Volume 52, Number 3, 1998 APPLIED SPECTROSCOPY 3750003-7028 / 98 / 5203-0375$2.00 / 0q 1998 Society for Applied Spectroscopy

Generation of Synthetic Background Spectra by Filteringthe Sample Interferogram in FT-IR

LUIS H. ESPINOZA, THOMAS M. NIEMCZYK,* and BRIAN R. STALLARDDepartment of Chemistry, University of New Mexico, Albuquerque, New Mexico 87131 (L.H.E., T.M.N.); and Sandia NationalLaboratories, Albuquerque, New Mexico 87185-0980 (B.R.S.)

The calculation of an absorbance spectrum depends on the mea-surement of a blank, or background spectrum. In many cases, suchas the determination of atmospheric constituents with the use ofopen-path Fourier transform infrared spectroscopy (FT-IR) or thedetermination of water vapor in a gaseous sample, it is very dif® cultto obtain a good background spectrum. The dif® culty is due to thefact that it is nearly impossible in these situations to measure aspectrum with no analyte features present. We present a method ofgenerating a background spectrum based on ® ltering the analytefeatures from the sample spectrum. When the ® ltering method isused, the accuracy of the results obtained is found to be dependentupon the analyte peak width, peak height, and type of ® lter em-ployed. Guidelines for the use of this background generation tech-nique for quantitative determinations are presented.

Index Headings: Fourier transform infrared spectroscopy; Gas-phase infrared spectroscopy; Background correction; Syntheticbackground.

INTRODUCTION

There are countless applications of spectroscopy whereabsorbance of an analyte is related to its concentrationby application of Beer’s law. The calculation of an ab-sorbance spectrum depends on the measurement of abackground spectrum. In most cases, the measurement ofa background spectrum is straightforward. There are,however, some spectroscopic applications where the mea-surement of a background spectrum is dif® cult. Such ap-plications include the determination of atmospheric com-ponents with the use of open-path Fourier transform in-frared (FT-IR) spectroscopy,1± 3 or determination of theconcentration of water vapor in a gaseous sample withinfrared spectroscopy. Ideally, a background spectrum isobtained by measurement of a blank (i.e., a sample thatcontains everything except the analyte). In open-path at-mospheric studies it is nearly impossible to eliminate theanalytes from the optical path of the measurement, andin the case of water vapor measurement, it is very dif® -cult to completely remove all water from the optical pathof the spectrometer.

A number of approaches have been developed to dealwith the problem of generating a background spectrumin these situations. In the case of water vapor determi-nation in a closed cell, the water vapor in the spectrom-eter can be reduced to 1± 10 ppb by using an evacuablespectrometer. More commonly, however, approaches thatinvolve ® tting a baseline to a single-beam spectrum areused.4 Baselines employing multiple straight lines as wellas high-order polynomials have been used.5 Note that the

Received 16 January 1997; accepted 26 September 1997.* Author to whom correspondence should be sent.

result of this baseline ® t is the removal of the high-fre-quency information, the narrow gas-phase absorptionpeaks, from an otherwise broad, slowly changing spec-trum.

In 1979, Hirschfeld suggested that a background spec-trum could be generated by removing the narrow absorp-tion bands due to gaseous molecules in the optical pathof the spectrometer, or in the sample cell, by ® ltering thehigh-frequency information from the single-beam spec-trum.6 The very small and narrow absorption bands, dueto a low concentration of a gaseous specie in the opticalpath of the spectrometer, have a very broad representationin the interferogram. Thus, they contribute very little tothe centerburst. A broad spectral feature contributes sig-ni® cantly to the centerburst. Therefore, a Fourier trans-form of the centerburst produces a single-beam spectrumin which the narrow spectral features have been sup-pressed. The ® ltering operation is most conveniently car-ried out by truncating or weighing the interferogram priorto performing the Fourier transform. We have investigat-ed this approach to the development of a `̀ synthetic back-ground’ ’ spectrum for the speci® c case of determinationof trace water in a gaseous sample. We present a proce-dure for performing the ® ltering operation and discussthe conditions under which the process can be used toproduce accurate and precise determinations.

EXPERIMENTAL

All spectral data were collected with a Nicolet Model800 FT-IR spectrometer. Data were collected with anInSb detector and KBr beamsplitter. The gas cell used inthese experiments was an 8 m Axiom cell consisting offour 2 m, 31.75 mm diameter nickel-coated brass tubesin a folded con® guration. The gas handling system con-sists of a specially designed and constructed apparatuswith moisture generation and reference measurementcomponents. The entire apparatus has been previously de-scribed.7

All data were collected at a nominal resolution of 1cm2 1, which corresponds to 24 576 point interferograms,with the use of a ® xed 10 min (620 scans) signal aver-aging period. The samples, unless otherwise noted, were1.0 ppm water in nitrogen. The experimental data wereprocessed on the Nicolet computer prior to transfer to aPC, where the classical least-squares (CLS) calibrationswere carried out. The data processing used standard Ni-colet routines for Happ± Genzel apodization.

The program to generate the synthetic backgroundspectra was written in Array Basic to operate within theGRAMS (Galactic Industries) environment. The programinitially ® nds the zero-path-difference (ZPD) point in the

376 Volume 52, Number 3, 1998

FIG. 1. Single-beam spectrum obtained after Fourier transformation ofthe multiplication of an interferogram with a 200 point width boxcarfunction.

FIG. 2. Single-beam spectrum obtained after Fourier transformation ofthe multiplication of an interferogram with a 78 point Gaussian func-tion.

FIG. 3. Sample single-beam spectrum of 500 ppb H2O.

interferogram, then multiplies the interferogram by the® lter function centered on the ZPD point. This process issimilar to apodization. The Gaussian ® lters are charac-terized by their width in interferogram points (1 cm2 1

resolution). The width is the full width at 1/e height. Thesingle-beam background spectra were then generated byFourier transforming the ® ltered interferogram.

A series of modeling studies using well-de® ned syn-thetic absorbance spectra were carried out to determinethe effects of the ® ltering operation on quantitative de-terminations. The modeling studies were carried out withprograms written in Matlab (The Math Works). Happ±Genzel apodization was applied to all sample interfero-grams prior to generating absorbance spectra. Two-sidedFourier transforms were employed for all model data.The CLS calibrations were carried out with software writ-ten in Array Basic to operate in the GRAMS environ-ment.

RESULTS AND DISCUSSION

A number of considerations must be taken into accountwhen generating the synthetic background spectrum.Most important are the form and width of the ® lter func-tion. The most straightforward approach to ® ltering theinterferogram is to use a boxcar function. The single-beam synthetic background spectrum that results from themultiplication of the interferogram by a 200 point widthboxcar function is shown in Fig. 1. Note the `̀ ringing’’in the spectrum. The ringing causes errors in determina-tions based on the absorbance spectra calculated fromthese synthetic background spectra. The ringing can beavoided with the use of a wider boxcar ® lter, but by thetime the ringing becomes insigni® cant, the boxcar ® lteris wide enough to let enough high-frequency informationthrough so that the water peaks, though somewhat muted,become visible in the synthetic backgrounds. No suitablecompromise between the ringing and incomplete ® lteringof the water peaks could be found when a boxcar ® lterwas used.

The ringing problem noted above is similar to that seenin high-resolution spectra when boxcar apodization isused. The problem is avoided with the use of differentfunctional forms for the apodization; one potentially use-ful ® lter function is a Gaussian. An interferogram, the

result of signal averaging 15 scans of the interferometerfor a 400 ppb sample of water, was multiplied by aGaussian function (maximum value of 1.0) centered atthe ZPD point. The single synthetic beam backgroundspectrum resulting from a ® ltering with a 78 point wideGaussian function is shown in Fig. 2. The entire single-beam sample spectrum and a blowup of the water region(3600± 3900 cm2 1) are shown in Fig. 3. The absorbancespectra obtained by ratioing the sample spectrum to thesynthetic background spectra created with two different-width Gaussian ® lters are shown in Fig. 4. Note that thewater vapor peaks in Fig. 4a and 4b look similar, butthere is a signi® cant difference in the baselines. Presum-ably, the baseline variation in Fig. 4a is due to the ® lterbeing too narrow to accurately reproduce the backgroundspectrum. A peak-by-peak CLS analysis8 of data pro-cessed by either width of the Gaussian ® lter produces agood calibration, but that might not always be the case.The accuracy of the CLS calibration is affected by theanalyte peak height and width, and the relationship ofthose variables to the width of the ® lter function.

The effects of these variables can most easily be ex-amined in a modeling study where the effects of analytepeak width, peak height, and ® lter function can be readilydetermined. The basic approach taken in the modelingstudy was to add peaks of known height and width to awater-feature-free single-beam background spectrum,

APPLIED SPECTROSCOPY 377

FIG. 4. Absorbance spectra obtained with the use of 78 and 233 pointwide Gaussian ® lters.

FIG. 5. Model single-beam spectrum showing added Gaussian peak ofknown peak height and peak width.

perform the ® ltering operation, and take note of the ef-fects of the ® ltering operation on the recovery of thewell-de® ned peak.

The water-feature-free single-beam background spec-trum was generated by recording a single-beam spectrumafter the spectrometer and sample cell had been thor-oughly dried. The residual water features, correspondingto about 400 ppb of water in the optical path of the spec-trometer, in this single-beam spectrum were removed byapplication of a 310 point wide Gaussian ® lter to theinterferogram prior to Fourier transforming to producethe spectrum. A model spectrum was then created by add-ing a Gaussian peak of speci® c height and width to thissingle-beam background. Such a model single-beam sam-ple spectrum is shown in Fig. 5. The overall shape of thespectrum in Fig. 5 is the result of the use of a Barr As-sociates bandpass ® lter (3448± 4081 cm2 1) to limit thebandpass of the spectrometer to the region of the waterabsorption.

The values (peak height and peak width) of the absor-bance peaks selected for the modeling are in the rangeof those actually measured in an experiment monitoringtrace water contamination in semiconductor grade gases.We have found that optimal quantitative results areachieved when making determinations from these gas-phase IR data via the use of a CLS calibration.7 Thus theerrors in quanti® cation due to the generation of the syn-thetic background were also determined with a CLS cal-ibration. In practice, the CLS model is applied across anumber of the analyte bands in the spectral data. Muchof the precision improvement achieved through the useof CLS calibration, when compared to a univariate de-termination, is the result of signal averaging across theseveral bands. The modeling studies are limited to a sin-gle band, with the assumption that a suite of bands, oflike strength and width, would be affected in a similarmanner by the background generation process.

A CLS calibration ® ts a pure component spectrum tothe unknown spectrum. In the modeling studies, the purecomponent spectrum was based on a synthetic absor-

bance spectrum of 0.1 absorbance unit peak height andappropriate peak width. The synthetic single-beam spec-trum was produced with the addition of a Gaussian fea-ture to a water-free single-beam background spectrum.The model absorbance spectrum was calculated by takingthe log of the ratio of the water-free single-beam back-ground to the synthetic single-beam spectrum. This mod-el absorbance spectrum should be perfect, as it is createdby ratioing a background plus a well-de® ned Gaussian tothe identical background.

The modeling studies were carried out by performingthe following steps: (1) adding the Gaussian peak ofknown height and width to the water-free single-beambackground model spectrum; (2) inverse Fourier trans-forming to produce an interferogram; (3) performing the® ltering step to produce a synthetic background interfer-ogram; (4) Fourier transforming to produce the syntheticbackground; (5) ratioing the model spectrum to the syn-thetic background to produce a model absorbance spec-trum; and (6) applying the CLS calibration to the modelspectrum to return a concentration. CLS modeling as-sumes a linear relationship between concentration and ab-sorbance, an assumption that has been shown to be validfor the range of absorbances modeled. The relative errorin the concentration is equivalent, on the basis of thelinear relationship between absorbance and concentration,to the relative error in absorbance. The CLS calibrationreturns a number that is directly proportional to concen-tration, but in this case concentration is totally arbitrary,i.e., the Gaussian absorption peak is arti® cial. Thus, allCLS results were maintained in `̀ CLS units’ ’ and errorswere reported in relative terms [i.e., (correct answer-cal-culated answer)/correct answer].

The errors measured that result from the generation ofthe synthetic background are a function of the width ofthe ® lter function used on the interferogram, the strengthof the absorbance peak, and the absorbance peak width.Figures 6a and 6b show the relative error measured as afunction of the absorbance peak height and peak widthfor two different ® lter functions. The ® lter function usedin Fig. 6a was a 156 point wide function, which corre-sponds to about 230 cm2 1 resolution, and the ® lter func-tion used in Fig. 6b was 1244 points wide, which cor-responds to approximately 28 cm2 1 resolution. When oneis using the 156 point wide Gaussian ® lter function, er-

378 Volume 52, Number 3, 1998

FIG. 6. Plots showing the relative errors as a function of the absor-bance peak height and peak width for 156 (a) and 1244 (b) point ® lterwidths.

FIG. 7. Plot showing the relative error vs. ® lter width for an absorptionpeak of 0.002 absorption unit height and different peak widths.

FIG. 8. Water vapor spectra showing two absorption peaks generatedby using different numbers of points in the Gaussian ® lter.

rors greater than 1% are only seen for the peaks withwidths greater than 8 cm2 1, and then only for the weakest(smallest absorption) of these peaks. The errors noted forthe 1244 point wide Gaussian ® lter function, shown inFig. 6b, are much more signi® cant. Again, however, theerrors are much more signi® cant for the wider peaks,reaching 50%. Relatively little error is seen for the peaksof 1 and 2 cm2 1 and width. Plots for ® lter functions in-termediate to these look similar; i.e., there are insigni® -cant errors for narrow absorption peaks regardless of theabsorption strength, but signi® cant errors for wider peaks.Similar plots from the use of ® lter functions wider than1244 points show signi® cant errors regardless of the ab-sorption peak height or peak width.

Figure 7 is a plot of relative error vs. ® lter width foran absorption peak that is 0.002 absorbance units highand varying in width. The general trend shown in Fig. 7is that seen in Figs. 6a and 6b; i.e., errors are much moresigni® cant for broader peaks. Note, however, that thereare minima in the curves for the peaks of 4 and 8 cm2 1

widths. The reason for the minimum is that when a ® lterfunction is used that is too narrow, the baseline in thebackground spectrum generated is not very smooth. Theundulating background affects broader peaks much moresigni® cantly than it does very narrow peaks. This is es-pecially the case when one uses a band-by-band CLScalibration, such as that used to process these data.

The practice of generating a synthetic background by® ltering the interferogram cannot be tested for absoluteaccuracy against true experimental data because all thecalibrations are based upon a linear relationship betweena value returned from the CLS analysis and a water con-centration based on a reference determination. We can,however, explore the background generation process andhow it changes the CLS value returned for a particularsample.

A CLS model was generated on the basis of the spec-tral data obtained from a 500 ppb sample of water innitrogen. The spectral data for this model were collectedat 1 cm2 1 resolution and a 10 min signal integration. TheCLS model was created for the two water absorptionpeaks at 3852.2 and 3854.1 cm2 1. The interferogram was® ltered with different width Gaussian ® lters. The resultsof three of these ® ltering operations are shown in Fig. 8.As noted above, very narrow ® lters result in curved base-lines. The 155 point ® lter, according to the modelingstudies above, ought be a ® lter width that produces good

APPLIED SPECTROSCOPY 379

FIG. 9. Plot showing the change in concentration as predicted by theCLS model against the number of points in the Gaussian ® lter.

quantitative results. Although no apparent differences ex-ist between the absorbance spectra produced with the 155and 1244 point ® lters, the wider ® lter does not entirelyremove the water features in the background. The spec-trum produced by the wider ® lters looks similar to thatproduced by intermediate ® lters, but the areas under thepeaks and the peak heights are decreased. This causes asigni® cant error when the data are subjected to CLS anal-ysis.

The change in the concentration as predicted by theCLS model in CLS units is plotted against the width ofthe Gaussian ® lter in Fig. 9. As can be seen, there is asmall error for extremely narrow ® lters, then a regionwith almost no error, followed by a region of increasingchange in the CLS value returned. As described above,relative errors in CLS units correspond directly to relativeerrors in concentration. Hence, use of ® lters with widthsin the intermediate region, i.e., the region of no CLSerror, will result in no concentration error.

CONCLUSION

It is dif® cult, if not impossible, to develop an appro-priate background spectrum to use in the generation ofan absorbance spectrum for some gas-phase samples. Themethod of ® ltering the high-frequency information, theresult of sharp absorption bands due to gas-phase species,from the interferogram and then using the ® ltered inter-ferogram to generate a synthetic background spectrum

produces good quantitative results as long as some guide-lines are followed. First, the ® ltering process can be suc-cessfully applied only when the absorption bands arevery narrow. Our results, both experimental as well asmodeling studies, indicate that there is no problem work-ing with data where the absorption bands are 2 cm2 1 orless in width, i.e., the typical width of small moleculegas-phase absorption spectra. Analogously, situationsmust be avoided where the single-beam background spec-trum has very narrow or sharp features, for the ® lteringprocess would distort or ® lter out these narrow features.Further, our results indicate that ® lters that are too narrowcause curving baselines and, hence, potential for error inthe data analysis step. Filters that are too wide do noteffectively ® lter out all the high-frequency information,thus resulting in changes in the peak heights when anabsorption spectrum is generated. The range of ® lters thatwe have found to work successfully are ® lters of 78points in width (corresponding to about 420 cm2 1 reso-lution) to 310 points in width (approximately 106 cm2 1

in resolution).

ACKNOWLEDGMENTS

We wish to thank David M. Haaland for suggesting this approachand, along with David Melgaard, developing the CLS software used.This work was performed in part at Sandia National Laboratories andwas supported by the U.S. Department of Energy under Contract DE-ACD4-94AL8500 and by SEMATECH.

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