatial independence of the RF phase can be achieved 
with the inventive pulse sequences as previously discussed. In the 
experiment described below, the aforementioned composite pulse cycle: 
G.sub..phi. -.pi..sub.x -G.sub..psi. -G.sub..psi. -.pi..sub.x -G.sub..phi. 
is used and the phases .phi. and .psi. of the gradient pulses are chosen 
equal, in which case the averaged Hamiltonian is proportional to I.sub.x 
and represents a planar gradient. This composite pulse can be used by 
sandwiching it between two homogeneous .pi./2 pulses of opposite phase as 
discussed above to produce the pulse sequence diagrammed in FIG. 4. 
As shown in FIG. 4, the basic homogeneous pulse sequence is the same as in 
the prior art sequence using B.sub.0 gradients and comprises two 
homogeneous .pi./2 pulses 400 and 402 separated by a time interval 
t.sub.1. RF gradient pulses 404 and 406, which produce a composite 
z-rotation, are applied both before and after the second homogeneous pulse 
402 and, for N-type selection, are equal. An FID 408 is collected during 
the t.sub.2 time interval 410. The RF gradient pulses 404 and 406 are, in 
turn, comprised of a composite pulse consisting of two homogenous pulses 
of opposite phase, 412 and 414 which sandwich one or more composite 
pulses. Each composite pulse comprises the plurality of pulses located 
within the parentheses and the notation ().sub.n indicates one or more 
reptitions of the composite pulse. More specifically, the composite pulse 
is comprised of one of the inventive pulse sequences discussed above. The 
particular pulse sequence shown in FIG. 4 corresponds to that shown in 
equation (11) above and comprises gradient pulses 418, 422, 424 and 428 
and homogeneous pulses 420 and 426. Alternatively, the pulse sequence 
shown in equation (15) could also be used. 
The total effect of the pulse sequence in FIG. 4 is a composite z-rotation 
where the rotation angle is a function of position in the transverse 
plane. Note, that the sequence does not work if the phase of the RF 
gradient is spatially dependent, since the composite z-rotation requires 
the phases of the RF gradient pulses and the pulse sandwich to be 
perpendicular 
FIGS. 5A and 5B show the N-type proton COSY spectrum of 
1-chloro,3-nitrobenzene in deuterated benzene, obtained with a single scan 
per t.sub.1 increment using the inventive pulse sequence shown in FIG. 4. 
The spectrum was obtained with a model AMX 400 spectrometer sold by Bruker 
Instruments, Inc. 19 Fortune Drive, Manning Park, Billerica, Mass. 01821 
operating at a proton resonance of 400 MHz. The experiment utilized a 
single RF coil driven by the same transmitter by means of active switching 
and capable of generating an RF gradient strength (measured in a nutation 
experiment) of 60 kHz/cm (14 G/cm). The total duration of the composite 
gradient pulse was 4 ms and 256 t.sub.1 increments were used with a single 
scan per increment. All data points were acquired without sample spinning 
and the data were processed by sine multiplication in both domains 
followed by a complex Fourier transformation. The data in FIGS. 5A and 5B 
are presented in magnitude mode; a conventional spectrum is shown in FIG. 
5A and a spectrum taken using the inventive pulse sequence is shown in 
FIG. 5B. The spectrum of FIG. 5B shows a complete suppression of the 
mirror diagonal, indicating a successful N-type selection. 
A second example illustrating the use of the inventive pulse sequences 
involves imaging of a sample by RF gradients. In particular, a 
spatially-varying RF magnetic field can be used to map the spatial 
distribution of spins inside the gradient coil. If the amplitude of the RF 
field varies over space, then spins at different locations experience an 
RF field with a different strength and they will therefore precess with a 
different rotation frequency .omega..sub.RF =.gamma.B.sub.1 (r) around the 
local direction of the RF field. This precession frequency can be measured 
in a so-called "nutation" experiment. The resulting nutation spectrum will 
then show a distribution of the RF amplitudes across the gradient coil, 
multiplied by a density function which represents the number of spins at a 
particular location in the coil. 
FIG. 6 illustrates an RF imaging experiment performed on a sample 
containing two capillaries of water 600 and 602, arranged parallel to each 
other and to the main magnetic field (shown schematically as field B.sub.0 
and indicated by arrow-head 604). The experiment is performed in a probe 
which contains, in addition to a homogeneous RF coil, a quadrupolar 
gradient coil. The geometry of the coil can be modeled by four wires 
parallel to the z-axis of the laboratory frame. The wires are located at 
the edges of a square and, in the case of a DC voltage, carry currents 
which alternate direction in neighboring wires (0.degree.+, 90.degree.-, 
180.degree.+, 270.degree.-). This probe is described in detail in U.S. 
Pat. No. 5,232,113, which is assigned to the same assignee as the present 
invention. The disclosure of this patent is hereby incorporated by 
reference. 
The gradient RF field generated by the quadrupolar coil has no constant 
contribution (B.sub.1.sup.c =0) and equal x and y gradient components 
(G.sub.x =G.sub.y). A nutation experiment performed with the inventive 
pulse cycle discussed above (G.sub..phi. -.pi.).sub.x -G.sub..psi. 
-G.sub..psi. -.pi.).sub.x -G.sub..phi.) enables the mapping of the spin 
distribution in a particular direction in the gradient coil. This 
direction can be varied by varying the phase of the gradient pulses. 
For instance, if the gradient pulse phases are chosen equal (.phi.=.psi.), 
then the averaged Hamiltonian is proportional to I.sub.x. The direction of 
amplitude variation, and, therefore, the direction of the image, can still 
be chosen by varying the value of the sum of .phi. and .psi.. If .phi. and 
.psi. are both equal to zero, the averaged Hamiltonian is equal to: 
EQU &lt;H&gt;=-.gamma.B.sub.1g G.sub.x I.sub.x (17) 
which results in a nutation spectrum corresponding to a projection of the 
spin distribution on the x-axis. FIG. 7 shows the nutation spectrum for 
this case, which corresponds to the imaging direction indicated by arrow 
A(606) in FIG. 6. 
If .phi. and .psi. are both equal to 90 degrees, then the averaged 
Hamiltonian is equal to: 
EQU &lt;H&gt;=-.gamma.B.sub.1g G.sub.y I.sub.x (18) 
which corresponds to an imaging direction perpendicular to the previous 
example. FIG. 8 shows the nutation spectrum for this case, which 
corresponds to the imaging direction indicated by arrow B (608) in FIG. 6. 
In general, any spatial direction and any spin dependence can be obtained, 
simply by varying the phases .phi. and .psi. of the gradient pulses. These 
sequences therefore allow the implementation of any type of NMR experiment 
involving gradients, such as RF imaging experiments, P/N-type selection in 
multidimensional experiments, solvent suppression techniques and coherence 
selection in NMR experiments. 
FIGS. 9 and 10 illustrates a third example using the inventive pulse 
sequences and show two possible multiple quantum filtering sequences that 
can be incorporated in NMR experiments and that filter out coherences of a 
certain order. In FIG. 9, the phases of the RF gradient pulses 904 and 906 
and the homogeneous RF pulses 900 and 902 are perpendicular to each other 
and are chosen here, for convenience, to be y and x, respectively. The 
gradient pulses 904 and 906 are composite pulses, made up from either of 
the inventive pulse sequences illustrated in lines (11) and (15). The 
notation mG.sub.y represents m times a certain gradient evolution, 
achievable by changing either the duration or the amplitude of the 
gradient pulse. The value of m determines the multiple quantum filtration, 
so for instance for m=2 the sequence acts as a double quantum filter, for 
m=3 as a triple quantum filter and so on. The pulse sequences depicted in 
FIGS. 9 and 10 are not complete pulse sequences, but are applied as part 
of an NMR pulse sequence in which, prior to the sequences of FIGS. 9 and 
10, multiple quantum coherences are created by a combination of RF pulses 
and free evolution time intervals. 
Although only a few illustrative embodiments have been described in some 
detail, the principles of the invention will immediately suggest other 
applications. For exmnple, the principles of the invention are applicable 
in a manner which will be apparent to those skilled in the art to 
applications including but not limited to other NMR experiments.