Near infrared spectroscopy X-1X. Near infrared spectroscopyReferences:- D. C. Harris och M. D. Bertolucci, Symmetry and Spectroscopy, Oxford UniversityPress, 1978.- J. M. Hollas, Modern spectroscopy, wiley, Chichester, 1987.- M. Karplus, R. N. Porter, Atoms & Molecules, Benjamin,1970.- E. F. H. Brittain, W. O. George, C. H. J. Wells, Academic Press,1970.- G. Herzberg, Spectra of Diatomic Molecules, Van Nostrand, 1950.- G. Herzberg, Electronic Spectra and Electronic Structure of Polyatomic Molecules,Van Nostrand, 1966.- K. P. Huber och G. Herzberg, Constants of Diatomic Molecules, Van Nostrand, 1979.- CRC Handbook of Spectroscopy.- Handbook of chemistry and physics, 55th Edition, R. C. Weast, Ed., CRC Press, 1974.- Near-infrared spectroscopy. Principles, instruments, applications, H. W. Siesler, Y.Ozaki, S. Kawata och H. M. Heise, Ed.s, Wiley, Weinheim, 2002.- M. Otto, Chemometrics. Statistics and computer application in analytical chemistry,Wiley, 1999.

X-2 Molecular spectroscopyX.1. The basicsThe infrared spectral range is from 10 to 12,500 cm�1corresponding to wavelengths from1 mm to 800 nm. It can be divided in three parts, the far infrared (FIR), mid infrared(MIR) and near infrared (NIR) regions. Crude limits and a few important applicationsare indicated in the table below.Region Wavenumber Wavelength VibrationsFar ir 10 - 400 cm�1 1 mm - 25 �m Lattice vibrations, rotationsMid ir 400 - 4000 cm�1 25 - 2.5 �m FundamentalsNear infrared 4000 - 12,500 cm�1 2500 - 800 nm OvertonesThe far infrared region contains numerous signals from the fundamental transition witha low frequency, combination bands, lattice vibrations, pure rotational transitions andmore. The mid infrared region is the region where most of the fundamental transitions oforganic compounds are observed. There are also various combination and overtone bands,of course. The near infrared region only contains overtones and combination bands,mostly overtones of the X-H stretching vibrations.Raman spectra are observed in the near infrared region in case the incident light used toinduce the Raman scattering is in that region. The transitions are the same as in infraredspectroscopy and the transitions energies usually correspond fall in the mid infrared region.More detailed discussion of Raman spectroscopy is given in a separate chapter.The fundamental frequency of theC-H stretching vibrations lies near 3000 cm�1 so thatthe �rst overtone is found near 6000 cm�1 (1.6 �m) and the second one near 9000 cm�1 (1.1�m). The exact band positions depend strongly on the anharmonicity of the vibrations.The fundamental N-H stretching frequency lies near 3400 cm�1 so that the �rst and secondovertones are found close to 7000 (1.4 �m) and 10,000 cm�1(1 �m), respectively. The O-Hstretching frequencys are still higher. Most of the other fundamental transitions lie below1600 cm�1 which means that the �rst, and in many cases also the second overtone lie in themid infrared region. Therefore they are usually ignored in the near infrared spectroscopy.The vibrations appear as parts of combination bands, of course.Please note that the vibrational freauencies are usually given as wavenumber ( cm�1) in themid infrared region while wavelengths (�m) are often used in near infrared spectroscopyto indicate the band positions.Near infrared spectroscopy is absorption spectroscopy. Therefore the selection rules

Near infrared spectroscopy X-3that were previously discussed in the chapter on general ir theory are used also in nirspectroscopy. However, the overtones of degenerate vibrations need to be treated speciallyas discussed earlier. From that discussion it follows that even if a fundamental transitionwould be symmetry forbidden the overtone may be symmetry allowed. Therefore a fewvibrations may be easier to detect in the nir spectrum than the mid infrared spectrum. Thisis the case, e.g., for the ethynyl group �C-H near 1.6 �m. Normally, the nir spectroscopyis not used for identifying compounds but for quantitative analysis.The exact positions of the absorption bands are di�cult to predict because the anhar-monicity plays an important role in the overtones. E.g., in water (H2O(l)) the situationis still more complicated due to the hydrogen bonds. A comparison of the fundamentalfreauencies is given in the table below.Normal vibration Wavenumber [cm�1]H2O(g) H2O(l)�1 3657 3404�2 1595 1643�3 3756 3404The lowest overtones and combination bands of liquid water H2O(l) in the near infraredregion are Wavenumber [cm�1] Assignment5260 a�1 + �2 + b�3, a+ b = 16800 a�1 + b�3, a + b = 28330 a�1 + �2 + b�3, a+ b = 210310 a�1 + b�3, a + b = 311960 a�1 + �2 + b�3, a+ b = 3The intensity of the overtones is very low. The intensity diminishes typically by a factorof 10 for each higher overtone. For example, consider the calculated oscillator strengthsfor the two C-H stretching vibrations in naphtalene.1 The notations are de�ned in FigureX.1.1 H. G. Kjaergaard and B. R. Henry, J. Phys. Chem. 99 (1995) 899.

X-4 Molecular spectroscopyHα

Hβ

Fig. X.1. Naphtalene.~� [cm�1] Oscillator strength f Assignment[3040 9� 10�6 j1 >]5957 2:8� 10�7 j2 > �5989 3:9� 10�7 j2 > �8759 3:3� 10�8 j3 > �8806 5:0� 10�8 j3 > �11445 4:5� 10�9 j4 > �11506 6:6� 10�9 j4 > �14014 6:6� 10�10 j5 > �14088 9:4� 10�10 j5 > �16467 1:1� 10�10 j6 > �16553 1:5� 10�10 j6 > �The aliphatic CH stretching vibrations tend to have 2-3 times higher oscilltor strengths.

Near infrared spectroscopy X-5X.2. InstrumentsThe near infrared spectroscopy is based on absorption and therefore the spectrometersare similar to those used in the conventional mid infrared or UV-vis regions. For the shortNIR wavelengths (< 2�m) UV-vis-NIR instruments are often used while for the longwavelengths (> 2�m) ordinary mid-ir instruments, usually FTIR spectrometers, aremost suitable. Certain optical elements, notably the gratings or the beam splitters, mustbe replaced when switching to the NIR region, of course. Instruments that are speci�callyconstructed for the NIR region usually need not have as high resolution as is commonin both mid-ir and UV-vis. On the other hand, the instruments must be very sensitivebecause the absorption bands are extremely weak. The NIR spectrometers are oftenused as analytical instruments on-line in idustrial processes which means that they mustbe robust and tolerate the harsh environment they are placed in.The most common spectrometer con�guration is transmission spectroscopy where thelight passes through the sample. The signal in the re�ection measurements is often quiteweak. The sample can be placed after the monochromator or interferometer. In this caseone must use a detector element that has a relatively large active area. This con�gurationis shown schematically in Figure X.2.Source Monochromator DetectorSampleFig. X.2. Transmission spectrometer in front of the sample. Instead of a monochromatoran interferometer may be used.If the sample is placed in front of the spectrometer the sample will be illuminated withintense broad band radiation from a thermal source. The spectrum is formed on a detectorelement with rather small dimensions, or an array detector of some kind, today usuallya CCD detector. The latter model can be more robust as no moving parts are needed.This is quite acceptable because the resolution does not need to be very high in mostapplications. The con�guration is shown schematically in Figure X.3.The most popular spectrometer type today is based on an interference �lter. The�lter is actually a Fabry-Perot interferometer that is shown schematically in Figure X.4.

X-6 Molecular spectroscopySource Monochromator DetectorSampleFig. X.3. Transmission spectrometer after the sample. Instead of a monochromator aninterferometer may be used.Intensity of the transmitted light reaches a maximum when the optical path length in theinterferometer is a multiple of the desired wavelength �p. If the thickness of the opticalelement is d and the refractive index is n the optical path will obey the criterionm�p = 2nd (X:1)for a beam that lies along the optical axis.

Fig. X.4. The principle of a Fabry-Perot interferometer.The light may also come at a small angle � as is shown in the �gure but in this case theoptical path length will be longer. Let the surfaces of the interferometer have a re�ectanceR. The the transmittance of the interference �lter can be expressed asT (�) = (1� R)2(1�R)2 + 4R sin2(2�nd cos �=�) : (X:2)

Near infrared spectroscopy X-7

cm-1

5000 10000 15000

T Ä%Å

0

20

40

60

80

100

R=90 %

R=50 %

R=10 %

Fig. X.5. Transmittance of a Fabry-Perot interferometer.Model curves computed using the above formula are shown in Figure X.5. The curves werecalculated for a �lter optimized for a wavelength (or 2nd) of 2 �m and the incident angle� = 5�.In spectrometers a rotating disk �lter with a varying thickness is used such that thewhole desired spectral range is covered. Such a disk is shown schematically in Figure X.6.Alternatively, a wedge-shaped �lter that moves back and forth may be used.Fig. X.6. An interferense �lter.The dispersive spectrometers are discussed in detail in Appendix D and the interferometrictechnique in Appendix E.The most common light sources are thermal, either tungsten-halogen sources orglobar. The �rst one is common in UV-vis spectrometers because it also emits intense UVand visible light but it is alse suitable in the NIR region down to approx. 2.5 �m (4000cm�1). A xenon lamp can be used in the range 0.2 to 2 �m. Globar (silicaon carbide)can be used in the range 1.1 to 100 �m. For certain speci�c measurements one can use lightemitting diodes (LED) which have a relatively narrown emission band. If the availableemission maximumhappens to correspond to the important absorption band of the samplethese are excellent sources. The choice of material will determine the wavelength of theemitted light. Thus GaAs will emit light at 940 nm and this can be used for determingoils and fats. GaAlAs will emit in the range 650 to 900 nm depending of the amount ofaluminium. InGaAs covers the range 1.1 to 1.6 �m which is perfect for determining themoisture in the sample from the OH overtone at 1.45 �m. A summary of detectors useful

X-8 Molecular spectroscopyin the NIR region is shown in Figure X.7. The most common type is the PbS detector thathas a broad sensitivity curve and can be used at room temperature even if the sensitivityincreases when cooled using a Peltier element. Multichannel detectors that are mixturesof various detector types, such as silicon, germanium and indium arsenide, are also popularbecause they are very sensitivite in a broad range.

1 2 3 4 5108

109

1010

1011

1012

1013

1014

D*

Wavelength (µm)

PbSe (300 K)

PbSe (196 K)

PbS (77 K)

PbS (196 K)

InSb (77 K)InAs (77 K)InGaAs (300 K)

Ge (77 K)

Fig. X.7. Detectors in NIR region.Optical properties of various window material useful in the NIR region are shown in FigureX.8. 2

2 S. Kawata, p. 75 in Near infrared spectroscopy, H. W. Siesler et al., Ed.'s, Wiley, 2002.

Near infrared spectroscopy X-9

µm0.8 1.0 2.0 3.0

T [%]

0

20

40

60

80

100

Si Ge

NaCl

LiF

KBr

KRS-5

Quarz

Fig. X.8. Optical materials for NIR region.

X-10 Molecular spectroscopyX.3. Sample handlingNear infrared spectroscopy is mainly used for quantitative analysis. Therefore thecalibration model must be reliable. The model itself is built using chemometrics but itmust be based on a representative training set that covers all observed and also futurevariations in the material. Only then can the model have predictive power. Consequently,the sampling techniques play a central role both when the model is constructed and laterin the production measurements.The samples must be taken at �bottle neck� points in the production line, i.e., at pointsthat all the material passes in a relatively small volume. Also when a spectrometer mea-sures a process on line the measuring points should be selected similarly. The training setmust cover all thinkable conditions of the material, e.g., the consistency, moisture content,temperature etc. For agrary products for example, one must consider the di�erent soilcompositions on the �elds from which the products are delivered, the di�erent harvestingmethods at the farms and even the annual changes in the weather conditions.The samples for near infrared spectroscopy usually need not be as carefully prepared as isoften the case in other branches of spectroscopy (UV-vis and mid-ir).The samples can be ground but the process is di�cult to control and may easily introduceadditional variations in the sample, depending on the machinery used, the moisture contentand temperature of the sample etc. Samples such as fruit or meat can sometimes be cut orshredded. Sometimes one may press juices from the samples for analysis. Some materialssuch as the diary products may need to be homogenized before analysis.The temperature of the samples is known to a�ect the NIR spectrum. if samples atdi�erent temperatures are not included in the training set the temperature must be ad-justed before the spectroscopic analysis. Themoisture content also a�ects the spectrumstrongly. Therefore samples with varying moisture content must be included in the calib-ration model. Also in this case one must control that the moisture content of the analysissample does not exceed the limits of the model. Note that some samples may loose waterduring storage before the analysis.It is customary in the NIR spectroscopy to use the relative absorbance instead of ab-solute absorbance. A reference measurement is obtained by letting the light pass througha ceramic plate giving the intensity Ir(�). The light intensity measured for the sample isIs(�). The relative absorbance is thenAs(�) = log�Ir(�)Is(�)� : (X:3)This corresponds to the di�erenceAs(�) = As � (�)�Ar � (�): (X:4)

Near infrared spectroscopy X-11The same measuring methods as in mid infrared spectroscopy can be used also in the nearinfrared spectroscopy. The most common method is transmission but trans�ection andspecular re�ection can be used. Fiber optics is in common use. In that method the end ofthe �ber truss must be pressed against the sample so that the light actually passes throughthe sample instead of being just re�ected from the surface. Thus this contact methodcorresponds in a way to di�use re�ectance.A vast amount of di�erent sample cells has been developed for various measuring condi-tions. It is usually the praxis that one does not buy just a spectrometer but an analysismethod complete with specially designed sample cells, sampling techniques and calibrationmodel.The calibration model is certainly as important part of the analysis equipment as is thespectrometer itself. It is based on chemometrics.

X-12 Molecular spectroscopyX.4. ChemometricsChemometrics is that part of statistics that is useful for plnanning of experiments andanalysis of results in chemistry. The most important methods are based onmultivariableanalysis; examples of such methods are the principal component analysis (PCA) andpartial least squares analysis (PLS). It is desired that all components and all contentrationintervalls that will present in the analysis samples are known and represented in the trainingset. Sometimes one cannot be sure that all conditions have been included in the trainingset. Sysch systems are called grey. In black systems the properties of the future analysissamples are completely unknown at calibration time.In the traditional Beer-Lambert method one uses a few solutions with known concent-rations and determines the absorption of each solution. In this way one has created atraining set. Then one plots a straight line for absorption vs. concentration. This consi-tutes the calibration model. Denote the concentration at a given wavelength by y and theabsorption at the same wavelength by x,x = log10�I0I � : (X:5)Beer-Lambert's law is then x = � � ` � y: (X:6)What one needs to calculate is the concentration and therefore the equation is modi�ed toread y = x�` : (X:7)The calibration model is a straight line,x = b1 � y + b0: (X:8)The intercept b0 is mainly determined by the disturbing components in the measurementand can be considered as an error term for the non-systematical variations.A corresponding classical multicomponent analysis uses the same solutions as above,let their number be m, but one does not use a single wavelength but the whole spectrum(i.e., the absorbances determined at n di�erent wavelengths). The absorbances are orderedin a m � n matrix X (m lines and n columns). Let every sample in the calibration setcontain l di�erent chemical components in varying concentrations. The concentrations ofeach component in all the calibration samples form a m� l matrix Y . Now one can writethe calibration model basically as above but as a matrix eauationX = Y RT +E: (X:9)

Near infrared spectroscopy X-13The matrix RT is a l � n matrix that contains the responses of each component at everymeasured wavelength and the m�n matrix E contains that part of the variations that themodel cannot explain. It is called the error term or resisual term. In case the spectra havebeen pretreated so that the mean of the residual terms is zero the last term can be omitted.If the spectra of the pure components are known the responses can be read directly andthe matrix RT is known. Then one does not need to any calibration. Instead, one cancalculate the concentrations of the analysis samples u from(y(u))T = (x(u))TR (RT R)�1; (X:10)where the vectors have n elements. If the spectra of the pure components are not availablethe response matrix must be determined fromRT = (Y T Y )�1 Y T X; (X:11)where the matrises describe the training set. The drawback of the classical least squaresmethod is that all the chemical components must be known when the model is calibrated.This leads often to an expensive calibration process.A possibility to formulate an alternative multicomponent method is indicated in the one-dimensional model. The desired quantity is the concentration y. To obtain this the calib-ratin model can be directly written asy = b0 + b1 � x: (X:12)This will give an inverse calibration model. I there is one chemical component but twospectra with n observations in each one will obtain the system of equations� y1 = b0 + b1x1;1 + b2x1;2 + : : :+ bnx1;n + e1y2 = b0 + b1x2;1 + b2x2;2 + : : :+ bnx2;n + e2 : (X:13)Write xi;0 = 1, i = 1; 2 after the intercept b0. The one can write the system of equationsin matrix form as y = X b+ e: (X:14)The least squares method gives the coe�cient bk for the n observation points asb = (XT X)�1 XT y: (X:15)If one measures the spectrum of an analysis sample at the same observation points onecan immediately calculate the concentration.The classical inverse method requires that one forms the inverse matrix (XT X)�1. Thismay be an instable process if there are interdependences between the variables. In or-der to avoid these complications one can use pseudo inverse matrices where one rotates

X-14 Molecular spectroscopythe coordinate axes basically via a unitary transformation but with a modi�cation. Oneintroduces namely a new matrix Z and writesX = Q1 Z Q2T Q1T Q1 = I Q2T Q2 = I: (X:16)The matrix Z is a quadratic matrix, the dimensions of which may be smaller than thoseof the matrix X. In that case the matrix Z forms a �lter. This is the mathematical basisof the partial least squares method (PLS).The principal component analysis method (PCA is a qualitative method where theobservations are calssi�ed in groups. In this method one seeks for a combination of variablesthat maximize the variations along the new coordinate axes.More information on the chemometric method is found in textbook in that �eld.

Near infrared spectroscopy X-15