- Email: [email protected]
Improved resolution of multiple-pulse proton images by oversampling
JOURNAL
OF MAGNETIC
RESONANCE
87,202-207
( 1990)
Improved Resolution of Multiple-Pulse Proton Images by Oversampling D. G. CORY,* Code 6122,
Chemistry
Division,
A. N. GARROWAY, AND J. B. MILLER Naval
Research
Laboratory,
Washington,
D.C.
20375-5000
Received November 30, 1989
In solid-state imaging, the strength of the magnetic field gradient is limited by the finite bandwidth of the multiple-pulse homonuclear line-narrowing sequence. Since the frequency width of the smallest resolvable voxel is fixed by residual broadening effects, the number of resolvable voxels is determined by this bandwidth restriction. The homonuclear decoupling sequences are conventionally sampled in quadrature once every cycle, leading to a Nyquist frequency of ( T~)-~, where T, is the cycle time. Here we consider sampling more than once per cycle in order to decrease the dwell and increase the bandwidth of the image. By sampling a complex data point twice per MREV-8 cycle, for example, the allowed gradient strength and, hence, the observed spatial resolution is doubled. Earlier work in spectroscopy with line-narrowing sequences (I) showed how to sample more than once per cycle, in order to increase the signal-to-noise ratio by adding together the multiple sampled signals. Until now, there has been little reason to try to increase the bandwidth of these sequences for imaging, since the line-narrowing deteriorates when one works off resonance, especially out to frequencies of the order of (27,)-l. Recently, we have demonstrated that multiple-pulse coherent averaging techniques can be successfully combined with short, approximately 4 /*s, magnetic field gradient pulses for imaging solid materials ( 2, 3). These methods were developed in response to the observation (4, 5) that resolution in ‘H imaging of solids is reduced as the dipolar decoupling efficiency of multiple-pulse techniques deteriorates far from resonance (6, 7). We found that for simple polymers under our experimental conditions (2)) the dominant contribution to this deterioration of the decoupling efficiency originates from phase evolution of the magnetization between the RF pulses and is not associated with an incorrect flip angle by the off-resonance RF pulses. This source of broadening is reduced by inserting short gradient pulses into carefully selected windows. Hence the bandwidth of the line-narrowing sequence is increased. In this Communication we take advantage of this increased excitation bandwidth to increase the sampling bandwidth (decrease the dwell) in such line-narrowing cycles by sampling more often than once a cycle; we refer to this procedure as oversam* National Research Council/Naval 0022-2364190
$3.00
Copyright 0 1990 by Academic Press, Inc. All rights ofreproduction in any form reserved.
Research Laboratory postdoctoral associate. 202
COMMUNICATIONS
203
MREV8
gradient FIG. I The MREV-S sequence with gradient pulses and acquisition windows employed in this study. For the spectra shown in Fig. 2, the cycle time was 60 ps, and the r/2 pulse was 2.5 /.A The operator corresponding to a linear term in 1, is shown for each window. In the oversampled MREV-S sequence, sampling occurs in the 1; windows (the first and third 2~ windows) and is indicated by the arrows.
pling. A fundamental limitation to the resolution obtainable in an image is the resonance linewidth in the absence of a magnetic field gradient (4, 5). If the imaging involved only data collection of a continuous free induction decay, the dwell could be arbitrarily reduced while the gradient was simultaneously increased to reach any desired resolution. Naturally, signal-to-noise considerations place a limit on such a modest proposal. With stroboscopically detected multiple-pulse signals, however, the dwell is conventionally taken to equal the cycle time which imposes a limit on the minimum dwell, making it difficult to reduce the dwell past a minimum cycle time. Oversampling reduces the dwell below this minimum cycle time limit. Here we will consider explicitly the example of sampling twice in an MREV-8 (8, 9) sequence modified for imaging (2) with short pulsed field gradients as shown in Fig. 1. The subcycles between gradient pulses and acquisitions are WAHUHA cycles; therefore this sequence will always retain the decoupling efficiency of an on-resonance WAHUHA sequence. The major improvement on going from a WAHUHA to an MREV-8 cycle is that the zero-order average dipolar Hamiltonian in the Magnus expansion vanishes regardless of duty cycle of MREV-8 ( 10,1 I ) . The line-narrowing efficiency of the MREV-8 cycle does not depend on which 27 window the observation takes place in, but each 27 window has a different effective preparation pulse. For observation of the magnetization in the first 27 window (an I, window, cf. Fig. 1) the effective preparation pulse is only a 7r/2 pulse and hence little magnetization is dephased by dipolar interactions. For sampling in the third 27 window the preparation pulse is both the r/2 pulse and a WAHUHA cycle; consequently more of the magnetization is dephased. Of course the remainder of the cycle refocuses much of this magnetization and this allows the process to be repeated. The result is that sampling in these two windows is not exactly equivalent. Under our experimental conditions, we have not observed any amplitude modulation. There is, however, a variation in the pedestal contributions to the signals which must be eliminated prior to Fourier transformation. Pedestals are often observed in multiple-pulse experiments as slowly decaying DC signals which originate from spin-locked magnetization. Static resonance offsets complicate this picture unless they are refocused during the subcycles, and for our purposes we will assume that such offsets are sufficiently small compared to the range of gradient shifts that they may be safely ignored.
204
COMMUNICATIONS
I”~‘,‘~~~,“~‘,~r”,“’
10
5
0
-5
-1OkHr
FIG. 2. Spin density profiles of the ferrocene sample shown in the figure. Spectrum A was acquired with a single acquisition every 127, and the gradients were set as large as possible while still avoiding aliasing. The actual gradient strength is difficult to quantify since the gradient is applied as an irregularly shaped pulse. If for simplicity the gradient pulse shape is taken to be rectangular, then a gradient of 150 mT/m or 50 kHz across the sample was used to acquire these spin density profiles. This is a reasonable estimate since our gradient system can deliver at most 300 mT/m. Spectrum B was acquired with two acquisitions every 127, hence doubling the spectral width. The gradient setting in B is identical to that in A. Spectrum C was acquired with gradient pulses twice as strong as those in spectra A and B, and was sampled twice per 127, hence doubling the spatial resolution of the spin density profile.
Experiments were carried out on a homebuilt 100 MHz spectrometer. The probe has been described previously (3). All ‘H spin density profiles were measured with the same phantom of ferrocene. The phantom geometry is shown in Fig. 2. Ferrocene was selected for these studies since it has a small proton chemical-shift anisotropy
205
COMMUNICATIONS
and not because of its somewhat reduced homonuclear fdipolar linewidth. For all displayed spectra, small pedestals were removed from the free induction decays prior to Fourier transformation to eliminate zero frequency artifacts. Figure 2A shows the pulsed gradient MREV-8 spin density profile of the phantom measured with acquisition of a complex pair of data points once every cycle. Figure 2B is an experiment identical to that displayed in Fig. 2A, but the complex magnetization has been sampled twice per cycle, or once every 67. As one would expect, this results in a doubling of the spectral width so that now the identical spin density profile which is shown in Fig. 2A is contained in the central portion of Fig. 2B. There are twice as many data points in Fig. 2B as there are in Fig. 2A; therefore the resolution of the two profiles is identical. Of course, Fig. 2B extends twice as far in frequency and also in space. The resolution may be increased by doubling the gradient strength as in Fig. 2C to obtain an image on the same spatial scale as that in Fig. 2A, but with twice the number of data points and therefore twice the resolution. The spin density profiles in Figs. 2A and 2C are very similar, but not identical. Part of the broadening in the over-sampled profile originates from the failure of the dipolar term to refocus. In addition, by doubling the gradient strength the falling edge of the gradient pulse extends slightly into the first pulse of the following solid echo, and this may cause additional broadening by effectively driving the pulse off-resonance. The gradient was doubled by doubling the pulsed output voltage of the audio amplifier as monitored by an oscilloscope; there is a small error associated with this procedure. Since for the oversampled MREV-8 sequence sampling takes place once a WAHUHA subcycle, are there benefits to this approach over simply imaging with a WAHUHA cycle and a single gradient pulse? Clearly both approaches have the same dwell. Depending on the phase evolution introduced by the gradient, some error terms in the average Hamiltonian are reintroduced; however, these do not necessarily recover their full value and appear for only certain portions of the image. These terms are also only reintroduced for large gradient evolutions which is just the situation necessary for them to be averaged by the gradient shift in a second averaging frame ( 23). Assuming that the zero-order dipolar average Hamiltonian is the dominant residual broadening term, the averaged Hamiltonian associated with this may be written down by considering the cycle to be composed of two WAHUHA cycles joined with a z pulse. The averaged Hamiltonians for the two WAHUHA cycles have been calculated previously as (ABC)(
CBA):
2
g'
=
-~~.P,,j[(Ai+Ci)B,+B,(A,+C,)l l
(ABC)(CBA): 2 g’ = + 4 c
Pi,j[(Ai
+
Ci)Bj
+ Bi(Aj
+
Cj)]
l
in the standard generalized notation of Mansfield (8) (for a complete description of this nomenclature refer to But-urn and Rhim (12)). To find the result of the gradient evolution on their sum, they are added together with the second appropriately phase shifted to yield
206 2g)~6
COMMUNICATIONS -?rCPi,j[(Ai~j+BiA,)(COSol-
1)
l
-(Ai~+CiAj)Sincr+(BiBj-CiC,)2COS(YSincu],
[2]
where LYis the angular evolution due to a single gradient pulse for the spin packet of interest, and @i,j is the strength of the dipolar coupling between spins i andj. From Eq. [ 21 we see that no portion of the reintroduced dipolar Hamiltonian is directly along the axis of gradient evolution (1, or A). Therefore at large gradient evolutions some error Hamiltonians are reintroduced, but these may be second averaged by this same gradient evolution and the full effect of the error is not observed. In this case it does appear that oversampling an MREV-8 cycle is preferable to using a WAHUHA cycle. As a footnote to this method, there is another mode of oversampling where during a single window a very large gradient is applied and data are rapidly collected during the course of a few microseconds. This approach is technologically difficult and has no apparent advantages over the method suggested here. Oversampling once will lead to a sensitivity gain of fi regardless of whether the data points are added together to increase the signal ( I ) or whether they are sampled to increase the signal bandwidth as we suggest here. This is a consequence of having a noise bandwidth which is much larger than the spectrum width so that by increasing the spectrum width the noise is folded in one less time resulting in a e decrease in the noise level of the spectrum. The noise bandwidth is a function of the sampling time (long window length) and thus is unaffected by the signal bandwidth in these experiments. Oversampling once without increasing the gradient strength (or oversampling in a cycle used for spectroscopy) results in a \Jz increase in the signal-tonoise ratio, no change in resolution, and a doubling of the spectral width. Doubling of the gradient strength, when coupled with oversampling once, results in a decrease in the signal-to-noise ratio of only fi (rather than the factor of 2 normally associated with doubling the gradient strength) while both the resolution and the spectral width are doubled. It has been demonstrated that by oversampling (i.e., sampling more than once a cycle) for certain multiple-pulse imaging experiments which incorporate gradient pulses and for which off-resonance effects are refocused or for which such effects are unimportant, the resolution of the image is increased corresponding to a decrease in the dwell. The most noticeable influence of oversampling on the acquired data is that the pedestals of the data acquired in the separate windows are not identical and should be corrected individually. It is also expected that a small amplitude imbalance exists between the two data sets, but in practice this has not been observed, and the present data analysis ignores this possibility. Oversampling opens the possibility of employing longer and more highly compensated sequences for imaging purposes without suffering from a prohibitively long dwell. ACKNOWLEDGMENTS D.G.C. acknowledges the receipt of a National Research Council/Naval Research Laboratory postdoctoral associateship. This work was sponsored in part by the Office of Naval Research.
COMMUNICATIONS
207
REFERENCES W.-K. RHIM, D. P. BURUM, AND R. W. VAUGHAN, Rev. Sci. Instrum. 47,720 ( 1976). J. B. MILLER, D. G. CORY, AND A. N. GARROWAY, Chem. Phys. Lett., in press. D. G. CORY, J. B. MILLER, AND A. N. GARROWAY, Mol. Phys.. submitted. J. B. MILLER AND A. N. GARROWAY, J. Magn. Reson. 82,529 ( 1989). D. G. CORY AND W. S. VEEMAN, J. Magn. Reson. 84,392 ( 1989). W.-K. RHIM, D. D. ELLEMAN, AND R. W. VAUGHAN, J. Chem. Phys. 59,374O ( 1975). A. N. GARROWAY, P. MANSFIELD, AND D. C. STALKER, Phys. Rev. B II, 121( 1975). P. MANSFIELD, M. J. ORCHARD, D. C. STALKER, AND K. H. B. RICHARDS, Phys. Rev. B 7,90 ( 1973). W.-K. RHIM, D. D. ELLEMAN, L. B. SCHREIBER, AND R. W. VAUGHAN, J. Chem. Phys. 60,4595 (1974). IO. W.-K. RHIM, D. D. ELLEMAN, AND R. W. VAUGHAN, J. Chem. Phys. 58, 1772 ( 1973). Il. M. MEHRING, Z. Naturforsch. A 27, 1634 ( 1972). 12. D. P. BURUMAND W.-K. RHIM, J. Chem. Phys. 71,944 ( 1979). 13. A. PINESAND J. S. WAUGH, J. Magn. Reson. 8,354 ( 1972). 1. 2. 3. 4. 5. 6. 7. 8. 9.
OF MAGNETIC
RESONANCE
87,202-207
( 1990)
Improved Resolution of Multiple-Pulse Proton Images by Oversampling D. G. CORY,* Code 6122,
Chemistry
Division,
A. N. GARROWAY, AND J. B. MILLER Naval
Research
Laboratory,
Washington,
D.C.
20375-5000
Received November 30, 1989
In solid-state imaging, the strength of the magnetic field gradient is limited by the finite bandwidth of the multiple-pulse homonuclear line-narrowing sequence. Since the frequency width of the smallest resolvable voxel is fixed by residual broadening effects, the number of resolvable voxels is determined by this bandwidth restriction. The homonuclear decoupling sequences are conventionally sampled in quadrature once every cycle, leading to a Nyquist frequency of ( T~)-~, where T, is the cycle time. Here we consider sampling more than once per cycle in order to decrease the dwell and increase the bandwidth of the image. By sampling a complex data point twice per MREV-8 cycle, for example, the allowed gradient strength and, hence, the observed spatial resolution is doubled. Earlier work in spectroscopy with line-narrowing sequences (I) showed how to sample more than once per cycle, in order to increase the signal-to-noise ratio by adding together the multiple sampled signals. Until now, there has been little reason to try to increase the bandwidth of these sequences for imaging, since the line-narrowing deteriorates when one works off resonance, especially out to frequencies of the order of (27,)-l. Recently, we have demonstrated that multiple-pulse coherent averaging techniques can be successfully combined with short, approximately 4 /*s, magnetic field gradient pulses for imaging solid materials ( 2, 3). These methods were developed in response to the observation (4, 5) that resolution in ‘H imaging of solids is reduced as the dipolar decoupling efficiency of multiple-pulse techniques deteriorates far from resonance (6, 7). We found that for simple polymers under our experimental conditions (2)) the dominant contribution to this deterioration of the decoupling efficiency originates from phase evolution of the magnetization between the RF pulses and is not associated with an incorrect flip angle by the off-resonance RF pulses. This source of broadening is reduced by inserting short gradient pulses into carefully selected windows. Hence the bandwidth of the line-narrowing sequence is increased. In this Communication we take advantage of this increased excitation bandwidth to increase the sampling bandwidth (decrease the dwell) in such line-narrowing cycles by sampling more often than once a cycle; we refer to this procedure as oversam* National Research Council/Naval 0022-2364190
$3.00
Copyright 0 1990 by Academic Press, Inc. All rights ofreproduction in any form reserved.
Research Laboratory postdoctoral associate. 202
COMMUNICATIONS
203
MREV8
gradient FIG. I The MREV-S sequence with gradient pulses and acquisition windows employed in this study. For the spectra shown in Fig. 2, the cycle time was 60 ps, and the r/2 pulse was 2.5 /.A The operator corresponding to a linear term in 1, is shown for each window. In the oversampled MREV-S sequence, sampling occurs in the 1; windows (the first and third 2~ windows) and is indicated by the arrows.
pling. A fundamental limitation to the resolution obtainable in an image is the resonance linewidth in the absence of a magnetic field gradient (4, 5). If the imaging involved only data collection of a continuous free induction decay, the dwell could be arbitrarily reduced while the gradient was simultaneously increased to reach any desired resolution. Naturally, signal-to-noise considerations place a limit on such a modest proposal. With stroboscopically detected multiple-pulse signals, however, the dwell is conventionally taken to equal the cycle time which imposes a limit on the minimum dwell, making it difficult to reduce the dwell past a minimum cycle time. Oversampling reduces the dwell below this minimum cycle time limit. Here we will consider explicitly the example of sampling twice in an MREV-8 (8, 9) sequence modified for imaging (2) with short pulsed field gradients as shown in Fig. 1. The subcycles between gradient pulses and acquisitions are WAHUHA cycles; therefore this sequence will always retain the decoupling efficiency of an on-resonance WAHUHA sequence. The major improvement on going from a WAHUHA to an MREV-8 cycle is that the zero-order average dipolar Hamiltonian in the Magnus expansion vanishes regardless of duty cycle of MREV-8 ( 10,1 I ) . The line-narrowing efficiency of the MREV-8 cycle does not depend on which 27 window the observation takes place in, but each 27 window has a different effective preparation pulse. For observation of the magnetization in the first 27 window (an I, window, cf. Fig. 1) the effective preparation pulse is only a 7r/2 pulse and hence little magnetization is dephased by dipolar interactions. For sampling in the third 27 window the preparation pulse is both the r/2 pulse and a WAHUHA cycle; consequently more of the magnetization is dephased. Of course the remainder of the cycle refocuses much of this magnetization and this allows the process to be repeated. The result is that sampling in these two windows is not exactly equivalent. Under our experimental conditions, we have not observed any amplitude modulation. There is, however, a variation in the pedestal contributions to the signals which must be eliminated prior to Fourier transformation. Pedestals are often observed in multiple-pulse experiments as slowly decaying DC signals which originate from spin-locked magnetization. Static resonance offsets complicate this picture unless they are refocused during the subcycles, and for our purposes we will assume that such offsets are sufficiently small compared to the range of gradient shifts that they may be safely ignored.
204
COMMUNICATIONS
I”~‘,‘~~~,“~‘,~r”,“’
10
5
0
-5
-1OkHr
FIG. 2. Spin density profiles of the ferrocene sample shown in the figure. Spectrum A was acquired with a single acquisition every 127, and the gradients were set as large as possible while still avoiding aliasing. The actual gradient strength is difficult to quantify since the gradient is applied as an irregularly shaped pulse. If for simplicity the gradient pulse shape is taken to be rectangular, then a gradient of 150 mT/m or 50 kHz across the sample was used to acquire these spin density profiles. This is a reasonable estimate since our gradient system can deliver at most 300 mT/m. Spectrum B was acquired with two acquisitions every 127, hence doubling the spectral width. The gradient setting in B is identical to that in A. Spectrum C was acquired with gradient pulses twice as strong as those in spectra A and B, and was sampled twice per 127, hence doubling the spatial resolution of the spin density profile.
Experiments were carried out on a homebuilt 100 MHz spectrometer. The probe has been described previously (3). All ‘H spin density profiles were measured with the same phantom of ferrocene. The phantom geometry is shown in Fig. 2. Ferrocene was selected for these studies since it has a small proton chemical-shift anisotropy
205
COMMUNICATIONS
and not because of its somewhat reduced homonuclear fdipolar linewidth. For all displayed spectra, small pedestals were removed from the free induction decays prior to Fourier transformation to eliminate zero frequency artifacts. Figure 2A shows the pulsed gradient MREV-8 spin density profile of the phantom measured with acquisition of a complex pair of data points once every cycle. Figure 2B is an experiment identical to that displayed in Fig. 2A, but the complex magnetization has been sampled twice per cycle, or once every 67. As one would expect, this results in a doubling of the spectral width so that now the identical spin density profile which is shown in Fig. 2A is contained in the central portion of Fig. 2B. There are twice as many data points in Fig. 2B as there are in Fig. 2A; therefore the resolution of the two profiles is identical. Of course, Fig. 2B extends twice as far in frequency and also in space. The resolution may be increased by doubling the gradient strength as in Fig. 2C to obtain an image on the same spatial scale as that in Fig. 2A, but with twice the number of data points and therefore twice the resolution. The spin density profiles in Figs. 2A and 2C are very similar, but not identical. Part of the broadening in the over-sampled profile originates from the failure of the dipolar term to refocus. In addition, by doubling the gradient strength the falling edge of the gradient pulse extends slightly into the first pulse of the following solid echo, and this may cause additional broadening by effectively driving the pulse off-resonance. The gradient was doubled by doubling the pulsed output voltage of the audio amplifier as monitored by an oscilloscope; there is a small error associated with this procedure. Since for the oversampled MREV-8 sequence sampling takes place once a WAHUHA subcycle, are there benefits to this approach over simply imaging with a WAHUHA cycle and a single gradient pulse? Clearly both approaches have the same dwell. Depending on the phase evolution introduced by the gradient, some error terms in the average Hamiltonian are reintroduced; however, these do not necessarily recover their full value and appear for only certain portions of the image. These terms are also only reintroduced for large gradient evolutions which is just the situation necessary for them to be averaged by the gradient shift in a second averaging frame ( 23). Assuming that the zero-order dipolar average Hamiltonian is the dominant residual broadening term, the averaged Hamiltonian associated with this may be written down by considering the cycle to be composed of two WAHUHA cycles joined with a z pulse. The averaged Hamiltonians for the two WAHUHA cycles have been calculated previously as (ABC)(
CBA):
2
g'
=
-~~.P,,j[(Ai+Ci)B,+B,(A,+C,)l l
(ABC)(CBA): 2 g’ = + 4 c
Pi,j[(Ai
+
Ci)Bj
+ Bi(Aj
+
Cj)]
l
in the standard generalized notation of Mansfield (8) (for a complete description of this nomenclature refer to But-urn and Rhim (12)). To find the result of the gradient evolution on their sum, they are added together with the second appropriately phase shifted to yield
206 2g)~6
COMMUNICATIONS -?rCPi,j[(Ai~j+BiA,)(COSol-
1)
l
-(Ai~+CiAj)Sincr+(BiBj-CiC,)2COS(YSincu],
[2]
where LYis the angular evolution due to a single gradient pulse for the spin packet of interest, and @i,j is the strength of the dipolar coupling between spins i andj. From Eq. [ 21 we see that no portion of the reintroduced dipolar Hamiltonian is directly along the axis of gradient evolution (1, or A). Therefore at large gradient evolutions some error Hamiltonians are reintroduced, but these may be second averaged by this same gradient evolution and the full effect of the error is not observed. In this case it does appear that oversampling an MREV-8 cycle is preferable to using a WAHUHA cycle. As a footnote to this method, there is another mode of oversampling where during a single window a very large gradient is applied and data are rapidly collected during the course of a few microseconds. This approach is technologically difficult and has no apparent advantages over the method suggested here. Oversampling once will lead to a sensitivity gain of fi regardless of whether the data points are added together to increase the signal ( I ) or whether they are sampled to increase the signal bandwidth as we suggest here. This is a consequence of having a noise bandwidth which is much larger than the spectrum width so that by increasing the spectrum width the noise is folded in one less time resulting in a e decrease in the noise level of the spectrum. The noise bandwidth is a function of the sampling time (long window length) and thus is unaffected by the signal bandwidth in these experiments. Oversampling once without increasing the gradient strength (or oversampling in a cycle used for spectroscopy) results in a \Jz increase in the signal-tonoise ratio, no change in resolution, and a doubling of the spectral width. Doubling of the gradient strength, when coupled with oversampling once, results in a decrease in the signal-to-noise ratio of only fi (rather than the factor of 2 normally associated with doubling the gradient strength) while both the resolution and the spectral width are doubled. It has been demonstrated that by oversampling (i.e., sampling more than once a cycle) for certain multiple-pulse imaging experiments which incorporate gradient pulses and for which off-resonance effects are refocused or for which such effects are unimportant, the resolution of the image is increased corresponding to a decrease in the dwell. The most noticeable influence of oversampling on the acquired data is that the pedestals of the data acquired in the separate windows are not identical and should be corrected individually. It is also expected that a small amplitude imbalance exists between the two data sets, but in practice this has not been observed, and the present data analysis ignores this possibility. Oversampling opens the possibility of employing longer and more highly compensated sequences for imaging purposes without suffering from a prohibitively long dwell. ACKNOWLEDGMENTS D.G.C. acknowledges the receipt of a National Research Council/Naval Research Laboratory postdoctoral associateship. This work was sponsored in part by the Office of Naval Research.
COMMUNICATIONS
207
REFERENCES W.-K. RHIM, D. P. BURUM, AND R. W. VAUGHAN, Rev. Sci. Instrum. 47,720 ( 1976). J. B. MILLER, D. G. CORY, AND A. N. GARROWAY, Chem. Phys. Lett., in press. D. G. CORY, J. B. MILLER, AND A. N. GARROWAY, Mol. Phys.. submitted. J. B. MILLER AND A. N. GARROWAY, J. Magn. Reson. 82,529 ( 1989). D. G. CORY AND W. S. VEEMAN, J. Magn. Reson. 84,392 ( 1989). W.-K. RHIM, D. D. ELLEMAN, AND R. W. VAUGHAN, J. Chem. Phys. 59,374O ( 1975). A. N. GARROWAY, P. MANSFIELD, AND D. C. STALKER, Phys. Rev. B II, 121( 1975). P. MANSFIELD, M. J. ORCHARD, D. C. STALKER, AND K. H. B. RICHARDS, Phys. Rev. B 7,90 ( 1973). W.-K. RHIM, D. D. ELLEMAN, L. B. SCHREIBER, AND R. W. VAUGHAN, J. Chem. Phys. 60,4595 (1974). IO. W.-K. RHIM, D. D. ELLEMAN, AND R. W. VAUGHAN, J. Chem. Phys. 58, 1772 ( 1973). Il. M. MEHRING, Z. Naturforsch. A 27, 1634 ( 1972). 12. D. P. BURUMAND W.-K. RHIM, J. Chem. Phys. 71,944 ( 1979). 13. A. PINESAND J. S. WAUGH, J. Magn. Reson. 8,354 ( 1972). 1. 2. 3. 4. 5. 6. 7. 8. 9.