Chemistry Reference
In-Depth Information
Mirror
M
1
Mirror
M
2
δ
BS
Broad band
IR source
Aperture
Sample
d
Detector
FIGURE 7.4
Principle of the FTIR spectrometer with Michelson interferometer, BS: Beam
splitter, δ: Mirror displacement,
d
: Sample thickness (absorption path length).
displacement. The output intensity
I
0
transmits the sample section and is focused on a
detector. The detector measures the intensity
I
of the infrared radiation as a function
of the mirror displacement δ - the interferogram
I
. For the broadband IR source the
measured interferogram is the result of the overlay of interferograms corresponding
to each wave number. In such case the main relation in t
h
e FTIR spectroscopy is
represented by the integral for the amplitude spectrum
B
(
δ
)
(
ν
)
of the investigated IR
radiation including all instrumental effects
+∞
B
(
ν
)
=
I
(
δ
)
·
A
(
δ
)
·
exp
(
i
·
2π
·
ν
·
δ
)
·
d
δ.
(7.5)
−∞
The IR amplitude spectrum
B
(
ν
)
is calculated from the interferogra
m
I
(
δ
)
by com-
puting the integral (7.5). For monochro
m
atic radiation the value
B
provides the
intensity of the source at a wave number ν as modified by the instrumental character-
istics. This procedure is implemented using a fast Fourier Transform in the standard
data process
in
g software of FTIR spectrometers. In the case
A
(
ν
)
(
δ
)
=
1, the amplitude
spectrum
B
. Because of the
limited displacement δ
max
of the moving mirror, the apodisation function
A
(
ν
)
corresponds to the Fourier transformed function
I
(
δ
)
(
δ
)
is intro-
duced. In the case
|
δ
|
>
δ
max
=
the apodisation function has a value
A
=
0, whereas
A
=
1 is valid for δ
∼
0. By use of the boxcar function
A
(
δ
)
=
1for
−
≤
δ
≤+
,
and
A
0 elsewhere, the spectrum is convoluted with the Fourier transformed
symmetric boxcar function (7.6).
(
δ
)
=
