| WO/2003/104430 | METHOD FOR OBTAINING DYNAMIC AND STRUCTURAL DATA PERTAINING TO PROTEINS AND PROTEIN/LIGAND COMPLEXES |
| WO/1988/004812 | APPARATUS FOR FORMING IMAGE |
| JP06133943 | MR IMAGING SYSTEM |
SOMASUNDARAM, Samuel (Dept. of Mechanical Engineering, King's College LondonStrand, London WC2R 2LS, GB)
JAKOBSSON, Andreas (Dept. of Electrical Engineering, Karlstad University, Karlstad, S-651 88, SE)
SMITH, John, Alec, Sydney (Chemistry Department, King's College LondonStrand, London WC2R 2LS, GB)
SOMASUNDARAM, Samuel (Dept. of Mechanical Engineering, King's College LondonStrand, London WC2R 2LS, GB)
JAKOBSSON, Andreas (Dept. of Electrical Engineering, Karlstad University, Karlstad, S-651 88, SE)
Claims
1. A method of testing comprising irradiating a sample, receiving a response signal and analysing the response signal by combining a plurality of resonance parameters, preferably as a function of a variable environmental parameter and a plurality of weighting parameters, wherein said weighting parameters preferably indicate proportions of components in said response signal.
2. A method according to Claim 1 , wherein the step of analysing the response signal comprises determining values of the weighting parameters.
3. A method according to Claim 1 or 2, wherein said components constitute a plurality of molecular environments.
4. A method according to Claim 3, wherein said plurality of molecular environments are a plurality of polymorphs of the same compound.
5. A method according to Claim 3 or 4, wherein the step of analysing the response signal comprises determining values of the weighting parameters in dependence upon the proportions of said sample's molecular environments.
6. A method according to any of the preceding claims, wherein the step of analysing the response signal comprises determining a value of the variable environment parameter, preferably in dependence upon the response signal.
7. A method according to any preceding claim, wherein the step of analysing the response signal comprises using a model of the response signal, the model combining the plurality of resonance parameters and the plurality of weighting parameters, at least one of the resonance parameters being a function of a variable environmental parameter.
8. A method according to Claim 3 or 4 or Claims 6 or 7 as dependent on Claim 3 or 4, wherein the number of molecular environments is unknown.
9. A method according to Claim 8, wherein the step of using the model further comprises determining resonance parameters and a weighting parameter corresponding to each molecular environment.
10. A method according to Claim 9, wherein each determined resonance parameter and weighting parameter is dependent on an actual molecular environment.
11. A method according to Claim 7, or any of Claims 8 to 10 as dependent on Claim 7, wherein the step of using the model further comprises fitting the model to the response signal by determining a value of the variable environmental parameter and the weighting parameter, and determining a value of at least one of the resonance parameters.
12. A method according to any of Claims 7, or any of Claims 8 to 11 as dependent on Claim 7, wherein the step of using the model further comprises determining the number of molecular environments in dependence upon the at least one weighting parameter.
13. A method of testing comprising: irradiating a sample comprising a plurality of molecular environments; receiving a response signal and analysing the response signal by fitting a model of the response signal to the actual response signal; the model comprising a plurality of resonance parameters each being a function of a variable environmental parameter, and a weighting parameter; and the step of fitting the model of the response signal to the actual response signal comprises determining a value of each of the resonance parameters, determining a value of the variable environmental parameter and determining a value of the weighting parameter.
14. A method according to any of Claims 2 to 13, wherein the step of determining a value of the at least one weighting parameter is carried out in dependence on a pre-determined relationship between the resonance parameters and the variable environmental parameter and/or a pre-determined relationship between the plurality of resonance parameters, preferably the relationship between the weighting parameter and the other parameters being linear.
15. A method according to Claim 14, wherein the step of determining a value of the at least one weighting parameter further comprises scaling the weighting parameters such that the sum of the weighting parameters is unity.
16 A method according to Claim 15, wherein a complex scaling is used.
17. A method according to any preceding claim, comprising determining the value of at least one further parameter.
18. A method according to Claim 17, wherein the value of the at least one further parameter is determined in dependence on a pre-determined relationship between the resonance parameters, the variable environmental parameter, and/or a pre-determined relationship between the plurality of resonance parameters and the determined value of the at least one weighting parameter, preferably the relationship between the at least one further parameter and the other parameters being linear.
19. A method according to Claim 18, wherein the value of the at least one further parameter is determined using a least squares technique.
20. A method according to any of Claims 9 to 19 in so far as they are dependent on Claim 6, wherein the step of determining a value of the at least one resonance parameter and/or the value of the variable environmental parameter is carried out in dependence on a pre-determined relationship between the resonance parameter and the variable environmental parameter and/or a predetermined relationship between the plurality of resonance parameters.
21. A method according to Claim 16, wherein the pre-determined relationship is a relationship between resonance frequency and temperature, and is preferably a linear relationship.
22. A method according to any of the preceding claims, wherein the step of analysing the response signal comprises using a model of the response signal, and further comprising determining the value of the variable environmental parameter and/or the value of the or each resonance parameter in dependence upon how well the response signal fits the model.
23. A method according to any of the preceding claims, preferably Claim 22, wherein the step of determining the value of the variable environmental parameter and/or the value of the or each resonance parameter is carried out using an iterative procedure.
24. A method according to Claim 23, wherein the iterative procedure comprises varying the value of the variable environmental parameter and/or the value of the or each resonance parameters and comparing the model to the response signal until the model is determined to match the response signal and/or until a pre-determined number of iterations have been performed.
25. A method according to Claim 24, wherein the iterative procedure comprises a 1 -dimensional search over the environmental parameter, and at least one multi-dimensional search over the or each resonance parameter.
26. A method according to Claim 25, wherein the multi-dimensional search is carried out in P dimensions, wherein P is a number of molecular environments present in said sample.
27. A method according to Claim 26, wherein the step of comparing the model to the actual response signal comprises generating a measure of how well the model matches the response signal.
28. A method according to Claim 27, wherein the model is determined to match the actual response signal when the measure of how well the model matches the response signal is within a pre-determined limit.
29. A method according to any of the preceding claims, comprising determining the value of the variable environmental parameter and/or the value of the or each resonance parameter and/or the value of the or each further parameter using a least squares technique, preferably a non-linear least squares technique.
30. A method according to any of Claims 9 to 29, comprising determining the value of the variable environmental parameter and/or the value of the or each resonance parameter and/or the value of the or each further parameter using a Maximum Likelihood Estimation technique.
31. A method according to Claim 30, wherein the Maximum Likelihood Estimation technique is a frequency selective Maximum Likelihood Estimation technique.
32. A method according to any of the preceding claims, wherein the step of determining the value of the variable environmental parameter and/or the value of the or each resonance parameter comprises determining the value of one of the parameters, fixing the value of that parameter at the determined value and then determining the value of another of the parameters.
33. A method according to any of the preceding claims, wherein the step of determining the value of the variable environmental parameter and/or the value of the or each resonance parameter comprises determining the value of at least two of the parameters simultaneously.
34. A method according to any of the preceding claims, wherein the method comprises determining, for at least one of the resonance parameters and/or for the environmental parameter, a range or set of values and determining the value of that parameter from that range or set of values.
35. A method according to any of the preceding claims, wherein the step of analysing the response signal comprises using a model of the response signal, and wherein components of the model are determined, wherein the step of using the model comprises selecting the components of the model.
36. A method according to Claim 35, wherein the model comprises at least one component representing a free induction decay.
37. A method according to Claim 35, wherein the model comprises at least one component stochastically representing a signal.
38. A method according to Claim 35, wherein the model comprises at least one component representing a steady-state free-precession.
39. A method according to Claim 35, wherein the model comprises at least one component representing an echo.
40. A method according to Claim 35 or 39, wherein the model comprises at least one component representing an echo decay.
41. A method according to any of Claims 35, 39 or 40, wherein the model comprises at least one component representing a train of echoes.
42. A method according to Claim 41 , wherein the component representing the train of echoes comprises a component representing the decay of the train of echoes.
43. A method according to Claim 42, wherein the component representing the decay of the train of echoes comprises a component representing the decay of peak echo amplitude.
44. A method according to any of Claims 41 to 43, wherein the model comprises at least one component representing a steady state signal associated with a train of echoes.
45. A method according to any of the preceding claims, wherein the step of analysing the response signal comprises using a model of the response signal, and wherein the model comprises a component which represents the response signal as at least one decaying sinusoid, and the or each decaying sinusoid corresponds to a respective resonance.
46. A method according to Claim 45, wherein at least one of the resonance parameters comprises a decay constant of the or at least one of the decaying sinusoids.
47. A method according to any of the preceding claims, wherein the step of analysing the response signal comprises using a model of the response signal, and wherein the model comprises at least one component representing an undesired signal.
48. A method according to any of the preceding claims, wherein the step of analysing the response signal comprises using a model of the response signal, and wherein the model comprises at least one component representing radio- frequency interference.
49. A method according to any of the preceding claims, wherein the step of analysing the response signal comprises using a model of the response signal, and wherein the model comprises at least one component representing a noise signal.
50. A method according to Claim 49, wherein the noise signal comprises a non-white noise signal.
51. A method according to any preceding claim, wherein the variable environmental parameter is one of temperature, pressure and magnetic field.
52. A method according to any of the preceding claims, wherein said components constitute a plurality of molecular environments, and wherein each and every said molecular environment is used to improve the signal-to-noise ratio of said response signal.
53. A method according to any preceding claim, wherein the response signal is a time-dependent signal.
54. A method according to any preceding claim, wherein the response signal comprises a radio-frequency response signal and/or the step of irradiating the sample comprises applying radio-frequency excitation to the sample.
55. A method according to Claim 54, wherein the excitation comprises pulsed excitation and preferably the excitation comprises a sequence of pulses.
56. A method according to any preceding claim, wherein the response signal comprises a resonance response signal, the resonance response signal being one of a nuclear quadrupole resonance (NQR) response signal, a nuclear magnetic resonance (NMR) response signal or an electron spin resonance (ESR) response signal.
57. A method according to any preceding claim, wherein the resonance parameters comprise at least one of frequency and relaxation time.
58. A method according to Claim 57, wherein the resonance parameters comprise at least one of spin-lattice relaxation time and spin-spin relaxation time.
59. A method according to any preceding claim, wherein the resonance parameters comprise a plurality of resonance frequencies.
60. A method according to any preceding claim, being a method for detecting the presence of a substance containing a given species of quadrupolar nucleus.
61. A method according to any preceding claim, being a method for detecting the composition of a substance containing a plurality of given species of quadrupolar nuclei.
62. A method of testing comprising: irradiating a sample comprising a plurality of molecular environments; receiving a response signal and analysing the response signal by fitting a model of the response signal to the actual response signal, said model being parametric.
63. A method according to Claim 62, wherein said parametric model is a demodulation technique such as the pencil technique.
64. A method according to Claim 62 or 63, wherein said response signal comprises components from each said molecular environment.
65. A method according to Claim 62, 63 or 64, wherein each said molecular environment is used to improve said response signal's signal-to-noise ratio.
66. A method according to any of Claims 62 to 65, wherein said response signal comprises a resonance response signal from each said molecular environment.
67. A method according to Claim 66, the resonance response signal being one of a nuclear quadrupole resonance (NQR) response signal, a nuclear magnetic resonance (NMR) response signal or an electron spin resonance (ESR) response signal.
68. A method according to any of Claims 62 to 67, wherein each said molecular environment is a polymorph of the same substance.
69. A method of testing a sample comprising predetermining a plurality of resonance parameters for different molecular environments and comparing the predetermined parameters with actual data.
70. A method according to Claim 69, further comprising performing an experiment to derive the actual data.
71. A method according to Claim 69 or 70, wherein the comparing step comprises the generation of a model.
72. A method according to Claim 71 , wherein the model is fitted to the actual data
73. A method according to any of Claims 69 to 72, further comprising producing an alarm signal when all expected molecular environments are detected.
74. A method according to any of Claims 69 to 72, further comprising producing an alarm signal when a predetermined proportion of expected molecular environments is detected.
75. Apparatus for testing a sample, comprising means for irradiating the sample, means for receiving a response signal and means for analysing the response signal by combining a plurality of resonance parameters preferably as a function of a variable environmental parameter and a plurality of weighting parameters, wherein said weighting parameters preferably indicate proportions of components in said response signal.
76. Apparatus for testing a sample, comprising means for irradiating the sample, means for receiving a response signal and means for analysing the response signal by fitting a model of the response signal to the actual response signal, the model comprising a plurality of resonance parameters each being a function of a variable environmental parameter and a plurality of weighting parameters, wherein the means for analysing the response signal is adapted to fit the model of the response signal to the actual response signal by determining a value of each of the resonance parameters, a value of the variable environmental parameter and a value of each weighting parameter.
77. Apparatus for testing a sample comprising means for irradiating a sample comprising a plurality of molecular environments; means for receiving a response signal and means for analysing the response signal by fitting a model of the response signal to the actual response signal, said model being parametric.
78. A computer program or computer program product adapted to perform a method as claimed in any of Claims 1 to 74.
79. Apparatus substantially as described herein with reference to and/or as illustrated in any of the accompanying drawings.
80. A method substantially as described herein with reference to and/or as illustrated in any of the accompanying drawings. |
ANALYSING NQR SIGNALS IN THE PRESENCE OF MULTIPLE POLYMORPHIC FORMS
The present invention relates to a method and apparatus for Nuclear Quadrupole Resonance (NQR) testing. In particular this invention relates to a method and apparatus for processing signals received from a sample containing multiple molecular environments, to analyse the sample, or to determine the composition of the sample.
There is strong interest in the potential applications of NQR, particularly for the non-invasive detection of hidden explosives and narcotics (e.g. detection of landmines and unexploded ordnance by the military; baggage screening for explosives, heroin and cocaine in the aviation industry), and as an analytical tool and characterisation method (e.g. in the pharmaceutical industry), where NQR promises significant advantages over other currently used methods.
This invention presents two sophisticated data processing algorithms, involving a parametric algorithm based on a model of the NQR signal echo train, which can be used in detectors. The invention may also be implemented for free induction decay signals, stochastic signals, steady-state free-precession signals and so on.
According to an aspect of the invention, there is provided a method of testing comprising irradiating a sample, receiving a response signal and analysing the response signal by combining a plurality of resonance parameters preferably as a function of a variable environmental parameter and a plurality of weighting parameters, the weighting parameters preferably indicating the proportions of components in said response signal.
By providing a plurality of weighting parameters the invention affords the advantage of allowing the proportions of substances within the sample to be determined. It further provides the advantage of allowing the number of different substances to be determined.
According to another aspect of the invention, there is provided a method of testing comprising: irradiating a sample comprising a plurality of molecular environments; receiving a response signal and analysing the response signal by
fitting a model of the response signal to the response signal; the model comprising a plurality of resonance parameters each being a function of a variable environmental parameter, and a weighting parameter; and the step of fitting the model of the response signal to the response signal comprises determining a value of each of the resonance parameters, determining a value of the variable environment parameter and determining a value of the weighting parameter. Thereby the invention affords the advantage of providing a model that accurately fits the response signal.
According to a further aspect of the invention, there is provided a method of testing comprising: irradiating a sample comprising a plurality of molecular environments; receiving a response signal and analysing the response signal by fitting a model of the response signal to the response signal, said model preferably being parametric. By providing a (parametric) model the invention thereby affords the advantage of providing more accurate results. Also, the invention may afford benefits over transform based techniques for example, such as reducing the time required to carry out the method.
According to a yet further aspect of the invention, there is provided a method of testing a sample comprising predetermining a plurality of resonance parameters for different molecular environments and comparing the predetermined parameters with actual data. By providing a plurality of predetermined resonance parameters the invention thereby affords the advantage of providing a test method to test a sample containing a plurality of molecular environments.
According to another aspect of the invention, there is provided an apparatus for testing a sample, comprising means for irradiating the sample, means for receiving a response signal and means for analysing the response signal by combining a plurality of resonance parameters as a function of a variable environmental parameter and a plurality of weighting parameters, the weighting parameters indicating the proportions of components in said response signal.
According to a further aspect of the invention, there is provided an apparatus for testing a sample, comprising means for irradiating the sample, means for receiving a response signal and means for analysing the response signal by
fitting a model of the response signal to the response signal, the model comprising a plurality of resonance parameters each being a function of a variable environmental parameter and a plurality of weighting parameters, the means for analysing the response signal being adapted to fit the model of the response signal to the response signal by determining a value of each of the resonance parameters, a value of the variable environmental parameter and a value of each weighting parameter.
According to a still further aspect of the invention, there is provided an apparatus for testing a sample comprising means for irradiating a sample comprising a plurality of molecular environments; means for receiving a response signal and means for analysing the response signal by fitting a model of the response signal to the actual response signal, said model being parametric.
The present invention further affords the following advantages:-
• The estimation of the proportions of different substances; the substances may be different polymorphic forms of the same substance or alternatively different substances entirely. • The exploitation of polymorphism; in effect the exploitation of different molecular environments to improve the response signal.
• The ability to assume that a large number of different substances are contained within the test sample without degrading quality of the result.
• The estimation of the number of different polymorphs present in the test sample.
• The ability to use any form of demodulation algorithm, such as a parametric technique -the pencil technique for example.
• The ability to convert the time-domain signal into the frequency domain.
• The ability to eliminate any undesirable frequencies once in the frequency domain (such as broadcast radio frequencies).
• The ability to search over a multi-dimensional space to determine the unknown parameters within the model; therefore the invention has the ability to distinguish between two parameters that are very close together in the frequency domain.
• It is not necessary to assume that the responses are close in terms of resonance.
• The applicability to multiple applications, not just explosives, but pharmaceutical, narcotics and quality control for example. • Could be applicable to other forms of detection such as NMR, although usually with solid state samples.
• Frequency ranges of interest may overlap.
• Reducing complexity by realising that with the present invention a matrix product can be simplified via the use of the formula for a geometric series. • Approximations of some parameters might be used to minimise the complexity of the method.
• The approximative method provides the advantage of only requiring a number of 1-D searches for simplicity.
• A less approximative method provides the method of a 1-D search over temperature (for example), then a multi dimensional search (depending on the number of polymorphs/substances) over the resonance parameters.
In an embodiment, the invention comprises a method for the analysis of an NQR signal from a sample containing multiple polymorphic forms of the same molecular species. Polymorphic forms, or polymorphs, are different crystalline forms of the same chemical compound.
The presence of polymorphs in a sample affects the characteristic spectra of the NQR signal such that it can be difficult to ascertain the sample constituents. Detection and quantification of polymorphic forms is in itself beneficial in the detection of explosives and narcotics, and is also important for use in quality control and as an analytical tool in the chemical and pharmaceutical industries. For example, pharmaceutical companies are obliged to state the precise polymorph of a given compound present in their products, and if there is a mixture of two or more, their relative proportions, as they may have differing pharmacological properties. This invention provides the advantage of enhancing the sensitivity of the NQR technique.
The present invention directly exploits the presence of such polymorphic forms, offering both improved probability of detection (for a given false alarm), and
allowing for an estimation of the relative proportions of the polymorphic forms present in the sample. This invention provides for fast and accurate detection even in the typical case where both the proportions of the polymorphs and the temperature of the sample are unknown. Numerical evaluation of the method by use of both simulated and real data demonstrates its utility, showing significant performance enhancement over the current state-of-the-art.
The invention has a more general applicability than its use with polymorphic forms, and a further embodiment of the invention enables the analysis of the NQR signal from a sample consisting of multiple distinct quadrupolar species, not necessarily polymorphic forms of the same substance.
Further features of the invention are characterised by the dependent claims.
The invention extends to methods and/or apparatus substantially as herein described with reference to the accompanying drawings.
Any feature in one aspect of the invention may be applied to other aspects. In particular, method aspects may be applied to apparatus aspects, or vice versa.
The present invention will now be described by way of non-limiting example with reference to the accompanying drawings, in which:
Figure 1 shows diagrammatically the 14 N quadrupole energy levels; Figure 2 is a block diagram of apparatus for NQR testing;
Figures 3 and 4 show the magnitude spectra of part of the v + region of a sample of TNT in monoclinic and mixed orthorhombic/monoclinic form, respectively; and Figures 5 to 11 are plots comparing the performance of a described detector to current state of the art detectors.
The following description is presented as follows:
• First, an introduction to nuclear quadrupole resonance is provided.
• Then, an example of NQR test apparatus is described, followed by a description of how NQR signals are detected and analysed.
• An outline of the data model of NQR signals containing multiple polymorphs as used by the current invention is then provided.
• Derivations of the two algorithms, describing the Hybrid Echo Train Approximate Maximum Likelihood (HETAML) and Frequency Selective HETAML (or FHETAML) detectors are then explained.
• A discussion of the use of certain approximations which can be made according to whether the primary use for the algorithms is analytical or for the purposes of detection then follows.
• A consideration of some alternative approaches to address the problem of polymorphs is then provided.
• Finally, an illustration is presented of an application of the algorithms to the detection of a sample of polymorphic TNT, containing a mixture, predominantly, of monoclinic and orthorhombic forms, the performance of the detectors being evaluated by using both data measured from an actual explosive and simulated data.
Introduction
Nuclear Quadrupole Resonance (NQR) is a solid state, typically pulsed radio frequency (RF) technique that can be used to detect signals from quadrupolar nuclei i.e. those, such as the 14 N nucleus, which behave as though they have a non-spherical charge distribution and therefore possess an electric quadrupole moment, a requirement that is fulfilled by roughly 50% of the periodic table.
When this type of nucleus is placed in a non-zero electric field gradient (EFG), different quadrupole energy levels arise since different nuclear orientations are energetically more favourable than others. The EFG seen by the nucleus is a result of the neighbouring charges, both electrons and nuclei, and is directly related to the chemical structure of the compound.
The compound specific nature of NQR is due to this relation between the EFG and the chemical structure of the compound, and its uniqueness means that there is little or no interference from other compounds that may be present.
This sensitivity of NQR signals to the chemistry of their originating species has led to the characterisation of the particular NQR frequency or frequencies for a large number of compounds containing quadrupolar nuclei.
The symmetry of the EFG, the magnitude of the nuclear electric quadrupole moment and the spin-quantum number of the nucleus all determine how the energy levels will be split. The 14 N nucleus has a spin-quantum number / = 1 and the energy levels, obtained by solving the quadrupolar Hamiltonian for a spin-1 nucleus, are shown in Figure 1 , with the three allowed transitions v + , v. and V 0 . The signals are acquired by applying pulsed RF radiation which drives transitions between the quadrupolar energy levels, and then measuring the response. Commonly, two types of signal are measured: the free induction decay (FID), which is the signal obtained immediately after an excitation pulse: and echoes, which are the signals obtained between a string of pulses. The latter having the advantage that a larger number of useful signals can be collected in a given time.
The use of NQR for the detection of explosives and narcotics is generating great interest as it offers distinct advantages over currently-employed methods such as the use of bomb-sniffing dogs and vapour detectors. Both of these apparatus suffer from environmental factors such as the presence of excessive moisture, and fail entirely when the explosives are hermetically sealed. Neither of these disadvantages affects NQR. Also, unlike Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI), to which it is related, NQR does not require a large static magnetic field to split the energy levels of the nucleus. Thus, NQR is attractive since it is an unobtrusive, non-invasive technique, ideally suited for such detection purposes.
The use of NQR in the pharmaceutical industry draws on its non-destructive, noninvasive nature, and also, since NQR is a solid state technique, it is able to capture important structural information often lost in solution-based methods, such as information concerning the crystallinity of compound, for example, the spin-phase memory decay time
In existing NQR techniques a sample is irradiated by a radio frequency (RF) signal and a radio frequency receiver then "listens" for a response signal. This is
typically done either by irradiating the sample using a single pulse and listening for a signal from the sample or by irradiating the sample using a series of pulses and listening for a signal in between them (often referred to as an "echo" technique).
Example of NQR test apparatus
An NQR test apparatus consists of a transmitter (to irradiate the sample), a receiver (to listen for response signals), signal processing circuitry (to analyse the response signal) and a controller (for timing of, for instance, pulses used to irradiate the sample, and for selection of the amplitude and phase of the pulses). A wide variety of apparatus are known for NQR testing, varying in accordance with whether it is intended for mine detection, baggage screening, or other applications. The present invention is applicable to ail such apparatus - one example of which is shown and described in US 6208136, the text of which is incorporated in its entirety herein by reference.
Similarly, the present invention is also applicable to signals excited by any one of a range of pulse sequences as are known in the art. Examples of such sequences include single-frequency excitation, phase cycling, PAPS, NPAPS, steady-state free-precession (SSFP), stochastic sequences, and so on.
The description of the apparatus in one embodiment is now described.
With reference to Figure 2, an apparatus for NQR testing includes a radio-frequency source 11 connected via a phase/amplitude controller 10 and a gate 12 to an r.f. power amplifier 13. The output of the latter is connected to an r.f. probe 14 which contains one or more r.f. coils disposed about or adjacent the sample to be tested (not shown), such that the sample can be irradiated with r.f. pulses at the appropriate frequency or frequencies to excite nuclear quadrupole resonance in the substance under test (for example, an explosive). The r.f. probe 14 is also connected to r.f. receiver and detection circuitry 15 for detecting nuclear quadrupole response signals. The detected signal is sent from circuitry 15 to a control computer 16 (or other control apparatus) for processing, and for signal addition or subtraction. The computer includes some means 17 for producing an alarm signal
in dependence upon whether a given threshold of detection for the presence of the particular substance of interest has been exceeded. The alarm signal would normally be used to activate an audio or visual alarm to alert the operator to the presence of the substance under test.
The control computer 16 also controls all pulses, their radio frequency, time, length, amplitude and phase. In the context of the present embodiment all of these parameters may need to be adjusted precisely; for example, phase may need to be varied in order to be able to generate echo responses.
Re-tuning of the r.f. probe 14, alteration of its matching and alteration of its Q factor may all need to be carried out dependent upon the nature of the sample. These functions are carried out by the control computer 16 as follows. Firstly, the computer checks the tuning of the r.f. probe 14 by means of a pick-up coil 18 and r.f. monitor 19, making adjustments by means of the tuning control 20. Secondly, the matching to the r.f. power amplifier 13 is monitored by means of a directional coupler 21 (or directional wattmeter), which the computer responds to via a matching circuit 22, which in turn adjusts the r.f. probe 14 by means of a variable capacitance or inductance. The directional coupler 21 is switched out by the computer 16 when not required, via switch 23. Thirdly, the Q factor of the r.f. coil is monitored by a frequency-switch programme and adjusted by means of a Q-switch 24 which either changes the coil Q or alternatively alerts the computer to increase the number of measurements.
The control computer 16 may be programmed in various methods of reducing or eliminating the spurious interference described above by controlling the pulse amplitudes and phases by means of the control 10. These methods can involve the use of a comparator 25 for comparing the response signals from different pulses by making appropriate changes to the phase of the receiver and detection circuitry 15, and passing the resultant signals to the remainder of the control computer 16 for further processing.
The control computer 16 is also used to analyse the response signals. The methods used for analysis of the response signals are described in more detail later. The control computer 16 may also be used to sum and/or signal average
response signals. Analysis may be carried out on individual response signals or on summed response signals or on averaged response signals.
Typically, appropriate software is run on the control computer 16 in order to carry out one or more of the analysis methods described below. In the preferred embodiment, the user may select which analysis method is to be used, depending on the nature of the testing to be carried out.
As described in more detail below the analysis may comprise estimating the values of resonance parameters and/or one or more variable environmental parameters
(for instance temperature), the estimation in the preferred embodiment being performed by fitting one or more response signals to a model. The control computer 16 in fitting the response signal or signals to the model, selects values of the various parameters included in the model and, in certain variants, also selects the form of the model and the components to be included in the model. Typically the control computer uses an iterative fitting procedure to fit the response signal or signals to the model.
In particular uses of the preferred embodiment, the results of the analysis procedure, for instance one or more of the fitted values of the parameters of the model, are outputted. The outputted results may be used for instance in a further analysis procedure (for instance in analysing, say, the purity of a sample) or in setting up a further measurement (for instance the fitted value of, say, temperature may be used in setting up another measurement on the sample, for instance a measurement using a different experimental technique).
The control computer 16 may be set up so that the fitting of the response signal or signals is performed with a pre-determined level of accuracy.
In the case where the apparatus is used for the detection of the presence or absence of a given substance, it may not be necessary to find the best fit to the response signals; an approximate fit may be suitable (in that case, typically, the response signal may be fitted using a series of 1 -dimensional fits of each parameter in turn rather than a full multi-dimensional fit of all parameters simultaneously).
In the case where the apparatus is used for analysis of a characteristic (for instance the purity) of the sample (or a particular substance included in the sample) under test then it may be important to find the best fit giving the most accurate values of the parameters. In that case, the response signal may be fitted using a full multi- dimensional fit of all parameters simultaneously.
Methods for searching for best or estimated fits are known in the art and may be used. Alternatively, methods for searching for best or estimated fits described explicitly herein may be used.
In alternative embodiments, response signals are passed to a further computer or processor for analysis. The analysis may be performed by dedicated circuitry or by suitable software.
Shown diagrammatically in Figure 2 and designated as 27 is some means, such as a conveyor belt, for transporting a succession of samples to a region adjacent the r.f. probe 14. The computer 16 is arranged to time the application of the excitation pulses substantially simultaneously with the arrival of a particular sample adjacent the probe. In alternative embodiments, instead of the sample being carried on a conveyor belt, it may actually be a person, and the r.f. probe may be in the form of a walk-through gateway or a hand-held wand.
Although the apparatus described above would usually employ rectangular pulses, other pulse shapes may be employed. Furthermore, although the radio-frequency probe would generally utilise a single coil for both transmission and reception of signals, any appropriate number of coils may be used, or different coils can be used for transmission and reception.
The detection and analysis of NQR signals
In practice, detection and analysis of NQR signals is complicated by the fact that many chemical compounds form distinct and different crystalline structures known as polymorphic forms or polymorphs. Each polymorph exhibits a different NQR signal, and the deconvolution of these responses for a sample containing a mixture of polymorphs is non-trivial. Furthermore, the presence of polymorphs
can result in low signal-to-noise ratios (SNR) and long data acquisition times. Therefore, detectors which can only examine responses from a single polymorph perform poorly when other polymorphs are also present. This can be a critical issue; for example, the accurate detection of trinitrotoluene (TNT), a common explosive, requires detection of both of its two main polymorphic forms, monoclinic and orthorhombic, and of mixtures thereof. It would therefore be highly beneficial to exploit the combined signals from all polymorphs contained in the sample under test in order to improve on the probability of detection (for a given false alarm).
It is also of significant interest in itself to determine the relative quantity of polymorphs present in a given sample. For example, where NQR finds use as an analytical tool in the pharmaceutical industry, detection and quantification of different polymorphic forms of chemical compounds is important as varying intermolecular interactions among polymorphs can give rise to different pharmaceutical properties in medical drugs.
Furthermore, there are detection systems which are able to simultaneously excite quadrupole nuclei from different compounds. The present invention can be used to beneficially combine these differing responses.
There are several different approaches to the analysis of NQR signals.
Fast Fourier Transform (FFT) methods, for example, are commonly used in the pharmaceutical industry. There, quantitative estimates of the different nuclear environments are obtained by integrating the associated spectral peaks.
Estimates of other NQR signal parameters are also commonly obtained by processing the spectrum; for example, Tξ is obtained by measuring the full- width-at-half-height of the resonant line. Estimates obtained in this manner are prone to variation, as subjectivity is introduced into the method, for example, the choice of integration interval in quantitative calculations. Additionally, overlapping spectral peaks and low signal-to-noise ratios (SNR) will make calculations more difficult.
It is therefore preferred to use parametric (model-based) methods. Typically, the analysis of the echo signals exploits the fine structure of the echo, and involves modelling the data as a sum of sinusoidal components. The technique is then to fit, in a weighted sense, the measured data to the data model using a search over constituent parameters.
This embodiment uses such a parametric model and presents detection algorithms for two different hybrid detectors which deal with the cases described above, both correctly accounting for combined NQR responses from multiple polymorphs, and allowing for quantitative estimates of the proportions of these polymorphs.
Of these two detection algorithms, the second algorithm presented in this invention constructs a detection variable from a frequency selective data set, allowing for significant robustness in cases where residual RF interference (RFI) is present.
This embodiment exploits the combined signals from all contained polymorphs to improve on the probability of detection (for a given false alarm), facilitating a faster and safer detection.
Extensive numerical evaluations using both simulated and measured NQR signals, and the comparison with the performance of current state-of-the-art detectors, indicates that the presented techniques offer a significantly improved probability of accurate detection for samples containing more than one polymorphic form.
The Data Model
In this and the following sections, this embodiment of the invention is described in mathematical terms but the skilled person will readily be capable of implementing this in data processing hardware and/or software, for instance on the control computer 16 in a preferred embodiment.
Background information concerning analysis of signals may be found in the following:- P. Stoica and R. Moses, Spectral Analysis of Signals, Prentice Hall, Upper Saddle River, N.J. 2005; S. M. Kay Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory, Prentice Hall, 1993; and S. M. Kay, Fundamentals of Statistical Signal Processing, Volume II: Detection Theory. Prentice Hall, Englewood Cliffs, N.J. 1998.
The use of a model of the NQR signal echo train, as produced by a PSL sequence, is now considered in detail, beginning with the derivation of a data model for trains of echoes, and then continuing with description of detectors based upon this data model.
In general, the idealised (noiseless) NQR echo signal from a particular polymorph can be modelled as for any non-polymorphic quadrupolar substance by a sum of sinusoidal components, or an "echo train". The m th NQR echo, produced by the p th polymorph, can be described by
t = to, ... , t N .i is the echo sampling time, not necessarily consecutive instances, but typically starting at t 0 ≠ 0 to allow for the dead time between an excitation pulse and the first measured echo (after the pulse). For simplicity, a uniform sampling starting at t 0 is assumed.
m = 0, ..., M-1 is the echo number; t sp , often called the tau spacing, is the time between the centre of the refocusing pulse and the echo centre. The term "refocusing pulse" refers to the pulse which refocuses the transverse magnetisation to produce an echo, as for example in a pulsed-spin locking (PSL) sequence.
μ = 2 t sp is the echo spacing in a PSL sequence.
cf m) denotes the number of NQR frequencies from the m th polymorph, which may be different to ό k \ for k≠m.
cck (p) , βk {p) , and η k {p) denote, for the p th polymorph, the (complex) amplitude, the sinusoidal damping constant and echo train damping constant of the rf h NQR frequency, respectively.
is the frequency shifting function of the A 111 NQR frequency component of the p th polymorph which, in general, depends on the (unknown) temperature, τ, of the exam ined sam pie.
An important point to note is that the number of sinusoidal components, d p
\ as well as the frequency shifting function for each spectral line,
Although the damping constants, β k (p \ are essentially known for a given sample, variations may exist between samples and therefore β k {p) is modelled as an unknown to allow for this uncertainty.
For NQR signals of many samples, such as for TNT, the frequency shifting function at likely temperatures of the sample can be modelled as
where a k {p) and b k {p) , for k=1,...,cf p) , are given constants.
It should be stressed that the frequency shifting functions for different crystalline structures are, in general, different. This will be equally true for samples, including both mixtures and compounds, containing two or more different quadrupolar nuclei whose resonance frequencies happen to lie within the measured frequency range.
Often, the relative ratio between the signal amplitudes is accurately known for a given examined sample and experimental set-up. To exploit this knowledge, a£ p) is set to be equal to p κ£ p \ where p and x// p) denote the common scaling constant due to the signal power and the a priori known relative (complex) scalings between the cf p) signal components (at time zero), respectively.
The observed NQR signal response from P polymorphs can therefore be written as
p
where y p denotes the proportion of the p th polymorph, and w(t) is an additive coloured noise. It is not necessary to know a priori the number of polymorphs, P
The HETAML Detector
The NQR signal response is rewritten in matrix form as follows:
w NM is defined in a similar way to y^w,
ω is an NM-by-P matrix (where each column represents a different polymorph) defined by
where (.) r denotes the transpose operator.
The Maximum Likelihood Estimator (MLE) is determined as
where and
where
and
i.e. the model is parameterised in terms of the common scaling constant due to signal power, p; the proportion of each polymorph, γ, temperature, τ; damping constants, β and the echo train damping function for each spectral line, η.
p and γ are linear and can be solved for algebraically; β, η and τ are non-linear quantities and need to be searched for.
Further, R w
denotes the noise covariance matrix
where £{.} and (./denote the expectation and the conjugate transpose, respectively.
As R w is typically unknown, one is normally forced to use an estimate of R w , say
^w in (14). Such an estimate can be formed in various ways; herein, a low-order approximative noise model derived from real noise data is used.
A prewhitened data model is therefore formed such that
where θNM is a zero-mean complex white Gaussian noise with variance σ e 2 , and
with [.] / c denoting /c" 1 index, and
Furthermore,
Using (16), the minimisation in (14) is written as
wher denotes the Frobenius norm.
Thus, the unstructured estimat
where
This assumes that the P polymorphs differ sufficiently to ensure the invertability of
should the matrix be poorly conditioned, a low-rank approximation of the inverse can instead be formed.
As the measured signal is complex, the unstructured estimate g τ is likely to be complex too, especially in the typical case where there are discrepancies between the model and the measured data. For instance, a zero order phase error, common in NQR measurements, would lead to a complex ST, where the algorithm applies a phase rotation to compensate for the error. Bearing this in mind, a complex scaling can be allowed by forming the estimate of γ k as
where denotes the /c" 1
element in
Let
Then, by inserting (26) into (23), the least squares estimate of p can be found as
yielding
and
Using the maximising (27), the Generalised Likelihood Ratio Test (GLRT) for an unknown noise model is formed
Using (30), the signal component is deemed present if and only if T( Z
NM) > $ and otherwise not, where $ is a predetermined threshold value reflecting the acceptable probability of false alarm G>/); here, Pf
From the essence of its derivation, this detector is therefore termed the Hybrid Echo Train Approximate Maximum Likelihood (HETAML) detector.
The FHETAML Detector
The HETAML detector presented above can be extended to formulate a Frequency Selective HETAML (or FHETAML) detector.
As the temperature of the sample can be assumed to lie within a known temperature range, one may use equation (2) to determine the range of frequencies in which each of the sinusoidal components may be present, and therefore derive a frequency selective detector that only considers these frequencies. This will reduce the impact of RF interference and also reduce the computational burden.
Consider the frequency regions formed by
with /fr k \ _ being L given, not necessarily consecutive, integers selected such that (31) only consists of the possible frequency grid points for each of the (cf 1) + ... + cf p) ) signal components; each such region is given by the minimal and maximal frequency values for that component considering the measured temperature and the size of the expected temperature uncertainty region.
Denoting the measured temperature
Each echo should be Fourier transformed individually since each refocusing pulse will reinitialise the signal.
The Fourier transformed (prewhitened) data vector for the m th echo and /c" 1 frequency bin can be expressed as
where E ™ = v fc e iv represents the /c* h frequency bin of the prewhitened noise sequence associated with the m th echo, θ λ /", and
with
where
and where EL" 1 is defined similar to Z L m .
Using (35), the data model for the whole echo train can be expressed as
where E LM is defined similar to Z L M, and
Using (38) the minimization in (14) can be approximated as
(The frequency domain data vector is typically of a significantly lower dimension than the time-domain representation as L « N).
The GLRT of the FHETAML detector is found to be reminiscent of (30).
From a computational view, the fact that the indices of
where
Expressions for the other polymorphs can be derived similarly.
The use of approximations for specific applications
To guarantee accurate estimates of all parameters, the full multidimensional minimisation described by (23) for HETAML, and by (40) for FHETAML, should be performed. The estimators/detectors that perform the full multidimensional search are termed the HETAML-MD and FHETAML-MD.
Finding the multidimensional minimum using a grid search would involve substantial computational effort. Fortunately, depending on the application, various approximations can be used in order to realise computationally efficient algorithms.
For analytical applications, where the SNR is relatively high compared to detection applications, it is accurate estimates of all NQR signal parameters which are of most importance. Therefore, the full multidimensional search is approximated by a series of 1-D searches over temperature, the sinusoidal
damping constants and the echo damping constants. The searches are iterated to give accurate parameter estimates.
For detection applications, the SNR is typically low and it is beneficial to reduce the number of parameters being estimated, by grouping parameters together; for instance, one can often make a number of useful approximations.
If temperature shifting functions for each echo train damping constant are available, i.e.
The approximations may also be used, enabling the
Similarly, one can form an approximation using (2P+1) 1-D searches over
The (approximative) Generalised Likelihood Ratio Test can be formed using the obtained estimate
These approximative detectors are termed the HETAML-a and FHETAML-a detectors.
However, typically, the joint search space over the common (sinusoidal and echo train) damping constants will not decouple. As a result, one should rather form a common P-D search space over the P common sinusoidal damping constants, and similarly a P-D search space over the P common echo train constants. The resulting approximate detectors, formed by an initial 1-D search over temperature, followed by a P-D search over the common sinusoidal damping constants and a P-D search over echo damping constants, are termed the HETAML-aPD and FHETAML-aPD.
Such an approximate maximisation of (27) (and similarly for the frequency selective versions), can beneficially be iterated to further improve the fitting.
Alternative approaches to the problem of polymorphs
Further embodiments of the invention addressing the problem of multiple polymorphs are now described
In one alternative, one may form a detector via an alternating projection approach, where one would initially assume the presence of only a single polymorphic form or substance, and treat any remaining form as part of the background noise. One can then form an estimate of the dominant frequencies of the assumed form or, alternatively, of the temperature matching these frequencies, using a weighted least squares approach. The estimated form is then subtracted from the data set, and the residual is used to estimate the second form, and so forth. Beneficially, one may also iterate the estimation steps such that after estimating all the present polymorphic forms, one proceeds to refine the estimates by subtracting all found forms, and then again estimating the considered form. The dominant frequencies of the estimated forms, or alternatively, a weighted combination of the frequencies matched to the found temperature estimates, can then be combined to form a detection variable.
In another alternative, one may form a detector by estimating a collection of all the dominant frequencies in the data set, using, for instance, a high-resolution frequency selective ESPRIT approach, and then using a weighted least squares fitting to combine the frequencies to their respective forms as well as the joint temperature estimate. These estimates can then be combined to form a detection variable, for instance, formed as a generalized likelihood ratio test.
An illustrative application of the invention: The detection of TNT
As an illustration of the applicability of the present invention to polymorph detection via NQR, the following demonstrates the detection of TNT using the proposed detectors.
TNT is a common explosive in landmines and currently poses a great challenge for the detection of landmines using NQR.
First, the masses of TNT typically found in anti-personnel mines result in low signal-to-noise (SNR) and long data acquisition times.
Second, the NQR signals generated by TNT are weak compared to the signals produced, for instance, by another common explosive found in landmines, RDX (cyclotrimethylene trinitramine, also known as Royal Demolition Explosive), and therefore many measurements often need averaging to yield a sufficient signal to noise ratio (SNR) to get the necessary high probability of detection required for landmine detection.
Third, the resonant lines in TNT have long spin-lattice relaxation times, resulting in long measurement repeat times.
Fourth, the TNT signals lie in the AM radio band where strong RFI will typically be present. Both passive RFI mitigation techniques, such as gradiometers to cancel the far field RFI, and active RFI mitigation techniques, such as adaptive noise cancellation techniques which require reference antennas to measure the non- stationary background RFI have been investigated in other work.
Detection of TNT is further complicated by the existence of at least two polymorphic forms, monoclinic and orthorhombic, with different NQR properties. TNT is almost always found as a mixture of these two polymorphs in varying proportions according to the origin of the explosive and the time - in the case of landmines - that the landmine has been in the ground. Rather than detecting signals from just one polymorphic form, it is an advantage to detect signals from both simultaneously and measure their relative proportion, which can be regarded as a characteristic of all mines in a given location.
As has been mentioned above, detectors which can only examine responses from a single polymorph perform poorly when other polymorphs are also present. This invention fully exploits the known data model of the NQR signal echo train in order to take correct account of the presence of polymorphic forms.
The isolated TNT molecule contains three NO 2 groups, two ortho and one para, i.e., two nitrogen environments as the two ortho groups are equivalent. However, in the crystal lattice, the unit cell, in both monoclinic and orthorhombic phases, contains two TNT molecules each lying in general positions (therefore each has three different NO 2 groups). Therefore, both monoclinic and orthorhombic TNT each contain six different nitrogen environments which leads to a total of 36 NQR transitions (resonant frequencies) i.e., 18 for monoclinic and 18 for orthorhombic.
Figures (3) and (4) show the magnitude spectra of part of the v + region of a monoclinic sample and a mixed orthorhombic/monoclinic sample, respectively. Inspection of the spectrum in Figure (4) indicates that the predominant polymorph in the mixed sample is orthorhombic TNT. Landmines often contain a mixture of these two forms, the proportions of which can vary between landmines (and over time in a given landmine) as the metastable orthorhombic form may change slowly to the more stable (at room temperature) monoclinic phase. The activation energy for the phase transition of orthorhombic to monoclinic is E act = 355~kJmor 1 .
Consider two of the polymorphic forms of TNT, namely the monoclinic (p=1) and the orthorhombic (p=2) polymorphs, i.e. P=2.
As detection is the problem of interest, the HETAML-a and FHETAML-a implementations, described earlier were implemented and compared to the ETAML-a, FETAML-a, AML and FSAML detectors described in International Patent Application Number WO 2006/064264, and the DMA-p, DMA-r and DMA-s detectors described in Y. Tan, S. L. Tantum, and L. M. Collins, Cramer-Rao Lower Bound for Estimating Quadrupole Resonance Signals in Non-Gaussian Noise, IEEE Signal Processing Letters, vol. 11 , no. 5, pp. 490-493, May 2004.
The performance of the detectors is evaluated using both measured NQR data and simulated data designed to mimic the measured data.
The measured data consisted of 1000 data files, 500 with TNT and 500 without, each containing four summed echo trains. Each echo train was generated using a
pulsed spin-locking (PSL) sequence and consists of 32 echoes, each echo consisting of 256 samples.
The first echo of the echo train was discarded before being input to the algorithms as it may be significantly distorted by contributions from the free induction decay (FID) produced by the preparation pulse in the PSL sequence.
To allow for the typical practical case where some residual RFI remains, the data collected in a partially shielded environment with only the coil, sample and probe tuning/matching circuitry being placed in a shield.
The sample, weighing 50Og, contained a mixture of monoclinic/orthorhombic TNT. Herein, this will be referred to as the "mixed" TNT sample.
The temperature of the sample was not artificially controlled, to allow for the realistic case where temperature fluctuations would exist, however, the ambient air temperature was measured as 301 K.
A solenoidal-type coil was used and its Quality (Q) was reduced to 30 in order to achieve the probe bandwidth necessary to observe the 8 lines used here for TNT detection.
A pure sample of monoclinic TNT sample was placed in the probe and using the same experimental set-up as used for the mixed TNT sample, the monoclinic a priori scalings were obtained. A pure sample of orthorhombic TNT could not be obtained, so a mixed sample of mainly orthorhombic TNT was placed in the probe and the orthorhombic a priori scalings were obtained by taking the monoclinic scalings into account.
The frequency shifting function constants and the a priori complex scalings for both orthorhombic TNT and monoclinic TNT are summarised in Table (1).
The temperature shifting functions (given in K) and the relative scalings for the 8 (dW = 4 and d^ = 4) NQR frequencies of TNT, for an excitation frequency of 841.5 kHz, in the region of 830-850 kHz.
Table 1.
Using these parameters, the HETAML algorithm was applied to a high SNR signal, obtained from the mixed TNT sample, yielding estimates of Ti= 0.3 and 72= 0.7.
The simulated data was generated using these proportions, (3), Table (1) and a sixth order AR noise model with AR coefficients c o =1 , Ci=-0.0006, c 2 =-0.0404, c 3 =-0.3932, c 4 =0.2868, c 5 =0.2510, c 6 =-0.2392.
The detectors were compared using simulated data with and without RFI, representing the cases of unshielded and shielded data, respectively.
The RFI is modelled using a simplistic model consisting of discrete sinusoids with random frequencies, uniformly distributed over the interval [-π, π], with zero mean unit variance normally distributed amplitudes.
The AML, FSAML and DMA approaches are generally applied to echoes, or echo trains that have been pre-processed to produce a single echo with stronger SNR, whilst HETAML, FHETAML, ETAML and FETAML detectors are applied to unprocessed echo trains. Hereafter, the AML, FSAML and DMA approaches were applied to the summed echo train, formed by adding all the M consecutive echoes, while the HETAML-a, FHETAML-a, ETAML-a and FETAML-a are formed on the full echo train signals allowing for the fine structure between the different
echoes. As the former estimators operate on a single echo, they cannot be formed on the full echo train.
The AML-based detectors and the DMA-s detector use a search region over temperature of [290,31O]K (in 100 steps), in order to account for temperature uncertainties.
To allow for uncertainties in the NQR sinusoidal damping parameters due possibly to different degrees of crystallinity of the sample, and for uncertainties in the NQR echo damping parameters in part due to varying t sp
, the following search regions were used; the common sinusoidal damping parameters, /? 0 (1)
and
These search spaces cover a large range of parameter values. In practice, the range of these searches should be significantly more restricted given typical prior knowledge about the sample temperature, sinusoidal damping parameters and echo damping parameters. This will further improve the performance of all the AML based methods. In order to represent the worst case, where little is known about the NQR parameters, the searches were unrestricted.
Figures (5) and (6) show the receiver operator characteristic (ROC) curves of the discussed detectors, for simulated data without RFI, using 1500 Monte-Carlo simulations at an SNR of -36 dB, where SNR is defined as SNR =
The figures clearly illustrate the improved performance of the proposed FHETAML-a and HETAML-a detectors over the recent AML and DMA approaches.
In this particular case, the DMA-s detector performed reasonably well; the reason for this is that the algorithm is not affected by different polymorphs, i.e., it finds
the dominant peak within the relevant frequency region, which here happens to be an orthorhombic peak.
It may also, at first, seem surprising that DMA-r performs better than DMA-p. This is because DMA-p is set to find the dominant monoclinic peak at the precisely given temperature, whilst DMA-r is set to find the same peak but with the temperature 5 degrees in error. This has, in fact, meant that the DMA-r detector is measuring the response from a stronger orthorhombic peak.
The poor performance of FSAML may be caused by the echo averaging.
In a realistic measurement environment, it is not possible to fully shield the sample and the antenna from RFI. As discussed earlier, there are techniques available for mitigating RFI, however, it is likely that significant amounts of residual interference will still remain. Here, the performance of the detectors was evaluated in the presence of RFI. Figures (7) and (8) confirm the earlier results, showing the ROC curves of the detectors, for simulated data with RFI present, using 1500 Monte-Carlo simulations at an SNR of -34~dB.
Finally, the algorithms were evaluated with real data. Figures (9) to (11) show the ROC curves of the detectors, for the measured data set (described earlier). The figures clearly show the beneficial performance of the hybrid detectors over the other detectors.
In summary, Nuclear Quadrupole Resonance (NQR) is a solid state radio frequency (RF) technique that is able to distinguish between different polymorphic forms of certain compounds. Quantification of these polymorphs is important in several pharmaceutical processes. Furthermore, being able to exploit the signals from multiple polymorphs, as well as from different quadrupolar nuclei, is beneficial in the detection of explosives and narcotics. In certain embodiments, this invention presents two hybrid estimators that provide estimates of the relative proportions of the polymorphs, as well as estimates of other NQR signal parameters, such as line width parameters, also important in pharmaceutical applications. The estimators are extended to form two hybrid detectors which offer improved probability of detection, as compared to recently proposed
detectors. The detectors are evaluated on simulated data and real data measured from a sample of TNT which contains at least two polymorphic forms, monoclinic and orthorhombic, with rather different NQR properties.
In other embodiments, this invention proposes two hybrid detectors that exploit NQR signals from multiple polymorphs, as well as allowing for estimation of the proportions of these polymorphs. These detectors ensure accurate detection even in the typical case where both the proportions of the polymorphs and the temperature of the sample are unknown. Numerical evaluation using both measured and simulated data show a significantly increased probability of detection (for a given false alarm) for the proposed HETAML and FHETAML detectors, over other current state-of-the-art detectors.
As a further example, other applications can be envisaged where the response signals from different compounds are closely spaced in which this invention would provide an improved performance and faster analysis. The widely used explosive "Semtex" consists of a mixture of the two explosives RDX and PETN, and both can be detected simultaneously by exciting the RDX doublet near 501 kHz and the intermediate v- frequency from PETN near 496 kHz, giving an improvement in the signal to noise ratio, faster analysis and a measure of the relative proportions of these two explosives so as to characterise the sample of
Semtex being detected.
The methods can be equally applied to two close signals from different nuclei in the same material. An example is the amphetamines, which are often found as hydrochlorides, in which the Cl 35 NQR signals usually observed between 2 and 3 MHz may lie close to N 14 NQR signals from the same material, so that both can be excited simultaneously and the relative proportions used as an additional method of characterising the material.
It will be understood that the present invention has been described above purely by way of example, and modification of detail can be made within the scope of the invention.
Each feature disclosed in the description, and (where appropriate) the claims and drawings may be provided independently or in any appropriate combination.