Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
  • G01R33/00—Arrangements or instruments for measuring magnetic variables
  • G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
  • G01R33/44—Arrangements or instruments for measuring magnetic variables involving magnetic resonance using nuclear magnetic resonance [NMR]
  • G01R33/441—Nuclear Quadrupole Resonance [NQR] Spectroscopy and Imaging

Definitions

• This invention relates to a method of and apparatus for detecting the presence of quadrupolar nuclei in a sample having at least one Nuclear Quadrupole Resonance (NQR) property (most particularly spin-lattice relaxation time, T : ) which varies with a given environmental parameter (for instance, temperature). It also relates to a method of configuring such apparatus.
• NQR Nuclear Quadrupole Resonance
• the invention has application to the detection in the field of 14 N quadrupole resonance signals from the explosives TNT, RDX, HMX or PETN concealed in parcels or luggage or on the person, or deployed in explosive devices.
• it has application to the detection of concealed drugs, such as heroin and cocaine, for instance at airports. If the substance is determined to be present, an alarm may be sounded.
• the temperature of the sample would be unknown, and may in fact vary widely. There may even be a significant temperature gradient within the sample.
• NQR measurements have the advantage that they do not require the sample to be placed in a strong magnetic field, and therefore do not require the large, expensive and sample-size limiting magnet structures which are needed for nuclear magnetic resonance (NMR) measurements.
• a method of detecting the presence of quadrupolar nuclei in a sample having at least one NQR property which varies with a given environmental parameter is known from International Patent Application No. PCT/GB92/00580 (British Technology Group Ltd.), whose disclosure is incorporated herein by reference.
• the method comprises in broad terms applying excitation to the sample to excite NQR resonance and detecting the NQR response signal, the excitation being such as to excite an NQR response signal which is detectable during the detection step over a predetermined range of the environmental parameter.
• sensitivity of detection is meant the number of selected nuclei (or amount of material) that can be detected at a given level of probability in a fixed volume of sample over a given test time. This sensitivity may be improved by Fourier transformation of the accumulated signals to give an absorption spectrum, the area under which is then measured by integration between appropriate limits.
• the invention was based on the discovery that the NQR properties of a sample, such as resonance frequency (v) and spin-lattice relaxation time (T j ), may vary considerably with a given environmental parameter, such as temperature, pressure or magnetic field, and that it was therefore necessary to take account of or compensate for these variations when carrying out NQR tests to cover a predetermined range of the environmental parameter.
• v resonance frequency
• T j spin-lattice relaxation time
• the given predetermined range of the environmental parameter might typically be the range of that parameter likely to be encountered in the field (possibly the national or global average range or maximum range of that parameter).
• the predetermined range might be ⁇ 10°C globally (possibly between 5°C and 25°C) or ⁇ 20°C (possibly between -10°C and +30°C). The range might be as much as from -30°C (corresponding to arctic conditions) to +40°C (corresponding to desert conditions). In some industrial applications, considerably wider temperature ranges may be encountered.
• the predetermined range may be, for example, ⁇ 1% (corresponding to a typical average daily pressure range) or _- 5% (corresponding to a maximum range), or even higher if the technique is being used to test conditions inside a pressure vessel.
• the substance under suspicion were the explosive RDX in airport luggage, it might be subjected to a temperature variation of -25 to +15°C about a mean of 20°C (i.e. a variation from -5 to +35°C).
• a temperature variation of -25 to +15°C about a mean of 20°C (i.e. a variation from -5 to +35°C).
• Different samples might be at different temperatures, and/or the same sample might have a non-uniform temperature.
• TJ spin-lattice relaxation time
• Present Figure 1 demonstrates that, at a given ratio of x/T- ( ⁇ 5), the signal is predicted to pass through a maximum as the flip angle is varied, this maximum moving to flip angles less than 119 degrees (c and to lower signal strengths as the ratio of ⁇ /T- drops below 1.
• the invention disclosed in PCT/GB92/00580 included a technique of compensating for the variation of T r
• This technique involved applying the excitation as a series of excitation pulses, at a plurality of different pulse repetition rates and/or so as to produce a plurality of different flip angles, so that a detectable NQR resonance response signal could be excited over the range of the relaxation time corresponding to the range of the environmental parameter, and indeed preferably so that the response signal had a substantially constant strength over that range.
• the present invention seeks to solve these problems.
• the invention is based on the realisation, pursuant to the present invention, that, provided the pulse repetition time and flip angle are selected carefully, they may be maintained at values which are constant for the particular test, without significant detriment to the sensitivity of the technique.
• a method of detecting the presence of a given quadrupolar nucleus in a sample, the resonance frequency and spin-lattice relaxation time of the nucleus varying with a given environmental parameter comprising determining a range of the resonance frequency which corresponds to a selected range of the parameter, applying excitation to the sample to excite nuclear quadrupole resonance, and detecting the resonance response signal, the excitation being such that a detectable resonance response signal can be excited over the resonance frequency range, and being such as to produce a constant flip angle of less than 45° actual.
• the term "constant" is not to be interpreted in a particularly precise sense; rather, it is to be interpreted in the context of the relatively low degree of precision usually associated with methods of detecting the presence of quadrupolar nuclei in a sample. For example, a 25% or even greater (for example 50%) variation in the flip angle over time would usually be acceptable.
• references to flip angles of a certain number of degrees "actual” are to be contrasted with values of "effective" flip angle, the two being related by a Bessel function in a manner which is well-known (see, for example, the Vega reference referred to above).
• a flip angle of 119° actual produces a maximum free induction decay, and so corresponds to a flip angle of 90° in Nuclear Magnetic Resonance, a flip angle of 119° actual thus corresponding to one of 90° effective.
• the excitation is such as to produce a constant flip angle, it will be understood that there may be circumstances in which the excitation produces flip angles which, whilst being constant (that is, not varying with time), may differ within the sample according to the the distance away from the excitation source.
• the term "detectable” preferably connotes a signal/noise ratio which, within the measurement time of the detection step, is significantly above the actual or expected noise levels, the degree of significance being determined, for example, by standard statistical methods, such as the upper Student's t-distribution.
• pulse repetition rate is simply the reciprocal of pulse repetition time.
• the technique of the present invention can detect relatively easily the presence of the relevant nuclei in circumstances where the given environmental parameter is unknown and may vary over a wide range, without there being a wide variation in the sensitivity of detection over the range of the environmental parameter. It can accomplish this by allowing in a simple fashion not only for the variation of the resonance frequency but also for the variation of the spin-lattice relaxation time with the given parameter.
• the excitation is pulsed excitation at a constant pulse repetition rate.
• the method further includes selecting an expected extreme value of the environmental parameter, being that extreme value for which the relaxation time has its shortest value (as opposed to the opposite extreme value for which the relaxation time has its longest value), and determining a measure of the ratio of the pulse repetition time to the shortest value of the relaxation time, the pulse repetition rate being such that said measure of the ratio is no more than a selected value.
• the detection technique can be considerably simplified over that disclosed in International Patent Application No. PCT/GB92/00580.
• the purpose of the selection of an expected extreme value of the environmental parameter (such as the highest expected value of temperature), the determination of said measure of the ratio, and ensuring that the pulse repetition rate is such that said measure is no more than a selected value is that, by judicious choice of the selected value, the detection technique can be relatively rapid whilst at the same time not being overly susceptible to variations in the environmental parameter.
• a method of configuring apparatus for detecting the presence of a given quadrupolar nucleus in a sample, the spin-lattice relaxation time of the nucleus varying with a given environmental parameter including means for applying pulsed excitation to the sample to excite nuclear quadrupolar resonance, the method including selecting an expected extreme value of the environmental parameter, being that extreme value for which the relaxation time has its shortest value, arranging the excitation means to apply excitation at a constant pulse repetition rate and such as to produce a constant flip angle, and determining a measure of the ratio of the pulse repetition time to the shortest value of the relaxation time, the pulse repetition time being such that said measure of the ratio is no more than a selected value.
• the invention extends to a method as directly aforesaid, for detecting the presence of the given nucleus in the sample, the apparatus further including means for detecting the resonance response signal, and including the step of operating the excitation and detection means to detect the presence of such nucleus.
• the invention further extends to a method of detecting the presence of a given quadrupolar nucleus in a sample, the spin-lattice relaxation time of the nucleus varying with a given environmental parameter, including selecting an expected extreme value of the environmental parameter, being that extreme value for which the relaxation time has its shortest value, applying pulsed excitation to the sample to excite nuclear quadrupole resonance, and detecting the resonance response signal, wherein the excitation is at a constant pulse repetition rate and such as to produce a constant flip angle, a measure of the ratio of the pulse repetition time to the shortest value of the relaxation time is determined, and the pulse repetition time is such that said measure of the ratio is no more than a selected value.
• the value of said ratio (of the pulse repetition time to the shortest value of the relaxation time) is no more than 20, more preferably no more than 10, yet more preferably no more than 3 or 5 or even 1.
• the particular importance of values of this order of magnitude is that it has been found that, all other parameters being the same, signal strength and hence sensitivity does not increase markedly at higher values. Thus tests conducted at higher values would be unnecessarily long. Therefore, for a rapid test, it is usually advantageous to utilise a value of this order of magnitude or lower. Even more preferably, such selected ratio value is no more than 0.2 or 0.3. If this is the case, theoretical analysis provided later indicates that, for sufficiently small flip angle, signal strength becomes more or less independent of the environmental parameter.
• the method includes further selecting an expected extreme value of the environmental parameter for which the relaxation time has its longest value, the ratio of, on the one hand, the repetition time, to, on the other hand, the relaxation time corresponding to a value of the environmental parameter centred between its expected extremes, being in the range 0.05 to 5, preferably 0.1 to 1.
• the ratio of, on the one hand, the repetition time, to, on the other hand, the relaxation time corresponding to a value of the environmental parameter centred between its expected extremes being in the range 0.05 to 5, preferably 0.1 to 1.
• the method preferably further includes selecting an expected extreme value of the environmental parameter for which the relaxation time has its longest value, determining a measure of the ratio of the pulse repetition time to the longest value of the relaxation time, and producing an alarm signal from the response signal in dependence on whether a predetermined threshold of detection has been exceeded, the threshold corresponding to a value of response signal strength which is no more than a value corresponding to said measure of the ratio of the pulse repetition time to such longest relaxation time.
• the method includes further selecting an expected extreme value of the environmental parameter for which the relaxation time has its longest value, and determining a measure of the ratio of the pulse repetition time to the longest value of the relaxation time, the value of signal strength corresponding to the value of the ratio of the repetition time to the shortest relaxation time being less than a selected number of times, preferably less than five times, more preferably less than three times, even more preferably less than twice, the equivalent signal strength value for the longest relaxation time.
• the sensitivity of detection can also be maintained within acceptable limits over this range.
• the values of pulse repetition rate and flip angle are chosen by a process of iteration between these two quantities.
• the excitation is such as to produce a flip angle of less than 45° actual. More preferably, the excitation is such as to produce a flip angle of less than 35°, even more preferably less than 25°, more preferably still less than 15°, yet more preferably less than 10°, yet more preferably still less than 5° actual. In fact, as will be explained later, the smaller the value of flip angle, the more effective the technique.
• the excitation is preferably applied at a single excitation carrier frequency, although it may be applied at two or more such frequencies.
• a particularly preferred feature is the use of so-called "shaped" pulses, as described in detail later, as well as in United Kingdom Patent Application No. 9319875 and International Patent Application No. PCT/GB94/02070. These can enable a broad frequency bandwidth to be excited at low power levels and using only a single excitation frequency.
• a shaped pulse may be thought of as one for which the time domain waveform of the excitation is either phase modulated or amplitude modulated, or both phase modulated and amplitude modulated.
• apparatus for Nuclear Quadrupole Resonance testing a sample comprises means for applying excitation to the sample over a selected excitation frequency range to excite NQR resonance, and means for detecting the NQR response signal, the phase of the excitation varying generally non-linearly with the excitation frequency over the selected range.
• the shaped pulses invention arises from the surprising discovery in the field of Nuclear Quadrupole Resonance that by applying excitation whose phase varies non- linearly with the excitation frequency, the peak power of the excitation can be reduced very significantly. In one example, peak power has been reduced by more than an order of magnitude. A very significant reduction in peak radio-frequency magnetic field has also been achieved.
• Guan's technique is deliberately limited to the time domain waveform of the excitation being only amplitude modulated, but not also otherwise phase modulated. (It will be understood that amplitude modulation by itself, when the amplitude varies between positive and negative values, involves modulation of the phase, say between 0 and 180 degrees.)
• the envelope of the modulus of the time domain excitation waveform has no zero crossings. This can have the advantage of reducing the peak power (and radio-frequency magnetic field) of the excitation considerably.
• the excitation applying means is adapted to apply excitation the time domain waveform of which is both amplitude and phase modulated. As opposed to the case where the waveform is only amplitude modulated, this arrangement can be utilised to produce an excitation waveform whose envelope has no zero crossings.
• the applying means includes means for producing two signals which are in relative quadrature, and means for combining the signals to form the amplitude and phase modulated excitation.
• the signal producing means includes means for generating a signal and for splitting the signal into two signals in relative quadrature.
• the generating means may be adapted to generate a carrier signal at a fixed amplitude.
• the generating means may be adapted to generate a signal having a varying amplitude.
• the applying means is preferably adapted to apply excitation the time domain waveform of which is amplitude modulated but not otherwise phase modulated. This embodiment may not permit such low peak excitation powers to be achieved as are achievable with other embodiments, but can be simpler to manufacture since there is no requirement to modulate the phase directly.
• the applying means is adapted to apply excitation the time domain waveform of which is modulated according to a chirp function.
• the chi ⁇ function may, for example, be a linear chi ⁇ function of the form cos( ⁇ t 2 ); that is, the modulation is pure phase modulation, the phase being modulated linearly with respect to the frequency off-set.
• the excitation applying means includes means for generating a carrier signal and means for modulating the carrier signal to produce excitation the phase of which varies generally non-linearly with the excitation frequency over the selected excitation frequency range.
• the modulating means suitably includes means for storing a representation of a modulating waveform for modulating the carrier signal.
• the variation of the phase of the excitation with the excitation frequency may, for example, be symmetric or antisymmetric with respect to the carrier frequency v 0 .
• the phase variation is preferably quadratic (that is, proportional to (v- v 0 ) 2 ); this has been found to give rise to low peak excitation powers.
• Another possibility is to vary the phase with statistical noise, but this can result in a noisy spectrum.
• a further disadvantage may be that the time domain waveform has many zero crossings, so that time is not used efficiently.
• phase variation is quadratic
• a plurality of excitation pulses are applied, in such a way as to generate at least one echo response signal. It may be advantageous to generate echo response signals, as opposed to free induction decay signals, especially in circumstances in which the spin-lattice relaxation time, T of the substance being tested is relatively long.
• the modulus of the frequency domain excitation spectrum is substantially constant over the selected excitation frequency range.
• the excitation can be uniform over the frequency range.
• the shaped pulses invention extends to a method of Nuclear Quadrupole Resonance testing a sample, comprising applying excitation to the sample over a selected frequency range to excite NQR resonance, and detecting the NQR response signal, the phase of the excitation varying generally non-linearly with the excitation frequency over the selected range.
• a selected NQR resonance may be excited, and, if so, the duration of the excitation is preferably less than twice the free induction decay time, T z *, appropriate to that resonance. This is an important feature, which can ensure that unacceptable loss of the NQR response signal does not arise before the signal is detected.
• the duration is in fact preferably less than 100%, 75% or even 50% of T 2 *.
• apparatus for Nuclear Resonance testing a sample comprising means for applying excitation to the sample over a selected excitation frequency range to excite nuclear resonance, and means for detecting the response signal, the applying means being adapted to apply excitation the time domain waveform of which is both amplitude and phase modulated.
• apparatus for Nuclear Quadrupole Resonance testing a sample comprising means for applying excitation to the sample over a selected excitation frequency range to excite NQR resonance, and means for detecting the NQR response signal, the phase of the excitation varying generally non- linearly with the excitation frequency over the selected range.
• the shaped pulses invention provides a method of extending the free induction decay time, T 2 *, of a sample, comprising applying excitation to the sample over a selected excitation frequency range to excite nuclear resonance, the phase of the excitation varying with the excitation frequency over the selected range.
• the nuclear resonance is suitably Nuclear Quadrupole Resonance or Nuclear Magnetic Resonance.
• the variation of the phase of the excitation is preferably non-linear.
• This aspect of the shaped pulses invention stems from the discovery pursuant to the present invention that if a nuclear signal is excited with a varying phase the length of the free induction decay may be greater compared with the case of simple excitation with constant phase. The reasons for this appear to be analogous to the reasons given below why the applied excitation itself is longer in such circumstances.
• the applied excitation should have considerable phase variation within the bandwidth of the nuclear signal.
• an appropriate test of the technique is a broader nuclear resonance line (compared with the 5210 kHz v + line), such as the 3460 kHz (v_) NQR line of RDX with a bandwidth of 0.5 kHz.
• the technique of this aspect of the shaped pulses invention can be particularly useful, for example, when T 2 * is less than T 2 , to obviate dead time problems due to probe ring down, or in circumstances where only small r.f. amplitudes and therefore small flip angles can be used.
• the environmental parameter is temperature.
• the expected upper extreme value may be less than 50°, preferably less than 40 or 30°C.
• the expected lower extreme value (for which the relaxation time for most substances has its longest value) may be greater than -30°C, preferably greater than -20 or - 10°C. It is expected that in most substances T, will decrease as the temperature rises; in cases where the reverse is true, the two extrema will need to be interchanged.
• the pulse repetition time is greater than, more preferably 2 or 3 times greater than, the free induction decay time of the quadrupolar nuclei, in order to allow time for the f.i.d. to be detected.
• the present invention extends to apparatus for detecting the presence of a given quadrupolar nucleus in a sample using pulsed excitation, comprising storage means in which is stored information for at least two types of nucleus having different NQR properties on suitable values of flip angle and pulse repetition rate to take account of expected variations in temperature, means responsive to the storage means for applying, for a given type of nucleus, pulsed excitation to the sample to excite nuclear quadrupole resonance, the excitation means being adapted to apply excitation at a constant pulse repetition rate and such as to produce a constant flip angle suitable for the particular substance, and means for detecting the resonance response signal.
• the requisite pulse repetition rate and flip angle selected may be dependent on the particular substance under test, so that different pulse repetition rates and flip angles may be appropriate to different substances. Apparatus features analogous to the method features described above may be provided.
• the apparatus may further include means for producing an alarm signal from the detected response signal in dependence on whether a predetermined threshold of detection has been exceeded.
• the excitation may be applied at a single excitation frequency, and may take the form of shaped pulses.
• Figure 1 (prior art) is a plot of the steady-state NQR response signal strength against flip angle for differing values of the ratio x/T-;
• Figures 2 show a time domain rectangular excitation pulse (Figure 2(a)) and its frequency domain equivalent (Figure 2(b));
• Figure 3 is a block diagram of a preferred embodiment of NQR testing apparatus according to the present invention.
• Figures 4(a) to 4(e) illustrate a first example of NQR test using shaped pulses
• Figures 5(a) to 5(f) illustrate a second example of NQR test using shaped pulses
• Figure 6 is a block diagram of a variant of the preferred embodiment of NQR testing apparatus
• Figures 7(a) to 7(f) illustrate a third example of NQR test, again using shaped pulses; and Figure 8 is a pulse timing diagram exemplifying the use of the preferred embodiment of the invention.
• the preferred embodiment of the present invention involves the use of pulsed radio-frequency excitation to excite Nuclear Quadrupolar Resonance in the substance whose presence it is desired to detect.
• Any suitable form of pulse sequence can be used, most usually a regular sequence of uniform pulses.
• the manner in which the excitation frequency, pulse repetition rate, flip angle and other parameters concerned with the excitation are chosen is discussed first. Details of the apparatus for putting the invention into effect, together with details of a particularly preferred type of pulse (a "shaped" pulse), are given later. Finally, an example of the operation of the invention is given.
• the invention makes allowance for variations both in resonance frequency and in spin-lattice relaxation time (T-) of the given quadrupolar nuclei.
• T- spin-lattice relaxation time
• Other NQR properties may also be taken into account, as taught in PCT/GB92/00580.
• frequency is compensated for in the manner taught in PCT/GB92/00580.
• only one excitation frequency is employed, the bandwidth of the excitation being sufficient, at that single frequency, to cover the entire frequency range of interest, that is, the range corresponding to the temperature range of interest.
• shaped pulses are particularly suitable for producing the requisite bandwidth at minimum radio-frequency power, and hence these are used in the preferred embodiment, although other types of pulse may also be suitable. Shaped pulses are described in more detail later.
• ⁇ and ⁇ axe constant for the duration of the particular detection test being carried out, even if that test is being conducted at more than one excitation frequency.
• flip angle may be different for a further test with the same sample, or for a separate test with a different sample. If more than one excitation frequency were employed, as an alternative to the excitation being such as to produce a single constant flip angle, it would be possible to employ a different (constant) flip angle and/or pulse repetition time for each frequency.
• Flip angle is also constant over substantially the entire region of interest in the sample, although this is in general terms not necessary provided flip angle is kept sufficiently low.
• Flip angle is rendered constant over the duration of the test by rendering constant the radio-frequency magnetic field B r ⁇ produced by the excitation applying means. Further, it may be rendered constant across the sample by the use of suitable types of the excitation coils employed to apply the excitation.
• the ratio x/T 1 for the two extreme values of temperature to which the sample is expected to be subjected. Since signal intensity does not increase significantly for values of this ratio above 5 or so, the value of the pulse repetition time, ⁇ , is selected so that, for the shortest value of ⁇ (corresponding for most substances to the higher extreme value of temperature), this ratio is no more than a selected value, say, 5. If it were higher, the test would be unnecessarily long, without there being any concomitant improvement in signal intensity and hence sensitivity.
• the value of signal strength corresponding to the lowest temperature extreme may acceptably be less than five times, preferably less than three times, more preferably less than twice, the equivalent signal strength value for the highest temperature extreme.
• the flip angle is chosen to be as small as possible. It may suitably be less than 45°, preferably less than 35°, more preferably less than 25°, more preferably still less than 15°, yet more preferably less than 10°, yet more preferably still less than 5° actual.
• pulse repetition time has an effect on the sensitivity of the tests in at least two different ways. Firstly, the longer the pulse repetition time (up to a certain limit), the greater is signal strength and hence sensitivity (see Figure 1). Secondly, and on the other hand, the shorter the pulse repetition time, the greater the total number of pulses that can be generated for a given duration of test, and hence the greater the number of free induction decays that can be accumulated. Signal to noise ratio, and hence sensitivity, increases as the number of detected pulses increases.
• flip angle has a direct effect on the sensitivity of the tests, in that, within certain limits, the lower the flip angle, the lower the signal intensity.
• a pulse at a lower flip angle is shorter than the equivalent pulse at a higher flip angle, more lower flip angle pulses can be utilised in a given test time; in other words, the pulse repetition time can be higher the shorter the pulse.
• the final values of pulse repetition rate and flip angle may need to be chosen by a process of iteration between these two quantities.
• a mid-point value of the ratio x/T. (that is, a value of the ratio corresponding to a value of temperature centred between its expected extremes) is likely to be in the range 0.05 to 5, preferably 0.1 to 1. In the context, it is not important what technique is used for evaluating such a centred value of temperature. It will be appreciated that a determination of the value of this ratio can be a useful check that the pulse repetition rate and flip angle have been chosen well.
• a typical process for configuring the detection apparatus would be as follows:- 1) Select upper and lower expected extreme values of temperature to which it is expected the sample will be subjected.
• the accumulated signal may be increased simply by increasing flip angle ⁇ .
• the accumulated signal may be increased by decreasing the pulse repetition time ⁇ to a new value ⁇ '. More f.i.d.'s are now collected in the given measurement time T m , and the signal to noise ratio is improved by the factor (x/x')' A . However, the signal strength of each individual f.i.d. is reduced, and, to compensate for this, flip angle ⁇ may need to be increased, such that, for example, the signal strength for each individual f.i.d. reverts to its original value before x was reduced.
• condition 2 ⁇ /T 1 «l may be satisfied if ⁇ /T j is less than 0.2 or 0.3 without the signal strength having significant dependence on the environmental parameter. It can thus be seen that there may be, for sufficiently low ⁇ , a significant range of ⁇ /Tj for which signal strength does not vary substantially. Hence, for an even wider range of ⁇ /T j , the variation of signal strength may lie within acceptable limits.
• step 10 in the procedure described above.
• Equation 2 valid for 2 ⁇ /T 1 «l, decreasing x makes the term in a_ larger, which diminishes S ⁇ ⁇ ; increasing ⁇ increases S_° and also a 2 , and so changes S ⁇ ⁇ .
• ⁇ is less than 30°, preferably less than 20°, the change in S ⁇ " dominates and the signal S ⁇ ⁇ increases.
• T half-height bandwidth ⁇ v and peak pulse power P
• P is proportional to 1/T 2 , provided that (in NQR) the product B rf T, and therefore the flip angle, remains constant.
• B rf is defined as the amplitude of the oscillating radio frequency field.
• the high power requirement is attributable to two main factors. Firstly, the sidelobes apparent in the frequency domain consume substantial power without contributing to the useful part of the spectrum (the central peak). Secondly, the range of excitation frequencies contained in the pulse are in phase at time zero. Hence there is a high coherency between the various frequencies at and very close to time zero, but destructive interference at other times. Thus the pulse is of short duration and high peak power.
• phase with frequency should be non-linear in order to ensure a proper scrambling of the phases.
• a linear phase variation merely has the effect of producing a time-shift, but does not have the effect of scrambling phases. It has been found, in fact, that for NQR testing a quadratic phase variation may be optimal.
• the apparatus comprises in general terms a control computer 100, means 102 for applying one, or more usually several, continuous radio-frequency excitation pulses to the sample covering a selected excitation frequency range and for a given duration, means 104 for generating shaped pulses for passing to the applying means 102, means 106 for detecting the NQR response signal, and an audio or visual alarm 108 which alerts the operator to the presence of the substance under test.
• each individual excitation pulse is shaped such that phase varies during the pulse, and preferably over a substantial proportion of the duration of the pulse, say, over at least 50%, more preferably at least 75 or 90%, most preferably over the entirety of the pulse.
• the phase modulation is preferably continuous in time, the excitation pulse itself being continuous in time (that is, there is no period during the pulse when the excitation is off, although the excitation may instantaneously pass through zero).
• the excitation pulse application means 102 includes a radio-frequency power amplifier 110 whose output is connected to an r.f. probe 112 which contains one or more r.f. coils disposed about the sample to be tested (not shown).
• the r.f. probe 112 also forms part of the detecting means 106 which also includes r.f. receiver and detection circuitry 120.
• the shaped pulse generating means 104 comprises a pulse programmer 130 for producing trigger signals to time the pulse, a spectrometer 132, manufactured by SMIS, United Kingdom, for generating a radio-frequency carrier signal at a known carrier reference frequency and fixed amplitude, the signal being gated by the trigger signals, a function generator 134, manufactured by Farnell, United Kingdom (Model No. SFG 25), for generating from a stored representation a waveform to modulate the amplitude of the carrier signal, the output of the function generator also being initiated by the trigger signals, and a double balanced mixer 136 for mixing the modulating waveform and the carrier signal and passing the mixed signal to the r.f. power amplifier 110. It will thus be appreciated that the shaped pulse generating means 104 is capable of applying to the sample a time-domain excitation waveform which is amplitude but not otherwise phase modulated.
• the computer 100 ultimately controls all pulses, their radio-frequency, time, width, amplitude and phase. It is arranged to time the application of the excitation pulses substantially simultaneously with the arrival of a particular sample adjacent the probe 112. It also acts to receive the detected NQR response signal from the detecting means 106 and to process it, carry out signal addition or subtraction, and finally trigger the alarm 108 if appropriate.
• the alarm 108 is arranged to be controlled by the computer 100 in such a way that an alarm is sounded or indicated in dependence on whether a predetermined threshold of detection has been exceeded, the threshold corresponding to a value of response signal strength which is no more than the value corresponding to the value of the ratio of the pulse repetition time ( ⁇ ) to the extreme longest value of the spin-lattice relaxation time (T.). (This extreme longest value is usually that corresponding to the lower temperature extreme.) This can ensure that a detectible resonance response signal is produced over the entire selected temperature range, that is, between the two extreme temperature values.
• the invention is based on the phase of the excitation varying generally non-linearly with excitation frequency.
• E(t) E rei ⁇ (t) + i.E ] ⁇ g . narv (t)
• a purely amplitude modulated time domain excitation waveform will in general not be adequate for the pu ⁇ oses of the present invention, so that the apparatus of Figure 3 would generally be inappropriate. However, there are special cases for which this apparatus can be used.
• a rectangular shape was selected for the frequency domain excitation spectrum.
• Figure 4(c) shows the modulus of the Fourier transform of the waveform of Figures 4(a) and 4(b). The deviation from a pure rectangular shape is caused by the truncation of the waveform.
• Figure 4(d) is the same as Figure 4(c), except that the imaginary part of the time domain waveform (see Figure 4(b)) was set to zero. It can be seen that Figure 4(d) does not differ excessively from Figure 4(c). This is because the imaginary part of the waveform was in any case small. Hence it is acceptable to ignore the imaginary part of the waveform and utilise as the modulating waveform purely the real part shown in Figure 4(a).
• Figure 4(e) shows the result of an experiment with the explosive RDX as the substance of interest.
• the NQR testing apparatus was used to excite one of the 1 N v + resonances of RDX (the one near 5192 kHz having a free induction decay time, T 2 *, of roughly 1.4 ms at room temperature and a line width of about 200Hz).
• the variation of the integrated area under the NQR signal detected by the detection means with respect to the carrier frequency of the spectrometer is presented.
• the circular data points represent an excitation pulse having a bandwidth (the selected excitation frequency range) of 20 kHz; the bandwidth for the square data points was 10 kHz. It can be seen that the two sets of experimental data points agree well.
• the peak power (P) for the pulse was 208W for a 90° effective pulse. This compares with a peak power of 2000W for the corresponding rectangular excitation pulse of the same excitation bandwidth.
• Figure 5(a) shows the modulus of the time domain waveform obtained by inverse Fourier transformation of the upper half-bandwidth.
• the dotted lines indicate where the waveform was truncated to create a 1ms pulse duration.
• Figure 5(b) shows the truncated real part of this waveform. This real part is the modulating waveform which was used to modulate the carrier signal.
• Figure 5(c) shows the real part of the Fourier transform of the truncated waveform of Figure 5(b), whilst Figure 5(d) shows the modulus of this transformation. The deviation from a rectangular shape is again due only to the truncation.
• the carrier frequency is shown as a dotted line. It is clear from Figure 5(d) that there is excitation of both sides of the carrier frequency.
• Figure 5(e) shows the result of a similar experiment to that described in relation to Figure 4(e), but using the modulating waveform of Figure 5(b) rather than that of Figure 4(a).
• the bandwidth of the excitation pulse was 20kHz.
• the plot in Figure 5(e) matches closely that in Figure 4(e).
• the peak power (P) for the pulse was 133W for a 90°- Hec . iv . pulse.
• Figure 5(f) is a similar plot to that shown in Figure 5(e), except that it was derived using a modulating waveform obtained by inverse Fourier transformation of the lower half-bandwidth. This modulating waveform is in fact the time reversal of that shown in Figure 5(b).
• Figures 5(e) and 5(f) differ only in that the former shows a peak in the NQR signal near 5192 kHz, whilst the latter shows a trough in the same region. If the NQR response signal were to follow the excitation closely, the region would be expected to be nearly flat (as shown in Figure 5(d)).
• the pulse duration is carefully controlled in relation to the T 2 * of the substance being tested, in order to prevent unacceptable loss of NQR response signal before detection.
• One way of maximising the pulse duration with respect to T 2 * would be to arrange for the NQR testing apparatus to generate a given number of pulses of the type described in relation to Figure 5(e), followed by an equal number of pulses of the type described in relation to Figure 5(f), or vice versa. Addition of the two sets of responses would then yield a substantially flat response over the excitation bandwidth. This technique may be important when testing the explosives TNT and PETN, since T 2 * is expected to be shorter for such explosives than it is for RDX.
• v + line of RDX mentioned above as having a T 2 * of roughly 1.4ms is an especially advantageous line to investigate.
• the other v + lines have T 2 *'s of less than 1ms, and hence would necessitate the use of a shorter pulse. This would have the disadvantage of raising the excitation pulse peak power.
• the generating means 204 of the variant is similar to the generating means 104, except that it is a double channel rather than a single channel arrangement. Hence it can produce a waveform which is phase as well as amplitude modulated.
• the variant again includes a pulse programmer 230 and spectrometer 232. However, two function generators 234a and 234b, and two double balanced mixers 236 are provided. In addition, a quadrature hybrid 0-90° splitter 238, a combiner 240 and resistors 242 and 244 are provided.
• the splitter 238 is a 5MHz splitter made by Mini Circuits (U.S.A.) and bearing Model Number PSCQ 2-5-1; the combiner 240 and mixers 236 are both made by Hatfield (U.K.) and bear the Model Numbers DP102 and MC 291 respectively.
• the resistors 242 are 56 ⁇ whilst resistors 244 are 560 ⁇ . The whole network of resistors 242 together with resistors 244 results in a resistance of 50 ⁇ seen by function generators 234.
• Spectrometer 232 is gated and the outputs of the function generators 234 are initiated by the pulse programmer 230 as described in relation to the first embodiment.
• the splitter 238 produces from the radio-frequency carrier signal two radio frequency signals in relative quadrature.
• the function generators 234a and 234b generate the real and imaginary parts respectively of the modulating waveform.
• the resistors 242 provide impedance matching with the cables from the function generators, whilst the resistors 244 convert the voltage output of the function generators to a current output for passing to the mixers 236. After mixing of the relevant modulating waveforms and carrier signals in the mixers 236, the two resultant waveforms are combined in the combiner 240 to form an amplitude and phase modulated signal for passing to the radio-frequency power amplifier 110.
• a single function generator could be provided.
• the output of the generator would be passed through a further quadrature hybrid, the two outputs of which would be passed to the respective mixers 236.
• This modification would produce the type of modulation known in the field of telecommunications as single side-band modulation with suppressed carrier.
• the modification has the possible disadvantage that the quadrature hybrid would work at very low frequencies.
• FIG. 7(a) the truncated modulus of the modulating waveform derived by inverse Fourier transformation of the desired rectangular frequency domain excitation spectrum is shown.
• the real and imaginary parts of this waveform are shown respectively in Figures 7(b) and 7(c).
• the modulus of the Fourier transform of this waveform is shown in Figure 7(d), whilst the real part of this spectrum is shown in Figure 7(e).
• the waveform shown in Figure 7(d) is not perfectly rectangular because the waveform of Figure 7(a) has been truncated.
• Figure 7(f) an oscillogram of the time domain excitation pulse is shown. This shows the effects of the modulating waveform on the radio frequency carrier signal.
• the peak power of the pulse was 1.44W.
• the peak magnetic field (B r£ ) for the excitation pulse was no greater than 0.16 mT at a flip angle of 30° e ⁇ a ⁇ ive and for a 15kHz excitation bandwidth. These are the lowest values of peak power and B rf of any of the examples. These low values were achieved mainly because the modulus of the time domain waveform had no zero crossing (compare Figure 7(a) with, for example, Figure 4(a)), but rather was relatively flat, so that power was distributed as evenly as possible throughout the duration of the excitation.
• shaped pulses described herein may be most satisfactorily employed in experiments with substances having signals exhibiting relatively small line widths.
• a small line width is preferable because it enables the excitation of large frequency ranges with low B rf field and low power. If only relatively broad lines are available, higher power may need to be used.
• RDX a good line is that at 5190 kHz, which has a line width of only about 200 Hz at room temperature.
• the apparatus was configured to detect the presence of the explosive RDX.
• the means for applying excitation was arranged to apply a sequence of regularly repeating pulses, as shown in the pulse timing diagram of Figure 8.
• the detection means was arranged to detect the free induction decays following each pulse.
• the pulses were shaped as described in relation to Figures 7 above, and were at a frequency, f, of roughly 5.2 MHz, so as to be able to excite the RDX resonance at 5.191 MHz at room temperature. They were of sufficient bandwidth (roughly 20kHz) to accommodate a temperature range of -5 to +35°C. They each had a duration (t,) of roughly 1ms.
• spin-lattice relaxation time, T ]5 varies by a factor of 100, between 500ms at the lower extreme of temperature and 5ms at the higher extreme.
• pulse repetition time, x was set to 25ms, giving a range of the ratio ⁇ /T, of 0.05 to 5.
• Flip angle, ⁇ was set to 30° actual.
• ⁇ was considerably greater than the sum of t f (which was 1ms) and the duration of the free induction decay appropriate to the substance and the selected frequency.
• the duration was approximately 2 or 3 times the free induction decay time, T 2 * of 1.4 ms.

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