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Claims  |
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What is claimed:
1. A method for spectral reconstruction comprising the steps of:
(a) obtaining the concentrations of a first component in a series of
mixtures of components, the concentrations of the first component
constituting a set of reference values;
(b) measuring spectral values for each mixture in the series of mixtures at
a series of wavelengths;
(c) cross-correlating, at a first wavelength, the spectral values for each
mixture in the series of mixtures with the corresponding reference values
for the one component at the first wavelength to obtain the spectral
contribution for the one component at the first wavelength;
(d) outputting the spectral contribution for the one component at the first
wavelength;
(e) repeating steps c and d at wavelengths other than the first wavelength,
until the spectrum of the one component is obtained.
2. A method as claimed in claim 1 wherein the cross-correlating step
comprises calculating:
##EQU5##
wherein n is the number of mixtures in the series of mixtures, x is the
mixture index, a(x) is the spectral value of the mixture x at the first
wavelength, b (x) is the reference value of the first component in the
mixture x, a is the average spectral value of all mixtures in the series
of mixtures at a first wavelength, b is the average fractional
concentration of the first component in the series of mixtures, and
C'.sub.ab is the value of the cross-correlation function between a(x) and
b(x).
3. A method as claimed in claim 2 wherein the spectrum is a near-infrared
reflectance spectrum.
4. A method as claimed in claim 1 wherein the cross-correlating step
comprises calculating:
##EQU6##
wherein n is the number of mixtures in the series of mixtures, x is the
mixture index, a(x) is the spectral value of the mixture x at the first
wavelength, b(x) is the reference value of the first component in the
mixture x, a is the average spectral value of all mixtures in the series
of mixtures at a first wavelength, b is the average fractional
concentration of the first component in the series of mixtures, and
C".sub.ab is the value of the cross-correlation function between a(x) and
b(x).
5. A method as claimed in claim 4 wherein the spectrum is a near-infrared
relectance spectrum.
6. A method as claimed in claim 1 wherein the spectrum is a near-infrared
reflectance spectrum.
7. A device for spectral reconstruction:
(a) means for obtaining the concentrations of a first component in a series
of mixtures of components, the concentrations of the first component
constituting a set of reference values;
(b) spectrometer means for obtaining spectral values for each mixture in
the series of mixtures;
(c) data storage means for storing the reference values and spectral
values;
(d) data input means for supplying the reference values and spectral values
to the data storage means;
(e) spectral reconstructor means for cross-correlating the corresponding
reference values and spectral values stored in the data storage means,
thereby providing a spectral contribution for the one component;
(f) data output means for outputting the spectral contribution for the one
component.
8. A device as claimed in claim 7 wherein the means for spectral
reconstruction cross-correlates the reference values and spectral values
according to the equation:
##EQU7##
wherein n is the number of mixtures in the series of mixtures, x is the
mixture index, a(x) is the spectral value of the mixture x at the first
wavelength, b(x) is the reference value of the first component in the
mixture x, a is the average spectral value of all mixtures in the series
of mixtures at a first wavelength, b is the average fractional
concentration of the first component in the series of mixtures, and
C'.sub.ab is the value of the cross-correlation function between a(x) and
b(x).
9. A device as claimed in claim 8 wherein the spectrometer means is a
near-infrared reflectance spectrometer.
10. A device as claimed in claim 7 wherein the means for spectral
reconstruction cross-correlates the reference values and spectral values
according to the equation:
##EQU8##
wherein n is the number of mixtures in the series of mixtures, x is the
mixture index, a(x) is the spectral value of the mixture x at the first
wavelength, b(x) is the reference value of the first component in the
mixture x, a is the average spectral value of all mixtures in the series
of mixtures at a first wavelength, b is the average fractional
concentration of the first component in the series of mixtures, and
C".sub.ab is the value of the cross-correlation function between a(x) and
b(x).
11. A device as claimed in claim 10 wherein the spectrometer means is a
near-infrared reflectance spectrometer.
12. A device as claimed in claim 7 wherein the spectrometer means is a
near-infrared reflectance spectrometer.
13. A method for reconstructing the spectrum of a specific component from a
series of multicomponent mixtures, each mixture capable of exhibiting a
composite spectrum, the method comprising:
(a) obtaining the concentration of the specific component in each mixture
in the series;
(b) measuring a composite spectral value for each mixture in the series at
a plurality of wavelengths; and
(c) for each of the plurality of wavelengths, cross-correlating an array
comprised of the measured composite spectral value for each mixture in the
series of mixtures with a correspondingly ordered array of the
concentration of the specific component in each mixture in the series of
mixtures to generate a reconstructed spectral value associated with the
specific component.
14. The method of claim 13 wherein the step of measuring the composite
spectral value for each mixture in the series comprises:
(a) selecting a plurality of wavelengths at which it is desired to have a
reconstructed spectral value for the specific component; and
(b) generating an array of composite spectral values at each of thc
selected wavelengths, each array of composite spectral values comprising
the measured spectral value of each mixture at one of the selected
wavelengths.
15. The method of claim 14 wherein the step of cross-correlating the array
of composite spectral values for each mixture with the correspondingly
ordered array of concentrations of the first component comprises
calculating:
##EQU9##
wherein, n is the number of mixtures in the series, x is the series index,
d is the displacement from the current x index, a(x) is the measured
spectral value of the xth mixture at a specific one of the selected
wavelengths, b(x) is the concentration of the first component in the xth
mixture, and C.sub.ab (d) is the value of the cross-correlation function
a(x) and b(x) at the displacement d.
16. The method of claim 14 wherein the step of cross-correlating the array
of composite spectral values for each mixture with the correspondingly
ordered array of concentrations of the first component further comprises
compensating the value of the cross-correlative function for experimental
noise and interference.
17. The method of claim 16 wherin the step of compensating the value of the
cross-correlation function comprises cross-correlating the array of
composite spectral values for each mixture with the correspondingly
ordered array of concentrations of the first component according to the
calculation:
##EQU10##
wherein, n is the number of mixtures in the series, series index, a(x) is
the measured spectral value of the xth mixture at a specific one of the
selected wavelengths, a is the average spectral value of all samples at
the same specific one of the selected wavelengths, b(x) is the
concentration of the first component in the xth mixture, b is the average
fractional concentration of a given component, the denominator in the
equation is the variance of b(x), and C'.sub.ab is the compensated and
normalized value of the cross-correlation function a(x) and b(x).
18. The method of claim 17 wherein the step of cross-correlating the array
of composite spectral values for each mixture with the correspondingly
ordered array of concentrations of the first component further comprises
compensating for mixtures in which the fractional concentration of another
component in the mixture influences the concentration of the specific
component for which the spectral reconstruction is desired.
19. The method of claim 1 or 13 further comprising repeating the
reconstruction of spectra for additional components of the mixtures. |
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Claims |
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Description |
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Background of the Invention
1. Field of the Invention
The present invention relates to a novel method and device for
reconstruction of spectra from spectral information obtained from complex
mixtures.
2. Description of the Prior Art
Spectroscopic methods may be used to measure spectral values of a series of
samples of known composition at several discrete wavelengths in order to
predict the concentration of one or more chemical species in an "unknown"
sample. Present methods require the use of a set of samples of known
composition whose spectra are employed as a "training set" of data
comprising a set of wavelengths and weighting coefficients for a
multilinear regression algorithm. The "training set" data then may be
applied to a spectrum of a sample of unknown composition to determine the
percent composition of the component or components in the sample. This
spectroscopic technique can be applied to many methods of spectroscopy and
has been applied successfully to samples in which almost complete spectral
overlap obscures individual bands; where no band is interferencefree; and
where background fluctuations far exceed spectral changes caused by the
compositional changes of interest.
Methods are also known for extracting a spectrum from complex mixtures.
Perhaps the most widely used of these techniques is termed spectral
stripping or curve-fitting. Spectral stripping requires that the spectrum
of each of the pure components of a mixture be known and that the spectrum
of the mixture be a linear combination of the pure components. Thus, for
spectral stripping the components must not exhibit complicating
interactions which affect the structure of the resultant spectrum. Such
complicating interactions include changes in symmetry, chemisorption,
physisorption and especially hydrogen bonding -- interactions which
prevent the spectra of most mixtures from being linear combinations of
their components. In near-infrared reflectance analysis, samples such as
wheat are analyzed for their moisture and protein content. Such spectra
exhibit complex intermolecular interactions between the components of the
sample.
The ratio method is a second method which can be used to generate
reconstructed spectra of components of a sample. This technique involves
generating a ratio from spectra of several samples containing the same
components in varying proportion. The resultant ratio is used to locate
regions of the spectrum where one component dominates. Indeed, the use of
the ratio method requires that each component must dominate the spectrum
in at least one "window" region and is thus limited to relatively simple
mixtures. However, in some spectroscopic regions (including the
near-infrared region of the spectrum) most transitions are very broad and
overlapping, which makes resolving components in the spectra of even
simple mixtures nearly impossible.
A third method for reconstructing spectra is factor analysis. The
eigenvectors of factor analysis provide spectral information on the
discrete contributors present, and their eigenvalues are related to
component concentrations. However, these eigenvectors represent only
independently varying entities, and are not necessarily associated with
specified (or indeed any) components. Even where such an association
exists, its detection requires very good spectral differentiation,
considerable expertise, or auxiliary chemical data. In the latter case,
factor analysis can actually be complemented by an abridged form of
spectral reconstruction. When the component sought contains independently
varying constituents, that component will itself never appear as a factor,
and its individual constituents might easily lie below the noise and be
indetectable.
It is thus an object of the present invention to provide a spectral
reconstruction technique that does not require the spectrum of the pure
component and that provides reproducible spectra even when components
exhibit complex intermolecular interactions.
It is yet a further object of the present invention to reconstruct spectra
from complex mixtures in which a significant degree of overlap occurs in
the region of the spectrum being studied.
It is yet a further object of the present invention to provide methods and
devices to produce spectra corresponding precisely to the component of
interest, even when the latter is ill-defined chemically.
It is yet another object of the present invention to provide a rapid,
convenient method for reconstructing near-infrared component spectra.
Based on a mathematical cross-correlation procedure, the technique
requires only a set of near-infrared spectra of samples in which the
concentration of the component of interest is known. Thus, the method of
the present invention avoids the difficulties of, and errors inherent in,
the use of spectra of pure components.
SUMMARY OF THE INVENTION
In one aspect, the present invention comprises a method for spectral
reconstruction which comprises first obtaining component concentrations in
a series of mixtures, which component concentrations constitute a set of
reference values. The spectral value of each member of that series of
mixtures is measured at a first wavelength, which spectral value possesses
unknown contribution from individual components in the mixture. The
spectral values for the series of mixtures are then cross-correlated with
the component concentrations in the series of mixtures at the first
wavelength, thereby obtaining the spectral contribution for the component
at that first wavelength. This operation may be repeated for a series of
wavelengths. The cross-correlation operation is then applied to the series
of spectral values for that series of wavelengths until the spectrum of
the component in the mixture is reconstructed.
In its device aspect this invention comprises means for obtaining the
concentrations of at least one component in a series of mixtures of
components, the component concentrations constituting a set of reference
values; spectrometer means for obtaining spectral values for each mixture
in the series of mixtures, the spectral values possessing unknown
contribution from components in the mixtures; data storage means for
storing reference values and spectral values; data input means for
supplying reference values to the data storage means; spectral
reconstructor means for cross-correlating the reference values and
spectral values thereby providing a spectral contribution for the one
component; and data output means for outputting the spectral contribution
for the one component.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 is the spectrum of pure cyclohexane and a spectrum reconstructed
from several mixtures of cyclohexane, benzene, iso-octane and n-heptane.
The scales of these spectra have not been normalized.
FIG. 2 is a spectrum of a typical hydrocarbon mixture composed of 12%
benzene, 43% iso-octane, 26% cyclohexane and 20% n-heptane.
FIG. 3 is a spectrum of pure benzene and a spectrum of benzene
reconstructed from hydrocarbon mixtures.
FIG. 4 is a spectrum of pure n-heptane and a spectrum reconstructed fro
hydrocarbon mixtures.
FIG. 5 is a spectrum of pure iso-octane and a spectrum reconstructed from
hydrocarbon mixtures.
FIG. 6 is a spectrum of pure water and a spectrum of wheat moisture
reconstructed from wheat samples.
FIG. 7 is a reconstructed spectrum of protein wherein the protein content
was determined in wheat samples by the Kjeldahl method and by the "as is"
method.
FIG. 8 is an embodiment of a device which utilizes the spectral
reconstruction methods of the present invention.
DETAILED DESCRIPTION OF THE INVENTION
The present invention provides a method and device for obtaining spectral
information from a sample whose component concentrations are known or
determined (the "reference values") and for generating a reconstructed
spectrum of the component or components of interest. Utilizing the methods
of the present invention, the common procedure of determining the
composition of unknowns through use of reference spectra of the components
is reversed. Instead "reference spectra" are generated based on
information concerning the quantitative composition of the sample.
From the correlation between known concentration values and the spectral
information, usually absorbance or reflectance information, of each sample
at individual wavelengths, the spectrum of the individual components can
be displayed. Such reconstructed spectra reflect the presence of the
components in a particular sample and can be used to deduce the nature of
matrix interactions.
Near-infrared reflectance analysis (NIRA) is an analytical spectroscopic
technique that utilizes the near-infrared diffuse reflectance of a series
of samples of known composition at several wavelengths to determine the
concentration of components in an "unknown" sample. To obtain the most
complete information from NIRA it would be desirable to have available the
near-infrared spectra of the individual components of the sample.
Unfortunately, pure components for spectral analysis are often
unavailable. In addition, the spectra obtained for pure components often
differ significantly from the spectra of mixtures containing that
component, expecially when the spectrum of the component is influenced by
the other components and its surroundings in the sample, e.g., samples
with strong matrix effects.
Any method may be used for measuring component concentration of the series
of samples to generate the reference values. For example, in the examples
described below for hydrocarbon mixtures, the series of reference values
were generated by knowing the weight of introduced component hydrocarbons.
Other methods which could have been used include the use of gas
chromatography or other methods, including methods involving wet
chemistry. Thus, there is no limitation in the present invention on the
methods for obtaining the reference values comprising the component
compositions of the series of samples.
While the examples of the present invention specifically describe the use
of near-infrared reflectance spectroscopy for measuring the spectral
information for the series of samples, it should be understood that
substantially any spectral method may be used in which the signal produced
thereby is proportional to the concentration of the component in the
sample. Examples include mid-infrared spectroscopy, far-infrared
spectroscopy, ultraviolet spectroscopy, visible spectroscopy, mass
spectrometry, nuclear magnetic resonance spectroscopy, microwave
spectroscopy, electron spin resonance spectroscopy, chromatography
techniques, flourescence spectroscopy, and the like.
In addition, no particular near-infrared reflectance spectrometer is
contemplated by the present invention. Thus, grating, Fourier transform
and filter instruments are contemplated for use in the present invention.
1. Methods for Spectral Reconstruction
The methods and devices of the present invention for spectral
reconstruction involve mathematical cross-correlation. The methods of the
present invention can be directly applied to reconstruct a spectrum of a
desired component in a complex mixture. A sequence of spectral values is
obtained for a series of mixtures at a particular wavelength in samples of
known concentration. Thus, concentrations of the desired component in that
same series of mixtures must be known. These concentrations constitute a
set of reference values. Cross-correlation of the spectral values and
reference values retains that portion of the signal which contains
spectral information attributable to the desired component. The methods of
the present invention further eliminates noise, which can be spectral
information or background from any other source. When the methods of the
present invention are repeated at a number of wavelengths over a selected
range, the spectrum of the desired component over that range of
wavelengths is obtained.
In its most general form the cross-correlation function can be written as
the summation:
##EQU1##
where n is the number of samples, x is the sample index and d is the
displacement from the current x index. C.sub.ab (d) is the value of the
cross-correlation function between signals a(x) and b(x) at the
displacement d.
In the application of Eq. 1 to NIRA, a(x) is the absorbance (or its
reflectance analog) of the xth sample at a specific wavelengt and b(x) is
the concentration of the desired component in the xth sample. In the
absence of noise or other absorbing components in the sample set, the
value of C.sub.ab (d) at d=0 depends only on the absorbance and
concentration of the desired component and all values of the
cross-correlation function at d.noteq.0 are zero. Although it would appear
trivial to extract the desired spectrum from repeated applications of Eq.
1 at various wavelengths, experimental noise, interference from other
sample constituents, and a limited number of samples cause the zero and
non-zero d terms of the cross-correlation function to contain small
undesired contributions. To overcome these errors, the average of the
non-zero d terms is subtracted from the value of C.sub.ab (d) at d=0. This
correction is shown in Eq. 2.
##EQU2##
wherein a is the average absorbance of all samples at a given wavelength
and b is the average fractional concentration of a given component. When
this calculation is repeated for a number of wavelengths and plotted
against wavelength, the resulting spectrum shows the correlation between
the sample absorbance and the concentration of the desired component.
Eq. 3 should be normalized so the resulting reconstructed spectrum appears
in convenient, concentration-independent units. This is performed by
dividing Eq. 3 by the variance of b(x), as shown in Eq. 4.
##EQU3##
In NIRA, C'.sub.ab in Eq. 4 has units of absorbance per unit
concentration. The application of Eq. 4 has been found to be useful in the
analysis of non-interacting solutes, in which the concentration of each
solute has no effect on the concentrations of other solute contained
therein.
However, some samples, especially solids, are comprised of mixtures where
the fractional concentration of each species influences the concentrations
of others, because the fractional concentrations must sum to unity. In
such a situation Eq. 4 contains a correlation attributable to the desired
component, as well as negative correlation caused by the effect of the
concentration of that component on the concentrations of all other
constituents.
The negative correlation in Eq. 4 can be eliminated by scaling Eq. 4 by the
true average concentration of "other" species and adding to the product
the average sample absorbance at that wavelength. This correction is shown
in Eq. 5, an expression which is valid as long as the concentration
[b(x)]is expressed as a dimensionless fraction.
##EQU4##
By applying Eq. 4 or Eq. 5 to spectral information obtained over a series
of wavelengths, the spectrum of the component may be reconstructed. The
correlation methods of the present invention rely on linearity of the
underlying function and, thus, Eq. 5 applies only in the absence of
nonlinear effects such as physical or chemical nonadditivity, e.g., as
Beer's law deviations. This limitation is not severe, because NIRA and
many other spectroscopic techniques mentioned above are based on
linear-response assumptions.
One advantage of the methods of the present invention is that each
reconstructed spectrum will receive only that noise which is phase
coherent with its analytical guiding values. All other noise appears as a
residual when component spectra are subtracted from the original data.
Spectral reconstruction requires more samples than does curve-fitting, and
accurate reference chemical values which are not necessary for ratio
deconvolution or factor analysis. However, NIRA applications also require
several samples and accurate reference chemical values. This compatibility
makes spectral reconstruction particularly well suited to elucidate the
spectral details of NIRA samples.
2. Devices for Spectral Reconstruction
A schematic diagram of a preferred embodiment of a device which implements
the process of spectral reconstruction is shown in FIG. 8. This system
comprises three principal subsystems: a spectrometer 1 capable of
measuring the spectral values of a series of samples 8 at a series of
wavelengths and storing the spectral values for processing; a data input
means 2 allowing input and storage of reference data for the component of
the samples for which a reconstructed spectrum is desired; and the
spectral reconstructor 3 which utilizes the spectral data for a series of
samples and the reference data for the component of interest,
mathematically cross-correlates the data and generates a spectrum
therefor.
The spectrometer configuration shown in FIG. 8 is designed for use in
near-infrared reflectance spectral reconstruction methods and can be
substantially any commercially available spectrometer. Described herein is
a scanning nearinfrared spectrometer such as a Cary Model 14. Commercial
Fourier transform instruments such as a Digilab Model 15C can also be
used. The monochromator 4 contains an optical energy source, such as a
tungsten-halogen lamp and means to select a narrow band of wavelengths,
such as optical filters or a diffraction grating. The output of the
monochromator is a narrow beam of monochromatic light. The wavelength
input to the monochromator is controlled by the wavelength sequencer 5,
which in a preferred embodiment consists of a stepper motor electronically
programmed to scan the wavelength over a preselected range thereby
providing the wavelength information for the spectrum of a sample. Beam
switcher 6 is controlled by beam sequencer 7 and alternately directs the
output energy to sample 8 or to detector 10. Samples are sequentially
introduced into the beam by sample sequencer 9, which may be manually or
automatically operated. Sample number (x) is stored on digital storage
device 16 for identification of the data for each sample. The
monochromatic beam directed to the sample, is either transmitted through
the sample or reflected from the sample whereby the sample absorbs some
energy, thereby producing an energy from the sample 8 containing the
desired spectral information. The detector 10 converts the optical
energies of the sample and reference beams to electrical signals. Said
signals are converted to digital form by the analog to digital converter
11 and separated by the demultiplexer 12 using timing information from the
beam sequencer 7. The ratio of intensities of the sample signal to the
reference signal which is the transmittance or reflectance of the sample,
is formed by divider 13. This may be any conventional digital divider
circuit. Transmittance or reflectance is converted to absorbance (a(x)) by
a conventional digital log 1/T converter 14. When performed at a series of
wavelengths, the absorbances (a(x)) together with the sample number, and
the wavelengths are placed in a digital storage device 16, by the storage
sequencer 15. Digital storage device 16 is preferably a magnetic disc or
tape to provide means for permanent data storage.
The data input means 2 is a conventional data input subsystem consisting of
a data input device 17, preferably a keyboard and display device, a
storage sequencer 18 which places the reference data values and sample
number in digital storage device 19. Preferably, the reference data values
for the component of interest, b(x), are stored associated with the
absorbance data, (a(x)), on digital storage device 19.
The spectral reconstructor 3, performs the spectral reconstruction process
whereby the absorbance data (a(x)) of the sample and the reference data
(b(x)) are processed to produce the reconstructed spectrum of the desired
component. The spectral reconstructor can be substantially any
minicomputer and can be a commercial DEC PDP11-34 or Data General Nova.
The first step of the process is the sequential retrieval of the b(x)
values and the a(x) values by retrieval sequencer 20. The retrieval
sequencer retrieves b(x) and a(x) information for all the samples in
sequence and passes the data to the averager 21 together with the total
number of samples (n). The averager 21 adds the data for all the samples
together in a digital register and then divides the sum by the total
number of samples using conventional digital techniques. The average of
the b(x) values (b) and the average of the a(x) values for each wavelength
(a) are then stored by storage sequencer 22 in storage 23, which
preferably is conventional digital random access memory, using the
reference data and wavelength information from the retrieval sequencer 20
to identify the data from the averager 21.
The process continues with the wavelength retrieval sequencer 24 selecting
a first wavelength, and retrieving b and a from storage 23.
Simultaneously, the wavelength retrieval sequencer 25, using the
information from the retrieval sequencer 24, selects a first x and
retrieves b(x) from digital storage device 19 and a(x) from digital
storage device 16.
The values of b(x) and b are passed from the retrieval sequencers 24 and 25
to subtractor 26, a conventional digital subtractor, which produces the
difference (b(x)-b), thence to squarer 27, a conventional digital
multiplier which produces (b(x)-b).sup.2, which is then passed to summer
28. The associated values of a(x) and a are passed from retrieval
sequencers 24 and 25 to subtractor 29, which is another conventional
digital subtractor, producing (a(x)-a), which is then passed to multiplier
30. The output of subtractor 26, (b(x)-b) is also passed to multiplier 30,
which produces the product (a(x)-a)(b(x)-b), which is then passed to
summer 31.
The wavelength retrieval sequencer 25 sequentially increments the sample
number x to retrieve the a(x) and b(x) data for each sample in turn
thereby sequentially providing the summers 28 and 31 with processed data
for each sample at each wavelength. Summer 28, which is a conventional
adder with an accumulator register, provides the summation from one to n
of all (b(x)-b).sup.2 at the conclusion of the sequence of sample data and
summer 31 produces the summation from one to n of all (a(x)-a)(b(x)-b) in
similar fashion. The outputs of summers 28 and 31 are passed to digital
divider 32 which divides the output of summer 31 by that of summer 28 by
conventional digital techniques, producing the result of Eq. 4.
The value of b from the wavelength retrieval sequencer 24 is passed to
subtractor 33 where the difference (1-b) is formed by conventional digital
techniques. The output of divider 32 is multiplied by the output of
subtractor 3 in multiplier 34, another conventional digital multiplier and
then passed to adder 35. Here, the value of a from the wavelength
retrieval sequencer 24 is added to the output of multiplier 34 by
conventional digital techniques to provide C".sub.ab at one wavelength of
the desired recontructed spectrum of component x, where C".sub.ab is
defined in Eq. 5. The output of adder 35 together with the value of the
wavelength retrieval sequencer 24 is then passed to output device 36,
which may be a data storage device, display printer, or plotter, to
produce one point of the reconstructed spectrum.
The process is continued by causing wavelength retrieval sequencer 24 to
increment to the next wavelength and repeating the above cycle of
processing to produce the next point of the reconstructed spectrum. The
cycle is repeated until all desired wavelengths have been processed and
the complete reconstructed spectrum of the desired component has been
obtained.
Example I
Spectral Reconstruction from Hydrocarbon Mixtures
Spectra of hydrocarbons were reconstructed from hydrocarbon mixtures
prepared as follows. Reagent-grade benzene and cyclohexane, and
spectranalyzed iso-octane and n-heptane were combined in varying
proportions to create 97 standard hydrocarbon solutions. These solutions
ranged from 3% to 100% concentration for each hydrocarbon. To minimize
error, each of the four hydrocarbons was rapidly introduced and weighed by
difference into a gas-tight vial. The error in each standard concentration
is estimated at b 0.05%. Infrared spectra were recorded by a
Fourier-transform spectrometer having a silicon beam splitter, a PbSe
detector operated at 300.degree. C., and a CaF.sub.2 flow-through cell.
The instrumental resolution was nominally 4 cm.sup.-1 and boxcar
apodization was employed. Reconstructed spectra were calculated according
to Eq. 5. The reconstructed spectrum of cyclohexane obtained from
hydrocarbon mixtures is shown in FIG. 1 along with a spectrum of pure
cyclohexane obtained during an independent run. A spectrum of a typical
hydrocarbon mixture (benzene, cyclohexane, iso-octane and n-heptane) is
shown in FIG. 2. A comparison of the reconstructed spectrum and that of
the mixture shows that even intense background features in the mixture do
not "bleed" through the reconstruction process and affect its accuracy.
Moreover, the identity of the vertical scales in FIG. 1 shows the fidelity
of the reconstructed spectrum; both the band location and amplitude are
the same as found in the spectrum of the pure compound. FIGS. 3-5 show the
pure and reconstructed spectra of the remaining components in the
hydrocarbon mixtures. Each of these compounds shows the same high degree
of similarity between the pure and reconstructed spectra as found for
cyclohexane. This similarity is not surprising; the compounds used to
create hydrocarbon mixtures are known to exhibit few intermolecular
interactions.
Although the reconstructed spectra of FIG. 1 and FIGS. 3-5 appear very
similar to those of the pure compounds, the spectra of the pure components
were not used or required to generate the reconstructed spectra.
Similarly, the spectral reconstruction technique is able to produce spectr
of individual mixture components even when the pure components cannot be
obtained. An example of this capability can be found in the determination
of moisture in wheat flour.
Example II
Spectral Reconstruction of Protein and Moisture in Wheat
Spectra were reconstructed for protein and moisture in wheat samples as
follows. A set of 50 near-infrared diffusereflectance spectra of
wheat-flour samples was obtained from USDA, Beltsville, MD. Each of these
spectra is comprised of 125 reflectance values obtained over the spectral
range 1000-2587.2 nm in increments of 12.8 nm. The reported instrumental
bandpass was 7 nm. Each of the four samples was characterized for protein
by 32 separate Kjeldahl measurements. A spectrum of distilled water was
obtained from a 0.5 mm transmission cell with CaF.sub.2 windows using the
Fourier transform spectrometer as described in Example I. Reconstructed
spectra were calculated according to Eq. 5.
An absorbance spectrum of pure water and the reconstructed spectrum of
moisture in wheat flour, shown in FIG. 6, are noticeably different. In
particular, the bands at 1450 nm and 1950 nm appear broader in the
reconstructed spectrum than in the spectrum of pure water. This change is
indicative of variations in hydrogen bonding caused by the protein matrix.
Additionally, two small peaks at 2150 nm and 2300 nm appear in the
reconstructed spectrum. These absorptions are due to protein and oil
respectively and show that the moisture, protein and oil content of wheat
are either biologically or chemically correlated.
FIG. 6 shows a spectrum of reconstructed moisture in wheat which reasonably
approximates pure water, but shows the spectral deviations of moisture in
wheat described by Hruschka et al., Applied Spectroscopy 36,261 (1982).
Spectral reconstruction is able to extract from a sample set the composite
spectrum of constituents responsible for sensory characteristics such as
flavor or taste. A similar capability is the spectral reconstruction of
Kjeldahl determined protein and "as is" protein.
"As is" protein has been defined as protein which has been determined by
the Kjeldahl method but which has been adjusted for the moisture content
of the sample. The reconstructed spectra of protein determined by the
Kjeldahl technique and by the "as is" measurement are reproduced in FIG.
7. These spectra are plotted on the same scale and are not offset. From
FIG. 7, both measurements generate the same spectrum, suggesting that both
measure essentially the same chemical species. However, there are some
slight differences in the relative intensities of several of the peaks.
For example, the moisture absorption band at 1950 nm is slightly smaller
in the "as is" protein spectrum than in the Kjeldahl spectrum, indicating
the "as is" measurement of protein reduces but does eliminate
interferences from moisture.
While the above examples describe certain methods of the present invention
they are not to be construed as limitations on the present invention. As
one skilled in the art would recognize, many modifications may be made in
the methods and devices of the present invention which fall within the
spirit and scope of the present invention.
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