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Introduction to FT-IR spectroscopy
INTRODUCTION
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Introduction to
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Discovery of infrared light
In the year 1800 the astronomer Friedrich Wilhelm Herschel analyzed the spectrum of sunlight. Herschel created the
spectrum by directing sunlight through a glass prism so that the light was divided into its different colors. He measured
the heating ability of each color using thermometers with blackened bulbs. When he measured the temperature just
beyond the red part of the spectrum he noticed some kind of invisible radiation. Much to his surprise he found that the
area close to the red part (i.e. an area apparently devoid of sunlight) had the highest heating ability of all. Herschel
concluded that there must be a different kind of light beyond the red portion of the spectrum, which is not visible to the
human eye. This kind of light became known as “infrared” (below red) light.
Herschel then placed a water-filled container between the prism and thermometer and observed that the temperature
measured was lower than the one measured without the water. Consequently, the water must partially absorb the
radiation. In addition, Herschel could prove that depending on how the prism was rotated (i.e. depending on the spectral
range) the difference in the temperatures measured for each color varied. This was the beginning of infrared
spectroscopy.
Infrared spectroscopy measures the infrared light that is absorbed by a substance. This absorption depends on the
wavelength of the light.
Friedrich Wilhelm Herschel
(1738 - 1822)
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The electromagnetic spectrum
Visible light and infrared light are two types of
electromagnetic radiation, but with different wavelengths, or
frequencies. In general, electromagnetic radiation is defined
by the wavelength  or the linear frequency . The
wavelength is the distance between two maxima on a
sinusoidal wave.
The frequency is the number of wavelengths per unit time.
Since all electromagnetic waves travel at the speed of light,
the frequency corresponding to a given wavelength can be
calculated as:
 = c/
According to the Plank’s Radiation Law, the frequency of
electromagnetic radiation is proportional to its energy.
E = h•
In infrared spectroscopy wavenumber is used to describe
the electromagnetic radiation. Wavenumber is the number
of wavelengths per unit distance. For a wavelength  in
microns, the wavenumber, ~, in cm-1, is given by
Sinusoidal wave of wavelength 
~ = 10000/
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The electromagnetic spectrum
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Interaction of radiation and matter
If matter is exposed to electromagnetic radiation, e.g. infrared light, the radiation can be absorbed, transmitted, reflected, scattered or undergo
photoluminescence. Photoluminescence is a term used to designate a number of effects, including fluorescence, phosphorescence, and Raman
scattering.
Matter
Photoluminescence
Incident light beam
Absorption
Transmission
Reflection
Scattering
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Interaction of radiation and matter
Vibration theory
IR spectroscopy is based on the absorption of infrared light by the substance to be measured. This absorption excites molecular vibrations and
rotations, which have frequencies that are the same as those within the infrared range of the electromagnetic spectrum.
The following simple model of an harmonic oscillator used in classical physics describes IR absorption. If atoms are considered to be particles with a
given mass, then the vibrations in a diatomic molecule (e.g. HCl) can be described as follows:
Mechanical model of a vibrating diatomic molecule
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Vibration theory
The molecule consists of mass m1 and m2 connected by a spring. At equilibrium, the distance between the two masses is r0. If the molecule is stretched
by an amount r = x1 + x2, then a restoring force, F, is produced. If the spring is released, the system will vibrate around the equilibrium position.
According to Hooke’s Law, for small deflections the restoring force is proportional to the deflection:
F = -k . r
Since the force acts in a direction opposite to the deflection the proportionality constant, or force constant, k, is negative in sign. The force constant is
called the spring constant in the mechanical model, whereas in a molecule the force constant is a measure of the bond strength between the atoms.
For a harmonic oscillator it is possible to calculate the vibrational frequency, , of a diatomic molecule as follows:
being the reduced mass.
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Vibration theory
On the basis of the equation above it is possible to state the following:
1)
The higher the force constant k, i.e. the bond strength, the higher the vibrational frequency, ~, (in wavenumbers).
3 absorption peaks for different force constants. Note that by convention, in infrared
spectroscopy wavenumbers are plotted right-to-left; i.e. highest wavenumber to the left.
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Vibration theory
2)
The larger the vibrating atomic mass, the lower the vibrational frequency, ~, (in wavenumbers).
3 absorption peaks for different atomic masses. Note that by convention, in infrared spectroscopy
wavenumbers are plotted right-to-left; i.e. highest wavenumber to the left.
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Vibration theory
For the harmonic oscillator model, the potential energy well is
symmetric. According to quantum-mechanical principles molecular
vibrations can only occur at discrete, equally spaced, vibrational levels,
where the energy of the vibration is given by:
Ev=(v + ½) h  
v = 0, 1, 2, 3, ...
Where h is Plank’s constant and v is the vibrational quantum number.
Even in case of v = 0, which is defined as the ground vibrational level,
a molecule does vibrate:
Ev= ½ h  
When absorption occurs, the molecule acquires a clearly defined
amount of energy, (E = h  ), from the radiation and moves up to the
next vibrational level (v = +1). If the molecule moves down to the next
vibrational level (v = -1), a certain amount of energy is emitted in the
form of radiation. This is called emission. For a harmonic oscillator, the
only transitions permitted by quantum mechanics are up or down to the
next vibrational level (v = 1).
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Potential energy curve for a harmonic oscillator
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Vibration theory
A more accurate model of a molecule is given by the anharmonic
oscillator. The potential energy is then calculated by the Morse
equation, and is asymmetric. The energy levels are no longer equally
spaced, and are given by:
Ev=(v + ½) h   - (v + ½)2 xGl h  
where xGl is the anharmonicity constant.
The anharmonic oscillator model allows for two important effects:
1) As two atoms approach each other, the repulsion will increase
very rapidly.
2) If a sufficiently large vibrational energy is reached the molecule
will dissociate (break apart). This is called the dissociation energy.
In the case of the anharmonic oscillator, the vibrational transitions no
longer only obey the selection rule v = 1. This type of vibrational
transition is called fundamental vibration. Vibrational transitions
with v = 1, 2, 3, ... are also possible, and are termed overtones.
Potential energy curve for an anharmonic oscillator
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Vibration theory
What kind of molecules absorb infrared light?
Infrared light can only be absorbed by a molecule if the dipole moment of the specific group of atoms changes during the vibration. The greater the
change in dipole moment, the stronger the corresponding IR absorption band will be.
Heteronuclear diatomic molecule
Vibrations not accompanied by changes in the dipole moment can not be excited by absorption of IR light, and are termed IR inactive. A consequence
of this is that homonuclear diatomic molecules, e.g. H2 or O2, do not have any IR spectrum.
Homonuclear diatomic molecule
Note: Raman scattering occurs if the polarizability of the of the bond changes during the vibration. This means that IR-inactive vibrations are Raman
active if the polarizability changes. Raman and IR spectra therefore complement each other.
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Separation of spectral ranges
The mid-infrared, or MIR, is the spectral range from 4,000 to 400 cm-1 wavenumbers. In this range fundamental vibrations are typically excited. In
contrast, in the ‘near-infrared’, or NIR, spectral range, which covers the range from 12,500 to 4,000 cm-1 wavenumbers, overtones and combination
vibrations are excited. The far infrared’, or FIR, spectral range is between 400 and about 5 cm-1 wavenumbers. This range covers the vibrational
frequencies of both backbone vibrations of large molecules, as well as fundamental vibrations of molecules that include heavy atoms (e.g. inorganic or
organometallic compounds).
NIR
15,000 cm-1
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400 cm-1
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Since the development of the first
spectrophotometers in the beginning of 20th
century a rapid technological development has
taken
place.
The
first-generation
spectrometers were all dispersive. Initially, the
dispersive elements were prisms, and later on
they changed over to gratings. In the mid
1960s IR spectroscopy witnessed a revival due
to the advent of spectrometers that utilized the
Fourier transform (FT-IR). These secondgeneration spectrometers, with an integrated
Michelson interferometer, provided some
significant advantages compared to dispersive
spectrometers.
Today,
almost
every
spectrometer
used
in
mid-infrared
spectroscopy is is of the Fourier transform
type. This is the reason why only FT-IR
technology will be described in the following.
Bruker Optics has specialized in the field of
FT-IR spectroscopy since 1974, and is one of
the leading manufacturers of FT-IR, FT-NIR
and FT-Raman spectrometers throughout the
world. The spectrometers are developed for
analytical chemistry, life science, process, and
many other fields.
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The working principle of an FT-IR spectrometer
Infrared light emitted from a source (e.g. a SiC glower) is directed into an interferometer, which modulates the light. After the interferometer the light
passes through the sample compartment (and also the sample) and is then focused onto the detector. The signal measured by the detector is called
the interferogram.
General FT-IR spectrometer layout
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Michelson Interferometer
The interferometer is the heart of an FT-IR
spectrometer. The collimated light from the infrared
source impinges on a beamsplitter, which ideally
transmits 50% of the light and reflects the remaining
part. Having traveled the distance L the reflected light
is hits a fixed mirror M1, where it is reflected and hits
the beamsplitter again after a total path length of 2L.
The transmitted part of the beam is directed to a
movable mirror M2. As this mirror moves back and
forth around L by a distance x, the total path length
is 2(L + x). The light returning from the two mirrors
is recombined at the beamsplitter, with the two beams
having a difference in path length of 2x. The beams
are spatially coherent and interfere with each other
when recombined.
Fixed
mirror M1
Movable
mirror M2
L
x
Source
L + x
Beamsplitter
x=0
Detector
Michelson interferometer
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Origin of the interferogram
The upper figure on the right shows the interferogram generated by the
detector for a monochromatic source. The interferometer splits and
recombines the two beams with a relative phase difference that
depends on the mirror displacement, or optical retardation. The two
beams undergo constructive interference, yielding a maximum detector
signal, if the optical retardation is an integral multiple of the wavelength
λ, i.e. if
2  x = n  λ
Detector signal
(n = 0, 1, 2, ...).
Destructive interference, and a minimum detector signal, occur if 2x is
a multiple of λ/2. The complete functional relationship between I(x) and
x is given by the cosine function
Optical Retardation
Monochromatic source detector signal
I(x) = S(ν)  cos (2 π ~
  x)
Spectrum
 = 1/λ, which is more common in FTIR
In which we use wavenumber, ~
spectroscopy. S(~
 ) is the intensity of a monochromatic spectral line at
wavenumber ~
 , as shown in the lower figure on the right. Intensity
shown as a function of frequency is called a spectrum, and can be
obtained by Fourier transformation of the signal that is a function of
optical retardation.
The cosinusoidal interference pattern from a monochromatic source is
very useful, because it enables a very precise tracking of the movable
mirror. All state-of-the-art FT-IR spectrometers use the interference
pattern of the monochromatic light emitted by an HeNe laser to monitor
the mirror position. The IR interferogram is digitized exactly at the zero
crossings of the laser interferogram.
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Frequency
Monochromatic source
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Origin of the interferogram
Nine wavelengths
Since spectrometers are equipped with a polychromatic
light source (i.e. many wavelengths) the interference
already mentioned occurs at each wavelength, as shown in
the upper figure on the right. The interference patterns
produced by each wavelength are summed to get the
resulting interferogram, as shown in the second figure.
Optical retardation
Resulting detector signal:
At the zero path difference of the moving mirror (x=0) both
paths all wavelengths have a phase difference of zero, and
therefore undergo constructive interference. The intensity is
therefore a maximum value. As the optical retardation
increases, each wavelength undergoes constructive and
destructive interference at different mirror positions.
Optical retardation
The third figure shows the intensity as a function of
frequency (I.e. the spectrum), and we now have nine lines.
Spectrum
consisting of 9 single frequencies
Frequency
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Origin of the interferogram
Spectrometers are equipped with a broadband light source, which yields a continuous, infinite number, of wavelengths, as shown in the figure on the
left. The interferogram is the continuous sum, i.e. the integral, of all the interference patterns produced by each wavelength. This results in the intensity
curve as function of the optical retardation shown in the second figure. At the zero path difference of the interferometer (x=0) all wavelengths undergo
constructive interference and sum to a maximum signal. As the optical retardation increases different wavelengths undergo constructive and destructive
interference at different points, and the intensity therefore changes with retardation. For a broadband source, however, all the interference patterns will
never simultaneously be in phase except at the point of zero path difference, and the maximum signal occurs only at this point. This maximum in the
signal is referred to as the “centerburst”
IR-source
Resulting detector signal
Optical retardation
Frequency
Frequency distribution of a black body source
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Resulting interferogram (detector signal after modulation
by a Michelson interferometer)
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Advantages of FTIR spectroscopy
IR spectrometer principle
1) The sampling interval of the interferogram, dx, is the
distance between zero-crossings of the HeNe laser
interferogram, and is therefore precisely determined by the
laser wavelength. Since the point spacing in the resulting
spectrum, d~
 , is inversely proportional to dx, FT-IR
spectrometers have an intrinsically highly precise
wavenumber scale (typically a few hundredths of a
wavenumber). This advantage of FT spectrometers is
known as CONNES’ advantage.
2) The JAQUINOT advantage arises from the fact that the
circular apertures used in FTIR spectrometers has a larger
area than the slits used in grating spectrometers, thus
enabling higher throughput of radiation.
Dispersive IR spectrometer
3) In grating spectrometers the spectrum S(ν) is measured
directly by recording the intensity at successive, narrow,
wavelength ranges. In FT-IR spectrometers all wavelengths
from the IR source impinge simultaneously on the detector.
This leads to the multiplex, or FELLGETT’S, advantage.
The combination of the Jaquinot and Fellgett advantages
means that the signal-to-noise ratio of an FT spectrometer
can be more than 10 times that of a dispersive
spectrometer.
FT-IR spectrometer
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The Fourier Transform
Data acquisition results in a digitized interferogram, I(x),
which is converted into a spectrum by means of the
mathematical operation called a Fourier Transform (FT).
The general equation for the Fourier Transform is applicable
to a continuous signal. If the signal (interferogram) is
digitized, however, and consists of N discrete, equidistant
points, then the discrete version of the FT (DFT) must be
used:
S(k . Δ~
)=
Σ I(n  Δx)  exp (i2πk  n/N)
The continuous variables x and ~
 have been replaced with
n  x and k  ~
,
representing
the
n discrete interferogram

points and the k discrete spectrum points. The fact that we
now have a discrete, rather than continuous, function, and
that it is only calculated for a limited range of n (i.e. the
measured interferogram has a finite length) leads to
important effects known as the picket-fence effect and
leakage.
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0.40
0.35
Zero-filling factor 2
1,806
1,804
1,802
1,800
Wavenumber, cm-1
1,798
1,796
0.45
Single channel
0.50
0.55
1,808
0.35
0.40
The picket-fence effect occurs if the interferogram
contains frequency components which do not exactly
coincide with the data point positions, k.Δ~
 , in the
spectrum. The effect can be thought of as viewing the
spectrum through a picket fence, thereby hiding those
frequencies that are behind the pickets, i.e. between the
data point positions k.Δ~
 . In the worst case, if a
frequency component exactly between two sampling
positions, a signal reduction of 36% can occur.
The picket-fence effect can be reduced by adding zeros
to the end of the interferogram (zero filling) before the
DFT is performed. This interpolates the spectrum,
increasing the number of points per wavenumber. The
increased number of frequency sampling positions
reduces the error caused by the picket-fence effect.
Generally, the original interferogram size should always
be at least doubled by zero filling, i.e. zero filling factor
(ZFF) of two is chosen. Zero-filling interpolates using
the instrument line-shape, and in most cases is
therefore superior to polynominal or spline interpolation
methods that are applied in the spectral domain.
Single channel
0.45
0.50
Zero filling
Zero-filling factor 8
1,808
1,806
1,804
1,802
1,800
1,798
1,796
Wavenumber, cm-1
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Apodization
A
In a real measurement, the interferogram can only be measured for a
BOXCAR
(no apodization)
finite distance of mirror travel. The resulting interferogram can be
thought of as an infinite length interferogram multiplied by a boxcar
function that is equal to 1 in the range of measurement and 0
elsewhere. This sudden truncation of the interferogram leads to a
sinc( ~
 ) instrumental lineshape. For an infinitely narrow
 )/ ~
 ) (i.e. sin( ~
spectral line, the peak shape is shown at the top of the figure on the
B
right. The oscillations around the base of the peak are referred to as
Triangular
“ringing”, or “leakage”.
The solution to the leakage problem is to truncate the interferogram less
abruptly. This can be achieved by multiplying the interferogram by a
C
function that is 1 at the centerburst and close to 0 at the end of the
Trapezoidal
interferogram. This is called apodization, and the simplest such function
is a ramp, or “triangular apodization”.
The choice of a particular apodization function depends on the
objectives of the measurement. If the maximum resolution of 0.61/L is
D
required, then boxcar apodization (i.e no apodization) is used. If a
HAPP-GENZEL
resolution loss of 50% (compared to the maximum resolution of 0.61/L)
can be tolerated, the HAPP-GENZEL or, even better, 3-Term
BLACKMAN-HARRIS function is recommended.
E
3-TERM BLACKMANHARRIS
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Phase correction
To this point, only the ideal case has been considered, in
which the point of zero path difference is the same for all
wavelengths. In practice, due to both optical and electronic
effects, this is not the case, and the sinusoidal interference
patterns for different wavelengths are slightly shifted with
respect to each other. These phase shifts, or “phase
errors” lead to asymmetry in the interferogram. This
asymmetry is corrected during the DFT using one of a
number of “phase correction” algorithms. The algorithm
generally used was developed by Larry Mertz, and is
therefore called “Mertz phase correction”.
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The spectral resolution
d
If a spectrum consists of a pair of narrow spectral lines a
distance d apart, then the interferogram exhibits a periodic
beat pattern that is repeated after at multiples of the optical
path difference of 1/d. The smaller the spacing between the
spectral lines, the greater the period of this beat pattern. For
an optical retardation of L, the “nominal resolution” is
therefore given by 1/L. The actual, measured, resolution is
also affected by optical considerations (most importantly
aperture size) and apodization. In the case of triangular
2
apodization, the instrument line shape is a sinc(~
 ) function,
and two lines with centers separated by 1/L will have a dip of
20% between them. This is the Rayleigh criterion for the
resolution of two lines.
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To calculate a transmission spectrum the following steps need to be
performed:
•An interferogram measured without any sample in the optical
path is Fourier transformed. This results in the single-channel
reference spectrum R().
Detector signal
Transmission spectrum
Optical retardation
0.10
Single-channel intensity
0.20
0.40
0.30
Fourier transformation
4,000
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3,500
3,000
Fourier Transformation
2,500
2,000
1,500
Wavenumber, cm-1
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1,000
500
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To calculate a transmission spectrum the following steps need to be
performed:
An interferogram measured without any sample in the optical
path is Fourier transformed. This results in the single-channel
reference spectrum R().
in the
singleto the
those
Optical retardation
0.10
0.20
0.30
0.40
Fourier transformation
Single-channel intensity
A second interferogram, measured with the sample
optical path, is Fourier transformed. This results in the
channel sample spectrum S(). S() looks similar
reference spectrum, but shows less intensity at
wavenumbers where the sample absorbs radiation.
Detector signal
Transmission spectrum
4,000
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3,000
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2,500
2,000
1,500
Wavenumber, cm-1
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500
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A second interferogram, measured with the sample
optical path, is Fourier transformed. This results in the
channel sample spectrum S(). S() looks similar
reference spectrum, but shows less intensity at
wavenumbers where the sample absorbs radiation.
in the
singleto the
those
4,000
3,500
3,000
2,500
2,000
1,500
Wavenumber, cm-1
1,000
500
1,000
500
Division
Transmittance [%]
80
40
60
The final transmission spectrum T() is obtained by dividing
the sample spectrum by the reference spectrum:
0.10
an interferogram measured without any sample in the optical
path is Fourier transformed. This results in the so-called singlechannel reference spectrum ().
100
To calculate the transmission spectrum the following steps need to be
performed:
Single-channel intensity
0.30
0.40
0.20
Transmission spectrum
20
T() = S()/R()
4,000
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3,000
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2,500
2,000
1,500
Wavenumber, cm-1
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IR Measurements
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IR Measurements
There are many measurement methods available for the analysis of
samples using IR spectroscopy. It is this multitude of different
measurement techniques which provides the necessary flexibility to
analyze many different types of samples. The method selected for
analysis usually can and should be optimized for the given sample.
This short guide, however, cannot explain all measurement methods in
detail. This guide will instead give an overview of the important factors
affecting IR sample analysis and will focus on the two most common
techniques: transmission and ATR (attenuated total reflection).
Sample preparation
The necessity for and nature of sample preparation depends on the
composition, physical attributes, and absorption properties of the
sample.
Additionally, the spectral range of interest and the
measurement method applied will determine how much and what type
of preparation will be needed. In this manuscript you will find details on
the sample preparation necessary for IR transmission analysis and
basic information on ATR spectroscopy. Generally speaking,
transmission analysis requires some preparation of the sample to
ensure that the sample is optically thin. ATR spectroscopy usually
requires little to no sample preparation.
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Measuring spectra in transmission
This section describes several common procedures for sample
preparation prior to collecting IR spectra in transmission. It is important
to select the best preparation method for a given sample. Some
samples may require trial and error to get an acceptable spectrum.
Irrespective of the physical sample condition, the material should be as
homogeneous as possible. Variations in concentration or chemical
compositions within the sample can lead to confusing or erroneous
results.
Chemical composition
The position of absorption peaks and their respective intensities
depend on the intrinsic chemical structure of the “unknown”. The
characteristic absorption features of the sample are an important
factor when selecting a suitable method to prepare the sample. To
obtain meaningful spectra, strongly absorbing samples must either
be very thin or diluted with a solvent or powder which are poorly
absorbing. Significant prior knowledge of the sample may be
necessary to predict whether strongly absorbing bands will be
evident. Reference spectra of the sample or components of the
sample can prove helpful.
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Concentration
The intensity of a peak in an absorption spectrum is directly
proportional to the concentration of the sample substance concerned,
as defined by the Lambert-Beer Law:
A=•b•c
A: Absorption maximum at a given wavelength
: Molar absorption coefficient (absorption probability at a given
wavelength)
b: Sample pathlength (for samples in a cell) or sample thickness
(pressed pellets for films)
c: Sample concentration
If ε of an absorption band is high, the concentration of the unknown (c)
needs to be lower to get a peak (A) with an acceptable intensity. If the
peak (A) is weak, the unknown may need to have a higher
concentration (increase c) or the sample has to be analyzed with a
higher layer thickness (increase b).
Physical properties
Special cells are required to analyze gas, liquids or solvents (unless a
free-standing liquid film on transparent substrate material is used).
Powders must be fine, of uniform grain size and as finely-ground as
possible. Very smooth, free-standing films may exhibit interference
patterns (also known as fringing), which may cause fine spectra details
to be concealed.
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FTIR spectroscopy
Sample preparation to measure spectra in transmission
A detailed description of all procedures necessary to prepare samples used
for analysis would be beyond the scope of this guide. This section describes
some methods normally used to prepare samples and provides further
information on how to select the right preparation method. Please note that
the most well suited preparation method (for a particular sample) may only
become evident after acquiring spectra using more that one technique. If
one method turns out to be inappropriate, select a second method you think
might be appropriate or ask your applications expert.
The following sample preparation methods are most common:
1.) No sample preparation (example: free-standing film)
2.) Apply a thin film between 2 thin, transparent support plates (NaCl,
KBr etc.).
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Thin film between support plates
Typically, a few droplets are applied between two thin
transparent support plates (sandwich). The sandwich is
fixed in the sample holder. The spacing between the two
support plates is very small (typically < 0.01mm), but
sufficient for most samples. If the solution is very volatile, it
may need to be filled in a sealed cell using very thin
spacers.
Proceed with care to prevent the solution from dissolving or
affecting the support plates (e.g. mounting an aqueous
solution with two NaCl support plates would not be a good
choice - the plates would dissolve).
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Introduction to
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Sample preparation to measure spectra in transmission
A detailed description of all procedures necessary to prepare samples
used for analysis would be beyond the scope of this guide. This section
describes some methods normally used to prepare samples and provide
further information on how to select the right preparation method. Please
note that the most suited preparation method (for a particular sample)
may only become evident after acquiring spectra using more that one
technique. If one method turns out to be inappropriate, select a second
method you think might be appropriate or ask your applications expert.
The following methods are the most common to prepare samples:
1.) No sample preparation (example: free-standing film)
2.) Apply a thin film between 2 thin, transparent support plates (NaCl, KBr
etc.).
3.) Dissolve a sample powder in a spectrophotometrically pure
solvent and
- apply the solution on a transparent support plate or
- fill it into an IR liquid cell
Dissolve solid sample in a solvent
It is very important to use solvents of high quality which are
spectrophotometrically pure to avoid spurious bands
associated with contaminates present in the solvent. The
solvent selected should not be highly absorbing within the
spectral range of interest. If the solvent within the particular
spectral range is highly absorbing, the bands of the
unknown may be concealed by solvent peaks and can thus
be overlooked. For the absorption properties of different
solvents, see the reference literature.
After solvating the sample, evaporate the solvent onto a
transparent support plate (salt window), yielding a thin
sample film. The window can then be fixed in a sample
holder for analysis.
Alternatively, you can fill the solution into a liquid cell for
analysis. A reference spectrum (background) of the cell
with the pure solvent should be used. The typical cell
capacity is between 0.1 and 1 ml. Microcells with lower
capacity are also available.
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Sample preparation to measure spectra in transmission
A detailed description of all procedures necessary to prepare samples
used for analysis would be beyond the scope of this guide. This section
describes some methods normally used to prepare samples and provide
further information on how to select the right preparation method. Please
note that the most suited preparation method (for a particular sample)
may only become evident after acquiring spectra using more that one
technique. If one method turns out to be inappropriate, select a second
method you think might be appropriate or ask your applications expert.
The following methods are the most common to prepare samples:
1.) No sample preparation (example: free-standing film)
2.) Apply a thin film between 2 thin, transparent support plates (NaCl, KBr
etc.).
3.) Dissolve a sample powder in a spectrophotometrically pure solvent
and
- apply the solution on a transparent support plate or
- fill it into an IR liquid cell.
4.) Grind a powder sample into fine particles using a mortar and
pestle and prepare a nujol suspension.
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Prepare a suspension
This method is useful if the sample can be ground to very
fine particles. The sample is finely ground and mixed with a
liquid in which the sample is not soluble. The resulting
suspension is smeared onto an IR transparent support plate
and analyzed. Nujol, a kind of paraffin oil, is frequently used
to prepare suspensions.
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Introduction to
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Sample preparation to measure spectra in transmission
A detailed description of all procedures necessary to prepare samples
used for analysis would be beyond the scope of this guide. This section
describes some methods normally used to prepare samples and provide
further information on how to select the right preparation method. Please
note that the most suited preparation method (for a particular sample)
may only become evident after acquiring spectra using more that one
technique. If one method turns out to be inappropriate, select a second
method you think might be appropriate or ask your applications expert.
The following methods are the most common to prepare samples :
1.) No sample preparation (example: free-standing film)
2.) Apply a thin film between 2 thin, transparent support plates (NaCl, KBr
etc.).
3.) Dissolve a sample powder in a spectrophotometrically pure solvent
and
- apply the solution on a transparent support plate or
- fill it into an IR liquid cell.
4.) Grind a powder sample into fine particles using a mortar and pestle
and prepare a nujol suspension.
5.) For optically thin solid samples, grind the sample into fine particles
and press the powder to obrain a very fine and even pellet.
6.) Grind a solid sample into fine particles and mix it with a
IR transparent powder (KBr etc.). Press the powder mixture to a
very thin pellet.
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Press a pellet
A solid sample is ground. The fine particles are mixed with a
supporting medium (e.g. NaCl, KBr) and pressed into a
pellet. The sample should be dilute with respect to the
medium (1-5%).
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Introduction to
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Sample preparation to measure spectra in transmission
A detailed description of all procedures necessary to prepare samples
used for analysis would be beyond the scope of this guide. This section
describes some methods normally used to prepare samples and provide
further information on how to select the right preparation method. Please
note that the most suited preparation method (for a particular sample)
may only become evident after acquiring spectra using more that one
technique. If one method turns out to be inappropriate, select a second
method you think might be appropriate or ask your applications expert.
The following methods are the most common to prepare samples :
1.) No sample preparation (example: free-standing film)
2.) Apply a thin film between 2 thin, transparent support plates (NaCl, KBr
etc.).
3.) Dissolve a sample powder in a spectrophotometrically pure solvent
and
- apply the solution on a transparent support plate or
- fill it into an IR liquid cell.
4.) Grind a powder sample into fine particles using a mortar and pestle
and prepare a nujol suspension.
5.) For optically thin solid samples, grind the sample into fine particles
and press the powder to obtain a very fine and even pellet.
6.) Grind a solid sample into fine particles and mix it with a
transparent powder (KBr etc.). Press the powder mixture to a
very thin pellet.
7.) Fill an evacuated gas cell with a gaseous sample .
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Gas cell
Gaseous samples can be injected into a gas cell
(evacuated) and analyzed. The intensity of the peaks
measured is influenced by the effective pathlength of the
cell, the gas pressure (which is proportional to the
concentration), as well as molar absorptivity.
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Principles of ATR
Since its development in the 1960s, ATR (attenuated
total reflection) has been established as a standard
method for both routine and research applications.
ATR IR analysis can be utilized in many different fields
of application without having the need of an extensive
sample preparation. ATR is a reflection technique
where the IR beam is directed through an internal
reflection element (IRE) with a high index of refraction.
The IR light is totally reflected internally off the back
surface, which is in contact with the sample. The
sample must have a lower index of refraction than the
IRE to achieve total internal reflection. Upon reflection
at the IRE/sample interface, the IR light penetrates
into the sample to a small degree and the IR data from
the sample is obtained.
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Refraction and reflection
If light impinges on a boundary separating two media, the path
of the light can be described by Snell’s Law.
n1 • sin = n2 • sin


N1
N2
incidence angle
refraction angle
refraction index of medium 1 (crystal)
refraction index of medium 2 (sample)
(Medium 1)
Substance n2

The bending of light occurs at the boundary where medium 1
meets medium 2. Above a certain incidence angle, the so-called
critical angle (see c) in the chart), total reflection evolves where
this angle G is considered to be:
 = 90°
or: sinG = n2 / n1
(e.g. G = 38° for ZnSe for samples with n = 1.5)
For incidence angles > G (see d) in the chart), light is totally
internally reflected. The light beam is reflected to the original
medium at the boundary between the two mediums. Upon
reflection at the IRE/sample interface, the IR light penetrates
into the sample to a small degree and the IR data from the
sample is obtained. The electromagnetic wave that penetrates
into the sample is called an Evanescent wave.




(Medium 2)
Crystal n1
a)
b)
c)
d)
ATR fiber optics utilize many internal reflections to pass light
from one distance point to another. Some light is lost in passing
through the crystal, where the effective length for fiber optic
cables is about 1 meter in the infrared. In the NIR, fiber optic
cables can be as long as 100 meters (quartz and glass are very
transparent in the NIR).
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Depth of penetration
Sample
The IR light beam penetrates the sample and the depth
of penetration DP can be quantitatively described by the
Harrick approximation:

dp 
2np(sin 2  nsp2 )1/ 2
 =
np =
 =
nsp =
ATR crystal
wavelength
refraction index, crystal
incidence angle
refraction index ratio between sample and crystal
Dp is defined as the distance between the sample surface and
the position where the intensity of the penetrating Evanescent
wave dies off to (1/e)2 or 13.5%, or its amplitude has decayed to
1/e.
Sample
n2

n1
Refraction index
n1 > n 2
ATR crystal
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Depth of penetration
The depth of penetration depends on several parameters:
Calculated depth of penetration for typical ATR crystals
1.) Incidence angle: this angle is determined by the design
of the ATR accessory and is constant for most ATR
accessories. There are ATR accessories which have the
capability to vary the angle of incidence. This can be
helpful for depth profiling near the surface of a sample
(within the 0.5-2.0 micron range).
Refraction index
Material
at 1,000cm-1
Diamond
Depth of
penetration*
at 45°
Depth of
penetration*
at 60°
2.4
1.66
1.04
Ge
4.0
0.65
0.5
Si
3.4
0.81
0.61
ZnSe
2.4
1.66
1.04
AMTIR**
2.5
1.46
0.96
*: The depth of penetration was calculated for a sample with a refraction angle of 1.4 at
1,000cm-1.
**: AMTIR: Ge33As12Se55 glass
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Depth of penetration
The depth of penetration depends on different parameters:
Calculated depths of penetration for some typical ATR crystals
1.) Incidence angle: this angle is determined by the design
of the ATR accessory and is constant for most ATR
accessories. There are ATR accessories which have the
capability to vary the angle of incidence. This can be helpful
for depth profiling near the surface of a sample (within the
0.5-2.0 micron range).
Refraction index
Material
at 1,000cm-1
2.) Refraction index of the ATR crystal: a higher index of
refraction yields more shallow depth of penetration. ATR
units with replaceable crystals can also be used for depth
profiling of the sample (within the submicron range).
Diamond
Depth of
penetration*
at 45°
Depth of
penetration*
at 60°
2.4
1.66
1.04
Ge
4.0
0.65
0.5
Si
3.4
0.81
0.61
ZnSe
2.4
1.66
1.04
AMTIR**
2.5
1.46
0.96
*: The depth of penetration was calculated for a sample with a refraction angle of 1.4 at
1,000cm-1.
**: AMTIR: Ge33As12Se55 glass
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Depth of penetration
The depth of penetration depends on different parameters:
1.) Incidence angle: this angle is determined by the design
of the ATR accessory and is constant for most ATR
accessories. There are ATR accessories which have the
capability to vary the angle of incidence. This can be helpful
for depth profiling near the surface of a sample (within the
0.5-2.0 micron range).
Transmission
0.4
0.6
0.8
ATR
0.0
0.2
Absorbance
3.) Wavelength of light: the longer the wavelength of the
incident light (lower wavenumber), the greater the depth of
penetration into the sample. This yields an ATR spectrum
that differs from the analogous transmission spectrum,
where band intensities are higher in intensity at longer
wavelength. However, the ATR spectrum is readily
converted to absorbance units by selecting the “convert
spectrum” option in the “manipulate” pull down menu in
OPUS.
1.0
2.) Refraction index of the ATR crystal: a higher index of
refraction yields more shallow depth of penetration. ATR
units with replaceable crystals can also be used for depth
profiling of the sample (within the submicron range).
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3,500
3,000
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2,500
2,000
1,500
Wavenumbers cm-1
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Comparing transmission and ATR measurements of a three-layer film
0.2
0.3
0.4
Film top side - ATR
0.1
This ability to analyze only the surface of a sample can be a
powerful tool for the chemist. Coatings on tablets, lubricants
on integrated circuit boards, and thin polymer films are just a
few of the many applications where ATR spectroscopy can
provide information not easily obtained by any other
analytical technique.
Film bottom side - ATR
Absorbance
The ATR spectra from the top and bottom layers of the thin
film are shown to the right with the top layer at the top and
the bottom layer shown on the bottom. The transmission
spectrum is the middle spectrum. Quick inspection clearly
shows that the top and bottom layers are different
compounds and the transmission spectrum contains bands
from all three layers.
Film in transmission
0.5
The ATR technique is a surface-sensitive method due to its
inherent low depth of penetration (micrometer range). An
advantage to surface analysis is demonstrated by the
following example: An analysis of a three-layer polymer film.
4,000
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3,000
2,500
2,000
Wavenumbers
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1,500
1,000
500
cm-1
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Selecting an adequate ATR crystal
When selecting the proper crystal for ATR analysis, sample
hardness must be taken into account as well as the desired
depth of penetration and spectral range. Diamond has a very
high degree of hardness, but very distinctive lattice bands
totally absorb between 2,500 and 1,600 cm-1. Most
compounds do not have vibrations in this area.
Material
Spectral range
ZnSe
20,000 -
500 cm-1
n = 2.4
130
ZnS
50,000 - 770 cm-1
n = 2.3
250
Ge
5,000 -
550 cm-1
n = 4.0
780
Si
8,333 -
33 cm-1
n = 3.4
1,150
50,000 - 2,500 cm-1
n = 2.4
9,000
Diamond
Refraction index
Hardness***
1,600 -
0 cm-1
KRS-5*
17,000 -
250 cm-1
n = 2.4
40
AMTIR**
11,000 -
725 cm-1
n = 2.5
170
*: KRS-5: TlI/TlBr
**: AMTIR: Ge33As12Se55 glass
***: Knoop hardness
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Number of reflections - effective path length
The number of reflections depends on the crystal type, the
dimensions of the ATR crystal, and the incidence angle of
the IR beam. A parallelogram-shaped crystal which contacts
the sample on two sides can be described by:
N = l / (d • tan)
N=
l =
d =
=
Number of reflections
Crystal length
Crystal thickness
Incidence angle
A ZnSe crystal with a length of 80 mm, a thickness of 4 mm
and an incidence angle of 45° yields N = 20 reflections.
The equation for the effective path length (DE) is:
DE = N • DP
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Selecting the adequate ATR unit
Aside from selecting the appropriate ATR crystal type,
you also have to consider the size of the crystal
(number of reflections). There is a direct relationship
between the number of reflections within an ATR
crystal and the intensity ratio of the resulting
spectrum. The higher the number of reflections, the
more distinctive the bands and the better the signalto-noise ratio. Similarly, the signal-to-noise ratio can
be enhanced by increasing the measuring time.
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Selecting the adequate ATR unit
Multiple bounce horizontal ATR (HATR): the sample
is horizontally placed onto the ATR crystal. Horizontal
ATR accessories are frequently used for routine
measurements, e.g. in case of high sample throughput.
The ATR crystals are fixed as troughs (for liquids) or
plates (for plane samples) in appropriate mountings.
Simple-reflection HATR: in contrast to HATR, single
reflection ATR utilizes a small ATR crystal, such that
only a single reflection takes place within the crystal
(good match for diamond). Single reflection ATR
accessories are mainly used when analyzing small
samples (> 1mm).
Vertical ATR (VATR): the sample is vertically placed
onto the ATR crystal. Vertical ATR is infrequently used
today.
Multipurpose Accessories: The ability to utilize a
single accessory for ATR AND external reflection
analysis can be convenient. The Bruker HELIOS and
Harrick Seagull are two good examples.
ATR Microscopy
Modern micro ATR units are equipped with a video
camera, enabling micro samples e.g. hair, fibers or
samples of micro structure (printed-circuit boards) to be
exactly positioned and analyzed. Samples as small as
20 microns can be quickly observed, positioned, and
analyzed with the Bruker HELIOS.
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Further applications of ATR spectroscopy
ATR spectrometry can also be used for for sample analysis
outside the sample compartment. Reaction monitoring in a
demanding environment outside the spectrometer is routinely
conducted utilizing ATR probe technology.
1.) ATR dipper
Light is direct coupled into an ATR crystal by a flexible
waveguide for analysis outside the spectrometer sample
compartment. This waveguide is composed of fixed mirrors
mounted in reflection coated (usually gold) light pipes. The
crystal can be immersed into the reaction solution to be
analyzed and monitored.
2.) MIR fiber coupling
Today, one can hardly imagine NIR spectroscopy without the
use of fiber optic measuring probes. Even in the middle
infrared (MIR), light can also be coupled out of the
spectrometer using fiber optics. However, fiber used in the
MIR is not as transparent as that utilized in the near infrared
and the cable length is limited to about 2 meters. Fiber
coupling to 100 meters can be accomplished in the NIR.
For any further information, please contact Bruker Optics:
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Evaluation of IR spectra
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Evaluation of spectra
Infrared spectroscopy is an extremely efficient analytical method
due to modest operating expenditure. The analytical results are
provided within a short period of time without the need of extensive
sample preparation. In particular, infrared spectroscopy provides
data which can be evaluated by quantity as well as by quality. The
following will describe the qualitative and quantitative evaluation of
acquired spectra.
•Qualitative evaluation of spectra
1. Identify an unknown substance
2. Check the identification of a known substance
•Quantitative evaluation of spectra
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Identify an unknown substance
a) Structural determination by interpreting spectra
A functional group within a molecule is considered as a harmonic oscillator (see vibration theory) which in a first approximation vibrates without being
affected by the rest of the molecule. This results in the fact that a particular functional group shows IR absorption bands within characteristic spectral
ranges: this is called group vibrations. This fact serves as the basis for spectral interpretation, whereby the position, (relative) intensity and halfwidth of a band decide whether a band can be assigned to a specific structural group.
20
Transmission [%]
40
60
80
100
Many functional groups of organic molecules show characteristic vibrations corresponding to absorption bands within defined ranges of the IR
spectrum. These molecular vibrations are mainly restricted to the functional group and do not affect the remaining molecule, i.e. such functional groups
can be identified by their absorption band. This circumstance, apart from a straightforward acquisition technique, makes IR spectroscopy to be one of
the simplest, fastest and most reliable methods when assigning a substance to its specific class of compounds. The position and intensity of the
absorption bands are extremely specific in the case of a pure substance. This enables the IR spectrum, similar to the human fingerprint, to be used as
a highly characteristic feature for identification.
4,000
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2,000
1,500
Wavenumber / cm-1
1,000
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500
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IR absorption of different organic molecular classes
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Identify an unknown substance
b.) Comparing with spectral libraries
Besides basic spectral interpretation, various comprehensive digital
spectral libraries have been compiled according to different
chemical classes and groups of substance. These are provided, for
example, by companies like Bruker and Sadtler. Apart from working
with existing spectral libraries, it is possible to create your own
libraries using modern spectroscopic software,see OPUS/SEARCH.
Different spectra regarding the number of bands and half-width,
may require different search algorithms. Therefore, OPUS/SEARCH
has the flexibility in providing various search options.
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Check the identity of a known substance
Infrared spectroscopy is a perfect analytical tool for quality control. It
gives the answer to the following question: “Does the quality of the
raw material delivered to the receiving department comply with the
specifications?” The underlying concept is very easy:
identical material = identical IR spectrum
The identification is done by comparing measured spectra with
reference spectra already saved. The method is based upon the
following considerations:
•chemically different materials result in different spectra
•real spectral differences exceed the reproducibility of
repeated measurements
•reference samples represent the expected sample variations
caused by supplier, batch, season, purity, grain size etc.
It is important to note that the reference samples can vary to a certain
degree, a circumstance that is experienced within quality control
every day. The spectrum of the material to be identified is compared
with the reference sample by means of a valid tolerance previously
defined. How to create a reference library and to compare spectra
will be described in the following.
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Reference library structure
2.) Calculate average
spectrum & threshold
values
Wavenumber / cm-1
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3.) Library structure &
validation

  
 

 
Absorbance
Absorbance
1.) Measure
reference sample


 
  


 






Wavenumber / cm-1
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Identifying new samples
1.) Measure new
samples
2.) Compare
with library
3.) Identify
material
Identified
sample:
material X
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Comparing spectra
Basically, to compare one spectrum with a reference library, the
Euclidean distance
spectral distance between two spectra is calculated, which also
Comparing spectra “point by point”:
defines the similarity between these two spectra. There are several
algorithms available to quantify the spectral distance. Depending on
the substance (or spectrum) and considering your type of problem
you have to select the most suitable comparison method. The
following describes the calculation of the Euclidean distance and
A( i ): Absorbance value at wavelength i
the comparison by factor analysis.
comparing two spectra point by point, i.e. the difference between
two spectra is reduced to one single numerical value. The Euclidean
distance can be used very well as the measured value when
comparing spectra. However, the size of this numerical value is not
standardized and has always to be considered as a relative value.
Acetylsalicylic acid
Salicylic acid
Calculating the distance:
D = ((Asample(i) - Areference(i))2)1/2
D = 3.2
0.2
Generally, this method can be used for all kinds of spectra.
Absorbance
0.6
0.8
The Euclidean distance is the sum of all single differences when
0.4
1.) Euclidean distance
1.0
1,2....i: Data points within the selected spectral range
12,000
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Difference used for
Euclidean distance
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6,000
Wavenumber / cm-1
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Comparing spectra
Factor analysis
2) Factor analysis
Factor analysis is a variance analysis which is widely used as
a general statistical method to analyze data. It is based on the
1. The factor loading collects the largest part of
the variance in the data record
search of differences (variances) within the reference data
record. Factor analysis is also called principal component
analysis, PCA. The main features comprise:
2. The factor loading collects the largest part of
the remaining variance
and so on …
• orthogonal data transformation
•substantial data compression: represents the data
record by only a few latent variables
2
Advantages of factor analysis:
• data compression
• reduces considerably noise components
1
The set of data points are represented better
by a translation and rotation of the axes
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Factor analysis
The factor analysis divides spectra into factors or factor loadings and
into the appropriate scores:
5 spectra
p
n
Scores
Spectra data matrix
d
=
p
Factors
d
n
Data matrix: n spectra with p data points
Scores:
d scores for each spectrum (d < n)
Factors:
d factors with p data points (d < n)
The result will be a reduced data record where the variances have
been transformed into different weighted factors (factor loadings).
Higher factors are generally ignored as they usually represent noise.
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Factors • Scores
1 Factor 1 5.216
Factor 2 -0.216
Factor 3 1.73E-02
Factor 4 -1.52E-02
Factor 5 3.17E-02
2 Factor 1 5.95
Factor 2 -0.103
Factor 3 4.97E-04
Factor 4 4.33E-02
Factor 5 5.65E-03
3 Factor 1 7.731
Factor 2 -0.699
Factor 3 3.67E-04
Factor 4 -1.15E-02
Factor 5 -2.04E-02
4 Factor 1 5.768
Factor 2 0.693
Factor 3 2.97E-02
Factor 4 -3.76E-03
Factor 5 -1.27E-02
5 Factor 1 7.13
Factor 2 0.441
Factor 3 -3.75E-02
Factor 4 -9.54E-03
Factor 5 4.46E-03
Fourier Transformation
Factors
1
2
3
4
5
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Introduction to
FTIR spectroscopy
Plot scores of factor 2 against 1
Factor 2
Acetylsalicylic acid
Salicylic acid
Glucose
Lactose
0.2
0.4
Absorbance
0.6
0.8
1.0
Factor analysis
12,000 11,000 10,000 9,000 8,000 7,000 6,000
Wavenumber / cm -1
5,000
4,000
Factor 1
Four pharmaceutical samples are each measured by NIR spectroscopy
several times. A factor analysis is performed of the spectral data. For
each spectrum, the scores of the first two factors are plotted. This
example shows how a complex set of data can be reduced to a
relatively simple 2D plot.
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Scores plot
Comparing spectra “point by point” by means of scores
between spectra or between spectra and average spectrum
For the calculation of the spectral distance D between two
spectra, the score coefficients T are used from the factor
analysis:
The MAHALANOBIS distance between spectra is corrected
for collinearity so different directions in a scatter plot are
weighted according to the variance
(below: 2D plot of T1 against T2, with contours of equal
Mahalanobis distance to the center)
T2
Ti
Score of factor i
1,2....i
Factors used
T1
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Quantitative evaluation of spectra
The basic principle for quantitative evaluation in optical
spectroscopy as well as in IR spectroscopy is the BouguerLambert-Beer Law which had already been defined in 1852.
Quantitative determinations by means of IR spectroscopy are
preferably performed in solution. Transmission T of a sample is
defined as:
T = I / I0
Io is the intensity of the incident light beam, I is the intensity of the
light beam leaving the sample. The percentage transmission (%T) is
100 • T. When traversing the measurement cell, the light intensity
decreases exponentially:
I = I0 • exp(-2.303 • c • b)
Where  is the molar absorption coefficient (in L mol-1 cm-1), c is
the sample concentration (in mol L-1) and b the thickness of the
measurement cell (in cm). The absorption coefficient  is a value
which depends on either the wavelength or the wavenumber, which
is typical for the compound analyzed. From the equation above, it
follows that:
log (I / I0) = - • c • b, or:
A = log (I0 / I) =  • c • b
where A is the absorbance. Because of the Bouguer-LambertBeer Law, the relationship between absorbance and
concentration of the absorbing substance is a linear function.
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Quantitative evaluation of spectra
In practice the relationship between concentration and absorbance
is empirically determined by calibration. Calibrating means finding
the mathematical connection between concentration and the
measurement values.
Calibration
4
3
In the first step, spectra of substances with known composition are
recorded. Then, these acquired spectra and the data available from
a reference analysis (concentration or substance properties) are
used to determine a calibration function. The software package
OPUS/QUANT provides several algorithms to do this.
X
2
1
In the second step, spectra of substances with an unknown
composition are measured and then used to determine the
properties of interest by means of the calibration function.
Wavelength
There are two different forms of calibration:
Univariate calibration (OPUS)
Analysis
Multivariate calibration (OPUS/QUANT)
Correlates considerably more spectral information using larger
spectral ranges with the reference values of the calibration set. This
leads to a higher degree of precision and reduced chance of error.
Partial Least Squares ((PLS) is an example of this method and is
implemented in OPUS/QUANT.
4
Absorbance
Correlates just one piece of spectral information (e.g. peak height or
peak area) with the reference values of the calibration set.
3
X
2
1
Concentration
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PLS regression
In PLS, the calibration involves correlating the data in the spectral
matrix X with the data in the concentration (or properties) matrix Y.
The X and Y matrices are reduced to only a few factors using all of
the available information. The final model consists of a score matrix
for X and a score vector for Y (in PLS-1) which are linearly related.
This means that the factoring of the spectral data is more suited for
concentration prediction.
1
2
M)
.
.
.
2)
X
=
1)
W1W2
.
.
.
.
.
W1W2 .
W11W21 .
. .
. .
WN
WN1
.
.
.
N
X
=
M
M W1MWM
2.
. .
WN
C1 C2 .
C12 C12 .
. .
. .
CL
C1L
M
. WN
Wavelength
C1 C2.
1)
..
.
M)
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1
C1
. .
1
C2. . .
C1M C1M.
. .
1
2
CL
1
CL
M
CL
Introduction
Y=
.
.
.
.
.
.
M CM CM.
1 2
L
Y
=
M
. .
Fourier Transformation
M
CL
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Introduction to
FTIR spectroscopy
Practical considerations
1.) Choice of concentration range
Analysis value
The concentration range of the calibration set should be
larger than the range of the samples to be analyzed.
2.) Choice of component values
• Individual component values should uniformly cover the
complete concentration range
• In the case of multi-component mixtures, the individual
concentration values must not decrease or increase to the
same degree (avoid collinearity)


 
 

 
  
  
 
 

 


 
 





 
 

 






Typical
concentration range
Reference value
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Practical considerations
3.) Number of calibration samples
• Simple systems:
• Typical systems:
• Complex systems:
~ at least 20 samples
~ 50-60 samples
~ 150 samples
4.) Selecting adequate spectral ranges for calibration
• Avoid spectral noise at the beginning and at the end of the
spectrum, where for example there may be a detector or window
cutoff
• Avoid ranges of total absorbance ( > 2.5 AU)
• Use large spectral ranges, if possible for calibration (“Full
Spectrum Calibration”)
5.) Parameters influenced by quality
• Quality of the measuring instrument (resolution capability,
stability, S/N-ratio, measuring precision, robustness, ...)
• Quality of reference data (frequently the quality of an IR/NIR
method is almost exclusively determined by the quality of the
reference data).
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If you have any further
questions about IR
spectroscopy, please
contact the application
team of Bruker Optics:
www.brukeroptics.com
North America:
Bruker Optics Inc
19 Fortune Drive
Billerica, MA 01821, USA
Phone: +1 978 439 9899
Fax:
+1 978 663 9177
[email protected]
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Europe:
Bruker Optik GmbH
Rudolf-Plank-Str. 27
76275 Ettlingen, Germany
Phone: +49 7243 504 600
Fax:
+49 7243 504 698
[email protected]
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Asia:
Bruker Optik Asia Pacific Ltd.
Suite 1116
Nan Fung Commercial Centre
19 Lam Lok Street, Kowloon Bay, Hong Kong
Phone: +852 2796 6100
Fax:
+852 2796 6109
[email protected]
Fourier Transformation
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