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dead volume) for solution introduction, this system is ideally suited for discrete sampling techniques such as FIA and HPLC. The thermospray system provides significant detection enhancement compared to conventional sample introduction systems. This enhancement can allow lower concentrations to be detected or provide adequate detection for low concentrationswith smaller sample volumes. These results are particularly encouraging, considering the observed limitations of our present postprobe system, and demonstrate the great potential of thermospray for making ICP-AES a practical detector for FIA and HPLC. Future studies will include the characterization of aerosol and transport properties, matrix/solvent effects, and HPLC applications. We are also modifying our present system to allow higher liquid flow operation and investigating improved probe designs. ACKNOWLEDGMENT The authors thank Marvin Vestal and Vestec Corp. for loan of the thermospray unit. LITERATURE CITED (1) Greenfield, S. Spectrochlm. Acta, Pari 8 1983, 386,93. (2) Lafrenlere. K. E.; Rice, G. W.; Fassel, V. A. Specfrochim. Acta, Pari 6 1985, 408, 1495.
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Faske, A. J.; Snable, K. R.; Boorn, A. W.; Browner, R. F. Appl. Spectrosc. 1985, 39, 543. Browner, R. L.; Boorn, A. W. Anal. Chem. 1984, 56, 786A. Browner, R. F.; Boorn, A. W. Anal. Chem. 1984, 5 6 , 875A. Bushee, D.; Krull, I. S.; Savage, R. N.; Smith, S. B. J . Llq. Chromafogr. 1982, 5 , 693. Florence, T. M.; Batley, G. E. CRC Crlf. Rev. Anal. Chem. 1980, 7 7 , 219. Lawrence, K. E.; Rice, G. W.; Fassel, V. A. Anal. Chem. 1984, 56, 292. Layman, L. R.; Lichte, F. E. Anal. Chem. 1982, 5 4 , 638. Blakely, C. R.; Vestal, M. L. Anal. Chem. 1983, 55, 750. Vestal, M. L.: Fergusson, G. J. Anal. Chem. 1985, 57, 2373. Meyer. G. A.; Roeck, J. S.; Vestal, M. L. ICP I n f . Newsl. 1985, 70, 955. Boumans, P. W. J. M. Line Coincidence Tables for Inductively Coupled Plasma Atomic Emission Spectrometry; 2nd ed.; Pergamon Press: New York, 1984.
J. A. Koropchak* D. H. Winn Department of Chemistry and Biochemistry Southern Illinois University Carbondale, Illinois 62901 RECEIVED for review April 7, 1986. Accepted June 2, 1986. This work was supported in part by a grant from the Office of Research Development and Administration, SIU-C. In addition, financial support for D.H.W. was provided by the Coal Research Center, SIU-C.
Species Discrimination and Quantitative Estimation Using Incoherent Linear Optical Signal Processing of Emission Signals Sir: What follows is a description of a simple apparatus for optical spectroscopic signal processing. This apparatus may be best suited for application in background interference limited emission spectroscopy for selective species detection. Operation is based on the established techniques of linear incoherent optical signal processing (OSP) (1) and optimal weight function estimation techniques (2, 3). The spectroscopic processor is made up of four components: an element to disperse the wavelength-dependent information into space-dependent information, a spatially variant optical transmission mask to filter the spectroscopic information, optical and/or electronic elements to spatially integrate the transmitted intensity and convert it to an electronic signal proportional to integrated intensity, and an electronic postprocessor to perform simple algebraic computations. The transmission characteristics of the optical mask are central to the operation of the processor. This mask takes the place of the slit in the image plane of a conventional monochromator. The optical transmission of the mask represents a mathematical function of space and, therefore, of wavelength beyond a dispersion element. The operation of this mask on the spatially dispersed information is to produce a mathematical product between the spectroscopic information and an orthogonalweight function recorded in the mask. This product is represented by the intensity beyond the mask. The orthogonal weight function is formulated such as to maximize the signal-to-noise ratio of the signal estimate while being orthogonal to, and therefore independent of, interferences (2, 3).
Linear OSP is basically a means to obtain a mathematical product of two values by passing light of an intensity representing one value through a transmission filter with a transmittance representing a second value. The intensity past the filter is the product. Extension of this procedure to obtain vector dot products is straightforward. One of the vectors is
defined as a spatially dependent intensity pattern. For example, this vector can be the output of a spectroscopic dispersion device. The intensity of each spatially dispersed wavelength or band of wavelengths represents an element of the vector. This dispersed intensity is imaged onto a spatially variant, achromatic transmission filter. The intensity at each wavelength band is imaged onto a different location on the transmission filter. The optical transmission of the filter defines the second vector. The transmitted intensity is a spatially ordered series of products of the intensities of the first vector elements with transmissions of the second. The vector dot product is the sum of these individual element product intensities. This summation or integration is performed by focusing the transmitted image to a spot that is smaller than the active area of a photodiode detector, or by using a large-area photodiode placed just after the mask. The current from this photodiode is directly proportional to the desired vector dot product. In an emission source, a species will emit over a characteristic spectrum, with an integrated emission intensity that is proportional to the quantity of this species in the source. Mathematically, the function that describes this emission is a wavelength-dependent function multiplied by a constant proportional to the amount of this species in the source. In many real situations, the total emission is made up of several overlapping spectra due to the many species in the source. An important factor in the formulation of the optical spectroscopic signal processor mask element is that it be such that the processed signal estimate is independent of spectral interferences. To optically process an emission signal made up of several component spectra, a vector function may be formulated such that it is orthogonal to the characteristic emission spectra due to interfering species ( 2 , 3 ) .The integrated product of this vector with the emission will result in a value that is independent of the amount of light emitted
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by the interfering species. This is a consequence of the orthogonal relationship between the interfering emissions and the vector used to process the total emission. The processing vector is also formulated such that it is not orthogonal to the characteristic emission pattern of the measured species. Thus, the integral product of the transmission and dispersed emission is directly proportional to the concentration of the desired species. There is an optimal way to formulate the signal processing vector function such that the signal-to-noise ratio of the result is a maximum. It is known that the best estimate of the signal magnitude occurs for a cross correlation of the signal with the impulse-response function, or “matched filter”,for that signal. Matched filtering is used in electrical engineering for signals that have “white” noise interference ( 4 ) . This filter can be extended to include cases where the noise power spectrum is not white. To do this, the signal is effectively preprocessed with a filter that transforms the noise into “white” noise, Whitening transformation and matched filtering can be performed in one step. In spectroscopy, the whitening filter corresponds to the determination of the orthogonal vector that will minimize the estimated contributions of the emitting interference species. This whitening process is the process of orthogonalization, and the resulting filter is a Kalman innovation ( 4 ) . Important implications of this type of processing are that the estimate is optimized in terms of the signal-to-noise ratio, the estimate is independent of interferences, and a wide-ranged frequency spectrum is used to calculate the signal estimate, thereby increasing the precision. Mathematical formulation of the optical filter is simplified if there is only one species of interest. This filter can be constructed by Gram-Schmidt orthonormalization ( 4 , 5 ) . For the purpose of illustration, consider a sample that has an analyte emission spectrum which is represented by the wavelength-dependent vector a, and a total emission magnitude x,. The spectral interference components are represented by a, and xL,i being the component index, in the same fashion. A column-ordered matrix of these n basis set vectors, A, is subsequently orthonormalized to yield the matrix, Q. Gram-Schmidt orthonormalization results in a set of orthogonal vectors that are related to the original basis set by the factorization matrix, R
A = QR
(1)
For an emission spectrum represented by the vector b, the problem is one of determining the individual emission magnitudes, xn,which are components of the vector x. This is the least-squares problem of determining x such that the 2-norm is a minimum minllAx - blln
(2)
By premultiplication of eq 2, the minimum 2-norm is equivalent to min(l(QTA)x - (QTb)l12
(3)
where T represents the transpose. Using eq 1 and the fact that the vector components of Q are orthonormal, the solution is
Rx
= QTb
(4)
The R factorization matrix, which effectively maps the stepwise orthonormalization process, is upper triangular. Subsequently, the least-squares coefficient of the last component of the orthogonalized set of vectors differs from the magnitude of the target species spectrum estimation by only a constant (6).This constant is the inverse of the last element of the factorization matrix since x = R-lQTb
(6)
1 RANSMISSION
Flgwe 1. Schematic representation of the optical spectroscopic signal processor. The source emission is dispersed, and the resulting spectrum is imaged at the transmission mask. The height of the image is such that both positive and negative components of the transmission mask are illuminated. The wavelength-ordered product of the emission spectrum with the mask transmission is integrated with the large-area photodiodes. The difference between the positive and negative integral components, as photodiode currents, is obtained with the differential amplifier.
and since QTb is a vector with elements equal to the dot products of b with the individual component vectors of QT. The correlation filter can be mathematically constructed by ordering the representations of the emission spectra such that the interference spectra come fist and the target species spectrum is the last vector in the matrix. After orthogonalization, the last vector, q,,, is the correlation filter for the target species. The dot product of q, with the emission spectrum, b, is the optimal estimate, x,. This dot product is defined as the correlation filter. The correlation filter is orthogonal to the interference, and thus the estimate is, in principle, unaffected by the interference species used in construction of this filter. The basic spectroscopic emission OSP apparatus is shown in Figure 1. Illustrated are the dispersion device, the mask, and the integration and detection devices. The device illustrated here is limited to the detection and quantitative estimation of only one species. A device that would detect and quantify several species simultaneously can be made by replicating the single element apparatus severalfold. A multielement transmission filter, imaging optics to integrate over spatial coordinate of wavelength dispersion, and a photodiode array would be used in this case. The dispersion device serves to order the wavelength-dependent intensity information into spatially dependent information. Either a monochromator or a spatially dispersing interferometer could be used. The correlation filter is a transmission filter element that is placed at the output image plane of the dispersion device. The spatially dispersed wavelength-dependent information is effectively multiplied by the spatially dependent transmission mask, and the integral is formulated with the large active area photodiodes. The correlation filter is defined as a pair of spatially variant transmission values recorded in the mask. The greater the absolute value of the correlation filter at a particular position on the mask, corresponding to a particular wavelength or band of wavelengths, the greater the optical transmission. A pair of vectors are required because only real, positive-valued products are defined in incoherent optical signal processing (7,8). The emission intensity can be either finite or zero, but not negative. In general, the correlation filter must contain both positive and negative values, since it is orthogonal to interference emissions which are positive valued only. In order to accomplish the signal processing, the correlation filter is divided into two component vectors: one containing the positive elements, the other the negative elements. The product of the source emission spectrum with the correlation filter is formulated after the dispersed emission passes through the filter mask. The difference between the positive and negative components of the integrated product is performed by electronic difference of the current from the two photodiodes.
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Either a permanent or a programmable transmission filter element can be employed. For a given emission source, a flame for example, the spectra are not dynamic in that they do not change on a measurement-to-measurementbasis. If the source temperature remains relatively constant, there is no need to change the filter function. Thus, a permanent transmission mask may be employed. Permanent transmission filter masks can be produced by several methods. One method is to use the emission and background spectra of the species to be analyzed as a basis set. This basis set is then orthogonalized using a digital computer. The resulting basis set and the factorization matrix (5)may then be used to produce enlarged dot density masks on a digital plotter. These enlarged masks could then be photographicallyreduced to proper dimensions. If programmability is required, for example in cases where the interferences vary substantially over time, then a liquid crystal device such as the ones found in the new “pocket” television sets could be used for the transmission mask. Promising applications are those that apply the optical correlation filter method to spectroscopic analyses which are background emission interference limited. One example is the detection of alkali and alkali earth elements by flame emission. Interferences due to the combustion products of the fuel and due to emission from other species in the sample will limit the detection. Another application will be found in ICP emission for quantitative estimation of atomic species. It is well-known that interference, as a consequence of the great number of emission lines relative to that of absorption, is a limiting factor in emission spectroscopies. In this case several correlation filter functions would be constructed such that they would be orthogonal to each other. The main advantage to incoherent OSP is that the optical spectrum or interferogram can be processed without conversion. By use of achromatic transmission elements, the processor will be unaffected by the chromaticity of the signal. Another advantage is in the short time required to “calculate” the signal estimate. OSP can perform parallel computations in the same time that is required to perform one computation. Thus, entire spectral libraries may be “searched” in one operation. A third advantage is that the data are already in a form that can be utilized by the processor. Only minor electronic level computations are required for the mathematical formulation of the signal estimate. Fourth, the cost of an optical processor can be much less than a large digital array processor. And finally, the physical size of the optical processor will allow construction of spectrometersthat contain all of the processing capabilities. It should not be difficult to add this processor to existing dispersion devices, since the only additional components required are transmission filters and photodiodes. One disadvantage is that the throughput of the signal may be low when there is a large overlap between target spectra and interference spectra (2,3). This is especially true if there is a large number of such interferences. The optical correlation filter transmission element will have a maximum total spec-
trum throughput on the order of the integrated spectral density and half of this per photodiode for two (bipolar) correlation filter vectors. The more elements in a matched filter “library”, the less total light throughput per element, scaling at best as 1/2N, N being the number of filter elements. However, the correlation filter maximizes the signal-to-noise ratio, and the throughput at wavelengths that are correlated to a particular spectrum should approach 100%. For large numbers of correlation filter elements in a single mask element, the spectroscopicsignal may be amplified with a image intensifier. Alternatively, the correlation filter can be time multiplexed in the spectral image plane so that only one pattern is correlated at a time ( I ) .
CONCLUSION The application of OSP to spectroscopic-based chemical analysis problems will result in more efficient means to both obtain signal estimates that are independent of background interferences and to perform rapid pattern recognition spectral analysis. Further, the OSP spectroscopic data analyzer will be a cost-effective alternative to processing of fast analytical signals. Specific applications of the OSP spectrum processor will be found for the real-time discriminationand quantitative estimation of luminescent spectroscopic signals that are background limited. A surprisingly straightforward application of optical signal processing to a particular class of problems currently limiting several analysis processes has been described here. This device could prove to make light work out of what with current technology requires large amounts of computer time, labor, and/or expensive analysis equipment. The device will be very well suited for use as a chemical sensor, which will respond to only the species of interest. This sensor would not have to be large in size and could be constructed from materials currently available.
LITERATURE CITED (1) Rhodes, W. T.; Sawchuk, A. A. In Optical Signal Processing fundementals; Lee, S. H., Ed.; Springer-Verlag: New York, 1981. (2) Morgan, D. R. Appl. Spectrosc. 1978, 37, 404-414; 1978, 37, 415-423. (3) Morgan, D. R. General Electric Technical Report R75ELS024, 1975. (4) Papoulis, A. Probablllty, Random Varlables and Stochastlc Processes, 2nd 4.;McGraw-Hill: New York, 1984. (5) Golub, G. H.; Van Loan, C. F. Matrix Computations; Johns Hopkins University Press: Baltimore, MD, 1983. (6) Blalkowski, S. E. Anal. Chem. 1986, 58, 1706-1710. (7) Casasent, D.; Jackson, J.; Neuman, C. P. Appl. Opt. 1983, 22, 115-124. (8) Casasent, D. Proc. IEEE 1984, 72, 831-849.
Stephen E. Bialkowski Department of Chemistry and Biochemistry Utah State University Logan, Utah 84322-0300 RECEIVED for review March 18,1986. Accepted June 19,1986. Support for this work and other projects from the Office of the Vice President for Research at Utah State University is gratefully acknowledged.
Sequencing Procyanidin Oligomers by Fast Atom Bombardment Mass Spectrometry Sir: Polymeric procyanidins (condensed tannins) are present in a wide distribution of plants, occurring in particularly high concentrations in some barks, leaves, and fruits ( I ) . These phenolic polymers complex with proteins and
therefore inhibit enzyme activity ( Z ) , are important contributors to the flavor of foods (3,4),and influence the nutritional value of plants (5, 6). Procyanidins are also credited with a role in protecting plants from microorganismsand insects (7,
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