- Email: [email protected]
14N magnetic resonance for materials detection in the field
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14
N magnetic resonance for materials detection in the field
B.H. Suits,a, A.N. Garroway,b J.B. Miller,b and K.L. Sauerb,c a
Department of Physics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931-1295, USA b Code 6122, Chemistry Division, Naval Research Laboratory, Washington, DC 20375-5342, USA c Physics Department, George Mason University, Fairfax, VA 22030-4444, USA
Abstract Nitrogen is prevalent in many materials, both naturally occurring and man-made. In particular, it is found in many explosives and other contraband materials. One technique for the detection of such materials in the field is the use of the magnetic resonance signal from the nearly 100% abundant, spin-1, 14N nuclei. Some of the difficulties with such measurements in the field include spurious signals from acoustic resonances, radio-frequency interference, and generally low signal-to-noise ratios. A summary of recent work by the authors to help mitigate these difficulties is presented. r 2003 Elsevier Inc. All rights reserved. Keywords: NQR; Materials detection; NMR; Field measurements
1. Introduction Nuclear magnetic resonance (NMR) spectroscopy is noted for its ability to distinguish between different chemical species making the technique an obvious candidate for materials detection applications. Of particular current interest is the ability to detect specific target species such as solid explosives for package, luggage, and possibly vehicle inspection and for finding buried landmines. Similar technologies could be used to detect other materials of interest, such as narcotics, and is not limited solely to explosives [1–3]. While it is quite straightforward to observe magnetic resonance signals for a wide variety of explosive materials in a laboratory setting, the ultimate application is to be able to identify the presence of these materials in the field with the smallest number
Corresponding author. Fax: +1-906-487-2933. E-mail address: [email protected] (B.H. Suits).
0926-2040/03/$ - see front matter r 2003 Elsevier Inc. All rights reserved. doi:10.1016/S0926-2040(03)00045-6
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of false-positive indications (i.e. the detection of an explosive when in fact one is not present) and false-negative indications (i.e. to detect that no explosive is present when in fact one is present). There are severe practical difficulties associated with the use of a large magnetic field for such measurements. The presence of benign magnetic materials (including magnetic recording media which would be erased) in packages and luggage and the difficulty of supplying a sufficiently large, uniform magnetic field for landmine applications are obvious problems. While NMR in Earth’s field has been successful for some applications, particularly in the oil industry [4], such techniques discriminate between different (liquid) materials based on differences in NMR relaxation times and there is a loss of the spectral resolution necessary to distinguish an explosive from a benign background. Furthermore, the ‘‘sample’’ here is a polycrystalline solid material and in this case, sample spinning is simply out of the question. Hence, one turns to techniques of zero-field NMR or nuclear quadrupole resonance (NQR). To use NQR, a nucleus with a spin I > 1=2 must be available. Since the materials of interest here are all solids containing a significant number of 14 N nuclei ðI ¼ 1Þ; 14N NQR spectroscopy is an obvious choice. Other potential nuclei which have been investigated, but which are not discussed here, include 35Cl, 37 Cl, and 39K. There have been a number of general papers written describing the use of 14N NQR to observe explosives [1–3,5]. The purpose of this work is specifically to summarize some of the recent results by the authors to explore, at a fundamental level, possible techniques and apparatus for 14N NQR detection of explosives in the field. The general goals of the research are to develop improved apparatus and/or techniques to: * * *
* *
increase the NQR sensitivity, mitigate radio-frequency interference in the field, separate desired NQR signals from other signals when they are present (e.g. due to magneto-acoustic and piezoelectric ringing), and/or eliminate the undesired signals, more efficiently collect signals, and develop new uses.
The basic instrumentation and techniques required for NQR measurements are the same as those required for traditional (non-spinning, wide-line) NMR, though without a magnet and possibly with a significantly wider range of operating parameters. The work presented here specifically involves the development of better probes and associated techniques to address some of the issues mentioned above. 2.
14
N NQR basics
There are some important differences between NQR and the more familiar high-field NMR. We start by reviewing well-known results [6] for the simplest
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pulsed NQR measurements in order to define terms and to set the stage for what follows. The nearly 100% abundant 14N isotope has a nuclear spin, I ¼ 1: The Hamiltonian for the interaction between a spin-1 nucleus and the electric field gradient (EFG) within a sample is given in the EFG’s principal axis system ðx; y; zÞ and in terms of the usual spin operators by HQ ¼
i hnQ h 2 Z ð3Iz I 2 Þ þ ðIþ2 þ I2 Þ ; 2 3
ð1Þ
where nQ characterizes the strength of the interaction and Z ð0pZp1Þ; is the asymmetry parameter (see Ref. [6] for more details). This Hamiltonian has the three eigenfunctions and corresponding energy levels shown in Fig. 1. The three possible NQR transition frequencies are given by Z n7 ¼ nQ 17 ; 3
2 n0 ¼ ZnQ : 3
ð2Þ
Typical transition frequencies for 14N are in the range from 0 to about 5 MHz with typical line widths of B100–1000 Hz. The large range combined with relatively narrow line widths make it extremely rare to find two different compounds with the same NQR frequencies. Hence, there is excellent chemical specificity. However, the low frequencies and the relatively low magnetogyric (gyromagnetic) ratio of 14N (7% that of 1H, 48% of 2H) conspire to make such measurements challenging. For simplicity in what follows, we assume below that Za0 or 1 to avoid degenerate energy levels and/or transition frequencies. If we apply an RF pulse in the laboratory reference frame ðx0 ; y0 ; z0 Þ which produces an RF magnetic field of magnitude B1, angular frequency o; along x0 ; then the interaction with the nucleus is described by the Hamiltonian H1 ¼ g1 _B1 Ix0 cos ot;
ð3Þ
where g1 is the magnetogyric ratio for the spin-1 nucleus and Ix0 ¼ cos a Ix þ cos b Iy þ cos d Iz ;
Fig. 1. The energy level diagram for a spin-1 nucleus in an electric field gradient.
ð4Þ
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where a; b; and d are the angles between the x0 -axis and the x-, y-, and z-axis, respectively. Since / þ jIx j0S ¼ /0jIx j þ S ¼ 1; / jIy j0S ¼ /0jIy j S ¼ i; ð5Þ / þ jIz j0S ¼ / jIz j þ S ¼ 1; and all other matrix elements are zero, the effective part of the RF magnetic field for the nþ transition, for example, is H1eff ¼ g1 _B1 cos a Ix cos ot _o1þ Ix cos ot;
ð6Þ
where we define o1þ ¼ g1 B1 cos a: It is straightforward to show that if o ¼ oþ 2pnþ ; that is we are exactly on resonance, then the effect of a pulse of duration tp of this RF is the same as that of a rotation by an angle W ¼ o1þ tp =2 about the x-axis. For the n0 and n transitions, an on resonance RF pulse corresponds to a rotation about the z- and y-axis, respectively. In the high-temperature approximation, neglecting constant terms that will not contribute to the signal as well as an overall scale factor, the density matrix in thermal equilibrium can be written as rð0Þ ¼ 3Iz2 þ ZðIx2 Iy2 Þ:
ð7Þ
At time, t; after the nþ on-resonance RF pulse one then has rðtÞ ¼ eiHQ t=_ eiWIx rð0ÞeiWIx eiHQ t=_ ;
ð8Þ
the expectation value /Ix S ¼ TrðrðtÞ; Ix Þ ¼ ð3 þ ZÞ sin 2W sin oþ t;
ð9Þ
and the expectation of the other two components of I will not contribute. The observed signal from the resulting nuclear magnetization is given in the lab frame by d/Ix S d/Ix S d/Ix S ; Sy0 ðtÞp cos b ; Sz0 ðtÞp cos d : ð10Þ Sx0 ðtÞp cos a dt dt dt That is, for the nþ transitions, only the component of the RF along the x-axis is important, and the resulting nuclear magnetization is linearly polarized along the xaxis. Similar results are found for the other two transitions along the other two axes. Note that the signal here is a maximum when W ¼ p=4 or o1þ tp ¼ p=2: Such a pulse is referred to as a p=2 pulse even though the actual rotation involved is p=4: For a polycrystalline sample, we must average over all EFG orientations giving, for the nþ transition, "sffiffiffiffiffiffiffiffiffiffiffiffiffiffi # 2p S% x0 ðtÞpnþ ðpþ p0 Þ cos oþ t J3=2 ðg1 B1 tp Þ ; g1 B1 tp S% y0 ðtÞ ¼ S% z0 ðtÞ ¼ 0;
ð11Þ
where J is a Bessel function and (p+p0) is the initial population difference between the |+S and |0S states. The maximum signal for a powder sample is obtained when
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g1 B1 tp E119 . The linearly polarized RF pulse along x0 results in a linearly polarized observable signal from the total nuclear magnetization which is also along x0 and it is in phase with the applied RF. Similarly, for powder measurements using the transitions at n0 and n one also obtains an observable signal only along x0 for an RF field applied along x0 :
3. Circularly polarized RF The use of a circularly polarized RF magnetic field was pursued as a possible means of improving the signal-to-noise ratio (SNR) and as a means to separate interfering acoustic signals from the desired NQR signal [7]. At first this may seem counterintuitive since, as was discussed above, the NQR excitation and resulting nuclear magnetization are inherently linearly polarized. For a circularly polarized RF magnetic field one has in the lab frame H1 ¼ g_B1 ðIx0 cos ot þ Iy0 sin otÞ
ð12Þ
and once again we will use the nþ transition as an example. Using spherical coordinates y and f which describe the orientation of the x-axis in the lab reference frame, the effective Hamiltonian can be written in the principal axis frame: H1eff ¼ g1 _B1 sin yðcos f cos ot þ sin f sin otÞIx ¼ g1 _B1 sin y cosðot þ fÞIx :
ð13Þ
With the new definition o1þ ¼ gB1 sin y; the analysis proceeds as above to give
Sx0 ðtÞ cos f ð14Þ cosðoþ t fÞ; poþ ðpþ p0 Þ sin y sin o1þ tp Sy0 ðtÞ sin f a linearly polarized signal, which must now be averaged over all orientations, that is all y; f: The resulting signal is given by the rapidly converging series expansion !
cos oþ t J1 ðg1 B1 tp Þ J3 ðg1 B1 tp Þ S% x0 ðtÞ ? ð15Þ p4 oþ ðpþ p Þ 3 15 sin oþ t S% y0 ðtÞ and the total signal is circularly polarized. The maximum of this signal is obtained when g1 B1 tp E102 . To understand why circular polarization is a benefit, consider three sets of nuclei which have their principal x-axis along the laboratory frame x0 -, y0 -, and z0 -axis, respectively. If RF is applied only along the x0 -axis, then only one set of nuclei will have a non-zero effective RF interaction, and hence only one set will produce a signal. On the other hand, circularly polarized RF in the x0 –y0 plane will excite two sets of these nuclei, albeit 90 out of phase with each other. These two sets then produce a linearly polarized nuclear magnetization along their respective axes, also 90 out of phase. When combined these two signals yield a circularly polarized magnetization. That is, a larger fraction of the available nuclei is effectively excited and contribute to the signal if circularly polarized excitation and detection is used.
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Fig. 2. Simplified schematic for excitation and detection of circularly polarized NQR signals. As shown a two-channel receiver is used. For single channel operation, the two signals can be multiplexed.
A simplified schematic for an experimental arrangement for a measurement using circular polarization is shown in Fig. 2. Two independent sets of coils are used and are driven out of phase. On the receive side, two linearly polarized signals are measured which can then be combined in software to obtain any desired polarization for the received signal. Fig. 3 shows the results of a single pulse experiment for linearly polarized excitation compared to circularly polarized excitation. For circular polarization, data from only one channel are shown. Since there are two such independent signals available which can be co-added (after appropriate phase shifts are applied), even though there is a slight loss in sensitivity for each receive channel, there is a net gain in the SNR of about 21%. There are additional benefits for the use of circular polarization. Referring back to Eq. (6), it can be seen that with linear polarization the distribution of effective RF magnetic fields across the sample is uniform from 0 to B1 : This wide distribution leads to inefficiencies similar to those seen in NMR with extremely inhomogeneous B1 fields. In particular, multiple pulse sequences are not as effective as they would be for a uniform B1 : With circular polarization, however, more of the nuclei are seeing an effective-B1 near to the value B1 : Hence, in effect, the RF field has been made significantly more homogeneous. For explosive detection applications, the most efficient data collection schemes utilize pulse sequences which produce an echo train, such as the spin-lock spin-echo (SLSE) sequence, and can be expected to work more efficiently for more homogeneous (effective) RF fields. Although beyond the scope of this article, composite pulse techniques have also been studied as an alternative method to compensate for the wide range of effective RF excitation which occurs for powder NQR. [8,9]. Another advantage of circular polarization is the potential to distinguish the NQR signal from other interfering signals. Such signals arise through a coupling between the applied RF field and an acoustic resonance via either a magnetostrictive or piezoelectric effect. In practice, these signals arise most often from a single source which responds with linear polarization. In practice these signals can drift with time
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0.5
NaNO 2 4.64 MHz
Relative Signal (arb. units)
0.4
Linear Polarization
0.3 0.2 0.1
Circular Polarization
0.0 -0.1 -0.2 -0.3 0
100
200
300
400
500
600
700
Nutation Angle (deg.)
Fig. 3. Experimental results compared to theory for linear and circularly polarized detection. Data from only one receiver channel are shown for circular polarization. The data shown are for the nþ transition from NaNO2 at 4.64 MHz at room temperature. Full details can be found in Ref. [7].
Fig. 4. Experimental results comparing the received signal for an NQR measurement of NaNO2 at 4.64 MHz (top) and the acoustic signal from a pair of pliers (bottom) when received data are combined in the same sense as the excitation (left) and in the opposite sense (right). The circularly polarized NQR signal is easily distinguished from the linearly polarized acoustic signal. Full details can be found in Ref. [7].
sufficiently rapidly so that they cannot be removed effectively by phase cycling and coherent averaging. Since the NQR signal from a powder has the same polarization as the excitation (whether it be linearly or circularly polarized along any axis) but the interfering signal will respond with linear polarization along an axis determined by the orientation of the interfering object, the two types of signals can be distinguished. This is illustrated in Fig. 4. The data in Fig. 4 are combinations of the two receive channels corresponding to two senses of circular polarization. On the left side of the figure, the polarization is in the same sense as that of the circularly polarized excitation. On the right it is the opposite—that is circularly polarized with the opposite sense of rotation. The top signal is an NQR signal from a powder sample, while that at the bottom is an acoustic signal from a pair of ‘‘locking’’ pliers. The circular polarization of the NQR signal compared to the linear polarization (which
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shows up equally for both senses of circular polarization) of the signal from the pliers is evident.
4. Three-frequency NQR As mentioned above, one of the problems with measurements in the field are couplings between acoustic resonances from benign materials and our applied RF field. After the RF is turned off, the acoustic system continues to ring and this can give rise to signals which mimic true NQR signals in many ways. The problem can be avoided, of course, if one does not apply an RF field at or near the NQR frequency. Hence, we have explored three-frequency (3f) NQR as a means to obtain an NQR signal without applying an RF field at the observation frequency [10]. For the NQR system, all three possible transitions shown in Fig. 1 are possible. The idea is to excite at two of these three frequencies and observe at the third. In concept this is similar to multiple quantum NMR except that all transitions are directly observable. The excitation can be accomplished using two separate, but closely spaced, RF pulses at two different frequencies, which we refer to as serial excitation, or by applying the two pulses at the same time, referred to as simultaneous excitation. Other excitation schemes are also possible. Here we will use as an example, excitation of the n0 and n transitions with observation at nþ ; however, other permutations yield similar results. The effect of an RF pulse applied at a single frequency is discussed above—for the n0 and n transitions it is a rotation about the z- and y-axis, respectively. Defining the effective RF fields o10 and o1 in a manner similar to the definition of o1þ in Eq. (6), one finds that for serial excitation where a first RF pulse of length t is applied at n and a second of length t0 at n0 ; the signal at nþ is proportional to Sp sinðo10 t0 =2Þ sinðo1 t Þ
ð16Þ
which is a maximum if the first pulse is a p=2 pulse and the second a p pulse. This expression will need to be averaged over all orientations. While the derivation is a bit complicated, it can be shown that the effect of an RF pulse applied simultaneously at two different resonance frequencies can also be written as a rotation of our spin-1 system. Defining O2 ¼ o210 þ o21 ; and tan x ¼ ðo1 =o10 Þ; a simultaneous RF pulse of duration tp will have the same effect as a rotation by an angle W ¼ Otp =2 about an axis which is in the y2z plane, at an angle x from the z-axis. Following through the analysis as was done in Eqs. (8)–(10), and keeping only those terms relevant for detection at nþ ; one finds that the signal is proportional to Sp sin x cos xðcos y 1Þ½ð3 Z cos WÞ cos2 x þ ð3 cos W ZÞ sin2 x Zð1 þ cos WÞ
ð17Þ
which has a maximum when W ¼ p and x ¼ p=8 (or 3p=8). For those values the signal is identical to what would be obtained in a traditional single-frequency
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Fig. 5. Simplified schematic for a three-frequency measurement using a single channel spectrometer.
measurement. Note that a rather complicated angular dependence relating the ðx; y; zÞ and ðx0 ; y0 ; z0 Þ coordinate systems has been hidden in the variables W and x and a powder average is necessary. Somewhat more complicated expressions have been obtained for various two-pulse echo sequences. That is, an initial pulse (either simultaneous or serial) at the two excitation frequencies, a delay, and then a second pulse (either simultaneous or serial) followed by observation at the third frequency. These results are presented elsewhere [10]. The signal at nþ following both serial and parallel excitations at n0 and n for powder samples was computed numerically and agrees very well with experimental measurements [10]. A simplified schematic of a configuration to perform these measurements using a single channel spectrometer while still allowing coherent averaging is shown in Fig. 5. Note that to obtain maximum sensitivity from a powder sample for either serial or parallel excitation, the three RF coils should produce mutually orthogonal RF magnetic fields at the sample, and for practical reasons they should have minimal (ideally zero) mutual inductance. Fig. 6 shows the effectiveness of this technique for removing acoustic ringing signals. Here acoustic signals from a slightly magnetized paper clip dominate when traditional single frequency techniques are used. Using the three-frequency technique with serially applied excitation pulses eliminates the acoustic signal. The price paid for removing this interference is a reduction in the signal strength by approximately a factor of two. Also visible in Fig. 6 is that the dead time after the RF pulse is significantly reduced using the 3f technique. The use of simultaneous excitation (not shown) is not nearly as effective at removing the acoustic signal, presumably due to non-linearities in the magnetic properties of the paper clip.
5. Gradiometer coils Since 14N NQR signals fall within a frequency range where there are a large number of radio broadcast stations (0.5–5 MHz which includes AM, shortwave, and
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NaNO2 4.64 MHz
Paper Clip
Relative Signal (arb. units)
6 NaNO2 4
1f
2 NaNO2 3f Serial (x 2) 0
Paper Clip
-2 0
1
2
3
4
Time (ms)
Fig. 6. A comparison of traditional single-frequency measurements (top) with the three-frequency technique using serial excitation (bottom) for NaNO2 and the acoustic signal from a paper clip. 3f serial excitation virtually eliminates the acoustic signal while the NQR signal has been reduced by only about a factor of two.
various other radio services), interference from those stations is a significant problem in an unshielded environment. Other sources of RF interference important in this frequency range include lightning, power line noise, and automotive ignition noise, to name a few. This is a particular problem for landmine detection since one cannot surround the ‘‘sample’’ with an electrical shield. In order to address problems of RF interference, another series of studies was pursued which includes a mix of theory and experiment involving RF gradiometer coils as one way to deal with this issue [11]. An RF gradiometer will have no magnetic dipole moment (and ideally no electric dipole moment) and so is a very poor antenna for distant sources. On the other hand, nearby sources, such as from the desired material to be detected, still give rise to usable signals. In addition, it was shown that deleterious effects due to soil conductivity (an issue for landmine detection) are much less of a problem for the gradiometer coil than for other coils [12]. Two simple gradiometer coil configurations are shown in Fig. 7. These coils should be coupled in an electrically balanced manner to avoid creating a large electric dipole moment between the coil and the surroundings. Fig. 8 illustrates the ability of a gradiometer coil to reject distant sources. Here identical NQR measurements were performed using the explosive RDX (hexahydro1,3,5-trinitro-1,3,5-triazine) as the sample, both inside and outside an electrically shielded cage using a simple, electrically balanced axial gradiometer. Measurements using a comparably sized coil of similar dimensions, but of traditional design, showed that the noise level outside the cage was approximately 25 dB larger than inside the cage. With the gradiometer coil, the two noise levels are comparable, within 1 dB. Full details can be found in Ref. [11].
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Fig. 7. Two simple examples of gradiometer coils include the axial gradiometer and the planar (figure-8) gradiometer configurations.
4
3.360 MHz RDX
Shielded
Signal (arb)
3
2
1
Unshielded
0 -30
-20
-10
0
10
20
30
Frequency (kHz) Fig. 8. NQR signals observed for an explosive material both inside and outside an electrically shielded environment. With a conventional coil of comparable size, the noise level outside the shield is approximately 25 dB larger than it is inside the shield (from Ref. [11]).
One disadvantage of simple gradiometers is that some signal loss occurs. In order to counter that loss, we have pursued asymmetric gradiometers designed to optimize the field produced within a designated inspection region subject to the constraints imposed by Maxwell’s equations. By reciprocity this optimizes the receive sensitivity in that region. Details of this work will appear elsewhere. Fig. 9 illustrates the
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Fig. 9. An asymmetric two-layer gradiometer coil designed to optimize the magnetic field within a specified sample region. The coil is circular (B22 cm outside diameter), the upper and lower layers are coaxial, and it is shown in cross-section. Shown are equally spaced contours of magnetic field strength (arb. units) for a unit current in the coil.
magnetic field, and by reciprocity the receive sensitivity, for one of our prototype asymmetric gradiometer coils.
6. Super-Q detection Probe sensitivity in general will depend on the quality factor of the RF detection coils used. This prompted us to investigate the very high quality factor ðQÞ limit for a detection coil [13], such as what one could achieve using superconducting coils. Normally in NMR (and NQR) one expects the receive sensitivity of a probe to depend (among other things) on the square root of its quality factor, Q: For transient (pulse) magnetic resonance, this result is derived assuming the bandwidth of the tuned detection coil is large compared to the bandwidth of the signal. With a very high Q; there is the potential to produce a tuned probe for 14N NQR that has bandwidth significantly smaller than the bandwidth of the signal to be measured. There are certainly a number of significant challenges with the practical use of very high Q coils, such as very long ring down times. Here, we put these other complications aside and simply investigate whether one can obtain a significantly improved SNR with a very high Q coil. That is, is there enough potential improvement to warrant the significant effort which would be necessary to deal with these other problems? It is certainly counterintuitive to make a measurement using a probe bandwidth smaller than the signal bandwidth since less signal will be collected and spectral resolution will be compromised. However, here we consider use as a materials detector and not for spectroscopy. That is, the spectrum of the target material is known, it is only necessary to determine whether or not it is present. Since the spectra from different chemical species do not overlap, the loss of spectral resolution is not important. What is important is the ultimate SNR for this detection and that depends not only on the signal, but on the noise as well. If we lose noise faster than we lose signal, there is a net gain in SNR.
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NF
1
10
0.01 dB 0.1 dB 1 dB 3 dB 6 dB 10 dB
2
2 2
(SNR) (units of A π /πP0)
0
10
135
Probe Limited
-1
10
-2
10
-3
10
Amplifier Limited
-4
10
-5
10
-3
10
-2
10
-1
10
0
1
10
10
2
10
3
10
4
10
Q'
Fig. 10. Predicted SNR improvements as the Q of the coil, normalized to the Q of the signal, is increased based on a simple model amplifier. Here NF refers to the noise figure of the amplifier. Other details, including definitions of the factors which define the vertical scale, are found in Ref. [13]. Results for real amplifiers will be similar.
Fig. 10 shows the principal result. Here, the Q of the probe is normalized by the Q of the resonance signal. Hence, when Q0 ¼ 1 the bandwidth for detection is the same as the bandwidth of the signal. Traditional high-resolution NMR measurements would be far to the left on this plot. Typical values for 14N NQR using copper coils designed for high Q and large samples are in the vicinity of Q0 E0:1: On the left side, the ultimate SNR (for detection) is determined predominately by the thermal noise of the probe. On the right the thermal noise from the probe continues to decrease compared to the desired signal, but ultimately the noise from the amplifiers dominates. It can be seen that some improvement can be had up to about Q0 E5 for state-of-the-art low-noise preamplifiers, but beyond that there is no further gain.
7. Conclusion Bringing NQR out of the laboratory and into the field has required many innovations by many researchers world wide (see Ref. [2]). Here, a number of results are summarized from recent studies by the authors to improve methods for 14N NQR detection of explosives in the field. Some of the unique challenges have been presented along with some possible methods to address those challenges. In particular we have investigated methods of probe design which take advantage of some of the unique properties of spin-1 NQR (e.g. the use of circularly polarized RF and 3f measurements) as well as basic properties of the coils which make up the probe (gradiometers and super-Q detection).
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Acknowledgments This work has been supported in part by the Office of Naval Research, US Army, and US Federal Aviation Administration. K.L.S. acknowledges a National Research Council fellowship and B.H.S. is supported in part under an NRL Broad Agency Announcement Grant N00173-01-1-G000.
References [1] A.N. Garroway, M.L. Buess, J.P. Yesinowski, J.B. Miller, Narcotics and explosive detection by 14N pure NQR, Proc. SPIE 2092 (1993) 318–327. [2] A.N. Garroway, M.L. Buess, J.B. Miller, B.H. Suits, A.D. Hibbs, G.A. Barrall, R. Matthews, L.J. Burnett, Remote sensing by nuclear quadrupole resonance, IEEE Trans. Geosci. Remote Sensing 39 (2001) 1108–1118 and references therein. [3] V.S. Grechishkin, N. Ya Sinyavskii, New technologies: nuclear quadrupole resonance as an explosive and narcotic detection technique, Phys. Usp. 40 (1997) 393–406. [4] R.L. Kleinberg, A. Sezginer, D.D. Griffin, M. Fukuhara, Novel NMR apparatus for investigating an external sample, J. Magn. Reson. 97 (1992) 466–485 and references therein. [5] M.L. Buess, A.N. Garroway, J.B. Miller, J.P. Yesinowski, Explosives detection by 14N pure NQR, in: J. Yinon (Ed.), Advances in Analysis and Detection of Explosives, Kluwer, Dordrecht, Netherlands, 1993, pp. 361–368; A.N. Garroway, M.L. Buess, J.P. Yesinowski, J.B. Miller, R.A. Krauss, Explosives detection by nuclear quadrupole resonance (NQR), SPIE Proc. 2276 (1994) 139–148. [6] J.A.S. Smith, Nuclear quadrupole resonance spectroscopy, general principles, J. Chem. Educ. 48 (1971) 39–49. [7] J.B. Miller, B.H. Suits, A.N. Garroway, Circularly polarized RF magnetic fields for spin-1 NQR, J. Magn. Reson. 151 (2001) 228–234. [8] G.Y. Li, X.W. Wu, Composite pulse sequences for pure NQR in powders, Chem. Phys. Lett. 204 (1993) 529–532. [9] A. Ramamoorthy, Phase-alternated composite pulses for zero-field NMR spectroscopy of spin 1 systems, Mol. Phys. 93 (1998) 757–766. [10] K.L. Sauer, B.H. Suits, A.N. Garroway, J.B. Miller, Three-frequency nuclear quadrupole resonance of spin-1 nuclei, Chem. Phys. Lett. 342 (2001) 362–368; K.L. Sauer, B.H. Suits, A.N. Garroway, J.B. Miller, Secondary echoes in three-frequency nuclear quadrupole resonance of spin-1 nuclei, J. Chem. Phys. 118 (2003) 5071–5081. [11] B.H. Suits, A.N. Garroway, J.B. Miller, Noise-immune coil for unshielded magnetic resonance measurements, J. Magn. Reson. 131 (1998) 154–158. [12] B.H. Suits, A.N. Garroway, J.B. Miller, Surface and gradiometer coils near a conducting body: the lift-off effect, J. Magn. Reson. 135 (1998) 373–379. [13] B.H. Suits, A.N. Garroway, J.B. Miller, Super-Q detection of transient magnetic resonance signals, J. Magn. Reson. 132 (1998) 54–64.
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14
N magnetic resonance for materials detection in the field
B.H. Suits,a, A.N. Garroway,b J.B. Miller,b and K.L. Sauerb,c a
Department of Physics, Michigan Technological University, 1400 Townsend Drive, Houghton, MI 49931-1295, USA b Code 6122, Chemistry Division, Naval Research Laboratory, Washington, DC 20375-5342, USA c Physics Department, George Mason University, Fairfax, VA 22030-4444, USA
Abstract Nitrogen is prevalent in many materials, both naturally occurring and man-made. In particular, it is found in many explosives and other contraband materials. One technique for the detection of such materials in the field is the use of the magnetic resonance signal from the nearly 100% abundant, spin-1, 14N nuclei. Some of the difficulties with such measurements in the field include spurious signals from acoustic resonances, radio-frequency interference, and generally low signal-to-noise ratios. A summary of recent work by the authors to help mitigate these difficulties is presented. r 2003 Elsevier Inc. All rights reserved. Keywords: NQR; Materials detection; NMR; Field measurements
1. Introduction Nuclear magnetic resonance (NMR) spectroscopy is noted for its ability to distinguish between different chemical species making the technique an obvious candidate for materials detection applications. Of particular current interest is the ability to detect specific target species such as solid explosives for package, luggage, and possibly vehicle inspection and for finding buried landmines. Similar technologies could be used to detect other materials of interest, such as narcotics, and is not limited solely to explosives [1–3]. While it is quite straightforward to observe magnetic resonance signals for a wide variety of explosive materials in a laboratory setting, the ultimate application is to be able to identify the presence of these materials in the field with the smallest number
Corresponding author. Fax: +1-906-487-2933. E-mail address: [email protected] (B.H. Suits).
0926-2040/03/$ - see front matter r 2003 Elsevier Inc. All rights reserved. doi:10.1016/S0926-2040(03)00045-6
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of false-positive indications (i.e. the detection of an explosive when in fact one is not present) and false-negative indications (i.e. to detect that no explosive is present when in fact one is present). There are severe practical difficulties associated with the use of a large magnetic field for such measurements. The presence of benign magnetic materials (including magnetic recording media which would be erased) in packages and luggage and the difficulty of supplying a sufficiently large, uniform magnetic field for landmine applications are obvious problems. While NMR in Earth’s field has been successful for some applications, particularly in the oil industry [4], such techniques discriminate between different (liquid) materials based on differences in NMR relaxation times and there is a loss of the spectral resolution necessary to distinguish an explosive from a benign background. Furthermore, the ‘‘sample’’ here is a polycrystalline solid material and in this case, sample spinning is simply out of the question. Hence, one turns to techniques of zero-field NMR or nuclear quadrupole resonance (NQR). To use NQR, a nucleus with a spin I > 1=2 must be available. Since the materials of interest here are all solids containing a significant number of 14 N nuclei ðI ¼ 1Þ; 14N NQR spectroscopy is an obvious choice. Other potential nuclei which have been investigated, but which are not discussed here, include 35Cl, 37 Cl, and 39K. There have been a number of general papers written describing the use of 14N NQR to observe explosives [1–3,5]. The purpose of this work is specifically to summarize some of the recent results by the authors to explore, at a fundamental level, possible techniques and apparatus for 14N NQR detection of explosives in the field. The general goals of the research are to develop improved apparatus and/or techniques to: * * *
* *
increase the NQR sensitivity, mitigate radio-frequency interference in the field, separate desired NQR signals from other signals when they are present (e.g. due to magneto-acoustic and piezoelectric ringing), and/or eliminate the undesired signals, more efficiently collect signals, and develop new uses.
The basic instrumentation and techniques required for NQR measurements are the same as those required for traditional (non-spinning, wide-line) NMR, though without a magnet and possibly with a significantly wider range of operating parameters. The work presented here specifically involves the development of better probes and associated techniques to address some of the issues mentioned above. 2.
14
N NQR basics
There are some important differences between NQR and the more familiar high-field NMR. We start by reviewing well-known results [6] for the simplest
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pulsed NQR measurements in order to define terms and to set the stage for what follows. The nearly 100% abundant 14N isotope has a nuclear spin, I ¼ 1: The Hamiltonian for the interaction between a spin-1 nucleus and the electric field gradient (EFG) within a sample is given in the EFG’s principal axis system ðx; y; zÞ and in terms of the usual spin operators by HQ ¼
i hnQ h 2 Z ð3Iz I 2 Þ þ ðIþ2 þ I2 Þ ; 2 3
ð1Þ
where nQ characterizes the strength of the interaction and Z ð0pZp1Þ; is the asymmetry parameter (see Ref. [6] for more details). This Hamiltonian has the three eigenfunctions and corresponding energy levels shown in Fig. 1. The three possible NQR transition frequencies are given by Z n7 ¼ nQ 17 ; 3
2 n0 ¼ ZnQ : 3
ð2Þ
Typical transition frequencies for 14N are in the range from 0 to about 5 MHz with typical line widths of B100–1000 Hz. The large range combined with relatively narrow line widths make it extremely rare to find two different compounds with the same NQR frequencies. Hence, there is excellent chemical specificity. However, the low frequencies and the relatively low magnetogyric (gyromagnetic) ratio of 14N (7% that of 1H, 48% of 2H) conspire to make such measurements challenging. For simplicity in what follows, we assume below that Za0 or 1 to avoid degenerate energy levels and/or transition frequencies. If we apply an RF pulse in the laboratory reference frame ðx0 ; y0 ; z0 Þ which produces an RF magnetic field of magnitude B1, angular frequency o; along x0 ; then the interaction with the nucleus is described by the Hamiltonian H1 ¼ g1 _B1 Ix0 cos ot;
ð3Þ
where g1 is the magnetogyric ratio for the spin-1 nucleus and Ix0 ¼ cos a Ix þ cos b Iy þ cos d Iz ;
Fig. 1. The energy level diagram for a spin-1 nucleus in an electric field gradient.
ð4Þ
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where a; b; and d are the angles between the x0 -axis and the x-, y-, and z-axis, respectively. Since / þ jIx j0S ¼ /0jIx j þ S ¼ 1; / jIy j0S ¼ /0jIy j S ¼ i; ð5Þ / þ jIz j0S ¼ / jIz j þ S ¼ 1; and all other matrix elements are zero, the effective part of the RF magnetic field for the nþ transition, for example, is H1eff ¼ g1 _B1 cos a Ix cos ot _o1þ Ix cos ot;
ð6Þ
where we define o1þ ¼ g1 B1 cos a: It is straightforward to show that if o ¼ oþ 2pnþ ; that is we are exactly on resonance, then the effect of a pulse of duration tp of this RF is the same as that of a rotation by an angle W ¼ o1þ tp =2 about the x-axis. For the n0 and n transitions, an on resonance RF pulse corresponds to a rotation about the z- and y-axis, respectively. In the high-temperature approximation, neglecting constant terms that will not contribute to the signal as well as an overall scale factor, the density matrix in thermal equilibrium can be written as rð0Þ ¼ 3Iz2 þ ZðIx2 Iy2 Þ:
ð7Þ
At time, t; after the nþ on-resonance RF pulse one then has rðtÞ ¼ eiHQ t=_ eiWIx rð0ÞeiWIx eiHQ t=_ ;
ð8Þ
the expectation value /Ix S ¼ TrðrðtÞ; Ix Þ ¼ ð3 þ ZÞ sin 2W sin oþ t;
ð9Þ
and the expectation of the other two components of I will not contribute. The observed signal from the resulting nuclear magnetization is given in the lab frame by d/Ix S d/Ix S d/Ix S ; Sy0 ðtÞp cos b ; Sz0 ðtÞp cos d : ð10Þ Sx0 ðtÞp cos a dt dt dt That is, for the nþ transitions, only the component of the RF along the x-axis is important, and the resulting nuclear magnetization is linearly polarized along the xaxis. Similar results are found for the other two transitions along the other two axes. Note that the signal here is a maximum when W ¼ p=4 or o1þ tp ¼ p=2: Such a pulse is referred to as a p=2 pulse even though the actual rotation involved is p=4: For a polycrystalline sample, we must average over all EFG orientations giving, for the nþ transition, "sffiffiffiffiffiffiffiffiffiffiffiffiffiffi # 2p S% x0 ðtÞpnþ ðpþ p0 Þ cos oþ t J3=2 ðg1 B1 tp Þ ; g1 B1 tp S% y0 ðtÞ ¼ S% z0 ðtÞ ¼ 0;
ð11Þ
where J is a Bessel function and (p+p0) is the initial population difference between the |+S and |0S states. The maximum signal for a powder sample is obtained when
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g1 B1 tp E119 . The linearly polarized RF pulse along x0 results in a linearly polarized observable signal from the total nuclear magnetization which is also along x0 and it is in phase with the applied RF. Similarly, for powder measurements using the transitions at n0 and n one also obtains an observable signal only along x0 for an RF field applied along x0 :
3. Circularly polarized RF The use of a circularly polarized RF magnetic field was pursued as a possible means of improving the signal-to-noise ratio (SNR) and as a means to separate interfering acoustic signals from the desired NQR signal [7]. At first this may seem counterintuitive since, as was discussed above, the NQR excitation and resulting nuclear magnetization are inherently linearly polarized. For a circularly polarized RF magnetic field one has in the lab frame H1 ¼ g_B1 ðIx0 cos ot þ Iy0 sin otÞ
ð12Þ
and once again we will use the nþ transition as an example. Using spherical coordinates y and f which describe the orientation of the x-axis in the lab reference frame, the effective Hamiltonian can be written in the principal axis frame: H1eff ¼ g1 _B1 sin yðcos f cos ot þ sin f sin otÞIx ¼ g1 _B1 sin y cosðot þ fÞIx :
ð13Þ
With the new definition o1þ ¼ gB1 sin y; the analysis proceeds as above to give
Sx0 ðtÞ cos f ð14Þ cosðoþ t fÞ; poþ ðpþ p0 Þ sin y sin o1þ tp Sy0 ðtÞ sin f a linearly polarized signal, which must now be averaged over all orientations, that is all y; f: The resulting signal is given by the rapidly converging series expansion !
cos oþ t J1 ðg1 B1 tp Þ J3 ðg1 B1 tp Þ S% x0 ðtÞ ? ð15Þ p4 oþ ðpþ p Þ 3 15 sin oþ t S% y0 ðtÞ and the total signal is circularly polarized. The maximum of this signal is obtained when g1 B1 tp E102 . To understand why circular polarization is a benefit, consider three sets of nuclei which have their principal x-axis along the laboratory frame x0 -, y0 -, and z0 -axis, respectively. If RF is applied only along the x0 -axis, then only one set of nuclei will have a non-zero effective RF interaction, and hence only one set will produce a signal. On the other hand, circularly polarized RF in the x0 –y0 plane will excite two sets of these nuclei, albeit 90 out of phase with each other. These two sets then produce a linearly polarized nuclear magnetization along their respective axes, also 90 out of phase. When combined these two signals yield a circularly polarized magnetization. That is, a larger fraction of the available nuclei is effectively excited and contribute to the signal if circularly polarized excitation and detection is used.
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Fig. 2. Simplified schematic for excitation and detection of circularly polarized NQR signals. As shown a two-channel receiver is used. For single channel operation, the two signals can be multiplexed.
A simplified schematic for an experimental arrangement for a measurement using circular polarization is shown in Fig. 2. Two independent sets of coils are used and are driven out of phase. On the receive side, two linearly polarized signals are measured which can then be combined in software to obtain any desired polarization for the received signal. Fig. 3 shows the results of a single pulse experiment for linearly polarized excitation compared to circularly polarized excitation. For circular polarization, data from only one channel are shown. Since there are two such independent signals available which can be co-added (after appropriate phase shifts are applied), even though there is a slight loss in sensitivity for each receive channel, there is a net gain in the SNR of about 21%. There are additional benefits for the use of circular polarization. Referring back to Eq. (6), it can be seen that with linear polarization the distribution of effective RF magnetic fields across the sample is uniform from 0 to B1 : This wide distribution leads to inefficiencies similar to those seen in NMR with extremely inhomogeneous B1 fields. In particular, multiple pulse sequences are not as effective as they would be for a uniform B1 : With circular polarization, however, more of the nuclei are seeing an effective-B1 near to the value B1 : Hence, in effect, the RF field has been made significantly more homogeneous. For explosive detection applications, the most efficient data collection schemes utilize pulse sequences which produce an echo train, such as the spin-lock spin-echo (SLSE) sequence, and can be expected to work more efficiently for more homogeneous (effective) RF fields. Although beyond the scope of this article, composite pulse techniques have also been studied as an alternative method to compensate for the wide range of effective RF excitation which occurs for powder NQR. [8,9]. Another advantage of circular polarization is the potential to distinguish the NQR signal from other interfering signals. Such signals arise through a coupling between the applied RF field and an acoustic resonance via either a magnetostrictive or piezoelectric effect. In practice, these signals arise most often from a single source which responds with linear polarization. In practice these signals can drift with time
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0.5
NaNO 2 4.64 MHz
Relative Signal (arb. units)
0.4
Linear Polarization
0.3 0.2 0.1
Circular Polarization
0.0 -0.1 -0.2 -0.3 0
100
200
300
400
500
600
700
Nutation Angle (deg.)
Fig. 3. Experimental results compared to theory for linear and circularly polarized detection. Data from only one receiver channel are shown for circular polarization. The data shown are for the nþ transition from NaNO2 at 4.64 MHz at room temperature. Full details can be found in Ref. [7].
Fig. 4. Experimental results comparing the received signal for an NQR measurement of NaNO2 at 4.64 MHz (top) and the acoustic signal from a pair of pliers (bottom) when received data are combined in the same sense as the excitation (left) and in the opposite sense (right). The circularly polarized NQR signal is easily distinguished from the linearly polarized acoustic signal. Full details can be found in Ref. [7].
sufficiently rapidly so that they cannot be removed effectively by phase cycling and coherent averaging. Since the NQR signal from a powder has the same polarization as the excitation (whether it be linearly or circularly polarized along any axis) but the interfering signal will respond with linear polarization along an axis determined by the orientation of the interfering object, the two types of signals can be distinguished. This is illustrated in Fig. 4. The data in Fig. 4 are combinations of the two receive channels corresponding to two senses of circular polarization. On the left side of the figure, the polarization is in the same sense as that of the circularly polarized excitation. On the right it is the opposite—that is circularly polarized with the opposite sense of rotation. The top signal is an NQR signal from a powder sample, while that at the bottom is an acoustic signal from a pair of ‘‘locking’’ pliers. The circular polarization of the NQR signal compared to the linear polarization (which
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shows up equally for both senses of circular polarization) of the signal from the pliers is evident.
4. Three-frequency NQR As mentioned above, one of the problems with measurements in the field are couplings between acoustic resonances from benign materials and our applied RF field. After the RF is turned off, the acoustic system continues to ring and this can give rise to signals which mimic true NQR signals in many ways. The problem can be avoided, of course, if one does not apply an RF field at or near the NQR frequency. Hence, we have explored three-frequency (3f) NQR as a means to obtain an NQR signal without applying an RF field at the observation frequency [10]. For the NQR system, all three possible transitions shown in Fig. 1 are possible. The idea is to excite at two of these three frequencies and observe at the third. In concept this is similar to multiple quantum NMR except that all transitions are directly observable. The excitation can be accomplished using two separate, but closely spaced, RF pulses at two different frequencies, which we refer to as serial excitation, or by applying the two pulses at the same time, referred to as simultaneous excitation. Other excitation schemes are also possible. Here we will use as an example, excitation of the n0 and n transitions with observation at nþ ; however, other permutations yield similar results. The effect of an RF pulse applied at a single frequency is discussed above—for the n0 and n transitions it is a rotation about the z- and y-axis, respectively. Defining the effective RF fields o10 and o1 in a manner similar to the definition of o1þ in Eq. (6), one finds that for serial excitation where a first RF pulse of length t is applied at n and a second of length t0 at n0 ; the signal at nþ is proportional to Sp sinðo10 t0 =2Þ sinðo1 t Þ
ð16Þ
which is a maximum if the first pulse is a p=2 pulse and the second a p pulse. This expression will need to be averaged over all orientations. While the derivation is a bit complicated, it can be shown that the effect of an RF pulse applied simultaneously at two different resonance frequencies can also be written as a rotation of our spin-1 system. Defining O2 ¼ o210 þ o21 ; and tan x ¼ ðo1 =o10 Þ; a simultaneous RF pulse of duration tp will have the same effect as a rotation by an angle W ¼ Otp =2 about an axis which is in the y2z plane, at an angle x from the z-axis. Following through the analysis as was done in Eqs. (8)–(10), and keeping only those terms relevant for detection at nþ ; one finds that the signal is proportional to Sp sin x cos xðcos y 1Þ½ð3 Z cos WÞ cos2 x þ ð3 cos W ZÞ sin2 x Zð1 þ cos WÞ
ð17Þ
which has a maximum when W ¼ p and x ¼ p=8 (or 3p=8). For those values the signal is identical to what would be obtained in a traditional single-frequency
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Fig. 5. Simplified schematic for a three-frequency measurement using a single channel spectrometer.
measurement. Note that a rather complicated angular dependence relating the ðx; y; zÞ and ðx0 ; y0 ; z0 Þ coordinate systems has been hidden in the variables W and x and a powder average is necessary. Somewhat more complicated expressions have been obtained for various two-pulse echo sequences. That is, an initial pulse (either simultaneous or serial) at the two excitation frequencies, a delay, and then a second pulse (either simultaneous or serial) followed by observation at the third frequency. These results are presented elsewhere [10]. The signal at nþ following both serial and parallel excitations at n0 and n for powder samples was computed numerically and agrees very well with experimental measurements [10]. A simplified schematic of a configuration to perform these measurements using a single channel spectrometer while still allowing coherent averaging is shown in Fig. 5. Note that to obtain maximum sensitivity from a powder sample for either serial or parallel excitation, the three RF coils should produce mutually orthogonal RF magnetic fields at the sample, and for practical reasons they should have minimal (ideally zero) mutual inductance. Fig. 6 shows the effectiveness of this technique for removing acoustic ringing signals. Here acoustic signals from a slightly magnetized paper clip dominate when traditional single frequency techniques are used. Using the three-frequency technique with serially applied excitation pulses eliminates the acoustic signal. The price paid for removing this interference is a reduction in the signal strength by approximately a factor of two. Also visible in Fig. 6 is that the dead time after the RF pulse is significantly reduced using the 3f technique. The use of simultaneous excitation (not shown) is not nearly as effective at removing the acoustic signal, presumably due to non-linearities in the magnetic properties of the paper clip.
5. Gradiometer coils Since 14N NQR signals fall within a frequency range where there are a large number of radio broadcast stations (0.5–5 MHz which includes AM, shortwave, and
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NaNO2 4.64 MHz
Paper Clip
Relative Signal (arb. units)
6 NaNO2 4
1f
2 NaNO2 3f Serial (x 2) 0
Paper Clip
-2 0
1
2
3
4
Time (ms)
Fig. 6. A comparison of traditional single-frequency measurements (top) with the three-frequency technique using serial excitation (bottom) for NaNO2 and the acoustic signal from a paper clip. 3f serial excitation virtually eliminates the acoustic signal while the NQR signal has been reduced by only about a factor of two.
various other radio services), interference from those stations is a significant problem in an unshielded environment. Other sources of RF interference important in this frequency range include lightning, power line noise, and automotive ignition noise, to name a few. This is a particular problem for landmine detection since one cannot surround the ‘‘sample’’ with an electrical shield. In order to address problems of RF interference, another series of studies was pursued which includes a mix of theory and experiment involving RF gradiometer coils as one way to deal with this issue [11]. An RF gradiometer will have no magnetic dipole moment (and ideally no electric dipole moment) and so is a very poor antenna for distant sources. On the other hand, nearby sources, such as from the desired material to be detected, still give rise to usable signals. In addition, it was shown that deleterious effects due to soil conductivity (an issue for landmine detection) are much less of a problem for the gradiometer coil than for other coils [12]. Two simple gradiometer coil configurations are shown in Fig. 7. These coils should be coupled in an electrically balanced manner to avoid creating a large electric dipole moment between the coil and the surroundings. Fig. 8 illustrates the ability of a gradiometer coil to reject distant sources. Here identical NQR measurements were performed using the explosive RDX (hexahydro1,3,5-trinitro-1,3,5-triazine) as the sample, both inside and outside an electrically shielded cage using a simple, electrically balanced axial gradiometer. Measurements using a comparably sized coil of similar dimensions, but of traditional design, showed that the noise level outside the cage was approximately 25 dB larger than inside the cage. With the gradiometer coil, the two noise levels are comparable, within 1 dB. Full details can be found in Ref. [11].
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Fig. 7. Two simple examples of gradiometer coils include the axial gradiometer and the planar (figure-8) gradiometer configurations.
4
3.360 MHz RDX
Shielded
Signal (arb)
3
2
1
Unshielded
0 -30
-20
-10
0
10
20
30
Frequency (kHz) Fig. 8. NQR signals observed for an explosive material both inside and outside an electrically shielded environment. With a conventional coil of comparable size, the noise level outside the shield is approximately 25 dB larger than it is inside the shield (from Ref. [11]).
One disadvantage of simple gradiometers is that some signal loss occurs. In order to counter that loss, we have pursued asymmetric gradiometers designed to optimize the field produced within a designated inspection region subject to the constraints imposed by Maxwell’s equations. By reciprocity this optimizes the receive sensitivity in that region. Details of this work will appear elsewhere. Fig. 9 illustrates the
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Fig. 9. An asymmetric two-layer gradiometer coil designed to optimize the magnetic field within a specified sample region. The coil is circular (B22 cm outside diameter), the upper and lower layers are coaxial, and it is shown in cross-section. Shown are equally spaced contours of magnetic field strength (arb. units) for a unit current in the coil.
magnetic field, and by reciprocity the receive sensitivity, for one of our prototype asymmetric gradiometer coils.
6. Super-Q detection Probe sensitivity in general will depend on the quality factor of the RF detection coils used. This prompted us to investigate the very high quality factor ðQÞ limit for a detection coil [13], such as what one could achieve using superconducting coils. Normally in NMR (and NQR) one expects the receive sensitivity of a probe to depend (among other things) on the square root of its quality factor, Q: For transient (pulse) magnetic resonance, this result is derived assuming the bandwidth of the tuned detection coil is large compared to the bandwidth of the signal. With a very high Q; there is the potential to produce a tuned probe for 14N NQR that has bandwidth significantly smaller than the bandwidth of the signal to be measured. There are certainly a number of significant challenges with the practical use of very high Q coils, such as very long ring down times. Here, we put these other complications aside and simply investigate whether one can obtain a significantly improved SNR with a very high Q coil. That is, is there enough potential improvement to warrant the significant effort which would be necessary to deal with these other problems? It is certainly counterintuitive to make a measurement using a probe bandwidth smaller than the signal bandwidth since less signal will be collected and spectral resolution will be compromised. However, here we consider use as a materials detector and not for spectroscopy. That is, the spectrum of the target material is known, it is only necessary to determine whether or not it is present. Since the spectra from different chemical species do not overlap, the loss of spectral resolution is not important. What is important is the ultimate SNR for this detection and that depends not only on the signal, but on the noise as well. If we lose noise faster than we lose signal, there is a net gain in SNR.
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NF
1
10
0.01 dB 0.1 dB 1 dB 3 dB 6 dB 10 dB
2
2 2
(SNR) (units of A π /πP0)
0
10
135
Probe Limited
-1
10
-2
10
-3
10
Amplifier Limited
-4
10
-5
10
-3
10
-2
10
-1
10
0
1
10
10
2
10
3
10
4
10
Q'
Fig. 10. Predicted SNR improvements as the Q of the coil, normalized to the Q of the signal, is increased based on a simple model amplifier. Here NF refers to the noise figure of the amplifier. Other details, including definitions of the factors which define the vertical scale, are found in Ref. [13]. Results for real amplifiers will be similar.
Fig. 10 shows the principal result. Here, the Q of the probe is normalized by the Q of the resonance signal. Hence, when Q0 ¼ 1 the bandwidth for detection is the same as the bandwidth of the signal. Traditional high-resolution NMR measurements would be far to the left on this plot. Typical values for 14N NQR using copper coils designed for high Q and large samples are in the vicinity of Q0 E0:1: On the left side, the ultimate SNR (for detection) is determined predominately by the thermal noise of the probe. On the right the thermal noise from the probe continues to decrease compared to the desired signal, but ultimately the noise from the amplifiers dominates. It can be seen that some improvement can be had up to about Q0 E5 for state-of-the-art low-noise preamplifiers, but beyond that there is no further gain.
7. Conclusion Bringing NQR out of the laboratory and into the field has required many innovations by many researchers world wide (see Ref. [2]). Here, a number of results are summarized from recent studies by the authors to improve methods for 14N NQR detection of explosives in the field. Some of the unique challenges have been presented along with some possible methods to address those challenges. In particular we have investigated methods of probe design which take advantage of some of the unique properties of spin-1 NQR (e.g. the use of circularly polarized RF and 3f measurements) as well as basic properties of the coils which make up the probe (gradiometers and super-Q detection).
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Acknowledgments This work has been supported in part by the Office of Naval Research, US Army, and US Federal Aviation Administration. K.L.S. acknowledges a National Research Council fellowship and B.H.S. is supported in part under an NRL Broad Agency Announcement Grant N00173-01-1-G000.
References [1] A.N. Garroway, M.L. Buess, J.P. Yesinowski, J.B. Miller, Narcotics and explosive detection by 14N pure NQR, Proc. SPIE 2092 (1993) 318–327. [2] A.N. Garroway, M.L. Buess, J.B. Miller, B.H. Suits, A.D. Hibbs, G.A. Barrall, R. Matthews, L.J. Burnett, Remote sensing by nuclear quadrupole resonance, IEEE Trans. Geosci. Remote Sensing 39 (2001) 1108–1118 and references therein. [3] V.S. Grechishkin, N. Ya Sinyavskii, New technologies: nuclear quadrupole resonance as an explosive and narcotic detection technique, Phys. Usp. 40 (1997) 393–406. [4] R.L. Kleinberg, A. Sezginer, D.D. Griffin, M. Fukuhara, Novel NMR apparatus for investigating an external sample, J. Magn. Reson. 97 (1992) 466–485 and references therein. [5] M.L. Buess, A.N. Garroway, J.B. Miller, J.P. Yesinowski, Explosives detection by 14N pure NQR, in: J. Yinon (Ed.), Advances in Analysis and Detection of Explosives, Kluwer, Dordrecht, Netherlands, 1993, pp. 361–368; A.N. Garroway, M.L. Buess, J.P. Yesinowski, J.B. Miller, R.A. Krauss, Explosives detection by nuclear quadrupole resonance (NQR), SPIE Proc. 2276 (1994) 139–148. [6] J.A.S. Smith, Nuclear quadrupole resonance spectroscopy, general principles, J. Chem. Educ. 48 (1971) 39–49. [7] J.B. Miller, B.H. Suits, A.N. Garroway, Circularly polarized RF magnetic fields for spin-1 NQR, J. Magn. Reson. 151 (2001) 228–234. [8] G.Y. Li, X.W. Wu, Composite pulse sequences for pure NQR in powders, Chem. Phys. Lett. 204 (1993) 529–532. [9] A. Ramamoorthy, Phase-alternated composite pulses for zero-field NMR spectroscopy of spin 1 systems, Mol. Phys. 93 (1998) 757–766. [10] K.L. Sauer, B.H. Suits, A.N. Garroway, J.B. Miller, Three-frequency nuclear quadrupole resonance of spin-1 nuclei, Chem. Phys. Lett. 342 (2001) 362–368; K.L. Sauer, B.H. Suits, A.N. Garroway, J.B. Miller, Secondary echoes in three-frequency nuclear quadrupole resonance of spin-1 nuclei, J. Chem. Phys. 118 (2003) 5071–5081. [11] B.H. Suits, A.N. Garroway, J.B. Miller, Noise-immune coil for unshielded magnetic resonance measurements, J. Magn. Reson. 131 (1998) 154–158. [12] B.H. Suits, A.N. Garroway, J.B. Miller, Surface and gradiometer coils near a conducting body: the lift-off effect, J. Magn. Reson. 135 (1998) 373–379. [13] B.H. Suits, A.N. Garroway, J.B. Miller, Super-Q detection of transient magnetic resonance signals, J. Magn. Reson. 132 (1998) 54–64.