effect of spectral resolution on pattern recognition analysis using passive fourier transform...

1382 Volume 53, Number 11, 1999 APPLIED SPECTROSCOPY0003-7028 / 99 / 5311-1382$2.00 / 0

q 1999 Society for Applied Spectroscopy

Effect of Spectral Resolution on Pattern RecognitionAnalysis Using Passive Fourier Transform Infrared SensorData

ARJUN S. BANGALORE,* JACK C. DEMIRGIAN, AMRIT S. BOPARAI, andGARY W. SMALLChemical Technology Division, (A. S. Bangalore, A. S. Boparai) and Environmental Research Division (J.C.D.), Argonne National

Laboratory, 9700 S. Cass Avenue, Argonne, Illinois 60439; and Center for Intelligent Chemical Instrumentation, Department of

Chemistry, Clippinger Laboratories, Ohio University, Athens, Ohio 45701-2979 (G.W.S.)

The Fourier transform infrared (FT-IR) spectral data of two nerve

agent simulants, diisopropyl methyl phosphonate (DIMP) and di-

methyl methyl phosphonate (DMMP), are used as test cases to de-termine the spectral resolution that gives optimal pattern recogni-

tion performance. DIMP is used as the target analyte for detection,

while DMMP is used to test the ability of the automated patternrecognition methodology to detect the analyte selectively. Interfer-

ogram data are collected by using a Midac passive FT-IR instru-

ment. The methodology is based on the application of pattern rec-ognition techniques to short segments of single-beam spectra ob-

tained by Fourier processing the collected interferogram data. The

work described in this article evaluates the effect of varying spectralresolution on the pattern recognition results. The objective is to

determine the optimal spectral resolution to be used for data col-

lection. The results of this study indicate that the data with a nom-inal spectral resolution of 16 cm 2 1 provide suf® cient selectivity to

give pattern recognition results comparable to that obtained by us-

ing higher resolution data. We found that, while higher resolutiondoes not increase selectivity suf® ciently to provide better pattern

recognition results, lower resolution decreases selectivity and de-

grades the pattern recognition results. These results can be used asguidelines to maximize detection sensitivity, to minimize the time

needed for data collection, and to reduce data storage requirements.

Index Headings: Spectral resolution; Qualitative analysis; Remote

sensing, Fourier transform infrared spectroscopy; Pattern recog-nition.

INTRODUCTION

Fourier transform infrared (FT-IR) spectroscopy is in-creasingly being used to analyze volatile organic com-pounds (VOCs) present in the atmosphere because of itscapability for remote and nondestructive measurements.1±4

Spectral resolution is one of the critical issues currentlyunder debate for both qualitative and quantitative analy-ses. It is still widely believed that one needs high-reso-lution data to analyze gaseous components, although sev-eral studies have indicated otherwise. The objective ofthis study is to determine the spectral resolution at whichFT-IR data need to be collected to obtain optimal resultswhen pattern recognition methods are used to implementan automated detection procedure for determining thepresence of a target analyte.

Several researchers have addressed the spectral reso-lution issue in the context of quantitative analysis eitherby using classical least-squares (CLS) or partial least-

Received 14 September 1998; accepted 22 June 1999.* Author to whom correspondence should be sent. Present address:

ChemIcon Inc., 7301 Penn Avenue, Pittsburgh, PA 15208.

squares (PLS).5±9 Hanst recommended 0.5 cm 2 1 resolu-tion for quantitative analysis.5 Grif® ths favored 8 and 16cm 2 1 resolution.6 Qin and Cadet have used 16 cm 2 1 spec-tral resolution in a study for monitoring process streamsfor several VOCs, although they used very broad spectralregions (4000±2500 and 1720±700 cm 2 1) for buildingcalibration models.7 Herget used open-path FT-IR mea-surements of auto exhaust.8 He obtained equivalent re-sults from 0.5, 1.0, and 2.0 cm 2 1 spectral resolution datafor VOCs in the presence of high concentrations of waterand carbon dioxide. The results deteriorated for data withresolution of 4.0 cm 2 1. Marshall et al. also studied open-path FT-IR data of several pure compounds and mixturesat several different spectral resolutions.9 They found thatfor qualitative analysis of pure compounds using absorp-tion spectra, a resolution of 1.0 cm 2 1 gave the best resultsoverall, although higher resolutions helped to reduce falsepositives slightly. For quantitative analysis, 8 cm 2 1 res-olution gave the best results. Jaakkola et al., in a recentresolution study using gas-phase FT-IR data, deduced thatlow-resolution data can produce better qualitative andquantitative results than higher resolution data.10 How-ever, they warned that the optimal resolution is applica-tion-speci® c and that the quantitative results are stronglyin¯ uenced by the multivariate algorithm employed.

The suitability of low-resolution FT-IR spectroscopyfor quantitative and qualitative analyses has been muchdebated. It is evident that currently there is no agreementon the optimal spectral resolution that can be used forquantitative or qualitative analyses. Generally, the highestresolution at which data can be collected is used for anal-ysis. The literature indicates that the optimal resolutionis often dependent on the speci® c data set employed inthe study. More work needs to be performed to resolvethis critical issue. Very few studies are found in the lit-erature that establish the optimal spectral resolution forqualitative analysis, although one can ® nd many studiesfor quantitative analysis. This study attempts to establishthe protocol for optimal spectral resolution for perform-ing automated identi® cation of target chemicals usingsingle-beam spectra.

The data analysis methodology is based on the appli-cation of pattern recognition techniques to segments ofthe single-beam spectra computed from the collected in-terferogram data. The spectral segments are treated aspatterns in a two-category pattern recognition analysis.The categories or classes consisted of (1) patterns con-taining the signature of the target analyte and (2) patterns

APPLIED SPECTROSCOPY 1383

not containing this signature. Piecewise linear discrimi-nant analysis (PLDA) is used to compute a set of lineardiscriminants that implement an automated classi® cationof the patterns into the two categories. Small and co-workers have used PLDA previously for the automateddetection of VOCs with passive FT-IR interferogramdata.3,11±14 The direct use of single-beam spectra elimi-nates the need for infrared background measurements thatwould be required if ratioed or difference spectra wereemployed. Such background measurements are dif® cultin passive FT-IR experiments because of natural meteo-rological variations in the atmosphere.

EXPERIMENTAL

Instrumentation. Data were collected with a MidacOut® elder FT-IR emission spectrometer (Midac, Irvine,CA). The instrument was equipped with a narrow-bandmercury cadmium telluride (MCT) liquid nitrogen-cooleddetector. The beamsplitter and exit window were con-structed of coated ZnSe. The spectrometer was interfacedto a personal computer that contained software writtenspeci® cally to collect and store multiple interferogramsin a single ® le.

A Mikron M340 (Wyckoff, NJ) blackbody source wasused as the infrared background during the data collec-tion. The blackbody was calibrated to NIST standards byMikron. The blackbody was allowed to equilibrate for atleast 30 min at each temperature before data were col-lected. The blackbody temperature was veri® ed dailywith the use of an Omegascope 2106S (Omega, Stam-ford, CT) pyrometer. The ori® ce of the blackbody wasplaced behind a ZnSe window to prevent vapors frombeing trapped in the ori® ce and causing contamination.

Procedures. Passive remote sensing conditions fordata collection were simulated in the laboratory by con-trolling both concentration and temperature. Quantitativereleases of chemicals were performed with a vaporizerdesigned at Argonne National Laboratory. The vaporizerconverted a liquid stream of dimethyl methyl phospho-nate (DMMP) (Aldrich, Milwaukee, WI) or diisopropylmethly phosphonate (DIMP) (Lancaster Synthesis Inc.,Windham, NH) into vapor that was released at a constantrate. A syringe pump delivered the liquid, using a 20 mLcalibrated syringe, to a sonic nebulizer that converted theliquid to a 15 m m aerosol. The aerosol was released intoa mixing chamber where it was mixed with air heated to130 8 C. The aerosol was then vaporized and swept intoa master chamber, where the heated air was mixed withnine parts of air at ambient temperature. The vapor thenpassed through a baf¯ e to ensure better mixing and exitedthrough a square ori® ce (10 cm 3 10 cm). All releaseswere completed in a hood to ensure that there were noresidual vapors present. The vaporizer ori® ce was placedso that the release was in front of the blackbody and thespectrometer was aimed at the blackbody. The integrityof the release was maintained for approximately 10 cm.Data were collected within 3 cm of the ori® ce.

The Midac spectrometer could be set for different scanrates and spectral resolutions. Single-sided interferogramsof 8192 (8K) points were collected that, upon Fourierprocessing, generated single-beam spectra with 4096(4K) points and a nominal spectral resolution of 8 cm 2 1.

DIMP data were collected at a 20 kHz scan rate andDMMP data were collected at a 40 kHz scan rate. Eachscan was a single interferogram, and no coaddition wasperformed.

Data Analysis. The interferogram data collected weretransferred to a Silicon Graphics workstation for furtherprocessing. The workstation was a MIPS R8000 singleprocessor Silicon Graphics computer (Silicon Graphics,Mountain View, CA) using the Irix operating system,Version 6.2. The computer had 128 megabytes of mainmemory and a total of 42 gigabytes of storage from bothinternal and external disks. The data analysis softwarewas written in Fortran 77 and was compiled with theSilicon Graphics Fortran 77 compiler with optimizationlevel 2 on a Silicon Graphics R4000 computer to obtain32-bit executable code. Fourier transform computationsperformed as a part of the data analysis made use ofsubroutines from the IMSL package (IMSL, Houston,TX).

RESULTS AND DISCUSSION

Instrumental Resolution. As described by Saarinenand Kauppinen,15 the instrumental spectral resolution ob-tained in an FT-IR experiment is the convolution of twobroadening functions, w v and wL, where w v describes aboxcar function arising from the nonzero area of the lightsource, and wL is the Fourier transform of the interfero-gram truncation function used (e.g., a sinc function if aboxcar truncation function is applied). An observed spec-tral band is thus the true band convolved with w v and wL.

The obtained instrumental resolution is controlled bythe larger of w v and wL. This implies that the optimalinstrumental setup is obtained when these two functionsare of approximately equal width. Instrumental resolutionis increased by increasing the maximum retardation (i.e.,length) of the collected interferogram and reducing thesize of the source aperture. These operations serve todecrease the widths of wL and w v , respectively. Similarly,reduced resolution is obtained by decreasing the lengthof the collected interferogram. Since wL then controls theinstrumental resolution, the size of the source aperturecan be increased to allow w v to match wL.

In a passive FT-IR remote sensing experiment of thetype performed in this work, an external infrared sourceis employed. In a typical remote sensing spectrometersuch as the Midac Out® elder instrument employed in thiswork, the optics are designed to produce a ® xed w v func-tion that roughly matches wL at the maximum allowedinterferogram retardation. In this case, the instrumentalresolution is controlled solely by wL.

To illustrate this instrumental con® guration, Fig. 1shows a plot of absorbance spectra of a low-pressuresample of methanol vapor at room temperature. The Mi-dac spectrometer was allowed to view the methanol sam-ple against an external blackbody source operating at 508 C. The narrow Q branch of the methanol C±O stretchingvibration at 1033 cm 2 1 is plotted for ® ve cases in whichthe interferogram length was increased in steps to achievenominal instrumental resolutions of 16 (dotted line), 8(short dashed line), 4 (dash-dot line), 2 (long dashedline), and 1 (solid line) cm 2 1. The loss of photometricaccuracy in the peak absorbance at each level of de-

1384 Volume 53, Number 11, 1999

FIG. 1. Absorbance spectra of methanol vapor collected with 1 (solidline), 2 (long dashed line), 4 (dash-dot line), 8 (short dashed line), and16 (dotted line) cm 2 1 resolution.

FIG. 2. Reference absorbance spectra of DIMP (solid line) and DMMP(dashed line).

TABLE I. Details of data set A.

Interferogramtype and

concentration(ppm-m)

Trainingset

Predictionset Total

DIMP-actives

5.0 389 711 11008.1 618 1032 1650

18.0 1221 979 220038.7 1772 428 2200

Sub-total 4000 3150 7150

DIMP-inactives

Pure background 3353a 8197 11550

DMMP-actives

9.1 533 567 110013.5 574 526 110031.8 585 515 110064.5 955 695 1650

Sub-total 2647b 2303 4950

Total 10000 13650 23650

a Total number of pure backgrounds (no DIMP or DMMP).b Number of DMMP-actives present as backgrounds.

creased resolution con® rms that wL is the controllingfunction up to a resolution of 1 cm 2 1. This effect can alsobe observed in the degradation of the shapes of the ro-tational bands in the R and P branches of the spectrum.On the basis of these observations, the instrumental res-olution was varied in this work by simply truncating thecollected interferograms to various shorter lengths.

Selection of Test Analyte. DIMP, widely used as anerve gas simulant, was chosen as the test analyte forthis investigation. The solid trace in Fig. 2 is a libraryreference absorbance spectrum of DIMP collected at 2cm 2 1 resolution.16 The strong P±O±C stretching vibrationat 995 cm 2 1 was targeted for the pattern recognition anal-ysis. The full width at half-height (FWHH) of this bandis approximately 17 cm 2 1. A second compound, DMMP,also used as a nerve gas simulant, was used as an inter-ferent. The dashed line in Fig. 2 is a reference absorbancespectrum of DMMP, also collected at 2 cm 2 1 resolution.16

DMMP shows four absorption bands of varying intensi-ties from very strong to weak in the 1200±700 cm 2 1 re-gion. The strong P±O±C stretching band of DMMP cen-tered around 1045 cm 2 1 overlaps somewhat with the 995cm 2 1 band of DIMP. Therefore, inclusion of DMMP asan interferent tests the ability of the methodology to dis-criminate the target analyte selectively.

Construction of Training and Prediction Data Sets.The data sets used for pattern recognition analyses wereassembled from single-beam spectra of DIMP, DMMP,background, and synthetically generated mixture spectracontaining signatures of both DIMP and DMMP. Back-ground spectra are de® ned as those collected when nei-ther DIMP nor DMMP was present in the ® eld of view(FOV) of the instrument. During the initial experimen-tation, all types of spectra except synthetic mixtures wereused. The spectra containing DIMP signatures werecalled analyte-actives and formed one of the two classesin the data set. Those that did not contain DIMP infor-mation were called analyte-inactives (DMMP-actives andpure backgrounds) and formed the other class in the dataset. The data sets were made progressively more dif® cultby adding synthetic mixture spectra containing the sig-natures of both DIMP and DMMP in various proportions.

The spectra that had signatures of both DIMP andDMMP were deemed to be analyte-actives.

The data sets were assembled with a pool of 23 650spectra. There were a total of 7150 DIMP-active spectraat four concentration levels (5.0, 8.1, 18.0, and 38.7 ppm-m), 4950 DMMP-actives at four concentration levels (9.1,13.5, 31.8, and 64.5 ppm-m), and 11 550 background spec-tra. Two representative subsets termed training and pre-diction sets were assembled from this pool of total spectraby using a procedure developed by Carpenter and Small.17

The spectra present in the training set were not includedin the prediction set and vice-versa. Table I shows thecomposition of the ® rst data set assembled, which is re-ferred to as data set A.

Construction of Databases with Different SpectralResolution. The data sets shown in Table I were assem-bled with spectra computed with 8K single-sided inter-ferograms. Figure 3B is an example of an 8K interfero-gram of 38.7 ppm-m DIMP. The interferogram points


FIG. 3. Interferograms of different lengths containing 38.7 ppm-mDIMP.

FIG. 4. Single-beam spectra obtained by Fourier processing the inter-ferograms shown in Fig. 3.

were sampled at every zero-crossing of the 632.8 nm He±Ne reference laser, and hence the maximum observabledigitized frequency according to the Nyquist theorem was15 798 cm 2 1. Upon Fourier processing, these interfero-grams produce single-beam (SB) spectra with 4K points.The spectral point spacing is calculated by the followingformula:

Point spacing 5 (Max. observable digitized frequency)/(No. of spectral points). (1)

The standard convention in FT-IR spectrometry de® nesspectral resolution as the width of three spectral points(i.e., twice the spectral point spacing). According to Eq.1, the point spacing of the 4K SB spectra is 3.86 cm 2 1,and the corresponding resolution is 7.71 cm 2 1. Figure 4Bdisplays the 0±3000 cm 2 1 range of the 4K SB spectrumobtained by Fourier processing the interferogram shownin Fig. 3B. The 8K interferogram data were used in theconstruction of other data sets of the same compositionas in Table I, but with different resolutions. The variouslower resolutions were obtained by truncating the 8K in-terferograms to 4K, 2048 (2K), or 1024 (1K) points. Forexample, a 4K interferogram is obtained by truncatingthe 8K interferogram to the ® rst 4K data points. Figures3C, 3D, and 3E show examples of 4K, 2K, and 1K in-terferograms obtained from an 8K interferogram (Fig.3B) by the above procedure, respectively, while Figs. 4C,

4D, and 4E show the 0±3000 cm 2 1 range of the corre-sponding SB spectra. The numbers of points in thesespectra are 2K, 1K, and 512 (1/2K), respectively. Thepoint spacing of the spectra changes according to Eq. 1,because the number of data points changes and the max-imum observable digitized frequency remains the same.It is evident from Fig. 4 that, as the spectral resolutiondecreases, the loss of information in the SB spectrumincreases.

One additional spectral data set was generated by zero-® lling the 8K interferograms to a length of 16K beforeperforming the Fourier processing step. This approachimplements an interpolation procedure that halves thespectral point spacing to 1.93 cm 2 1. This procedure canincrease the photometric accuracy of the spectrum andwas implemented to evaluate its effect on the pattern rec-ognition results.

The two vertical lines in Fig. 4 show the 100 cm 2 1 SBspectral region between 950 and 1051 cm 2 1 used for anal-ysis in the current study. Figure 5 shows the 1250±750cm 2 1 region of the corresponding absorbance spectra, ob-tained by ratioing the SB spectra in Fig. 4 with suitable,similarly processed background spectra. Loss of infor-

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FIG. 5. The 1250±750 cm 2 1 segment of absorbance spectra obtainedby ratioing the single-beam spectra in Fig. 4 and suitable backgrounds.

TABLE II. Spectral point spacing of data sets.

Interferogramlength

Single-beamspectrum length

Point spacing(cm 2 1)

16394 8192 1.938192 4096 3.864096 2048 7.712048 1024 15.601024 512 30.86

mation with the decrease in resolution is more apparentin Fig. 5. Table II shows the details of the data sets usedin this study including the number of data points in theinterferogram, the number of data points in the SB spec-trum, and the spectral resolution. The data sets describedin Table I were assembled separately for the spectra pro-duced from the 16K, 8K, 4K, 2K, and 1K interferogramdata.

Overview of Methodology. The data analysis meth-odology employed in this work utilizes short segments ofSB spectra that contain analyte information. Pattern rec-ognition methods are then applied to these spectral seg-ments to obtain an automated yes/no decision regardingthe presence of the analyte. Since the methodology isbased on the direct analysis of segments of the SB spec-tra, a separate reference or background measurement isnot required.

The spectral segments can be treated as vectors of npoints. These segments encode both the intensities andshapes of bands in the SB spectra. Each vector can berepresented as a point or ``pattern’ ’ in n-dimensionalspace, where the coordinate axes correspond to speci® cspectral resolution elements. These points in n-dimen-

sional space cluster in different regions on the basis ofwhether the pattern has analyte information or not. Clus-tering of data points in higher dimensional space allowsthe use of pattern classi® cation methods to make a yes/no decision regarding the presence of the analyte.

Principal component analysis (PCA) allows visualiza-tion of a higher dimensional data space in lower dimen-sions by projecting the data points to lower dimensionswhile preserving the inter-point relationships among thedata points. Figure 6 is a plot of the ® rst and secondprincipal components of the 100 cm 2 1 segments of thetraining data set shown in Table I. The ® gure clearlyshows the separate clustering of DIMP-actives andDIMP-inactives (DMMP-actives and the pure back-grounds).

The PLDA pattern recognition method used in this re-search18,19 is based on the sequential construction of linearseparating surfaces or discriminants that de® ne regions ofthe data space occupied by points belonging to speci® ccategories of data (e.g., analyte-active and analyte-inac-tive). The linear discriminants together approximate anonlinear surface separating the different data categories.These discriminants are moved to optimal locations byusing a numerical optimization method such as Simplexoptimization. The ® rst discriminant is calculated and op-timized to separate as many DIMP-active patterns as pos-sible. Any misclassi® ed DIMP-active patterns are heavilypenalized, resulting in the so-called ``single-sided’ ’ dis-criminant. This discriminant de® nes a boundary such thatonly DIMP-active patterns are on the ``pure’ ’ side of theboundary, while a mix of DIMP-active and DIMP-inac-tive patterns are on the ``mixed’ ’ side. After optimizationof the discriminant, DIMP-actives on the pure side areremoved from further consideration. A second discrimi-nant is calculated and optimized to separate additionalDIMP-active patterns from the mixed group. This pro-cedure is repeated until no more DIMP-active patternscan be separated.

An n-dimensional vector corresponding to a new orunknown SB spectrum can be classi® ed or assignedmembership by computing the orientation of the pointrelative to the discriminant. This procedure results in thecalculation of a parameter called the discriminant score.The discriminant score is a threshold value computed bythe application of the piecewise linear discriminant to thespectral segment. Spectra that produce discr im inantscores greater than zero are judged to contain the DIMPsignature, based on the orientation of the pattern withrespect to the previously computed discriminant surface.The percentage of DIMP-actives correctly classi® ed (dis-criminant scores . 0) is used as the measure of spectralselectivity. The performance of the methodology is gen-erally judged by considering both the percentage of


FIG. 6. Principal component scores plot of training set of data set A displaying the projection of the 951±1050 cm 2 1 single-beam spectral segmentsonto the ® rst two principal components. DIMP-actives are plotted as hexagons, while DIMP-inactives are plotted as triangles.

TABLE III. Details of data set B containing mixture spectra.

Interferogramtype

Trainingset

Predictionset Total

DIMP 3200 2520 5720DIMP 1 DMMP 800a 630 1430Background 6000b 10500 16500(DMMP) (2647)c (2303) (4950)

Total 10000 13650 23650

a Total of 20% DIMP-actives were replaced with mixture interfero-grams.

b Total number of pure backgrounds and DMMP-actives.c Number of DMMP-actives present as background.

DIMP-actives correctly classi® ed and the percentage offalse detection (DIMP-inactives incorrectly classi® ed asDIMP-actives). In all the pattern recognition experimentsperformed, the false detection rate was well below 1%,and therefore, the DIMP-classi® cation percentage aloneis used as the criterion for evaluation of methodology.

Overview of Parameter Optimization. The spectralsegment used in this study for pattern recognition anal-ysis was either the 951±1050 cm 2 1 region or a subset ofthis range. Two variables optimized were the length andposition of the segments. These parameters alter the spec-tral selectivity that is available to the pattern recognitionanalysis. A factorial design study was used to optimizethese variables. The ® ve different values for segmentlength were 100, 80, 60, 40, and 20 cm 2 1. The numberof actual data points in these spectral segments varieddepending on the spectral resolution. The segment widthof 100 cm 2 1 had one segment location (951±1050 cm 2 1).For the 80 cm 2 1 width, the ® rst segment location was951±1030 cm 2 1. This window was moved by 10 cm 2 1

until the maximum of 1050 cm 2 1 was reached. Thus,there were three segment locations in the 951±1050 cm 2 1

range (951±1030, 961±1040, 971±1050 cm 2 1). Similarly,there were ® ve segment locations of 60 cm 2 1 width, sev-en segment locations of 40 cm 2 1 width, and nine segment

locations of 20 cm 2 1 width. Thus, there were 25 PLDAexperiments for a data set with a particular resolution.With ® ve different resolutions, a total of 125 PLDA ex-periments were conducted for each data set. The patternrecognition results for all the data sets were analyzed toestablish the optimal spectral resolution.

Data Sets. Examination of the pattern recognition re-sults obtained from data set A indicated that the data setswere not very challenging for analyses. Therefore, otherdata sets with progressively increased dif® culty were as-sembled, with the use of not only pure component andbackground spectra but also synthetic mixture spectra ob-tained by averaging DIMP and DMMP interferograms invarying compositions. The averaged interferograms werethen Fourier processed to obtain the synthetic mixturespectra. The total number of interferograms for each classin the training and prediction sets of all the data setsremained the same.

Data set B was obtained by replacing 20% of theDIMP-active spectra with mixture spectra. The mixturespectra were obtained by averaging one DIMP and oneDMMP interferogram before Fourier processing. Inter-ferograms from three levels of concentration of DIMP(8.1, 18.0, and 38.7 ppm-m) and DMMP (13.5, 31.8, and64.5 ppm-m) were used. Interferograms of 5.0 ppm-mDIMP were not used for the reason that the weakestDIMP data may be near the limit of detection. It wasthought that reduction in the DIMP concentration throughaveraging might produce spectra with undetectable DIMPsignatures. The composition of data set B is shown inTable III.

Data set C was obtained by replacing another 5% ofthe pure DIMP-actives from data set B with new mixturedata, bringing the total percentage replaced to approxi-mately 25%. Interferograms with concentrations of 5.0and 8.1 ppm-m for DIMP and 9.1 and 13.5 ppm-m forDMMP were used for generating the mixture data. TheDIMP data used in the construction of this data set have

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TABLE IV. Details of data set C containing mixture spectra.

Interferogramtype

Trainingset

Predictionset Total

DIMP 3000 2362 5362DIMP 1 DMMP 800 630 1430DIMP 1 DMMP (New) 200a 158 358Background 6000b 10500 16500(DMMP) (2647)c (2303) (4950)

Total 10000 13650 23650

a Approximately 5% of DIMP-actives were replaced with new mixtureinterferograms thus bringing the total replaced to 25%.


TABLE V. Details of data set D containing mixture spectra.

Interferogramtype

Trainingset

Predictionset Total

DIMP 2800 2204 5004DIMP 1 DMMP 1000 788 1788DIMP 1 DMMP 1

DMMP (New) 200a 158 358Background 6000b 10500 16500(DMMP) (2647)c (2303) (4950)

Total 10000 13650 23650

a Approximately another 5% DIMP-actives were replaced with newmixture interferograms thus bringing the total replaced to 30%.


FIG. 7. Pattern recognition results for 100 cm 2 1 wide single-beamspectral segments.

weaker absorptions than those used in data set B and thusthe resulting signal-to-noise (S/N) ratio is smaller thanthat of data set B. The composition of data set C , whichis more challenging than either data set A or B, is shownin Table IV.

Data set D was obtained by replacing another 5% ofthe pure DIMP-actives from data set C with new mixturedata, bringing the total percentage replaced to approxi-mately 30%. The mixture spectra were obtained by av-eraging one DIMP-active with two DMMP-active inter-ferograms before the Fourier processing step. DIMP datawith concentrations of 5.0, 8.1, and 38.7 ppm-m wereused, while all four concentrations were used for DMMP.Since one DIMP-active and two DMMP-actives were av-eraged to generate the mixture interferograms, the newmixture spectra had lower S/N ratios than those generatedpreviously. The composition of data set D is shown inTable V.

Analysis of Data Set A. Two discriminants wereenough in most of the cases to almost completely separatethe DIMP-actives from the DIMP-inactives for all thedata sets. For this reason, all pattern recognition resultspresented are based on piecewise linear discriminantsconsisting of two individual linear discriminant functions.Generally, the training and prediction results tracked eachother, although the training percentage was slightly betterthan the prediction percentage.

The 100 cm 2 1 Wide Segment. Figure 7 shows thepattern recognition results for data sets with differentspectral resolutions. The percentage of DIMP-actives cor-rectly classi® ed is plotted for both training and predic-tion. For the data sets with spectral point spacings of1.93, 3.86, and 7.71 cm 2 1, the training and predictionpercentages are comparable. The analyte informationpresent in the spectral segment provides enough selectiv-ity to ensure that the spectral resolution does not haveany effect on the pattern recognition performance. Thefalse detection rate is less than 0.5%. The training andprediction classi® cation percentages decrease for the dataset with a point spacing of 15.60 cm 2 1, which can beattributed to the decreased DIMP information in the spec-tral segment, resulting in reduced selectivity (see Figs. 4and 5). For the data set with a point spacing of 30.86cm 2 1, the classi® cation percentages decrease further witha corresponding increase in the percentage of missed de-tection. The highest percentage of DIMP-actives correctlyclassi® ed in prediction for this data set is about 54%.Thus, selectivity is at the lowest and accounts for severedegradation in the results. The same trend was noticed

for all segment widths for this data set; therefore, no fur-ther results for this data set are discussed.

The 80 cm 2 1 Wide Segment. Figure 8 shows the pat-tern recognition results for the data sets with differentspectral resolutions. As described earlier, there were threesegment locations, and the ® gure shows the results for allthe locations. The results are very similar to those ob-tained with the 100 cm 2 1 segment. For the data sets withpoint spacings of 1.93, 3.86, and 7.71 cm 2 1, the resultsare comparable and are insensitive to segment location.For the data with 15.60 cm 2 1 point spacing, the perfor-mance begins to decrease as the segment location movesaway from the initial position. As the segment locationmoves away, DMMP spectral information increases witha corresponding decrease in the DIMP information. Theability of the discriminants to classify DIMP correctlydecreases.

The 60 cm 2 1 Wide Segment. Figure 9 shows the re-sults for all ® ve segments with a width of 60 cm 2 1. Theresults are very similar to those obtained with the 100and 80 cm 2 1 wide segments. The pattern recognition re-sults are comparable for the data sets with point spacingsof 1.93, 3.86, and 7.71 cm 2 1. However, the performancestarts to decrease in the 991±1050 cm 2 1 spectral segment.This result can again be attributed to both a decrease inDIMP spectral information and an increase in DMMPspectral information. For the data set with a point spacingof 15.60 cm 2 1, the performance initially increases, reach-


FIG. 8. Pattern recognition results for 80 cm 2 1 wide single-beam spec-tral segments.

FIG. 9. Pattern recognition results for 60 cm 2 1 wide single-beam spec-tral segments.

es a maximum, and then decreases as the segment loca-tion moves away from the initial position. Therefore,there is an optimal segment location for this data set forwhich performance is much better. The percentage of theDIMP-actives correctly classi® ed for the 961±1020 cm 2 1

optimal segment is 93.6%, which is slightly lower thanthe corresponding classi® cation percentages for the otherdata sets.

The 40 cm 2 1 Wide Segment. Figure 10 shows theresults for all seven spectral segments of data set A . Onecan see a trend in the pattern recognition results. Theperformance increases, reaches a maximum, and then de-creases. The peak performance is seen in the spectral re-gion with maximum DIMP information and minimumDMMP information. The performance is comparable forthe data sets with point spacings of 1.93, 3.86, and 7.71cm 2 1, while it decreases for the data set with a pointspacing of 15.60 cm 2 1. The same explanation given forthe 60 cm 2 1 wide segment holds here also.

The 20 cm 2 1 Wide Segment. Figure 11 shows theresults for all nine spectral segments of data set A . Thetrend seen with the 40 cm 2 1 wide segments is more pro-nounced here. The peak performance occurs in the spec-tral regions where there is maximum DIMP information

and minimum DMMP information. The performancegradually tails off on both sides of the peak due to agradual decrease in DIMP information content and cor-responding increase in DMMP information content.

The results of the analysis of data set A clearly revealthat the pattern recognition performance is not affectedby spectral resolution for data sets with point spacings of1.93, 3.86, and 7.71 cm 2 1, while the performance de-creases for the data set with 15.60 cm 2 1 point spacing.At a point spacing of 30.86 cm 2 1, no reliable DIMP clas-si® cations can be made. It is evident that using a 3.86 or1.93 cm 2 1 point spacing does not increase the selectivity,as indicated by the lack of improvement in the patternrecognition performance. For 15.60 and 30.86 cm 2 1 pointspacings, the selectivity decreases as re¯ ected by thepoorer pattern recognition results. Therefore, it can beconcluded that comparable or acceptable pattern recog-nition results can be obtained by using data with a pointspacing of 7.71 cm 2 1 (nominal 16 cm 2 1 resolution).

Analysis of Data Set B. The experimental designstudy used in the analysis of data set A was repeated withdata set B. The results obtained were virtually identicalto those produced by data set A . Thus, inclusion of datacontaining the signatures of both DIMP and DMMP did

1390 Volume 53, Number 11, 1999



not make the data analysis more dif® cult, as was antici-pated. The methodology is robust enough to reject theinterfering, strong DMMP band to produce comparableresults. These results reinforce the conclusion that datasets with a point spacing of 7.71 cm 2 1 provide suf® cientselectivity in order to obtain good pattern recognition re-sults.

Analysis of Data Set C. The same experimental de-sign study was performed with data set C . The resultsobtained with this data set were very similar to thoseproduced by data set B. Again, data with a point spacingof 7.71 cm 2 1 were observed to give comparable or ac-ceptable pattern recognition performance.

Analysis of Data Set D. This data set contained mix-ture spectra obtained by averaging not only one DIMPand DMMP interferogram each, but also one DIMP andtwo DMMP interferograms. Thus, the signal due toDIMP is much smaller in the mixture data, thus makingthe data set more dif® cult to analyze.

The experimental design study described above wasimplemented with this data set. However, because anal-ysis of the results revealed that they were again verysimilar to those obtained with data sets A , B, and C , they

are not discussed in detail. This observation again lendssupport to the conclusions drawn above.

CONCLUSION

The results described in this paper demonstrate thatpassive FT-IR data collected with a nominal spectral res-olution of 16 cm 2 1 will provide enough selectivity in or-der to get optimal pattern recognition results, rejectingadjacent interfering spectral bands and the background.Collection of data with higher resolution or data in whichzero-® lling has been used to reduce the spectral pointspacing does not increase the selectivity for typical com-pounds of the bandwidths investigated here. However,lower resolution data deteriorates the selectivity, as evi-denced by poorer pattern recognition results. Therefore,it can be inferred that collection of data with a nominal16 cm 2 1 spectral resolution for passive FT-IR remotesensing experiments provides acceptable or comparablepattern recognition classi® cation without compromisingselectivity. The match of the optimal resolution to theFWHH of the analyte bands (e.g., the DIMP band con-sidered here with an FWHH of 17 cm 2 1) is consistentwith previous studies that focused on quantitative anal-


ysis.15 This result helps to substantially reduce both thestorage space needed to store high-resolution data and thetime required to collect the data. Both factors are impor-tant in FT-IR remote sensing applications that form themotivation for the current work.

A further advantage of reducing the size of the col-lected interferogram is the corresponding reduction innoise in the SB spectrum. Since the noise in the inter-ferogram is considered to be constant throughout itslength, a longer interferogram will contain more totalnoise to be spread across the ® xed spectral bandwidth.Reducing the interferogram length by a power of two isexpected to reduce the noise in the SB spectrum by afactor of 2½. Furthermore, since a shorter interferogramrequires a shorter scan time, additional signal averagingcan be performed in the same total data acquisition time.

In the experiments performed in the current work, sin-gle-scan interferograms were used as is typical in manyFT-IR remote sensing applications, and the spectra cor-responding to each resolution level were obtained fromthe same interferogram. The spectra at lower resolutionthus received the bene® t of lower noise levels accordingto the 2½ relationship described above. This fact doescomplicate the interpretation of the results, since the dif-ference in the pattern recognition results can be attributedto a combination of changes in both resolution and noiselevels. The key factor in considering this point is thesimilarity in the pattern recognition results for data setsA through D . These data sets differed signi® cantly in theDIMP signal strength, and thus, changes in the noise lev-el would be expected to have the greatest effect on dataset D in which the DIMP signal strength was the weakest.However, the parallel nature of the results from the fourdata sets suggests that the resolution rather than the noiselevel was the controlling factor in determining the patternrecognition performance.

Finally, the methodology described here for detectingDIMP has advantages speci® c to the remote sensing ap-plication. In remote sensing experiments, the natural var-iation in the meteorological conditions affects the infraredbackground radiation emitted by various terrestrial ob-jects. Collecting representative and stable backgrounds inpassive FT-IR remote sensing experiments is impossible.The methodology implemented here does not require col-lection of stable background interferograms because it

uses SB spectra for data analysis that are not ratioed ordifference spectra that are typically used in conventionalanalyses. In addition, the methodology requires only asmall segment of the single-beam spectrum containinganalyte information, which signi® cantly reduces the com-putation time required to analyze the data.

ACKNOWLEDGMENTS

This research was supported by the Department of Army under Con-tract W-31-109-Eng-38. The authors wish to acknowledge Scott E. Car-penter and Roger J. Combs for helpful discussions and Susan Machafor collecting the data used in this research.

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