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How to Deal with Some Spurious Fringes in Fourier Transform Infrared
Spectrometers
Article in Applied Spectroscopy · November 2008
DOI: 10.1366/000370208786049132 · Source: PubMed
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Jean-Joseph Max
Université du Québec à Trois-Rivières
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spectroscopic techniques
How to Deal with Some Spurious Fringes in Fourier Transform
Infrared Spectrometers
JEAN-JOSEPH MAX AND CAMILLE CHAPADOS*
ITF Labs, 400 Montpellier, Montréal, QC, Canada, H4N 2G7 (J.-J.M); and Département de chimie–biologie, Université du Québec à Trois-
Rivières, Trois-Rivières, QC, Canada G9A 5H7 (C.C.)
Faulty fringes coming from an infrared spectrometer may creep into a
spectrum. Because these come from one faulty interferogram out of many
used to obtain the spectrum, these may pass unnoticed. However, they
cause some problems in the data treatment of factor analysis and other
spectral analysis. We present a method for detecting the faulty fringes and
give a simple method to eliminate them at the interferogram accumulation
level.
Index Headings: Faulty interferograms; Anomalous fringes; Correcting
procedure; Infrared spectroscopy; IR spectroscopy.
Received 2 March 2008; accepted 8 July 2008.
* Author to whom correspondence should be sent. E-mail: Camille.
Chapados@uqtr.ca.
INTRODUCTION
Fringes are often observed in infrared (IR) spectra. These
result from multiple reflections at the surface of polymer-like
thin films and IR cells with neatly polished IR windows
separated by micrometer spacers. 1–5 These fringes are sample
dependent. In Fourier transform infrared (FT-IR) spectrometry
other fringes are encountered that are instrument dependent. To
decrease the noise level in the spectra, 20, 50, 100, 1000, or
even more interferograms are accumulated, averaged, and
Fourier transformed to obtain the spectrum. There is a small
drift from one interferogram to another that the spectrometer
tracking device replaces at the center burst. In most cases the
displacement is minimal and the tracking device does its job
correctly. However, when the deviation is too great, the
tracking device does not operate properly and a deviant
interferogram is obtained that is averaged with the others. This
will introduce fringes that are added to the species spectrum. If
one deviant spectrum out of 100 or more is obtained, the fringe
pattern may pass unnoticed. However, when subtracting one
spectrum from another in order to look at the variation process
or for more sophisticated data treatment such as factor
analysis 6–12 and band-enhancement techniques, 13 these errant
fringes render the operation impossible.
When the above situation occurs in limited interferogram
accumulations such as twenty, one easily sees the spectrometer
malfunction; that set is discarded and another one is taken.
However, in a lengthy experiment where several interferogram
accumulations are made over a long period of time, one is
frustrated to find after data treatment that an errant interferogram
has crept into the accumulated spectra. One way to deal
with this matter is to redo the experiment, hoping that the
spectrometer will behave properly. Here we present an
experimental situation that illustrates the problem and the
method that we developed to replace the errant interferogram in
the proper track without discarding an otherwise good
experiment.
THEORETICAL CONSIDERATIONS
Most FT-IR spectrometers use a Michelson interferometer to
obtain interferograms. These are Fourier transformed (FT) by a
fast Fourier transform algorithm (FFT) to obtain the IR
intensity spectrum. Taking first the background power
spectrum and, second, the spectrum of the sample, their ratio
gives the transmission spectrum that is transformed into
absorbance units for quantitative analysis. FTs have linear
properties, i.e., the FT of a sum is equal to the sum of the
individual FTs. 14 This property is used in FT-IR spectroscopy
to increase the signal-to-noise ratio. Several interferograms
obtained by individual scans of the interferometer are averaged
so that the noise level decreases with the square root of the
number of scans.
In most commercial FT-IR spectrometers, the exact location
of the mobile mirror in the Michelson interferometer is not
measured. Rather, a laser beam is superimposed on the infrared
(IR) beam to produce an interference pattern in the interferometer.
These laser interferences are used to trigger the IR
interferograms: at each laser interference maximum (or
minimum), a measure of the intensity of light is obtained,
giving one data point of the interferogram. Due to the sampling
interval (k laser ), the maximum frequency obtained through FT of
the interferogram is given by ˜m FFT max ¼ (1/100k laser ). According to
Shannon’s theorem, the maximum frequency recovered for the
IR spectrum is half the latter value: ˜m max ¼ (1/200k laser ). 14
In the default mode, the Nicolet 510P spectrometer shows in
real time the center burst region of the interferograms after
centering. When we look at these we see from time to time that
one scan is far out of the center. More recent models (such as
the Nicolet Impact 420) do not display, in the default mode,
such interferograms. Therefore, the operator cannot see this
type of error, which occurs occasionally.
Because the exact location of the mobile mirror is not
measured, one needs to be sure that the interferograms to be
Volume 62, Number 10, 2008 APPLIED SPECTROSCOPY 1167
0003-7028/08/6210-1167$2.00/0
Ó 2008 Society for Applied Spectroscopy

averaged are properly centered. This is achieved by locating the
interferogram center bursts situated at the interferogram
maximum intensity peaks. These are centered at the same
position (position ‘‘0’’ on the path difference) after which they
are averaged. Every FT-IR spectrometer has its own modus
operandi. However, because of instrument peculiarities, it
occasionally happens that some of the interferograms are outside
the adjustment region, which is around 6 10 samples (this value
is only indicative because it is a manufacturer’s property). The
out-of-bound interferograms cannot be properly centered. In
such cases, the resulting averaged interferograms will contain an
erroneous intergerogram that will generate in the spectrum a
wave similar to a sine. The FT of one single spike is a true sine
wave, the frequency of which depends on its location in the input
function. 14
EXPERIMENTAL AND DATA TREATMENT
Infrared Measurements. The IR measurements are obtained
with a model 510P Nicolet FT-IR spectrometer that has
a DTGS (deuterium triglycine sulfate) detector. Two KBr
windows isolate the measurement chamber from the outside.
The samples are contained in a closed Circle cell (SpectraTech,
Inc.) equipped with a ZnSe crystal rod (8 cm long) in an
attenuated total reflection (ATR) configuration where the beam
is incident at an angle of 458 with the rod’s axis and makes 11
internal reflections of which nearly 6.4 are in contact with the
liquid sample. The cell effective number of reflections was
calibrated with the pure water spectrum at 25 8C given by
Bertie and Lan. 15
The spectral range of this system is 6000 to 650 cm 1 .
Compared to the rest of the range, the intensity of the source is
weaker in the 6000 to 4800 cm 1 region, which will generate
higher noise levels. The spectra are taken under a nitrogen flow
to ensure low CO 2 and water vapor in the spectrometer. Each
spectrum represents an accumulation of 140 scans at 2 cm 1
resolution (0.965 cm 1 sampling interval). Model 510P being a
single-beam spectrometer, a background reference is taken
with the empty cell carefully dried before measuring the sample
spectra.
The IR measurements consisted of obtaining the ATR
background and sample interferograms. These are transformed,
respectively, into spectral intensities R 0 and R using the usual
FFT algorithm, with the Happ–Genzel apodization function
and coefficient (0.46). The ratio of R/R 0 is the intensity I for the
spectral range being studied. Thereafter, the 5547 data points (I
(˜m) vs. ˜m (in cm 1 )) of each spectrum are transferred to a
spreadsheet program for numerical analysis. The intensities I
are transformed into absorbance units, log (1/I) (abbreviated in
some cases as AU). The numerical data of each interferogram
accumulation are transferred to the spreadsheet program for
data treatment.
Chemicals and Solutions. Deionized freshly distilled water
was used. The cell is filled with this water and tightly closed. A
heating device ensures a slow, orderly increase of the sample
temperature. This is measured with a copper–constantan
thermocouple imbedded in the cell. In a series of sample
measurements covering the temperature range 29.1 to 91.1 8C,
we found that out of the 492 spectra taken, five were obtained
at the constant temperature of (90.66 6 0.06) 8C. All the
spectra looked alike. However, closer examination showed
some differences where none were expected. The bad spectra
caused false data treatment, which alerted us to the matter and
prompted us to find a remedy.
Correction of the Improper Interferograms. The
Correction Equation. Each deviant interferogram that produces
an oscillation in the absorbance spectrum can be corrected. Let
Int(d) be the measured power at path length difference d,withd 2
[ a, þ b], where a and b belong to the set of natural numbers.
Int(d) is an accumulation of n scans that are averaged:
IntðdÞ ¼ 1 n
X n
i¼1
Int i ðdÞ
The perturbation of concern is due to one or more scans not
properly aligned to the center burst of the remaining
interferograms. Hence the perturbed interferogram, Int*(d),
can be written as follows:
" #
Int ðdÞ ¼ 1 X n p
Int i ðdÞþ Xp Int m ðd þ d m Þ ð2Þ
n
1
1
where Int i (d) represents the correctly co-added scans, Int m (d) is
the non-properly aligned interferograms, and p is the number of
these interferograms. Equation 2 is transformed into:
n 3 Int ðdÞ ¼ Xn
1
p
Int i ðdÞþ Xp 1
Int m ðd þ d m Þ
Therefore, the properly centered interferograms can be
obtained by the following:
X n
1
p
Int i ðdÞ ¼n 3 Int ðdÞ
X p
1
Int m ðd þ d m Þ
Finally, the corrected averaged interferogram is obtained by
Int corr ðdÞ ¼ 1
n
¼ 1
n
X n
p
Int i ðdÞ
p
" 1
#
p n 3 Int ðdÞ
X p
1
Int m ðd þ d m Þ
Since we do not have the individual interferograms, we use the
following approximation as a first-order perturbation:
Int m ðd þ d m Þ ’ Int ðd þ d m Þ
Equation 6 represents a first-order approximation because
Int m (d þ d m ) contains no perturbation, while Int*(d þ d m )
contains 1/n perturbation (one or more shifted scans out of n
scans). Hence, one obtains the equation used for correcting the
faulty interferograms:
" #
Int corr ðdÞ ’
n
n p Int 1 X p
ðdÞ Int ðd þ d m Þ ð7Þ
n
1
Determination of Parameters p and d m . In Eq. 7, the
parameters p and d m must be determined. We begin with d m .
Each shifted scan co-added to the proper ones will produce a
small sine wave after FFT. The period (in cm 1 ) of this sine
wave is directly determined by the shift, d m , and the
wavelength that determines the interferogram sampling step,
ð1Þ
ð3Þ
ð4Þ
ð5Þ
ð6Þ
1168 Volume 62, Number 10, 2008

FIG. 1. ATR IR spectra of liquid water at 90.66 6 0.06 8C. (a) Five
consecutive spectra (separated by 0.3 AU) obtained from 140 co-added scans.
(b) Difference spectra (separated by 0.05 AU) obtained from the spectra in (a):
spectrum n minus spectrum 4 or 2: (2–4); (1–2); (3–2); (3–4); and (5–4) (see
text). Intensities are in ATR absorbance units (AU).
k laser , as follows:
Period ¼ ð1=100k laserÞ 1
¼
dm 100k 3 dm
The constant k laser is the laser wavelength (here it is 632.8
nm). Since an approximation of the period can be obtained
from the perturbed spectrum, an iterative procedure starting
from the estimated value of d m and monitored by the resultant
interferograms can be operated to obtain the exact value of d m .
The amplitude of each shifted interferogram is a multiple of the
inverse of the total number of co-added scans: 1/n.
RESULTS AND DISCUSSION
Experimental Spectra. Starting Spectra. To illustrate the
usefulness of the method, we present five spectra recorded
successively at a temperature that varied less than 60.06 8C.
Figure 1a shows the five original spectra without any
correction, some of which contain sine waves. These are not
evident on casual observation. However, they can be detected
by careful evaluation in the 5650 to 3650 cm 1 region, where
no sample band is present. We describe a better way to observe
them in the next section.
The Difference Spectra. Figure 1b illustrates the difference
between spectra where the numbers refer to the original spectra
of Fig. 1a. The difference spectra enhance the perturbing sine
ð8Þ
FIG. 2. (a) Interferograms of the water spectra in Fig. 1a (separated by 1000
amplitude units). (b) Differences between the interferograms (separated by 10
amplitude units): (2–4); (1–2); (3–2); (3–4); (5–4) (see text).
waves in three of the five spectra in Fig. 1a. The top spectrum
in Fig. 1b (spectrum 2 minus spectrum 4) shows a null
spectrum (only noise remains). This indicates that no
oscillating pattern is present in spectra (2) and (4) and that
these are of good quality. However, the other difference spectra
in Fig. 1b show three different oscillating patterns: in Fig. 1b
(trace 1–2), a large period (around 895 cm 1 ) is present; the
three others (traces 3–2, 3–4, and 5–4) contain shorter periods
(around 370 cm 1 ), two of which have twice the amplitude of
the bottom difference spectrum (trace 5–4).
At this stage, we can expect that the use of difference
spectra, abundantly used in factor analysis (FA), will present
difficulties in data treatment. If perturbed spectra are obtained,
one can either discard the faulty spectra, which will result in a
gap in the series, or take another series of measurements. The
latter is time consuming, and success is not assured.
The Experimental Interferograms. The oscillations observed
in the difference spectra (Fig. 1b) come from faulty
interferograms generated by the instrument.
Original Interferograms. Figure 2a shows the five interferograms
related to the five spectra of Fig. 1a. For clarity, only
the center burst region is shown ( 100 , d , 100). All five
interferograms look alike, with minute differences not evident
at first sight. These are revealed in the next section.
The Difference Interferograms. The difference interferograms
are shown in Fig. 2b with an amplitude scale expansion
of 120. The top interferogram difference (2–4) shows very low
amplitude in the center burst region (around 1/780 ¼ 0.13% of
APPLIED SPECTROSCOPY 1169

FIG. 3. (a) Difference interferograms and (b) spectra obtained after correction
of the perturbed interferograms: (1), (3), and (5) in Fig. 2a (see text). The
differences and presentation are the same as in Figs. 2b and 1b, respectively.
the maximum intensity). Both averaged interferograms (accumulation
of 140 scans) are almost identical without any side
burst. The small intensity difference comes from low
temperature 16,17 and instrument differences between the two
spectra. These are normal and do not generate a sine pattern in
the spectra. From this we conclude that interferograms (2) and
(4) are good and that the corresponding spectra are devoid of
spurious fringes.
Using the good difference interferogram (2–4) as the
measuring stick, we find (Fig. 2b) that the interferogram
differences (1–2, 3–2, 3–4, and 5–4) are faulty because side
bursts are observed. This indicates that interferograms (1, 3,
and 5) and related spectra are faulty. Interferogram (1) is
perturbed in the following way: the difference interferogram
(1–2) displays two patterns similar to the center burst of
interferogram (1), one positive exactly at the center burst
position and one negative at a location 17. From Eq. 8, we
find that position 17 corresponds to an oscillation period of
930 cm 1 [1/(100 3 632.8 nm 3 17)]. This value is close to the
estimated value from Fig. 1b (895 cm 1 ). The positive
perturbation at the center burst location is due to a missing
scan that could not be properly centered. Recall that the normal
interferogram center burst is negative (Fig. 2a). The amplitude
of 5.5 is related to interferogram (2) center burst intensity value
of 780 to give around 0.705%. One over this value gives
around 142, which corresponds almost to the number of scans
(140). This indicates that the evaluation rationale is correct.
The faulty interferograms (1, 3, and 5) show perturbations
situated on one side or the other of the center burst position, as
illustrated in the interferogram differences (Fig. 2b). For that of
the (1–2) difference, the counterpart is located at position 17.
This perturbation is similar to the original interferogram (Fig.
1a, trace 1), but shifted on the path length axis from the center
burst position. It has no counterpart on the positive side of the
path length axis. This clearly indicates that it represents one
shifted scan that had been added to the other properly centered
scans.
Interferogram (3) is perturbed because the difference
interferograms (3–2 and 3–4) (Fig. 3b) display two patterns
similar to the center burst of the original interferogram, one
positive at the exact center burst position and one negative at a
location (þ43). The position þ43 corresponds to an oscillation
period of 368 cm 1 , obtained from Eq. 8 [1/(100 3 632.8 nm 3
43)]. This value is the same as the fringe difference of 370
cm 1 observed in Fig. 1b (traces 3–2 and 3–4). This indicates
that the interferogram perturbation of spectrum (3) is different
than that of spectrum (1). The perturbation amplitude is almost
twice that in interferogram (1). This means that two shifted
scans were co-added. Since the counterpart to the center burst
perturbation is located at one single place (the þ43 position)
with twice the amplitude of the (1–2) difference interferogram,
it means that, in this case, two faulty scans are present but
shifted exactly at the same position. Finally, interferogram (5)
is perturbed similarly but with half the amplitude of the
perturbation of interferogram (3).
The Corrected Interferograms. With the above information
on the perturbed interferograms, one can now correct the
perturbation by applying Eq. 7 with the determined parameters
d m and p. For interferograms (1, 3, and 5), they are ( 17, 1;
þ43, 2; and þ43, 1), respectively. Using the same presentation
as in Fig. 2b, Fig. 3a shows the interferogram differences
obtained after correction of the three perturbed interferograms.
The four bottom difference interferograms are similar to the top
one, which was obtained with the original two good
interferograms. As before, the small intensity differences come
from the slight temperature and instrumental differences
between the spectra. Figure 3a shows clearly that the applied
corrections from Eq. 7 worked adequately.
Absorbance Spectra Obtained with the Corrected
Interferograms. Given the corrected interferograms, we can
now recalculate the corresponding spectra. To illustrate
convincingly the corrections made, we obtained the same
difference spectra as those illustrated in Fig. 1b, which showed
faulty spectra. These are displayed in Fig. 3b. The five ‘‘null’’
spectra show only noise whose intensities are stronger in
regions of low light intensities where strong absorption bands
are present (m OH , 3600–3100 cm 1 ; d HOH , 1680–1600 cm 1 ;
and m L , , 850 cm 1 ) and in the region where the IR beam is
weak (.4050 cm 1 ). These indicate eloquently that the
corrected spectra are without spurious fringes (Fig. 3b).
CONCLUSION
In the long series of spectra obtained in FT-IR spectrometers
coming from series of interferograms, a faulty interferogram
may creep in among the good ones. The FT of these will give
the IR spectrum, but the faulty one will generate a sine wave
pattern that is added to the spectrum. Because the faulty
The pattern is not exactly a sine wave. Attempts to subtract a sine curve
from the absorbance spectrum were fruitless.
1170 Volume 62, Number 10, 2008

interferogram is only one out of the many (usually more than
20 and often more than 100) taken for the spectrum, the
spurious fringe may pass unnoticed because it is weak. For
qualitative identification of a sample, this minimally affects the
bands and usually does not influence their assignment.
However, for quantitative measurements, the spurious fringes
perturb the data treatment, which cannot be adequately
completed. By taking the difference between two spectra, we
show how to detect the spurious fringes. From these
differences, the correcting parameters to be introduced into
the correcting equation are determined. Applying the correction
to the three faulty interferograms corrected these adequately,
which yielded the spectra after FT. The difference spectra of
these showed no spurious fringes and illustrate eloquently the
effectiveness of the corrective procedure.
ACKNOWLEDGMENTS
This work was supported in part by NSERC of Canada and in part by ITF
Labs.
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APPLIED SPECTROSCOPY 1171