Biomedical Engineering Reference
In-Depth Information
11.3.4
Fourier Transform Infrared Spectroscopy for GPCR
Study
Fourier Transform Infrared Spectroscopy (FTIR) offers an analysis based on infra-
red spectra from absorption, emission, photoconductivity or Raman scattering from
complex biological macromolecules. Mostly FTIR is to measure the absorption
spectra from each wavelength. A typical setup for FTIR is shown in Fig.
11.11
. As
the name of this technique implies, the Fourier transformation as below is required
to convert the acquired data to the actual spectra in a reciprocal space [
134
] where
ω
is the angular frequency.
^
∞
=
∫
−
2
πω
xi
f
( )
ω
f
()
x e
dx
−∞
The measured interferogram,
I
, is given by
^
∞
=
∫
This measure intererogram is converted into the computed spectrum denoted
I
by
Fourier transformation.
Ix
( )
I
( ) cos(2
ν πνν
x d
)
0
^
∞
∫
I
( )
ν
=
2
I x
( ) cos(2
πν
x
)
dx
0
The Michelson's interferometer is the core of the FTIR spectrometer for splitting
beam into two paths so that the paths of the two beams are different resulting in
interference. Assuming the distance between two paths is
l
, the light intensity can
be described as:
2
2
2
I
==++
E
E
E
2
EE
·
cos( )
θ
1
2
12
which can be approximated to
I l
( )
=+
21
cos(
kl
)
This intensity can be transformed into the spectrum by Fourier transformation as
below:
ikx ikx
ee
−
+
∞
∞
∞
∫
∫
∫
=+ = +
1 cos( ) ()
kl G k dk
G k dk
()
G k
()
dk
2
0
0
0
1
1
∞
−∞
∫
ikx
=
I
(0)
+
G k e
( )
dk
2
2
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