1118 Volume 51, Number 8, 1997 APPLIED SPECTROSCOPY0003-7028 / 97 / 5108-1118$2.00 / 0q 1997 Society for Applied Spectroscopy

Classi® cation of Vegetable Oils by FT-IR

DONALD B. DAHLBERG,* SHAWN M. LEE, SETH J. WENGER, andJULIE A. VARGOApplied Chemometrics, Department of Chemistry, Lebanon Valley College, Annville, Pennsylvania 17003

The Fourier transform infrared (FT-IR) spectra of 27 brands of 10types of cooking oils and margarines were measured without tem-perature control. Attempts to predict the vegetable source andphysical properties of these oils failed until wavelength selection andmultiplicative signal correction (MSC) were applied to the FT-IRspectra. After pretreatment of the data, principal component anal-ysis (PCA) was totally successful at oil identi® cation, and partialleast-squares (PLS) models were able to predict both the refractiveindices [standard error of estimation (SEE) 0.0002] and the viscos-ities (SEE 0.52 cP) of the oils. These models were based predomi-nately on the FT-IR detection of the cis and trans double-bond con-tent of the oils, as well as small amounts of de® ning impurities insesame oils. Efforts to use selected wavelengths to discriminate oilsources were only partially successful. These results show the po-tential utility of FT-IR in the fast detection of substitution or adul-teration of products like cooking oils.

Index Headings: FT-IR; Pattern recognition; Principal componentanalysis; Partial least-squares; Vegetable oils; Refractive index; Vis-cosity.

INTRODUCTION

Verifying the authenticity of raw materials is a majorexpense for industry. Failure to identify counterfeit oradulterated feed stocks can be even more expensive whenit results in inferior products that then require disposal.The analysis problem is exacerbated when a counterfeitmaterial closely resembles the authentic material. A typ-ical example of such a situation is edible vegetable oils,which are predominantly mixtures of the same triglyc-erides, differing only in the relative amounts of each. Inspite of the chemical similarities of vegetable oils, smalldifferences in their composition can lead to substantialdifferences in price and health properties.1 This consid-eration makes edible oils a prime candidate for alterationby chemical means and for substitution or doctoring withless expensive oils.

Pattern recognition, coupled with a variety of analyti-cal techniques, has been successfully applied to the iden-ti® cation of many foods over the years. Gas chromatog-raphy (GC) has been applied to the classi® cation of pep-permint oils,2 olive oils3 and several types of wines.4,5,6

Mineral analysis techniques have been applied to wines7

and fruit juices.8 Sometimes a variety of techniques arecombined, as in the classi® cation of apple juice, usinghigh-performance liquid chromatography (HPLC) for thedetermination of sugars, titration for acidity, refractome-try for 8 Brix, and ultraviolet spectrometry for L-malicacid.9 All these techniques are costly and time consumingand do not lend themselves to on-line analysis.

Both near-infrared (NIR) and mid-infrared (MIR) spec-

Received 8 July 1996; accepted 22 January 1997.* Author to whom correspondence should be sent.

troscopy quickly and easily provide a great deal of in-formation about the composition of materials such as ed-ible oils. NIR is generally considered to span from thered end of the visible region near 12,800 cm2 1 to thebeginning of the MIR region at about 4000 cm2 1, whileMIR spans the region from this point to about 200 cm2 1.Because NIR detects weak overtone and combination vi-brations and is close to the visible region, it has certainadvantages, including lower absorbencies, which toleratelonger pathlengths, and the ability to use inexpensive,broad-band optical ® bers to transmit the light betweenthe sample and the instrument.10 The utility of this tech-nique has recently been demonstrated in the classi® cationof vegetable oils and the detection of adulterated oliveoils.11,12 The narrower and stronger peaks associated withthe fundamental vibrations of MIR can provide greatersensitivity and selectivity than the broad peaks of NIR.This consideration can be very important when the dif-ferences between samples are subtle. Although the ap-plication of MIR to edible fats and oils has been exam-ined for years,13,14 the advent of the faster and more stableFourier transform infrared spectroscopy (FT-IR) makesMIR a more viable candidate for at-line or on-line anal-ysis. Optical conduits, immersion probes, and attenuatedtotal re¯ ectance (ATR) cells can make sample handlingmuch easier.15,16

Chemometric classi® cation and calibration techniquesare very sensitive to instrumental variations.17 Driftingtemperature has proven to be a problem in both NIR andFT-IR spectroscopy, often requiring careful thermostatingof the sample and/or instrument.18,19 This problem couldgreatly decrease the robustness of the technique in anon-line situation where environmental conditions may bemore dif® cult to control. It is possible to include tem-perature in the chemometric model,20 but this approachnecessitates a larger learning set. In the present study,multiplicative signal correction (MSC) was used to cor-rect for temperature variations experienced during the ac-quisition of the FT-IR spectra of edible oils. MSC orig-inally stood for multiplicative scatter correction and wasdeveloped as a data pretreatment technique to correct forvarying light scatter in re¯ ective spectroscopy.21 Calibra-tion models are based on the assumption that the path-length of the light through the sample is constant. Evenpowerful calibration techniques, such as principal com-ponent regression (PCR) and partial least-squares (PLS),have dif® culty modeling systems when this assumptionfails. MSC has since proven to be a valuable techniquein correcting for this and other phenomena that result ineither a baseline shift (additive effects) or an ampli® ca-tion of the spectrum (multiplicative effect).22

Multiplicative scatter correction assumes that varyingenvironmental in¯ uences, such as light scattering and

APPLIED SPECTROSCOPY 1119

temperature variations, can have two effects on the spec-trum of a sample as described by the model

xi 5 xi,true ai 1 b i, (1)

where xi is a vector representing the distorted spectrumof a sample, xi,true represents the expected spectrum froma stable instrument, ai is a constant representing a mul-tiplicative effect such as a varying light pathlength, andb i is an additive effect or baseline offset. The multipli-cative- and additive-effect constants vary from sample tosample but are constant for each wavelength within asample.

One impractical way of obtaining xi,true would be tomeasure the spectrum many times under varied condi-tions and use the mean of that spectrum. If the values ofai and b i are random from sample to sample, then theirmeans would then approach 1 and 0, respectively. Whileconstructing a learning set, one has already taken nu-merous spectra under varying conditions, and each ofthese spectra, although not of the same sample, containsa substantial sampling of multiplicative and additive ef-fects. If the spectra contain large regions of baseline andrelatively constant absorbencies, then the distorting con-stants may be approximated by performing a linear re-gression of the spectrum to be corrected against the meanof all the spectra of the learning set according to theequation

xi 5 xÅ ai 1 b i (2)

where xŠis the mean spectrum of the learning set. Theresulting constants, ai and b i, can then be used to createan estimate of the true spectrum, xà i,true, by using the equa-tion

xà i,true 5 (xi 2 b i)/ai. (3)

A very clear description and discussion of the techniquecan be found in a paper by Isaksson and Nñ s.23

Principal component analysis (PCA) is a pattern rec-ognition technique that has been described in detail inmany papers.24 Each sample can be represented as a pointin multidimensional space, one dimension for each wave-length of the spectrum. Such hyperspace is very dif® cultfor humans to visualize or interpret. In PCA, a new co-ordinate system can be de® ned as linear combinations ofthe old coordinates, so that most of the variance or in-formation that resides in the data is concentrated in onlya few of the new coordinates, often called principal com-ponents. This approach can be expressed mathematicallyas the decomposition of the data matrix, D, into the prod-uct of two other matrixes, the scores, P, and the transposeof the loadings, T,

D 5 PTT. (4)

If D has the dimensions of samples by wavelengths, thenthe loadings matrix, T, will have the dimensions of wave-lengths by principal components and represents the rec-ipes by which each of the principal components was con-structed from the old variable, the wavelengths. Thescores matrix, P, has the dimensions of samples by prin-cipal components and represents the location of the sam-ples in this new principal components space. If the pro-cess is successful in concentrating most of the useful in-formation into the ® rst few principal components, the

samples can then be represented as points in the spacedescribed by just the ® rst two or three principal compo-nents. The other principal components are assumed tocontain minor characteristics of the samples and noiseand can be ignored. Often the scores± scores plots of the® rst few principal components will result in the samplesclustering into groups of similar characteristics, separatedfrom other clusters of samples with differing character-istics. The loadings provide a sort of `̀ compass’’ in thisabstract principal component space, pointing the directionof the old variables, which are more easily understoodby the chemist. A major advantage of PCA is that it is afull-spectrum technique in that it uses the redundancy ofthe information from many variables to help reduce thein¯ uence of noise and to exploit subtle difference in theproperties of the samples in order to make more de® nedgroupings of the samples.

Although cluster membership can often be determinedby visual examination of the scores± scores plots, soft in-dependent modeling of class analogy (SIMCA) is a morestatistically de® ned method of cluster analysis.25,26 SIM-CA involves building a PCA model for a given class andencompassing the resulting model with a decision shelldetermined by a statistically de® ned distance from thecenter of the model. If unknown samples fall inside thisshell, they are assigned as being members of the class,and if they fall outside this shell, they are assigned as notbeing members of the class.

Since the scores are a concentrated form of the originalspectra and thus contain the structural information ofthese spectra, they can also be used in the prediction ofphysical and chemical properties. A model can be con-structed from a learning set of data by regressing a phys-ical property such as viscosity against these scores. Theresulting regression coef® cients can then be used to pre-dict the viscosity of new samples from their spectra. Thisis the basis of the full-spectrum calibration technique ofPCR. In the related technique of PLS, the scores are con-structed not from PCA, but through a cooperative routineinvolving information from both the spectra and the prop-erty to be predicted. This approach often leads to a modelrequiring fewer principal components to describe the sys-tem.

The purpose of this work is to test the effectiveness ofMSC in correcting FT-IR spectra for environmental vari-ations such as temperature and to determine whetherFT-IR is capable of both classifying edible oils accordingto their vegetable source and predicting physical prop-erties of these oils.

EXPERIMENTAL

All oils and margarines were obtained from local retailoutlets and are described in Table I. The oil samples in-cluded 24 brands of oils from 10 vegetable sources plustwo margarines and one commercial mixture of oils. One-year-old bottles of two brands were added to the studyin order to examine the effects of aging and/or variationsin a brand with time. A sealed NaCl cell (pathlength0.015 mm) was ® lled with the oils. Margarines requiredwarming above their melting point and ® ltering through® lter paper before ® lling of the cells. The cells werecleaned with dichloromethane and dried with air. FT-IR

1120 Volume 51, Number 8, 1997

TABLE I. Origins of edible oils used in this study.

Oil origin Number of brands FT-IR replicates Refractive index 25 8 C Viscosity (cP @ 35 8 C) Iodine valuea

AlmondCanola

Corn

Corn margarineOlive (American light)

13

3

11

533333343

1.47001.47181.47191.47211.47291.47291.47291.46991.4729

39.3538.2037.5938.1634.5434.6334.5442.0134.54

98.6

122.6

Olive (Italian light)Olive (Italian)Olive (Italian extra virgin)Olive (Spanish extra virgin)Peanut

Saf¯ ower

Sesame (light)

11112

2

1

333353535

1.46791.46791.46801.46811.46911.46951.47461.47501.4716

41.6041.2040.9141.3740.9140.8332.7932.3438.08

81.1

93.4

145

Sesame (dark)

Sesame± soy (60± 40%)Soybean

Soybean margarineSun¯ ower

Walnut

3b

12

13b

1

57534444445

1.47231.47171.47161.47271.47311.47341.46821.47371.47411.47341.4753

37.2738.1538.4036.2034.0333.8746.6833.5734.3036.4229.56

106.6

130.0

125.5

a J. J. Harwwod and R. P. Geyer, Biology Data Book (Federation of American Societies for Experimental Biology, Washington, DC, 1964), pp.380± 82.b Including 1 yr of one brand and 2 yr of a second brand.

FIG. 1. Superimposed FT-IR spectra of 112 samples of 27 types ofoils from 10 vegetable sources. The bars under the spectra mark theregions used in the construction of chemometric models.

spectra were taken on a Nicolet 5-DX FT-IR system at4-cm2 1 resolution. From three to seven replicate spectrawere taken of each oil. An effort was made not to takereplicas of a given sample on the same day, in order tovary the environmental conditions under which each oilwas analyzed. The spectra were then transferred from the5-DX data processor of the FT-IR to a Macintosh II com-puter. The resulting spectra were combined to form a datamatrix by using the matrix algebra software package MAT-LAB.27 Each spectrum contained 1556 measurementsfrom 3600 to 600 cm2 1.

The refractive indices of the oils were measured on a

Bausch and Lomb Abbe-3L refractometer thermostatedat 25.0 8 C. The viscosities of the oils were determined at35.0 8 C by using a size 300 Oswald viscometer calibratedwith ethylene glycol. The viscosity of ethylene glycol at35 8 C was taken as 10.953 cP through interpolation ofdata from other temperatures.28 The densities were deter-mined to be 1.093 g/mL for ethylene glycol and 0.902g/mL for the oils at 35 8 C.

Data Pretreatment and Analysis. Figure 1 shows thesuperposition of 112 complete FT-IR spectra of the 29oil samples. During the course of the 2-month study, thesalt cell gradually became increasingly cloudy, causinglight scattering and slanting of the baseline. Matlab rou-tines were written to shift the baseline and ramp the spec-tra in such a way that each spectra had a zero baselinenear 2200 and 3300 cm2 1. Similarly, a Matlab routinewas written to perform MSC of the spectra to correct forthe fact that, as the temperature of the room changed,there was a change in the density of the oil and/or in thepathlength of the cell. Finally, only the regions from 3020to 2992 cm2 1 and from 1476 to 668 cm2 1 were used inthe analyses, as indicated by the bars under the spectrain Fig. 1. This approach excluded the baseline regionsand the regions where the absorbance of contaminatingwater vapor and carbon dioxide confuse the analysis.Much of the C± H stretch region and the carbonyl stretchregion were also removed, because these absorbencieswere above 2 and the resulting noise and nonlinearityconfused the analysis. The remaining 435 wavelengthsincluded the cis-vinyl C± H stretch and most of the ® n-gerprint region. The ® nal matrix was then mean-centeredand analyzed by using the PCA algorithm NIPALS.29,30

APPLIED SPECTROSCOPY 1121

FIG. 2. First two scores from the PCA model of mean-centered datawithout multiplicative signal correction.

FIG. 3. MSC plot of the 1556 wavelength spectrum for sample 66, awalnut oil, vs. the mean of all spectra in the learning set.

FIG. 4. First two scores from the PCA model of mean-centered datawith multiplicative signal correction. Major loadings are indicated byvectors and labeled wavenumbers.

The PLS algorithm, as described by Haaland and Thom-as, was used to model the refractive index and the vis-cosity of the oils.31 Twenty-nine mean spectra of all rep-licates for each of the samples of oil were used to con-struct the learning set. The number of principal compo-nents kept in the model was chosen through aleave-one-out cross-validation technique. The standarderrors of estimation (SEE) of the models were calculatedfor the learning set by using the equation

2(y 2 y )e mOSEE 5 (5)! n 2 1 2 nPC

where ye is the estimated value of the property in thelearning set, ym is the measured value of this property, nis the number of samples in the learning set, and nPC isthe number of principal components used to build themodel.

RESULTS AND DISCUSSION

PCA. Figure 2 is a scores± scores plot from a PCA ofthe mean-centered data that had not been subjected toMSC. Along the ® rst principal component, several of thesesame samples are highly isolated from the other oils,including other samples of sesame oil. These outlier ses-ame samples were measured during a time when theroom air conditioning failed, causing the ambient tem-perature to rise some 10 8 F. This increase in temperaturemost likely caused the oil to expand, changing the mo-larity of the neat oils. Even with the removal of thesesamples, more normal variations in ambient conditionsprevented satisfactory separation of the various oil typesby PCA.

Since the thinning of the oil from thermal expansionis a multiplicative effect, MSC is a good candidate tocorrect the problem. Figure 3 depicts the determinationof the multiplicative and additive constants for sample66, a walnut oil. Here, the spectra for this sample wereplotted for each of the 1556 wavelengths against themean of all 112 samples. The resulting linear regressionyields a slope of 1.067 and an intercept of 2 24.8. Theadditive effect is negligible in comparison to the ampli-tude of the peaks, because the data had previously beencorrected for baseline offset, but the slope revealed a6.7% multiplicative effect, presumably due to a temper-

ature variation when this spectrum was taken. Similarplots were then performed on each of the other 111 spec-tra and corrections made according to Eq. 3. The multi-plicative constants ranged from 0.916 to 1.337. The cis-vinyl C± H stretch and ® ngerprint regions of these cor-rected spectra were then subjected to PCA as had beendone with the uncorrected data. The scores± scores plotfor the ® rst two principal components (PC1 and PC2)resulting from MSC-corrected data is shown in Fig. 4.For ease of interpretation, the vectors depicting the wave-lengths associated with the largest loadings have beensuperimposed onto the same plot. The pretreatment withMSC has resulted in the separation of most of the oilsaccording to plant origin with the use of two principalcomponents. Although the ellipses around the clusters inthe ® gures are only for visual clarity in identifying thegroups and are not statistically determined, we have usedSIMCA to show that the closest of clusters (soybean andcorn) are totally distinguishable within a 95% con® dencelevel. The apparent overlap of some of the sesame oilswith the canola oils is resolved with the third principalcomponent (PC3), as shown in Fig. 5. Discrimination of

1122 Volume 51, Number 8, 1997

FIG. 5. First and third scores from the PCA model of mean-centereddata with multiplicative signal correction. Major loadings are indicatedby vectors and labeled wavenumbers.

FIG. 6. PCA loadings for PC3.

FIG. 7. Two-wavelength discriminant analyses of oils, trans C± H bend(967 cm2 1) vs. cis C± H stretch (1005 cm2 1).

oils by brand proved to be possible only in a limitednumber of cases.

Most of the resolution of the oils is achieved alongPC1 through a negative relationship with the absorbancein the 3005-cm2 1 region, the cis-vinyl C± H stretch. PC1contained 79% of the variance of the system. The vectorfor the 1399-cm2 1 cis-vinyl C± H in-plane bend alsopoints in the same direction. Almost directly opposed tothe cis-alkene vectors is the 1464-cm2 1 vector, which isfrom CH2-scissoring of saturated alkanes. Thus, the vec-tor drawn from the olive oils to the saf¯ ower oils marksthe direction of increasing average unsaturation of theoils and increasing iodine values as listed in Table I. Thedifference between the cis-vinyl C± H stretching and alkylC± H bending absorbencies determines the position alongthis line. This result is expected in light of the fact thatArnold and Hartung showed that the ratio of absorbenciesfor vinyl and alkyl C± H stretches is linearly correlated tothe iodine values of oils.32

The second principal component, which contained16% of the variance, is dominated by and negatively cor-related with the trans-vinyl C± H in-plane bend at 967cm2 1. Trans-alkenes are not natural in these oils and re-sult from the partial hydrogenation of the oils in the pro-cess of making the higher melting margarines. The hy-drogenation process both decreases the unsaturation andrearranges some of the remaining alkenes from the cis tothe trans isomeric form.33 Thus, the margarines are foundalong a line that is both in the saturation (positive PC1)and trans (negative PC2) directions from the oils fromwhich they were made. The clusters labeled `̀ Sun ’ 91’’and `̀ Sun ’ 92’’ represent the same brand of sun¯ ower oilfrom those two years. The relative position of these twooils may indicate some reformulation of the oil throughpartial hydrogenation of the 1992 oil compared to that ofthe 1991 oil.

As shown in Fig. 5, the third principal component isresponsible for separating the sesame oils from the canolaoils and contains 3.6% variance. Sesame oils A and Bwere the traditional dark oriental sesame oils, while ses-ame C was light in color. A fourth brand, which waslabeled as a 60/40% sesame/soybean oil mixture, is foundin between the oils from which it was made in both Figs.

4 and 5. This result suggests the possibility of usingFT-IR and SIMCA in the detection of adulterated oils, aproject presently being pursued in this laboratory.

The dark sesame oils contain up to 0.9% of lignan andsesamin and smaller amounts of sesamolin and sesamol.34

Figure 6 depicts the loadings for PC3. Many of the wave-lengths with major negative loadings in PC3 (1246, 1096,1057, 1039, 936, and 806 cm2 1) match up very well withthe IR spectrum of sesamin as tabulated by Qianrong etal.35 PC3 is, thus, primarily interpreted as being nega-tively related to the concentration of these impurities inthe oils. The light sesame oil contains much less of thesesubstances and thus appears in between the dark sesameand nonsesame oils. The NIR study of vegetable oils bySato failed to pick up these impurities and thus failed toachieve the degree of discrimination between sesame andcanola oils that we obtained with FT-IR.11 Finally, thereseems to be no signi® cant difference between the year-old and fresh sesame oils labeled as sesame A.

Discriminant Analysis. Having identi® ed the mostimportant wavelengths in the ® rst three principal com-ponents in the PCA study, it should be possible to usethese wavelengths alone to discriminate between the oils.Figures 7 and 8 employ the absorbencies at 3005, 967,and 1041 cm2 1, respectively, in order to represent the ® rstthree principal components by using the wavelength withthe largest loading magnitude for each oil. The separation

APPLIED SPECTROSCOPY 1123

FIG. 8. Two-wavelength discriminant analyses of oils, 1041 cm2 1 vs.cis C± H stretch (1005 cm2 1). FIG. 9. PLS estimation of refractive indices of oils vs. measured re-

fractive indices. A line of unity slope and zero intercept has been su-perimposed.

FIG. 10. PLS estimation of viscosities (cP) of oils vs. measured vis-cosities. A line of unity slope and zero intercept has been superimposed.

between oil types is nearly as good as in the full-spectrumapproach of PCA. A notable exception is the overlap ofthe corn and soybean oils when only the three wave-lengths are used. Soybean oil is higher in tri-unsaturatedlinolenic acid, while corn oil is higher in mono- (oleic)and di-unsaturated (linoleic) acids,11 giving soybean oil aslightly higher iodine value (130 vs. 123). However, thecis-vinyl C± H stretch at 3005 cm2 1 is insuf® cient to re-solve these oils. The absorbencies at 1148, 1118, and1096 cm2 1 appear to be important to the discriminationof these two oils. These small peaks probably belong tothe C± C-stretching region of 850± 1150 cm2 1, which issensitive to changes in the fatty acid backbone.36,37

PLS. Figures 9 and 10 show the PLS-estimated vs. themeasured refractive indices and viscosities, respectively,of the 24 brands of oils, two margarines, and one oilmixture. In both cases, four principal components gavethe minimum error in cross-validation. The lines throughthe points are lines of perfect prediction, i.e., lines ofunity slope and zero intercept. A linear regression of theestimated vs. the measured properties leads to slopeswithin 1% of unity and intercepts near zero. The SEEwere 0.0002 for the refractive indices and 0.52 cP for theviscosities. These value translate to 2.2% and 2.8%, re-spectively, of the ranges of these properties in the learn-ing set.

In both PLS models, the ® rst two principal componentsdescribed the cis and trans alkenes, respectively. Theloadings and percent variances contained in these twoprincipal components were virtually identical to those inthe PCA study. PC3 in the refractive-index model andPC4 in the viscosity model contained about 2% of thevariance and described the sesame oils. They were verysimilar to the PC3 from the PCA study. PC4 in the re-fractive-index study seemed to be modeling the canolaoils, while PC3 in the viscosity model seemed to be mod-eling some of the canola oils and some of the sesameoils. Both contained about 1% of the variance.

CONCLUSION

Fourier transform infrared spectroscopy and PCA wereable to easily distinguish edible oils according to theirvegetable origins. Absorbencies corresponding to the cisdouble-bond content were predominately responsible for

this discrimination. Partially hydrogenated vegetable oilswere distinguished through the trans C± H-bending ab-sorbance. Finally, sesame oils were uncovered throughthe detection of absorbencies characteristic of the spectraof small amounts of impurities unique to these oils. Thegreater sensitivity of FT-IR over NIR to these impuritiesallowed FT-IR to show better discrimination with respectto sesame and canola oils. The same spectral propertiesdetected by PCA were similarly involved in the PLSmodels for the prediction of the refractive indices andviscosities of the oils.

A major drawback to the method as applied in thisstudy was the dif® culty and time involved in samplepreparation caused by using a ® xed-pathlength IR cell.The use of a horizontal ATR cell would greatly speed upsample handling. A further advantage of this techniqueis that ATR tends to attenuate the stretching region morethan the ® ngerprint region of mid-infrared spectra. Thisfactor would decrease the absorbencies in the C± H andcarbonyl stretching regions, bringing them into the rangeof reliable values and allowing the retention of their valu-able information in the model.

1124 Volume 51, Number 8, 1997

ACKNOWLEDGMENT

The authors are grateful to the Exxon Educational Foundation for agrant supporting undergraduate summer research.

1. J. Dupont, P. J. White, and E. B. Feldman, J. Am. Coll. Nutr. 10,577 (1991).

2. N. Harmann and S. J. Hawkes, J. Chromatogr. Sci. 8, 610 (1970).3. M.-P. Derde, H. W. Krueger, and R. H. Reesman, J. Assoc. Off.

Anal. Chem. 67, 721 (1984).4. A. C. Noble, R. A. Flath, and R. R. Forrey, J. Agric. Food Chem.

28, 346 (1980).5. W.-O. Kwan and B. R. Kowalski, J. Agric. Food Chem. 28, 356

(1980).6. I. Moret, G. Scarponi, and P. Cescon, J. Sci. Food Agric. 35, 1004

(1984).7. W.-O. Kwan and B. R. Kowalski, J. Food Sci. 43, 1320 (1978).8. S. Bayer, J. A. McHard, and J. D. Winefordner, J. Agric. Food

Chem. 28, 1306 (1980).9. L. S. Pilando and R. E. Wrolstad, J. Food Compos. Anal. 5, 10

(1992).10. S. J. Swarin and C. A. Drumm, Spectroscopy 7(7), 42 (1992).11. T. Sato, J. Am. Oil. Chem. Soc. 71, 293 (1994).12. I. J. Wesley, R. J. Barnes, and E. A. J. McGill, J. Am. Oil. Chem.

Soc. 72, 289 (1995).13. R. T. O’ Connor, J. Am. Oil. Chem. Soc. 33, 1 (1956).14. D. Chapman, J. Am. Oil. Chem. Soc. 42, 353 (1965).15. W. M. Doyle, Process Control Qual. 2, 11 (1992).16. F. R. van de Voort, Food Res. Int. 25, 397 (1992).17. Y. Wang and B. R. Kowalski, Appl. Spectrosc. 46, 764 (1992).18. C. A. Young, K. Knutson, and J. D. Miller, Appl. Spectrosc. 47, 7

(1993).

19. F. R. van de Voort, J. Sedman, G. Emo, and A. A. Ismail, FoodRes. Int. 25, 193 (1992).

20. V. Bellon-Maurel, C. Vallat, and D. Gof® net, Appl. Spectrosc. 49,563 (1995).

21. P. Geladi, D. MacDougall, and H. Martens, Appl. Spectrosc. 39,491 (1985).

22. H. Martens and T. Nñ s, Multivariate Calibration (John Wiley andSons, New York, 1989), Chap. 7, pp. 345± 350.

23. T. Isaksson and T. Nñ s, Appl. Spectrosc. 42, 1273 (1988).24. S. Wold, K. Esbensen, and P. Galadi, Chemom. Intel. Lab. Syst. 2,

37 (1987).25. S. Wold, Pattern Recognition 8, 127 (1976).26. S. Wold and M. SjoÈ stroÈ m, in Chemometrics: Theory and Applica-

tion, B. R. Kowalski, Ed., ACS Symp. Series (American ChemicalSociety, Washington, DC, 1977), Chap. 12.

27. The Mathworks Inc., Natick, Massachusetts.28. CRC Handbook of Chemistry and Physics, D. R. Lide, Ed. (CRC

Press, Ann Arbor, Michigan, 1990), 71st ed., pp. 6± 143.29. Y. Miyashita, T. Itozawa, H. Katsumi, and S.-I. Sasaki, J. Chemom.

4, 97 (1190).30. H. Martens and T. Nñ s Multivariate Calibration (John Wiley and

Sons, New York, 1989), Chap. 3, pp. 111± 112.31. D. M. Haaland and E. V. Thomas, Anal. Chem. 60, 1193 (1988).32. R. G. Arnold and R. E. Hartung, J. Food Chem. 36, 166 (1971).33. H. W. Lemon and C. K. Cross, Can. J. Res. 27B, 610 (1949).34. L. A. Appelqvist and A. Kamal-Eldin, J. Am. Oil. Chem. Soc. 68,

693 (1991).35. L. Qianrong, R. S. Ward, and A. Pelter, Spectrosc. Lett. 25, 301

(1992).36. R. G. Sinclair, A. F. McKay, and R. N. Jones, J. Amer. Chem. Soc.

74, 2570 (1952).37. R. G. Sinclair, A. F. McKay, G. S. Myers, and R. N. Jones, J. Amer.

Chem. Soc. 74, 2578 (1952).