WO1996010163A1 - Detection device and method - Google Patents
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- WO1996010163A1 WO1996010163A1 PCT/GB1995/002304 GB9502304W WO9610163A1 WO 1996010163 A1 WO1996010163 A1 WO 1996010163A1 GB 9502304 W GB9502304 W GB 9502304W WO 9610163 A1 WO9610163 A1 WO 9610163A1
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- 238000001514 detection method Methods 0.000 title claims abstract description 23
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- 238000005079 FT-Raman Methods 0.000 description 1
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
- G01J3/28—Investigating the spectrum
- G01J3/2846—Investigating the spectrum using modulation grid; Grid spectrometers
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01J—MEASUREMENT OF INTENSITY, VELOCITY, SPECTRAL CONTENT, POLARISATION, PHASE OR PULSE CHARACTERISTICS OF INFRARED, VISIBLE OR ULTRAVIOLET LIGHT; COLORIMETRY; RADIATION PYROMETRY
- G01J3/00—Spectrometry; Spectrophotometry; Monochromators; Measuring colours
- G01J3/28—Investigating the spectrum
- G01J2003/2866—Markers; Calibrating of scan
Definitions
- the present invention relates to a device for and method of multiplex detection of a plurality of signals characteristic of a plurality of samples. More particularly, the invention relates to techniques for the multiplex detection of signals by a spectrometer.
- the invention might, for example, be utilised in the control of mixing processes such as the gelatinisation of starch.
- spectrometers receive signals from one radiation source and one sample, and display the results as a single spectrum of the sample.
- each sample (carrying spectral information characteristic of that sample) were combined and then detected in a number of experiments.
- each individual signal was modulated using an encoding scheme.
- the combined signal was then decoded to reveal the individual signals.
- the encoding and decoding was carried out using Hadamard and inverse Hadamard transforms.
- the present invention seeks to overcome these problems.
- a device for the multiplex detection of a plurality of signals characteristic of a plurality of samples comprising: encoding means for causing the respective signal characteristic of each sample to be modulated according to a respective different sine function, or a respective different cosine function, or a respective different mixed sine and cosine function; and
- the present "sine/cosine transform" technique invention can afford the advantage over the
- the present invention can enable the simultaneous acquisition of an arbitrary number of signals using one spectrometer or at least a reduced number of spectrometers, thus achieving a considerable cost saving in situations where several instruments might formerly have been required if a sequential sample acquisition scheme were used.
- the invention Whilst a major advantage afforded by the present invention is the ability to operate with a reduced number of spectrometers, in many circumstances the invention can also provide an improved standard deviation of noise as compared with sequential sample acquisition schemes. These circumstances are where the noise is generated in the combining and detecting means. For instance, in the case of FT-NMR, the noise is generated mainly in the radio-frequency detection coils and in the detection preamplifier.
- sine function As used herein, the terms “sine function”, “cosine function” and “mixed sine and cosine function” include, for example, sine squared functions and the like. The different, say, sine functions according to which the respective signals are modulated may differ solely according to their frequency. Also, as used herein, the term “mixed sine and cosine” function includes such functions as might be encountered for example with Fourier and
- samples includes both a number of separate, distinct specimens and also a number of portions of the same specimen.
- the encoding means is adapted to cause each signal to be modulated such that the magnitude of the modulated signal does not fall below zero.
- This feature is of importance if the invention is being used to detect signal intensities of any kind, such as radiation. Intensities by their very nature can not fall below zero; it is important that the sample multiplexing scheme can cope with this limitation.
- the encoding means is adapted to cause each modulated signal to be centred on a baseline level having a magnitude greater than zero.
- the encoding means may be adapted to cause each signal to be modulated according both to a sine squared and to a cosine squared function.
- each signal may be caused to be modulated according to a sine, cosine or mixed sine and cosine function, with a baseline offset from the zero intensity level.
- the encoding means is adapted to cause each signal to be modulated such that negative half-cycles of the function are inverted, whereby the magnitude of the modulated signal does not fall below zero.
- each signal is a radiation signal, in which event the device suitably includes at least one source of radiation for irradiating the samples to generate said signals.
- the radiation may be electromagnetic, and may for example be light, whether at its visible or invisible wavelengths.
- the encoding means comprises a respective pair of polarising filters for each sample, the filters of each pair being movable relative to each other to modulate their respective signal.
- the encoding means may comprise a respective graded filter device for each sample, each filter device being movable to modulate its respective signal.
- the encoding means comprises a respective modulating member for each sample, each modulating member being movable and being shaped such that movement of the member can modulate its respective signal.
- the modulating member may, for example, involve a specially shaped slit on a rotatable disc or on a translatable plate, or it may involve a disc with a series of apertures of various sizes.
- the encoding means is arranged such that the matrix is unitary. This can ensure that each of the decoded signals includes noise with the same standard deviation.
- the encoding means is arranged such that the matrix is purely real. This can lead to the invention being easier to implement than in cases, such as where a Fourier transform is used, where the matrix is complex.
- sampling instants is preferably no less than the number of samples, since this is usually necessary for the successful performance of the test.
- sampling instants is meant preferably the instants at which the combining and detecting means detects the combined signal or signals.
- real time the instants at which the combining and detecting means detects the combined signal or signals.
- such sampling instants may represent uniformly spaced instants during a single experiment; in another preferred embodiment (the “pseudo-time” embodiment), such sampling instants may represent separate experiments spaced by an arbitrary (but nevertheless typically regular) time interval.
- the encoding means is adapted to cause each signal to be modulated at a respective different frequency; in other words, the functions by which the respective samples are modulated differ as to frequency.
- the remaining modulations More preferably, relative to the modulation having the lowest frequency, the remaining modulations have frequencies which are integral multiples of such lowest frequency modulation.
- the encoding means is adapted to cause each signal to be modulated according to the transform kernels of a discrete cosine, discrete sine or discrete Hartley transform, since these can be the easiest to implement, especially if the symmetric versions of the first two of these transforms are used.
- the discrete cosine and Hartley transforms are described in detail later; it will be understood that the discrete sine transform is simply the sine analogy of the cosine transform.
- a discrete Fourier transform may also be used to advantage.
- the detection device of the present invention may include decoding means for decoding the output of the combining and detecting means into a plurality of signals, such that each signal is characteristic only of its respective sample.
- the decoding means would normally operate according to the inverse transform of that used in the encoding means. In the case of a spectrometer, the inverse transform would recover spectra from each sample when used in conjunction with the further standard inverse transform conventionally required to calculate spectra from the observed signals.
- the device may also include a further encoding means for causing the signal from each sample to be encoded with information characteristic of that sample.
- the encoding would be wavelength encoding, to ensure that each wavelength arriving at the combining and detecting means is encoded in some way, to make it distinguishable from all the other wavelengths which may arrive.
- Such wavelength encoding might be achieved by a diffraction grating, by a simple filter system, or by a Fourier transform device such as a Michelson interferometer or a Nuclear Magnetic Resonance pulse generator.
- An analogous further decoding means may also be provided.
- the device may also include sample receiving means such as a series of sample mounts.
- the invention extends to a method of multiplex detecting a plurality of signals characteristic of a plurality of samples, comprising:
- Figure 2 is a schematic diagram of a second preferred embodiment of the invention.
- Figure 3 is a schematic diagram of a third preferred embodiment of the invention.
- Figure 4 is a schematic diagram of a fourth preferred embodiment of the invention.
- Figure 5 illustrates the shape of a modulating member for use in any of the preferred embodiments
- Figure 6 is a flow diagram illustrating the operation of a set up phase in the invention.
- Figure 7 is a flow diagram illustrating the operation of a multiplexing phase in the invention using a first multiplexing scheme
- Figure 8 is a flow diagram illustrating the operation of a multiplexing phase in the invention using a second multiplexing scheme
- Figure 9 is a flow diagram illustrating the operation of a multiplexing phase in the invention using a third multiplexing scheme
- Figure 10 is a flow diagram illustrating the operation of a multiplexing phase in the invention using a fourth multiplexing scheme
- Figure 11 is a flow diagram illustrating the operation of a processing phase in the invention.
- Figure 13a is a schedule of coefficients cos( ⁇ jk ) to be used in a Discrete
- Figure 13d is a schedule of coefficients cos 2 ( ⁇ /4- ⁇ jk /2) to be used in a
- Figures 14a to 14e show five synthetic spectra illustrating the signals characteristic respectively of five samples
- Figures 15a to 15e illustrate the results of multiplexing the spectra shown in Figures 14a to 14e respectively in five different multiplexing experiments to yield five experimental spectra;
- Figures 16a to 16e illustrate the results of demultiplexing the waveforms shown in Figures 15a to 15e to recover the original spectra shown respectively in
- the first three embodiments of the present invention are similar to the three embodiments disclosed in International Patent Application No. PCT/GB91/01019 referred to earlier, the main differences relating to the manner in which the sample multiplexing encoding is effected and the manner in which the signals detected by the detector are decoded.
- the first embodiment of detection device is a multiplexing Fourier Transform Infra-Red (FT-IR) spectrometer. It comprises generally, in succession, a source ("Source") of radiation, a primary encoder ("Primary Encoder"), a splitter (not explicitly shown in this figure), a sample multiplexing encoder (A or B), a plurality of samples (“Samples”), a combiner (not shown explicitly in this figure) and a detector (“Detector”).
- the paths of the radiation from the source to the detector are denoted by arrows.
- the source is a source of infra-red radiation, such as a flash lamp or laser.
- the source might be a microwave generator.
- the primary encoder is a Michelson interferometer, by which wavelength information (that is, radiation intensities at various wavelengths) is encoded into a series of intensities sorted as a function of the displacement of a moveable mirror in one arm of the interferometer.
- wavelength information that is, radiation intensities at various wavelengths
- the splitter serves to split the signal from the primary encoder and to transmit this on to the samples or the sample multiplexing encoder, dependent upon whether the "A" or "B" configuration is adopted.
- the splitter might be some form of lens or fibre optic device or a partly-silvered mirror set at an angle to the radiation path..
- the sample multiplexing encoder is placed in the path of the radiation from the radiation source, either before the samples (as designated at A), or after the samples (as designated at B). Encoding is accomplished by one of a variety of means described shortly. The signal characteristic of each sample is encoded independently of the other such signals.
- the encoder comprises a respective pair of close- coupled linear polarising filters for each sample, the filters of each pair being rotatable relative to each other to modulate their respective signal.
- the filters of each pair are rotatable relative to each other to modulate their respective signal.
- the attenuation of the signals obtained by each pair is proportional to cos 2 ⁇ , where ⁇ is the angle between the planes of polarization.
- the encoder comprises a respective graded filter device for each sample, each such device being movable to modulate its respective signal.
- the filter device might, for example, comprise a series of neutral density filters of variable thickness and/or variable optical density selectively interposable in the radiation path. These filters are mounted on a sliding bar or a rotating filter wheel, so that the filter appropriate to each sample and experiment number can be selected.
- the filter device might comprise a single filter with varying optical density. The density could vary in discrete steps, or it could vary continuously if the filter is only moved in discrete steps.
- the encoder comprises a respective modulating member for each sample, each modulating member being movable and being shaped such that movement of the member can modulate its respective signal.
- An appropriately shaped member is shown in Figure 5. This consists of a rectangular flat plate 1 having a cut-out 2 in the shape shown in the figure, the plate being slidable across the path of the radiation to vary the occlusion of the radiation beam from the source. The two sectors of the cut-out are each shaped according to a sine (or cosine) function, so that equal increments of displacement of the plate would cause the radiation signal from the relevant sample to be modulated according to a sine (or cosine) function.
- the modulating member could be a suitably shaped rotatable disc.
- the encoder comprises a wheel with holes of the appropriate sizes. The wheel is rotated to select the appropriate hole before a new experiment is conducted.
- samples themselves are physical (material) samples, and might be of any type, provided (in this particular embodiment) they are suitable for infra-red spectroscopy. They might, as just one example, be food samples. Although three samples are shown in Figure 1, any number of samples (greater than one) could be used. Five or six might be a typical number.
- the combiner serves to combine the radiation signals from the individual samples so that a single composite signal is detected by the detector.
- the combiner might be some form of lens or fibre optic device. If the combiner were a fibre optic device, it could include optical fibres or other light guides extending from each individual sample to carry the various signals to a point at which they are all combined, and a single further optical fibre or other light guide to transmit the combined signal on to the detector. It will be understood that for many uses the samples may be physically separated from each other.
- the combiner (and also the splitter) is mounted in a rigid fashion so as to prevent changes in the relative phase of the individual signals due to variation during the course of the experiment.
- the detector is of a standard form used in FT-IR spectroscopy such as can convert the detected signal to digital form for subsequent analysis. It includes not only a sensor for sensing the composite signal, but also, in the preferred embodiment, means for decoding and analysing the signal to produce information relating to each of the individual samples.
- the decoding and analysing means would usually incorporate implementing software (for more details of which see Figures 6 to 11 and the description relating thereto).
- the second embodiment of detection device is similar to the first embodiment. The only difference resides in the position in the radiation path of the primary encoder. It will be understood that, for an FT-IR spectrometer, it is largely immaterial whether the primary encoder is placed before or after the samples.
- the third embodiment of detection device is similar to the second embodiment, the difference residing in the number of sources provided. Whereas in the second embodiment only one source is provided, in the third embodiment the same number of sources are provided as samples. This might be advantageous if, for example, the sample multiplexing encoder A were to operate directly on each source, say by varying the input voltage to the flash lamp so as to modulate its output. Further advantages of using multiple sources are firstly that they can ensure that a larger signal arrives at the detector and secondly that failure of a single source need not result in total signal loss but only in loss of signal from one sample.
- the fourth embodiment of detection device is similar to the second embodiment, the main difference residing again in the number of sources which are provided.
- the device is configured as a Fourier Transform Raman Spectrometer such as detects the effects of Raman scattering.
- the sample itself could be the source of radiation (although this is not necessarily the case), so that no independent source need be provided at all.
- the encoding and decoding performed in the present invention may be defined in terms of an "encoding" matrix C having matrix coefficients C jk such that the experimental observations a] which measure the combined signal presented to the detector (data-handling system) are related to the unknown individual signals s k from each sample, k, as follows:
- the unknowns s k are recovered by solving Equation (1) using the inverse of matrix C.
- Equation (1) is in fact quite general, and defines not only the sample multiplexing encoding but also where appropriate the encoding of the signals from the samples with wavelength information (that is, using the primary encoder). If this double level of encoding takes place, each of the elements of the vectors in Equation (1) is itself a vector and each of the element of the matrix C is itself a matrix. Equation (1) would then be solved by double inversion of the matrix.
- the relevant elements in the encoding matrix are determined by the physical technique used and the construction of the spectrometer.
- a simple case of wavelength multiplexing is that of a dispersive instrument, such as a conventional grating Infra-Red (IR) spectrometer or continuous wave nuclear magnetic resonance (NMR) spectrometer.
- the coefficients C jk for the wavelength encoding comprise a unit matrix.
- wavelength information that is, radiation intensities s k at various wavelengths
- FT-IR Fourier transform infrared
- FT- ⁇ MR pulsed Fourier transform nuclear magnetic resonance
- wavelength information that is, radiation intensities s k at various wavelengths
- Michelson interferometer into a series of intensities d j sorted as a function of the position of a moveable mirror in one arm of the interferometer.
- FT- ⁇ MR the encoding of wavelength information is achieved by the application of excitation pulses and by the consequent precession and dephasing of the nuclear magnetic moments within the sample.
- Intensity values s k as a function of frequency are encoded and recorded as a series of induced voltages d j (the so-called "free induction decays”) measured at successive time intervals after the excitation of the sample.
- Equation (1) can be solved by carrying out an inverse Fourier transform of the data d j , with or without additional data processing such as apodisation.
- the coefficients C jk are the transform kernels of any appropriate sine, cosine or other transform, capable of modulating the respective signal characteristic of each sample according to a respective different sine, cosine or mixed sine and cosine function.
- a large family of suitable such transforms (including various discrete cosine and discrete sine transforms) is disclosed in Table 1 of a paper by Jain, A. K. entitled “Fundamentals of digital image processing", Prentice Hall, 1989, p.150.
- Other such transforms include the discrete Hartley transform and the discrete Fourier transform.
- references to the discrete Hartley transform are firstly a paper by Bracewell, R.N., J.Opt. Soc. Am., 73, 1832-1835 (1983), and secondly a paper by Williams, C.P. et al., Anal. Chem., 61, 428-431 (1989).
- the discrete Fourier transform may in many circumstances be needlessly complicated, since generally the quantities to be transformed are real rather than complex quantities.
- the sine or cosine (or Hartley) transform is a real transform
- the Fourier transform is a complex transform.
- the C jk are cosine terms, each of which corresponds to a phase angle ⁇ jk .
- the values ⁇ jk must be chosen such that each source signal s k is modulated by a "frequency" which can be distinguished from the frequencies of the other sources.
- the data d j must be sampled with steps in ⁇ jk small enough to satisfy the Nyquist sampling condition for all the modulation frequencies.
- the detection device of the present invention preferably operates by encoding the signal from each sample with a separate characteristic frequency.
- the relevant coefficients of the matrix C are fixed by the physical processes involved.
- the coefficients are chosen directly by the user. It has been determined pursuant to the present invention that there are four important limitations on the possible choices:
- Equation (1) It must be possible to solve Equation (1).
- the basic requirement is that the determinant of C should be non-zero. In order to obtain accurate numerical solutions, it is also desirable that C should not be ill-conditioned.
- the experimental errors or signal-to-noise ratios of the decoded s k values should be at least as good as, or better than, the errors obtained when measuring the s k values directly by some sequential technique. Further, the change in the signal-to-noise ratio should preferably be the same for all the s k .
- the latter requirement imposes a tight constraint on the matrix C; it must be unitary.
- the encoding matrix is preferably not only unitary but also real, that is, its inverse is equal to its transpose, when the quantities being transformed are real numbers. More generally, however, if the transformed quantities are complex (that is, there are two quantities measured by a quadrature detection scheme) the transformation matrix must be complex unitary. The unitary property also guarantees that the transformation is invertible.
- the matrix C can be constructed and implemented for any order N. Changing N should not require radical redesign of the spectrometer.
- the encoding matrix must be real and unitary if the signal-to-noise properties are not to be adversely affected by the encoding/decoding scheme.
- f(x) is an array of experimental data subject to gaussian measurement errors, in other words f(x) is a realisation of an array of gaussian random variables f(x) with expectation values (f(x)) and standard deviations ⁇ f ( x).
- f(x) is an array of experimental data subject to gaussian measurement errors
- f(x) is a realisation of an array of gaussian random variables f(x) with expectation values (f(x)) and standard deviations ⁇ f ( x).
- the transformed array F(u) will also be a realisation of an array of gaussian random variables F(u) with expectation values (F(u)) given by and standard deviations a F (u) given by the Pythagorean rule for the addition of noise variances,
- DCT Discrete Cosine Transform
- the DCT has an encoding matrix such that, in the present invention, the signals characteristic of each sample can be modulated according to a respective different cosine function. It is to be noted that the first array element of the transformation matrix has a different form from the other array elements.
- g(u,x) and h(x,u) defined in (16) therefore satisfy the necessary and sufficient conditions (5) and (6) for forward and inverse transformation kernels.
- g(u,x) is the kernel of the Discrete Cosine Transform (DCT). 6.
- DCT Discrete Cosine Transform
- SDCT SYMMETRIC DISCRETE COSINE TRANSFORM
- the SDCT has an encoding matrix such that, in the present invention, the signals characteristic of each sample can be modulated according to a respective different cosine function.
- the first term in the summation is zero except when u + u' +1 is zero, which never happens.
- DHT Discrete Hartley Transform
- DFT Discrete Fourier Transform
- the Discrete Hartley Transform may be defined, using the foregoing notation, as a transform with the symmetric kernel
- the kernel (23) satisfies the condition (5) for the forward and inverse transformation kernels, and may similarly be shown to satisfy (6).
- the kernel (23) may be rewritten in a simpler form by employing the identity
- the Discrete Hartley Transform is a mixed sine and cosine transform, like the Discrete Fourier Transform; however, unlike the DFT but like the Discrete Cosine and Symmetric Discrete Cosine Transforms, the DHT is a purely real transform. It is therefore easier than the DFT to implement. In practice, the DCT, SDCT and DHT have been found to be equally easy to implement, and have produced results of approximately equal quality. 8. THE MULTIPLEX ADVANTAGE
- the computed s k will have the same standard deviations as the d j , that is ⁇ (2/N) ⁇ . But if we had measured the s k directly using the same detector D ⁇ , the measured values would have had standard deviations ⁇ . Therefore the multiplexing scheme gives a reduction of ⁇ (2/N) in the noise level, or equivalently an enhancement of ⁇ (N/2) in the signal-to-noise ratio.
- the origin of a multiplexing advantage in this instance lies in the choice of what is actually measured, the quantities d) defined by (33).
- Scheme / modulates the sample signals by a cosine function. This scheme is not applicable to cases where the signals are intrinsically non-negative, such as radiation intensities.
- the other three multiplexing schemes are designed to circumvent this problem, with some loss of efficiency in the signal-to-noise enhancement which is achieved by multiplexing.
- Schemes III and IV use cosine-squared functions to modulate the signal intensities. All of these schemes use the Symmetric Discrete Cosine Transform; other like transforms may also be used. 9.1 Multiplexing Scheme I
- the computed s k have standard errors ⁇ (2/N)a, that is, the signal-to-noise enhancement using the multiplexing scheme is ⁇ (N/2).
- either (36) or (37) provides the relevant values of the phase angle ⁇ jk for each sample k and each experiment j.
- the frequency of modulation of the signal from the third sample would be five times as great as that from the first sample.
- the signal-to-noise enhancement can be derived in a different way as follows.
- the modified scheme is required to encode each signal such that the magnitude of the modulated signal does not fall below zero. Broadly speaking, this can be achieved in one of two ways.
- the negative portion of the modulation may be inverted, the inverted portions of the modulated signal either being caused to be presented to the detector at a different time from the positive, non-inverted portions, or being caused to be presented to a separate detector.
- Multiplexing Scheme II below represents such an approach.
- this may be achieved by centring the sine (or cosine) function on a baseline signal having a magnitude greater than zero, that is, by imposing a sinusoidally oscillating modulation of the signal upon some constant background level.
- the zero level of the modulation thus corresponds to the background level, and the negative modulation can be represented by a positive signal which is nevertheless less than the background level.
- the problem of recovering the signals from the individual samples is then simply one of baseline correction followed by inverse transformation. Two specific schemes to achieve this are presented as Schemes III and IV below. These schemes rely on the fact that a modulation of the form cos ⁇ superimposed on a constant background can be regarded, by a standard trigonometric identity, as equivalent to a modulation of the form cos 2 ( ⁇ /2) with the background removed.
- a first set of N experiments is performed in which the N measured data d + j are weighted sums of the signals s k as in (35), but, for values of j, k for which cos ⁇ jk ⁇ 0, the modulation function is set to zero, that is, the contribution of s k to d + j is zero when cos ⁇ jk ⁇ 0.
- the N measured data are again weighted sums of the s k , but, for values of j, k for which cos ⁇ jk > 0, the modulation function is set to zero, that is, the contribution of s k to d ⁇ ⁇ is zero when cos ⁇ jk > 0.
- the modulation function is taken to be - cos ⁇ jk .
- the signals are modulated by a positive factor in the range 0 to 1. This is physically realizable for signals such as light intensities which are intrinsically non- negative.
- the modulated signals have the appearance of a half-wave rectified waveform.
- N experiments are performed with the N quantities d + j being measured by the first detector, and another N quantities d j being measured in parallel by the second (identical) detector.
- the difference of the two datasets is calculated to derive the dy.
- N experiments are performed using one detector, or N experiments using two identical detectors D ⁇ .
- the first N measurements are of data d c j , which are sums of the s k weighted by cosine-squared functions.
- the phase angles are ⁇ jk /2, where the ⁇ jk are given by (36):
- the signals are modulated by a positive factor in the range 0 to 1, which is physically realizable.
- the difference of the two datasets is next calculated, employing a standard trigonometric identity:-
- the s k can be recovered by the transform (45).
- This multiplexing scheme is particularly preferred, since it has a requirement for fewer experiments to be carried out, or for fewer spectrometers.
- the first N measurements are of data d c j which are sums of the s k weighted by cosine- squared functions, as in (46) above.
- the (N+ 1)th. measurement is a quantity d c N+1 which is just the sum of the unweighted signals:-
- references herein to the modulation of the signals from the various samples according to different sine, cosine or mixed sine and cosine functions are to be understood to include references both to real time and to virtual time operation. Also, where reference is made to each signal being modulated at a different frequency, the frequency is to be understood as either a real frequency or a "pseudo-frequency".
- the spectral elements comprising the signals from every sample, are monitored by the spectrometer for a series of time intervals ⁇ t during which time-dependent modulation of the signal takes place.
- a number of optical signals could be attenuated by rotating sectors or moving graduated filters in the light path, the modulation of each signal being according to a different, say, cosine function.
- the combined signal from all the sources is an interferogram, which is collected (digitized) in an appropriate manner. Inverse Fourier or cosine transformation of the time domain signals then gives a set of spectrometer responses separated by the frequency differences of the intensity modulations. For dispersive instruments, this corresponds to a set of spectra, while for multiplexing instructions a second set of transforms is required before spectra are obtained.
- the size of the transforms depends on the number of cycles of modulation which are used, and this may be reduced to a minimum level in which the number of samples in the time domain, for each spectral element, is no more than the number of sources used.
- the signals from each sample are modulated according to sine or cosine functions each having a different pseudo-frequency, the modulation taking place between the various sampling instants, with the sampling instants representing different experiments.
- Virtual time modulation may be important in circumstances where real time modulation might involve difficulties with synchronising the signals from the various samples.
- time separation between may be arbitrary, hence giving rise to the concept of a "pseudo" frequency. Whilst the actual time separation between the experiments can be arbitrary, it will be appreciated from the analysis presented below that the modulation employed for each sample will progress from experiment to experiment with uniform phase shift increments, and, further, that the phase shift increments will differ from sample to sample.
- the detection device is set up according to the steps outlined in this figure.
- the desired sample multiplexing encoding transform is selected in Step 12. This might be the Symmetric Discrete Cosine Transform, as described in detail above.
- Step 16 the spectrometer configuration is selected.
- the number of sources and the order of the primary and sample multiplexing encoders and samples is selected, in accordance, for example, with the principles discussed in relation to the preferred embodiments of the invention described above.
- the desired multiplexing scheme for instance one of Schemes I to IV described above. It is noted in passing that Scheme I would only be suitable in situations where the signal to be modulated has negative as well as positive values, such as would be the case with electrical signals.
- Step 20 the appropriate multiplexing scheme is executed, as described next.
- Step 108 the relevant signal is modulated by cos ⁇ jk , where ⁇ jk is given by Equation (37).
- Step 110 the signals from each sample are combined (added together) and the result is recorded as d j (see Equation (35)).
- Step 112 the experiment number y is incremented (that is, a new experiment is embarked upon), and the procedure reverts to question Step 106 until the requisite number of experiments has been completed.
- Step 208 the relevant signal is modulated by cos ⁇ jk , where ⁇ jk is given by Equation (37), if cos ⁇ jk is greater than 0, and otherwise by zero (see Equation (40)).
- Step 210) the signals from each sample are combined (added together) and the result is recorded as d + j (see Equation (39)).
- Step 212 the experiment number j is incremented (that is, a new experiment is embarked upon), and the procedure reverts to Question Step 206 until the requisite first N experiments have been completed.
- Step 206 the answer to Question Step 206 is "yes", and processing proceeds to Step 214, where y is again set to 1.
- y is again set to 1.
- Step 216 it is enquired whether the second set of N experiments has been completed, this time for the "negative" part of the modulation. If “no”, then processing proceeds to Steps 218 to 222. If “yes”, then processing proceeds to Steps 224 to 232.
- Step 218 in which, for each sample k, the relevant signal is modulated by -cos ⁇ jk , where ⁇ jk is given by Equation (37), if cos ⁇ jk is less than 0, and otherwise by zero (see Equation (42)). Then (Step 220) the signals from each sample are combined (added together) and the result is recorded as d j (see Equation (41)). Finally (Step 222), the experiment number j is incremented (that is, a new experiment is embarked upon), and the procedure reverts to Question Step 216 until the requisite second N experiments have been completed.
- Step 224 the implementing software sets the value of the experiment number/ to 1.
- Question Step 226 it is enquired whether the value of/ is greater than N. If the answer is "yes”, then the experiment is finished and the processing phase begins (Step 232, for details of which see later).
- Step 308 for each sample k, the relevant signal is modulated by cos 2 ( ⁇ jk /2), where ⁇ jk is given by Equation (37). Then (Step 310) the signals from each sample are combined (added together) and the result is recorded as d c j (see Equation (46)). Secondly, and likewise, in Step 318, for each sample k, the relevant signal is modulated by sin 2 ( ⁇ jk /2), where ⁇ jk is again given by Equation (37).
- Step 320 the signals from each sample are combined (added together) and the result is recorded as d s j (see Equation (47)).
- Step 328 the total signal d j for each experiment is computed as the sum of d c j and d s j (see Equation (48)), analogously to the procedure adopted in Step 228.
- the experiment number, j is next set to 1 (Step 404).
- the implementing software then enquires whether the value of/ is equal to N+ 1. If the answer is "no”, then Steps 408 to 412 are proceeded with. If "yes” , then Steps 414 to 426 are proceeded with.
- Step 408 the relevant signal is modulated by cos 2 ( ⁇ jk /2), where ⁇ jk is given by Equation (37).
- Step 410 the signals from each sample are combined (added together) and the result is recorded as d c j (see Equation (46)).
- Step 412 the experiment number j is incremented (that is, a new experiment is embarked upon), and the procedure reverts to Question Step 406 until N experiments have been completed.
- Step 414 a further baseline correction experiment is conducted in Steps 414 and 416. Specifically, in Step 414, a final experiment is conducted in which for each sample k, ⁇ jk is set to zero, so that cos 2 ( ⁇ jk / 2) is equal to 1; in other words, none of the signals are modulated. Then, for this one experiment, all of the (un-modulated) signals are combined (added together) and the result is recorded as d c N+1 (see Equation (49)).
- Step 418 the processing proceeds to determine the value of d j for each experiment.
- the implementing software sets the value of the experiment number, j, to 1.
- question Step 420 is reached, in which an enquiry is made as to whether/ is greater than N. If the answer is "yes”, then the experiment is finished and the processing phase begins (Step 426, for details of which see later). If the answer is "no”, then the value of d j is computed as 2d c j - d c N+1 (see Equation (50) - Step 422). Step 424 ensures that this is carried out for each of the N experiments.
- the processing phase is carried out in the analysis means of the detection device as follows.
- the sample number k is first set to 1 (Step 502).
- enquiry is made as to whether the sample number in the processing phase is equal to N+1.
- Step 506 ensures that this process is carried out for each of the N samples.
- Step 510 at which any additional processing which might be required is carried out. Such processing might, for example, be apodization or Fourier transformation of the signals s k . Then (Step 512), the processed signals are displayed, possibly as spectra, and/or further analysed. Processing is concluded at the Stop Step 514.
- Figures 12 and 13a to 13d the salient features of the operation of the invention using the Discrete Fourier Transform are now described, where these differ markedly from the features described in relation to Figures 6 to 11.
- Figures 13a to 13d are provided the corresponding values of cos( ⁇ jk ), sin( ⁇ jk ), cos 2 ( ⁇ jk /2) and cos 2 ( ⁇ /4 - ⁇ jk /2), respectively.
- Figures 13a and 13b cover the case where the signals may be negative as well as positive
- Figures 13c and 13d cover the case where the signals are intrinsically non-negative.
- the coefficients in Figures 13a and 13b are used to modulate the signals (assigned to the first five samples) and (assigned to the second five samples) in a series of ten experiments to measure the quantities and according to Equation
- Modulation (attenuation) of the signals by factors of cos 2 ( ⁇ jk /2) and cos 2 ( ⁇ /4 - ⁇ jk /2) can, as usual, be achieved by rotating a pair of cross-polarising filters relative to each other by the appropriate angles. In all cases, the angles should be normalised to the range 0 - 90° since this is the effective range of cross-polarising filters.
- test can be performed with a Discrete Fourier Transform as just described, it has no particular advantage over the Discrete Cosine, Symmetric Discrete Cosine or Discrete Hartley Transforms, and it has the disadvantage of added complexity. The latter three transforms are therefore preferred.
Abstract
Description
Claims
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EP95932824A EP0783671A1 (en) | 1994-09-28 | 1995-09-28 | Detection device and method |
AU35718/95A AU3571895A (en) | 1994-09-28 | 1995-09-28 | Detection device and method |
CA002199146A CA2199146A1 (en) | 1994-09-28 | 1995-09-28 | Detection device and method |
JP8511513A JPH10506711A (en) | 1994-09-28 | 1995-09-28 | Detecting device and method |
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JP (1) | JPH10506711A (en) |
AU (1) | AU3571895A (en) |
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Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
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WO1998023057A1 (en) * | 1996-11-19 | 1998-05-28 | Rdl Commercial Technologies Corporation | High capacity spread spectrum optical communications system |
US6236483B1 (en) | 1998-07-30 | 2001-05-22 | Codestream Technologies Corporation | Optical CDMA system using sub-band coding |
EP1150250A1 (en) * | 2000-04-27 | 2001-10-31 | CSEM Centre Suisse d'Electronique et de Microtechnique SA | Method of encoding information which can be represented by vectors |
Citations (2)
Publication number | Priority date | Publication date | Assignee | Title |
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WO1992000509A1 (en) * | 1990-06-22 | 1992-01-09 | British Technology Group Plc | Spectrometers |
EP0522796A1 (en) * | 1991-07-09 | 1993-01-13 | General Electric Company | Method and apparatus for obtaining pure-absorption two-dimensional lineshape data for multidimensional NMR spectroscopy using switched acquisition time gradients |
-
1994
- 1994-09-28 GB GB9419557A patent/GB9419557D0/en active Pending
-
1995
- 1995-09-28 JP JP8511513A patent/JPH10506711A/en active Pending
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- 1995-09-28 AU AU35718/95A patent/AU3571895A/en not_active Abandoned
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Publication number | Priority date | Publication date | Assignee | Title |
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WO1992000509A1 (en) * | 1990-06-22 | 1992-01-09 | British Technology Group Plc | Spectrometers |
EP0522796A1 (en) * | 1991-07-09 | 1993-01-13 | General Electric Company | Method and apparatus for obtaining pure-absorption two-dimensional lineshape data for multidimensional NMR spectroscopy using switched acquisition time gradients |
Non-Patent Citations (4)
Title |
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BRACEWELL: "DISCRETE HARTLEY TRANSFORM", JOURNAL OF THE OPTICAL SOCIETY OF AMERICA, vol. 73, no. 12, 1 December 1983 (1983-12-01), pages 1832 - 1835 * |
KNUDSEN ET AL.: "MIXED DOMAIN FILTERING,ETC.", IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS FOR VIDEO TECHNOLOGY, vol. 1, no. 3, 1 September 1991 (1991-09-01), pages 260 - 268 * |
SAGHRI ET AL.: "NEAR LOSSLESS BANDWIDTH COMPRESSION,ETC.", OPTICAL ENGINEERING, vol. 30, no. 7, 1 July 1991 (1991-07-01), pages 934 - 939 * |
VASSILIADIS ET AL.: "SINGLE CHANNEL DEMODULATOR,ETC.", IEEE TRANSACTIONS ON MEDICAL IMAGING, vol. 10, no. 4, 1 December 1991 (1991-12-01), pages 638 - 641 * |
Cited By (4)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
WO1998023057A1 (en) * | 1996-11-19 | 1998-05-28 | Rdl Commercial Technologies Corporation | High capacity spread spectrum optical communications system |
US5867290A (en) * | 1996-11-19 | 1999-02-02 | Rdl Commercial Technologies Corporation | High capacity spread spectrum optical communications system |
US6236483B1 (en) | 1998-07-30 | 2001-05-22 | Codestream Technologies Corporation | Optical CDMA system using sub-band coding |
EP1150250A1 (en) * | 2000-04-27 | 2001-10-31 | CSEM Centre Suisse d'Electronique et de Microtechnique SA | Method of encoding information which can be represented by vectors |
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EP0783671A1 (en) | 1997-07-16 |
JPH10506711A (en) | 1998-06-30 |
AU3571895A (en) | 1996-04-19 |
GB9419557D0 (en) | 1994-11-16 |
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