Correcting Attenuated Total Reflection–Fourier Transform Infrared Spectra for Water Vapor and Carbon Dioxide

Correcting Attenuated Total Reflection–Fourier TransformInfrared Spectra for Water Vapor and Carbon Dioxide

SUSANNE W. BRUUN, ACHIM KOHLER, ISABELLE ADT, GANESH D. SOCKALINGUM,MICHEL MANFAIT, and HARALD MARTENS*Biochemistry and Nutrition Group, BioCentrum-DTU, Technical University of Denmark, building 224, Søltofts Plads, DK-2800 Kgs. Lyngby,

Denmark (S.W.B.); Center for Biospectroscopy and Data Modelling, Matforsk, Norwegian Food Research Institute, N-1430 Aas, Norway (A.K.,

H.M.); Unite de Sensometrie et de Chimiometrie, ENITIAA, BP 82225, 44322 Nantes Cedex 3, France (A.K.); Unite MeDIAN CNRS UMR 6142,

UFR Pharmacie, IFR 53, Universite de Reims Champagne Ardenne, 51 rue Cognacq-Jay, 51096 Reims Cedex, France (I.A., G.D.S., M.M.);CIGENE/IKBM, Norwegian University of Life Sciences, N-1430 Aas, Norway (H.M.); and The Royal Veterinary & Agricultural University, 1870

Frederiksberg C, Denmark (H.M.)

Fourier transform infrared (FT-IR) spectroscopy is a valuable technique

for characterization of biological samples, providing a detailed fingerprint

of the major chemical constituents. However, water vapor and CO2 in the

beam path often cause interferences in the spectra, which can hamper the

data analysis and interpretation of results. In this paper we present a new

method for removal of the spectral contributions due to atmospheric

water and CO2 from attenuated total reflection (ATR)-FT-IR spectra. In

the IR spectrum, four separate wavenumber regions were defined, each

containing an absorption band from either water vapor or CO2. From two

calibration data sets, gas model spectra were estimated in each of the four

spectral regions, and these model spectra were applied for correction of

gas absorptions in two independent test sets (spectra of aqueous solutions

and a yeast biofilm (C. albicans) growing on an ATR crystal, respectively).

The amounts of the atmospheric gases as expressed by the model spectra

were estimated by regression, using second-derivative transformed

spectra, and the estimated gas spectra could subsequently be subtracted

from the sample spectra. For spectra of the growing yeast biofilm, the gas

correction revealed otherwise hidden variations of relevance for modeling

the growth dynamics. As the presented method improved the interpre-

tation of the principle component analysis (PCA) models, it has proven to

be a valuable tool for filtering atmospheric variation in ATR-FT-IR

spectra.

Index Headings: Fourier transform infrared spectroscopy; FT-IR spec-

troscopy; Attenuated total reflection; ATR; Atmospheric correction;

Atmospheric absorptions; Principal component analysis; PCA.

INTRODUCTION

In biological sciences, Fourier transform infrared (FT-IR)spectroscopy has proven to be an important tool for measuringan overall chemical fingerprint of very different samples. Forthe monitoring of biological processes in fluids like fermen-tation and enzymatic reactions, the attenuated total reflection(ATR) FT-IR technique has turned out to be very useful.1 Thistechnique prevents saturation of the water peaks for aqueoussamples, as a micrometer scale path length is achieved. Thus,FT-IR spectroscopy is a versatile tool that allows fornondestructive simultaneous quantification of a rich diversityof chemical constituents (proteins, lipids, carbohydrates, freevs. bound water, etc.) and certain physical properties (e.g., lightscattering). The multi-component detection is beneficial, forexample, in the real-time monitoring of biofilms, growndirectly on the ATR crystal.2,3 The relevant information isextracted from FT-IR spectra by use of chemometric methods.

However, the analysis of FT-IR spectra is often hampered by

IR absorptions due to uncontrolled, varying amounts of watervapor and CO2 in the light path. The atmospheric absorption ofwater vapor demonstrates characteristic absorption bands, eachshowing a symmetric pattern of fine spectral lines andinvolving the excitation of a chemical bond vibration. As eachvibrational state is associated with many rotational levels (J),spectral lines appear symmetrically in two branches of theband, resulting from transitions involving DJ ¼þ1 and DJ ¼�1, respectively. These lines are high-frequent compared to theabsorptions from liquids and solids.4 For CO2, the absorptionlines are less resolved, and a high instrument resolution isneeded in order to see the individual lines of the CO2 bands.

These atmospheric absorptions represent an experimentalnuisance, creating unwanted but systematic patterns, whichoften cannot be completely avoided by purging of theinstrument with gaseous N2 or using background subtraction.The concentrations of water vapor and CO2 are likely to varybetween the background measurement and the samplescanning. This problem is, for example, encountered whena process is followed over a long time in the ATR cell (e.g.,biofilm development). For ATR-FT-IR measurements ofaqueous samples, evaporation from the sample itself mayincrease the humidity in the sample compartment and give riseto the problems, especially if the measurements are carried outat elevated sample temperatures. In this situation, the problemis not solved by purging, which is also expensive and timeconsuming.

The CO2 bands are not as wide as the water vapor bands andthe major band is found in a spectral region devoid ofabsorptions from the main biochemical components (lipids,proteins, and carbohydrates). On the other hand, the watervapor absorptions overlap with some important bands fromproteins and lipids, and, in particular, the presence of watervapor absorptions in the amide I region (1700–1600 cm�1)presents a problem in analysis of protein secondary structuresbased on the amide I band. Even small contributions fromwater vapor may hamper this analysis and lead to incorrectband assignments, as these absorptions are amplified by theresolution enhancement (e.g., by Fourier self-deconvolution).5

Thus, it appears necessary to correct the spectra for theatmospheric contributions in order to obtain useful sampleinformation or to improve accuracy and precision of the FT-IRcalibration models. The correction is also advantageous whenclassifying biological samples based on their FT-IR spectra, asthe presence of water vapor absorptions in, e.g., the in-formation-rich protein amide I region, may cause confusion.However, as the subbands of amide I show line widths

Received 3 April 2006; accepted 9 June 2006.* Author to whom correspondence should be sent. E-mail: [email protected].

Volume 60, Number 9, 2006 APPLIED SPECTROSCOPY 10290003-7028/06/6009-1029$2.00/0

� 2006 Society for Applied Spectroscopy

comparable to those of the water vapor lines, information maybe lost if simple low-pass filtering is used for reducing thewater vapor effects. Commonly, a gas absorption spectrum iscollected and stored in the beginning of each measurementseries, and the subtraction from each sample spectrum isaccomplished by use of an algorithm in the spectroscopicsoftware. The main problems associated with this approachrelate to difficulties in determining the correct subtractionfactor and in obtaining exactly the same gas composition andthe same band shapes for the reference and the samplespectrum.6 As regards the latter problem, the sample itself mayinfluence the spectral shape due to the influence on the beamgeometry. Also, temperature and pressure influence the shapeof the gas spectrum. In addition, a low instrument resolutioncauses distortion of the spectral lines and results in non-linearities.6

The present paper shows a model-based preprocessing toolfor ATR-FT-IR spectra to minimize water vapor and CO2

spectral contributions. Successful removal of these interfer-ences is demonstrated for different types of samples, measuredwith the same instrument.

NOTATION AND TERMINOLOGY

I means measured light intensity, while A means absorbance,defined as log10(I), or log10(I/I0), when mentioned explicitly.I(m) means measured intensity at m cm�1. Ai,k means estimatedabsorbance in sample i at wavenumber channel k.

EXPERIMENTAL

All measurements were performed on a Bruker Equinox 55FT-IR instrument, equipped with a liquid-nitrogen-cooledMCT detector, scanning from 4000 cm�1 to 600 cm�1. Thenominal instrument resolution was 4 cm�1, but the spectralreadings were recorded at 2 cm�1 intervals. Aqueous andbiofilm samples were measured on a horizontal ATR ZnSecrystal. Each spectrum resulted from coaddition of at least 128scans (if not otherwise mentioned) obtained in single-beammode. Background spectra were obtained on the empty sampleholder.

Four FT-IR experiments were carried out, as described in thefollowing. Gas model spectra for water vapor and CO2 wereobtained from Experiment 1 (providing a data set of onlyatmospheric absorptions) and Experiment 2 (providing a dataset also with liquid water absorptions). The model performanceis tested on a basic and a realistic/complex data set, obtainedfrom Experiments 3 and 4, respectively.

Experiment 1: Gas Calibration Measurements. A total of120 FT-IR spectra of various concentrations of water vapor andgaseous CO2 were obtained using an empty sample compart-ment, monitoring the gradual replacement of room air with N2

gas. The N2 purging was started after closing of the samplecompartment and spectra were recorded once a minute for 60minutes Each spectrum resulted from coaddition of 32 scans.This time series experiment was performed twice and the datawere used for estimating primary gas spectra.

Experiment 2: Water Calibration Extension Measure-ments. Milli-Q water (distilled and ion-exchanged) and varioussalt solutions of low concentrations (0.2–1.0 M) of NaCl,MgSO4, or NaClO4 (prepared in Milli-Q water) were measuredon the ATR crystal, mounted in a closed sample cell, whichallowed for temperature control by circulation of heating or

cooling water in the space around the ATR cell. A total of 205sample spectra were recorded with different levels of watervapor and CO2 in the sample compartment. Water wasmeasured at different temperatures between 8 and 60 8C, whilesalt solutions were measured at 15, 22, and 29 8C. The FT-IRinstrument was kept at room temperature in all measurements.These ATR-FT-IR spectra of aqueous solutions were used todefine secondary ‘‘nuisance’’ gas spectra and to developa between-regions calibration model (discussed later).

Experiment 3: Water Test Measurements. Water spectraat different temperatures and with different water vapor andCO2 levels were measured by placing Milli-Q water in theATR cell at one temperature (about 22 8C), closing the samplecompartment, and starting N2 purging. The spectra were read atconsecutive points in time while the sample was changedgradually towards another temperature (about 10 8C) by slowlydecreasing the temperature of the cooling water. The FT-IRinstrument itself was kept at room temperature. In total 25spectra were recorded in this time series. These spectra wereused for testing how well the ‘‘nuisance’’ gas modeling workedfor samples similar to some of the calibration samples.

Experiment 4: Yeast Cell Culture Test Measurements.Candida albicans (strain SC 5314, ATCC collection) wasgrown in 10 mL Sabouraud Medium (bioMerieux, France) for24 hours. Three hundred microliters (300 lL) of this culturewas added to 3 mL of fresh medium and placed on the ATRcrystal at room temperature (21 8C) and a biofilm was allowedto develop. Biofilm growth was monitored by ATR-FT-IRspectroscopy during 19 hours and a total of 58 spectra werecollected at intervals of 20 minutes throughout the growthperiod. Sixty-four scans were coadded for obtaining each finalspectrum. These samples were used for testing how thecorrection for water vapor and CO2 performed for samplespectra that were very different from the calibration samplespectra.

Determining Four Primary Gas Model Spectra. Thespectra in Experiment 1 were used for establishing the main gasabsorbance model. Component loadings for a two-componentbi-linear model were defined for the water vapor and CO2

regions by the following analysis: The two contiguous timeseries in Experiment 1 were generated in order to avoidpossible day-to-day variations in the instrument. Furthermore,to minimize even minute-to-minute instrument variationeffects, the temporal absorbance difference spectra betweenconsecutive spectral readings

Di;k ¼ Ai�1;k � Ai;k ð1Þ

were computed within each of the two time series, for spectra i¼ 2, 3, . . . at wavenumber channels k ¼ 1, 2, . . . , 1764(corresponding to the region 4000–600 cm�1).

The two H2O(g) ranges (k¼1:400; i.e., 4000:3231 cm�1 andk ¼ 1001:1450; i.e., 2072:1205 cm�1, see Table I) were

TABLE I. The four defined gas regions.a

Wavenumbers (cm�1) Absorption band

Water vapor region 1 4000–3231 Sym. and asym. stretching m1,3

Water vapor region 2 2072–1205 Bending m2

CO2 region 1 2442–2208 Asym. stretchingCO2 region 2 914–600 Bending

a Sym: symmetric. Asym: antisymmetric.

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modeled separately. The motive for this was to secure highflexibility in future gas-removal applications, since the tworegions are very different with respect to other componentsabsorbing there. (The two region models will then be linkedquantitatively; see below.) Likewise, two CO2 ranges (k ¼809:930; i.e., 2442:2208 cm�1 and k ¼ 1601:1764; i.e.,1400:600 cm�1) were modeled separately. In each of thesefour wavenumber regions an uncentered principal componentanalysis (PCA), i.e., a singular value decomposition (SVD) wasperformed. The first two principal component (PC) loadingvectors of Di,k¼k1:k2 were extracted, placed back in the commonwavenumber-basis 4000–600 cm�1 (outside the defined range,the value was set to zero), and saved as primary gas spectra forthat region.

Determining Secondary Gas Model Spectra. The perfor-mance of the primary gas model with 4þ4 gas components thusobtained from the spectra in Experiment 1 was then checked inthe water spectra from Experiment 2: The gas effects in thefour regions were estimated and corrected for as described inthe next section. However, the resulting gas-corrected spectraindicated some remaining high-frequency absorbance varia-tions in the water vapor and CO2 regions. It was thereforedecided to expand the gas model. High-frequency spectra weredefined as the gas-reduced water spectra minus their smoothedversions (smoothed with a 22 cm�1 wide moving-averagefilter). These high-pass filtered spectra showed one clearremaining high-frequent variation pattern in each of the twoH2O(g) regions and in the first CO2 region 2442:2208 cm�1

(the last CO2 region at the lower end of the spectrum was toonoisy for further modeling). One additional non-randomsecondary ‘‘nuisance’’ gas model spectrum was thus definedin each of these three wavenumber regions, as the first principalcomponent vector, obtained by SVD of each set of differencespectra.

As a result, the final gas models had a primary and twosecondary model spectra in each of the water vapor regions andin the first CO2 region, and a primary and one secondary modelspectrum in the last CO2 region, i.e., in total 11 gas modelspectra. Each of these spectra has non-zero values inside one ofthe four independently modeled gas regions, and zeroelsewhere in the 4000–600 cm�1 wavenumber range.

Correction for the Gas Model Spectra. The concentrationsof water vapor and CO2 in a measured spectrum of sample i,Ai,k, k¼ 1, 2, ... , K, may be approximated by the model shownin Eq. 2:

Ai;k ¼XJ

j¼1

cijkjk þ di;k þ ei;k ð2Þ

where ci,j represents the concentration ‘‘score’’ of gas element j¼ 1, 2, ... , J, respectively, whose absorbance at channel k is kj,k

Contribution di,k represents relevant but unmodeled chemicaland physical absorption effects in sample i’s absorbance atchannel k, e.g., from desired sample constituents or undesiredinstrument effects, while ei,k represents residuals, including thepresumably random measurement error at this channel.

In the present case, the gas parameters kj,k in Eq. 2 may nowbe considered known. The number of gas components J equals11; kj,k represents the four primary gas spectra obtained fromExperiment 1, representing ‘‘average’’ water vapor or CO2

spectra in the four above-mentioned wavenumber regions, andthe seven secondary gas component spectra from Experiments

1 and 2, representing other systematic gas contributions in thewavenumber regions.

Even though the elements in kj,k are known, it can bedifficult to assess their concentrations ci,j, because the‘‘interesting’’ chemical and physical absorption effects di,k

can create large alias errors in these gas score estimates. Onone hand, if the ‘‘interesting’’ absorbance contribution di,k inEq. 2 had been very small compared to the J gas contributionsci,jkj,k, then di,k could have been ignored, and the gasconcentration scores [ci,j, j ¼ 1, 2, ... , J] could have beenestimated by, e.g., least squares regression of absorbancemeasurements Ai,k on [kj,k, j ¼ 1, 2, ... , J] over wavenumberchannels k ¼ 1, 2, ... , K. On the other hand, if di,k had beenlarge but the spectra of the chemical constituents or physicalphenomena causing di,k had been known, then the problemcould have been solved by simply expanding the regressionmodel accordingly.

However, in many cases the chemical and physicalcontributions in di,k are too large to be ignored, while thecasual contribution spectra behind di,k are unknown. Thus, inorder to develop a more general gas correction model,applicable even in such situation, we here estimate the gasscores only based on reliable high-frequent parts of the spectra.

If we assume that the ‘‘non-gas’’ contributions di,k havemuch smoother spectral features than the gases, then the high-frequency part of the non-gas elements will be small and can bemore or less ignored. A common way to extract high-frequentspectral information is to take derivatives, and this will be usedhere: For each sample i with spectrum Ai,k, a simple spectralsecond derivative was computed according to Eq. 3:

Gi;k ¼ 2Ai;k � Ai;k�1 � Ai;kþ1; k ¼ 2; 3; . . . ð3Þ

Similarly for each gas model element j with spectrum kj,k, thesame simple second derivative was computed according to Eq. 4:

hj;k ¼ 2kj;k � kj;k�1 � kj;kþ1; k ¼ 2; 3; . . . ð4Þ

Moreover, we assume that the second derivative of theunknown but smooth sample contribution spectrum di,k, k ¼1, 2, ... can be approximated by a simple unknown offset fi atall channels in the second derivative. The second-derivativemodel can then be written:

Gi;k ¼XJ

j¼1

ci;jhj;k þ fi1k þ ei;k ð5Þ

Gas concentrations ci,j in each sample spectrum i are thenestimated (ci,j) by least squares regression of Gi,k on [hj,k, j¼ 1,2, ... , J; 1k] according to Eq. 5, by minimizing the residual sumof squares in ei,k over the K wavenumber channels.

Indirect Gas Predictions. In case the spectra contain theamide I band from proteins, the above-mentioned assumptionsabout smoothness of the real sample spectra di,k may not hold.The scores (‘‘concentrations’’) of the water vapor componentsin the second H2O(g) region (2072:1205 cm�1, containing theamide I region) may instead be predicted indirectly from theestimated scores of the three water vapor components in thefirst region (2442:2208 cm�1) by Eq. 6, where M¼3 representsthe three components of the first H2O(g) region, and N ¼ 3represents the three components of the second region:

APPLIED SPECTROSCOPY 1031

ci;n ¼XM

m¼1

ci;mbm;n þ b0;n n ¼ 1; 2; . . . ;N ð6Þ

Likewise, the scores of the N¼2 CO2 components in its secondwavenumber region were predicted from M ¼ 3 CO2

components in the first region by Eq. 6. The model parametersbj,m and b0,m in Eq. 6 were here estimated by full-rank ordinaryleast squares (OLS) regression using the scores ci,j¼ [ci,n, ci,m]obtained in Experiment 2, for water vapor and for CO2

separately. The indirect score estimation models were thenused for the prediction of gas component scores in Experiment4, since samples in this experiment contain proteins.

Gas Correction. With the gas scores ci,j thus obtained in allfour gas wavenumber regions, the sample spectra are then gas-corrected by subtracting the gas scores ci,j, multiplied by thecorresponding gas model spectrum kj,k:

Ai;k;gas�corrected ¼ Ai;k �XJ

j¼1

ci;jkj;k ð7Þ

Test of the Final Model. The final extended gas model thusconsisted of three model spectra in each of the water vaporregions, three model spectra in the main CO2 region, and twomodel spectra in the second CO2 region. This final gas modelwas applied for correction of the independent test sets fromExperiments 3 and 4.

Evaluation of the gas model performance was done byinspection of scores and loadings from a PCA before and afterthe gas correction. In addition, water vapor indices were usedfor comparison of water vapor absorptions in the spectra. Theindex was calculated for each spectrum as Amax � Amin in the1847–1837 cm�1 region in the second derivative and used asa conventional measure of the water vapor level.7

To illustrate how the gas correction can be combined withmore established spectral preprocessing, the spectra fromExperiment 4 will finally be submitted to extended multipli-cative signal correction (EMSC)8 as described in Martens etal.9 All results were computed and displayed in the authors’software using Matlab (TM) version 7.0.

RESULTS

Experiment 1: Estimation of Four Primary Gas ModelSpectra. Figure 1a shows the raw data (intensity I(m) spectra)from the first of the time series in Experiment 1, showing watervapor and CO2 in room air being gradually replaced with N2

purging gas and hence leaving smaller and smaller intensityreductions. Two characteristic water vapor absorption patternsare evident in the 4000–3500 cm�1 and 2000–1200 cm�1

ranges. These are the results of rotation-vibration (‘‘rovibra-tional’’) transitions, associated with the stretching and bendingvibrations of H2O, respectively. Moreover, the double CO2

absorption band around 2350 cm�1 is seen, as well as a weakerCO2 band around 670 cm�1, involving CO2 antisymmetricstretching and CO2 bending, respectively.10 Only the latterCO2 absorption demonstrates a so-called Q-branch in themiddle of the band. Each water vapor and CO2 band wascontained in one of the four defined spectral regions, accordingto Table I.

In the first of two defined water vapor regions (4000–3231cm�1), the atmospheric water bands overlap only little withprotein absorptions, whereas the interference is more dramaticin the second water vapor region (2072–1205 cm�1), as this

region contains amide bands from proteins as well asabsorption bands from lipids. The first of the defined CO2

regions (2442–2208 cm�1) is outside the absorption regions forthe common biochemical constituents, whereas the secondregion (914–600 cm�1) contains some important backbonevibrations of macromolecules.

‘‘Nuisance’’ Spectra from Experiment 1. The temporalabsorbance difference spectra Di,k, Eq. 1, in Fig. 1b show moreclearly the four gas absorptions, which are amplified in Figs.1c–1f. The peak sizes decrease with purging time. The SVD ofeach gas element region showed that the first componentaccounted for more than 99% of the total variance, while thesecond component, although small, also showed systematiccontributions. This indicated that one major and one minorspectral pattern of gas variation could be observed in eachregion. This was seen within each of the two time-series in thisexperiment. The two replicate PC loading vectors were verysimilar, for both component 1 and for component 2, in each ofthe four spectral regions. Hence, their mean (shown in Figs.2a–2d) was subsequently used for each region.

The first component loading (highest curve in each of thefour plots) is seen to be almost non-negative, as expected forchemical absorbances. The spectral patterns of these primarycomponents resemble typical water vapor or CO2 spectra. Thesecond component loadings (lowest curve in each of the fourplots in Figs. 2a–2d) has been amplified for visual clarity. Theyshow both negative and positive absorbances. They do modelsome small systematic variation around the typical gasspectrum in each region, and their inclusion in the model istherefore likely to improve the removal of the atmosphericabsorptions for similar measurements. But their interpretationis not clear.

The concentration scores of the eight primary ‘‘nuisance’’

FIG. 1. Calibration spectra from one time-series in Experiment 1. Infraredspectra of room air were measured consecutively in time during purging withN2(g) to obtain different concentrations of water vapor and CO2. (a) Intensityspectra I(m). (b) Absorbance spectra A(m) ¼ �log10(I(m)). (c) Water vaporsegment 1. (d) Water vapor segment 2. (e) CO2 segment 1. (f) CO2 segment 2.


gas components ci,j, j ¼ 1, 2, ... , 8 were estimated in the twotime series. Figure 3 shows that they all decrease as a functionof gas purging time, as expected. The figure also reveals that inthis experiment, very similar water vapor scores are estimatedfrom each of the two regions of water vapor absorptions, andthe same is found in the case of CO2 estimation from the twoCO2 regions. When the estimated gas concentration score forthe second component was plotted against the correspondingestimated score of the first component, it was found to displaya curved but temporally smooth and highly reproduciblerelationship (not shown here), in each of the four gaswavenumber regions. The cause of this is not yet clear. Itmay be that the second component in each case models a weakbut systematic spectral effect of partial pressure of water vaporand of carbon dioxide. Alternatively, it may reflect a nonlinearinstrument response or a temporal change in the instrument.

Experiment 2: Estimation of Three Secondary Gas

Model Spectra. Absorbance spectra of the 205 aqueoussolutions measured in the ATR cell are shown in the top panelof Fig. 4. These samples come from several measurementseries taken over two months. In each measurement series,a background spectrum was measured and subtracted.Moreover, in each spectrum the absorbance at 4000 cm�1 hasbeen subtracted, as a simple baseline correction. The threeinsets display the two water vapor regions and the main CO2

region, each after a local baseline correction.The spectra display the three broad absorbance peaks around

3300, 1640, and 800 cm�1 from liquid water plus a major peakaround 1100 cm�1 (due to the presence of anions SO4

2- andClO4

� in some of the samples). However, as the three insetsshow, the presence of some high-frequency water vaporcontributions is evident, as well as contributions from the firstCO2 double peak. In contrast, the second CO2 peak is notreadily visible.

The spectra were corrected for the eight primary gas‘‘nuisance’’ spectra by the procedure described by Eqs. 1–5 inthe Methods Section: The second-derivative transformedsample spectra were regressed on the second-derivative trans-formed model spectra (plus a constant, representing the secondderivative of a local second-degree polynomial in the givenwavenumber range). These estimated gas content scores wereused for determination of the main spectral gas contributions,which were subsequently removed from the non-transformedspectra by Eq. 6. The gas-corrected spectra are seen in themiddle panel of Fig. 4. Again, the three insets display the twowater vapor regions and the main CO2 region, each after a localbaseline correction. The difference between the top and middlepanels, i.e., the gas contributions estimated and subtracted, areshown in the bottom panel of Fig. 4. The gas estimates havemainly positive or negative gas peaks in each region, illustratinghow the samples may have higher or lower gas content thana reference sample (background spectrum).

Ideally, the high-frequency residuals of the corrected spectra(i.e., after subtracting the low-pass filtered versions of thespectra) should only contain measurement noise. However,

FIG. 4. Calibration spectra of water and salt solutions at different temperaturesobtained by ATR-FT-IR in Experiment 2. (Top) Raw absorbance spectra.(Middle) Spectra corrected for the eight primary gas model spectra. The insertsamplify the three main gas regions, after local baseline correction. (Bottom)Estimated gas spectra, i.e., Middle � Top.

FIG. 3. Gas scores for two time-series in Experiment 1. Estimated levels of theprimary gas components. Upper curves, starting near 1: the first component inthe four wavenumber segment models. Lower curves, starting near 0.5: thecorresponding second components.

FIG. 2. Primary gas model spectra obtained from Experiment 1 by singularvalue decomposition (SVD) of each gas region. Two component loadingspectra are defined in each wavenumber region. In each region, the loadingvectors for the first and the second component were normalized to correspondto a score value of 1 and 0.5, respectively, in an arbitrary sample (#2 in timeseries 1 in Experiment 1). (a) Water vapor segment 1. (b) Water vapor segment2. (c) CO2 segment 1. (d) CO2 segment 2.


upon closer inspection, these high-frequency residuals display

some remaining systematic high-frequency patterns in three of

the four gas-channel regions (Fig. 5a). Therefore, a separate

SVD of the residuals in each of these three regions was

performed. The first component loading was extracted (Fig. 5b)

and these were projected (see, e.g., Martens and Naes 1989)11

on the primary ‘‘nuisance’’ spectra. The orthogonalized

residuals (Fig. 5b) were used as secondary loadings, i.e.,

secondary ‘‘nuisance’’ spectra (orthogonal to the already

established ‘‘nuisance’’ spectra). They may account for

deviations from the atmospheric spectra in Experiment 1,caused by the samples and the ATR device.

Indirect Gas Prediction Model. To what extent do the twodifferent water vapor regions give similar estimates of watervapor concentration in a given sample’s spectrum? Figure 6shows various relationships between water vapor scores fromregions 1 and 2, for components 1, 2, and 3, respectively, inExperiment 2. The top row shows the estimate from region 1versus the estimate from region 2. Considering that the loadingspectra for the first two (primary) components have beenobtained from a rather different measurement situation(Experiment 1) than the present, the similarity between thescores from the two regions is good (as seen from the closenessto the diagonal where the abscissa equals the ordinate). Onlya scaling difference is seen for the first component (Fig. 6a),while an offset is seen for the second and much smallercomponent (Fig. 6b). As the two regions resulted in rathersimilar scores in Experiment 1, the deviations seen forExperiment 2 (Figs. 6a and 6b) may be related to the largedifferences between the spectra in the two experiments (of theempty sample compartment and of water on the ATR).

Figure 6c shows that the two regional loading spectra for thethird (secondary) components obtained in Experiment 2 reflectmuch of the same systematic variation phenomenon, pre-sumably related to varying water vapor concentrations. Hence,the two wavenumber regions gave clearly related scoreestimates.

To prepare for a situation where protein and lipid signalsmake water vapor concentration estimation difficult in watervapor region 2, linear full-rank calibration models wereestablished from the gas score estimates in Experiment 2 topredict the water vapor component scores in region 2 fromthose in region 1. (Region 1 is a region with only a few andrelatively broad protein bands (e.g., amide A and amino acidNH stretch), which do not interfere with the gas score

FIG. 5. Secondary gas model spectra from residuals in Experiment 2. (a)High-frequency residuals in the spectra from Fig. 4b. (b) Loading of the firstcomponent from SVD of the residuals in Fig. 5a for three gas regions (the twowater regions and the main CO2 region). (c) The secondary model spectra,obtained by orthogonalizing the spectra in Fig. 5b on the primary model spectra(Figs. 2a–2d).

FIG. 6. Score relationships for water vapor in Experiment 2. (Left, center, and right) Components 1, 2, and 3. (Top) Score estimate in region 1 (ordinate) versusscore estimate in region 2 (abscissa). (Bottom) Score estimate in region 2, predicted from score estimates in region 1 (ordinate) versus score estimate in region 2(abscissa).


estimation.) The component scores in region 2 were regressedon to the component scores in region 1 by OLS regression.Figures 6d–6f show the prediction ability of the water vaporscore models. For each of the three components in region 2 itseems that its water vapor scores can be successfully predictedfrom the water vapor scores in region 1, at least for these typesof spectral measurements. The degree of over-fitting in thepredicted scores in Figs. 6d–6f is considered negligible, sincethe number of observations (205) is far higher than the numberof independent parameters (4) estimated for each component inEq. 4.

Similar calibration models were developed for predictingCO2 scores in the second CO2 range from the first CO2 range.However, the modeling of (small) CO2 effects in the secondrange was less successful in this region. In fact, detailedmodeling below about 856 cm�1 was found to be difficult dueto large day-to-day instrument drift, which in turn probably isdue to low lamp/detector signal strength in this region.

These calibration models to predict region 2 from region 1for water vapor and CO2 will be used in Experiment 4 to avoidconfounding with proteins and lipids.

Experiment 3: Test of Model on Attenuated TotalReflection–Fourier Transform Infrared Spectra of Aque-ous Samples. Absorbance ATR-FT-IR spectra obtained onpure water dropping gradually from 21 to 10 8C are shown inFig. 7a. The absorbance at 4000 cm�1 was subtracted fromeach spectrum to correct for irrelevant baseline variations. Thegas peaks and the temperature effect on the water spectrumbecome apparent after mean centering each channel (Fig. 7b).In Figs. 7c and 7d, the mean-centered and gas-corrected spectra(Eq. 7) are shown, based on two ways to perform the gas score.Figure 7e shows the gas component model spectra used. In Fig.7d the estimate of gas component scores ci,j, j ¼ 1, 2, ... , 11was based on the spectral second derivatives, as described byEqs. 3, 4, and 5, respectively.

As one of many alternative estimation possibilities, in Fig.7c the gas component score estimation was based directly onthe least squares solution of Eq. 2, assuming non-gascontributions dik to be negligible. For each gas type (watervapor, CO2), the primary gas model component spectrum fromits two regions (containing zero outside its region) was firstsummed into a common primary water vapor or CO2

FIG. 7. Test of the gas model, using ATR-FT-IR spectra of pure water at different temperatures, obtained in Experiment 3. Raw absorbance spectra (a) before and(b) after mean centering. Mean-centered spectra after subtraction of gases, (c) estimated in raw absorbance and (d) in second derivative. (e) Gas model spectra.


component spectrum. The same was done for the secondarycomponents, resulting in a total of three water vaporcomponent spectra and three CO2 component spectra, i.e., J¼ 6 in Eq. 2. The high amount of remaining water vapor in Fig.7c illustrates the alias problem that can arise when basing thegas score estimation directly on the actual absorbance spectrainstead of on their second derivatives. Compared to this, thegas correction based on estimation of gas scores in the secondderivative (Fig. 7d) effectively eliminated the gas nuisanceeffects.

Figure 8 illustrates the consequences for the subsequent dataanalysis when applying no gas correction or when using thetwo different approaches to the gas correction:

Simple PCA, i.e., SVD of the mean-centered spectra in Figs.7b–7d, was used in order to extract the major systematicpatterns of variation in the FT-IR spectra as the liquid watersample cooled from about 21 8C to about 10 8C. The PCloading spectra and the PC scores, both scaled by the size ofthe component, are shown on the left and right side,respectively, of Fig. 8. One PC seems to dominate the datain all three cases. This variation is presumed to reflect thetemperature-dependent changes between a weakly and a strong-ly hydrogen bonded state of liquid water.

The scores of the first PC are not affected by water vapor andCO2 nuisances, as these are minor effects compared to thetemperature-induced variation in liquid water. However,looking at the loading spectra (left-hand side of Fig. 8), whichare intended to represent the effect of temperature on liquidwater, these are strongly contaminated by irrelevant high-frequent water vapor signal in the case of the untreated data(Fig. 8a) and the over-simplified gas score estimation (Fig. 8c).

It was not possible to use regression for estimation of thewater temperature effect, since the precise temperatures werenot known for these samples. Anyway, this approach wouldhave been to no avail, as the temporal change in thetemperature of the liquid water sample in the ATR is stronglyconfounded with the temporal change in water vaporconcentration inside the instrument.

In contrast, the gas-corrected spectra based on second-derivative estimates (Fig. 7d) gave an estimated temperatureeffect on the liquid water (Fig. 8e) with little or no trace of thewater vapor or CO2.

Experiment 4: Yeast Cell Culture Test Measurements.Figure 9 summarizes the effect of preprocessing on in situspectra of the live cell culture of C. albicans, growing on theATR surface. The absorbance spectra measured, A ¼�log10(I(m)) (Fig. 9a) are rather similar to that of pure water(Fig. 7a) except for a higher baseline at the lower wave-numbers. After having subtracted the mean of these spectra,Fig. 9b shows that the variation in this data set is dominated byirrelevant water vapor and CO2 contributions, presumably frominside the FT-IR instrument, plus a weaker variation around1000 cm�1 from the samples themselves.

The concentrations of the water vapor and CO2 componentswere estimated in second derivative in the upper wavenumberregions (above 2200 cm�1) but not in the lower wavenumberregions (below 2200 cm�1), for fear that informative, high-frequent signals from proteins, etc., might be lost. Instead, thescores in the lower wavenumber region were predicted fromthose in the upper region by the calibration models obtained inExperiment 2 (Fig. 6).

The second row in Fig. 9 shows the gas-corrected

FIG. 8. Results from PCA models of the spectra, obtained in Experiment 3. (a, b) Raw spectra. (c, d) After gas correction, estimated in raw absorbance. (e, f) Aftergas correction, estimated in second derivative. (Left) The spectral variation patterns found, i.e., PCA loadings versus wavenumber. (Right) Sample models, i.e.,scores versus time.


absorbance spectra before and after mean centering. (Thewavenumbers below 856 cm�1 were weighted to zero becausethe measurements were considered unreliable in this region.)Apparently, most of the water vapor and CO2 contributionshave been removed, revealing other systematic variationpatterns in several regions. However, some minor gas(especially CO2) contributions are still evident. Therefore, tofurther reduce the CO2 effect, each spectrum was linearlyinterpolated locally under the CO2 peak, i.e., from 2442 cm�1

to 2208 cm�1. Moreover, the light scattering of the C. albicanssuspension may be expected to change with growth time. Lightscattering effects in the spectra may result from changes inrefractive index of the sample over time. As the refractiveindex affects the penetration depth of the IR light, this variationmay cause multiplicative scaling effects. Also, additivebaseline effects appear. For removal of this physical variation,the spectra were subjected to EMSC.

The wavenumber regions between 1582 and 1453 cm�1

were down-weighted by a factor of 0.01 in the EMSCparameter estimation in order to suppress the effects of theclear sample absorbance variations in this region, presumablydue to proteins, lipids, etc. The region below 856 cm�1 waslikewise down-weighted due to instrument variations and lowsignal/noise in this region. For catching the multiplicative lightscattering effect and additive baseline variations, each spectrumwas approximated by the mean spectrum from Fig. 9c plusa second-degree polynomial in the wavenumber domain. Theestimated polynomial baseline effects were subtracted and theresult divided by the estimated multiplicative light scatteringparameter. The corrected spectra, which are shown in the

bottom of Fig. 9, display many regions with chemicalvariations.

Each of the three data matrices displayed in Figs. 9b, 9d, and9f were submitted to PCA. The loading and score vectors areshown in the left and center parts of Fig. 10, while the two firstPC scores are plotted against each other in the right part of thefigure. The untreated absorbance data (row 1) give PCAloading vectors dominated by irrelevant gas contributions.Hence, the obtained scores probably reflect the trivial purgingof gases. After removal of the gas absorptions (row 2), theircontributions to the loadings are greatly reduced, and theloadings now show peaks from the chemical constituents.Thus, the scores reflect chemical changes during the cellgrowth, but also physical changes, and the jumps observed inthe score plots are probably related to some physicalmeasurement variations. The additional step for removal ofremaining CO2 and light scattering effects (row 3) causes thescores to show much smoother development over time. Thus, itseems that the physical variations have been removed in thisstep, leaving mainly chemical information, and the course ofthe scores may reflect two growth phases: an initial fast anda final slower phase.

DISCUSSION

The above-presented preprocessing approach appears suit-able for reducing the atmospheric contributions to ATR-FT-IRspectra, thereby facilitating the analysis of the interestingvariations in the samples. As seen from the conventional watervapor indices in Table II, and as shown above, the empiricalgas model was able to effectively reduce the contaminatingwater vapor patterns, even in the spectra of C. albicans, which

FIG. 9. In situ ATR-FT-IR spectra of C. albicans. (Top) Input absorbance spectra. (Middle) After correction for the primary and secondary water vapor and CO2

spectra. (Bottom) After subsequent interpolation under the main CO2 peak, and EMSC to correct for light scattering, etc. (Left) (a, c, e) Absorbance data. (Right) (b,d, f) Mean-centered absorbance data.


are very different from the calibration spectra. Interestingly,correction of the C. albicans spectra caused the largest decreasein the water vapor index (Table II). Likewise, in Fig. 9 is seena tremendous effect of removing the gas contributions from theC. albicans spectra. After the correction, the scores in the firstthree principal components are no longer influenced by thegases, and it is possible that they could be used for modelinggrowth dynamics of C. albicans. In contrast, without suchremoval of the gas absorptions, many more principalcomponents would be needed in this modeling and theinteresting loadings would contain more noise and irrelevantphenomena. In addition, if purging rate and growth rate werethe same, it could be hard to obtain chemical information aboutthe samples from the loading plots, as these would also containthe gas signatures.

The subtraction of atmospheric absorptions in FT-IR spectrais a necessity in protein secondary structure analyses that arebased on the amide I band (1700–1600 cm�1). In order toensure correct amide I band assignments, the overlapping watervapor band needs to be almost completely eliminated prior tothe analysis.5 Thus, mathematical treatments for removal of the

water vapor spectrum have been proposed, and in many cases,the algorithms are included in the spectroscopic software. Themethod proposed here is thought to improve the amide Ianalysis considerably, as it reduces the high-frequent bands inthe amide I region of the second-derivative water spectra.

The water vapor peaks are relatively narrow compared to ourspectral resolution. In the two vapor regions the average widthof visually discernible peaks was found to be about 14 cm�1.So with our 4 cm�1 wavenumber resolution, there are only twoor three clear spectral readings per vapor peak. Under theseconditions an accurate modeling of the water vapor requiresa very stable instrument. According to the results ofGoormaghtigh et al.,12 using a nominal resolution of 0.5cm�1 would likely improve the gas removal. However, thiswould increase the noise and the measurement time. Thus, weuse a resolution that is commonly used for measurements ofbiological samples.

Temperature variations in the measurement chamber maycontribute to some variation in the gas spectra, as thepopulations of molecules occupying the higher rotationallevels become increased at the expense of others withincreasing temperature.4 This causes the maximum of the twobranches to move further away from the center of the rotation-vibration band. In addition, temperature- and pressure-de-pendent line broadening effects arise.4 However, the smallvariations around room temperature that are commonly foundbetween measurement days are believed to cause only minortemperature effects in the gas spectra. In addition, thecalibration samples are expected to cover some temperaturevariations, due to the different temperatures of the ATR cell (upto 60 8C) in the calibration measurements. However, theperformance of the preprocessing tool at very differenttemperatures was not tested.

Free Matlab (TM) software code for establishing and usinga model of ‘‘nuisance’’ contributions from water vapor and CO2

FIG. 10. Results from PCA of in situ ATR-FT-IR spectra of C. albicans. (Left) (a, d, g) PCA loadings versus wavenumber. (Middle) (b, e, h) PCA scores versustime. (Right) (c, f, i) PCA score for PC1 (abscissa) versus PC2 (ordinate). ‘‘Time¼ 0’’ represents the start of the measurement series.

TABLE II. Average water vapor content index (3103) for the data sets inthe experiments, before and after subtraction of the estimated gas modelcontributions. (The maximum index for each data set is shown inparentheses).

Input spectra

Gas-corrected(2 componentsin each watervapor region)

Gas-corrected(3 componentsin each watervapor region)

Experiment 1 5.242 (37.754) 0.295 (0.570) –Experiment 2 3.181 (9.748) 1.193 (2.783) 0.885 (1.515)Experiment 3 1.058 (2.392) – 0.805 (0.826)Experiment 4 4.977 (21.989) – 0.143 (0.832)


in IR spectra can be downloaded at www.umb.no/specmod,where the actual values of the gas component spectra obtainedin the present paper can also be found. The methods presentedhere are considered rather generic. But the gas componentspectrum values are considered valid only for the present type ofATR-FT-IR measurements in our Bruker instrument; beforethey can be used in another experimental setup, they may needsubstantial calibration transfer modification.

ACKNOWLEDGMENTS

Astrid Oust is thanked for providing the empty-instrument gas measurementtime series. Isabelle Adt is grateful for financial support by the Conseil

Regional de Champagne-Ardenne, Achim Kohler and Ganesh D. Sockalingumby the Aurora Franco-Norwegian mobility program.

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3. P. A. Suci, J. D. Vrany, and M. W. Mittelman, Biomaterials 19, 327(1998).

4. H. M. Heise and H. W. Schrotter, ‘‘Rotation-Vibration Spectra of Gases’’,in Infrared and Raman Spectroscopy: Methods and Applications, B.Schrader, Ed. (Wiley-VCH, Weinheim, 1995). Chap. 4.3, p. 256.

5. S. E. Reid, D. J. Moffatt, and J. E. Baenziger, Spectrochim. Acta, Part A52, 1347 (1996).

6. ‘‘Atmospheric vapor compensation on the Spectrum 100 FT-IR and 100NFT-IR spectrometers’’, Technical note (http://las.perkinelmer.com/content/RelatedMaterials/atmosphericvaporcompensationspectrum100tch.pdf).

7. D. Helm, H. Labischinski, and D. Naumann, J. Microbiol. Meth. 14, 127(1991).

8. H. Martens and E. Stark, J. Pharmaceut. Biomed. 9, 625 (1991).9. H. Martens, J. P. Nielsen, and S. B. Engelsen, Anal. Chem. 75, 394 (2003).

10. P. J. Hendra, Internet J. Vib. Spectrosc. (www.ijvs.com) 5, 2 (2001).11. H. Martens and T. Næs, Multivariate Calibration (John Wiley and Sons,

Chichester, UK, 1989).12. E. Goormaghtigh and J.-M. Ruysschaert, Spectrochim. Acta, Part A 50,

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Documents

Correcting Attenuated Total Reflection–Fourier Transform Infrared Spectra for Water Vapor and Carbon Dioxide