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Unformatted text preview: Fourier Transform Infrared Spectrometer 1 A Fourier Transform Infrared (FTIR) spectrometer is based on a Michelson in
terferometer. An FTIR spectrometer is capable of determining the spectral content of
a light source. This is accomplished by scanning one of the mirrors of the Michelson in
terferometer and recording the output interferogram as a function of the optical path
difference between the two interfering beams. In an FTIR, the wavelength of a wave is
typically represented by its wavenumber 'u where v = —
A
and A is the freespace wavelength. For the case of two narrow linewidth waves of wavenumbers v1 and v2 and amplitudes A1 and A2, the spectrum is given by delta func tions. The resulting amplitude interference may be represented by
A(6) 2 A1 cos(27rvl 6) + A2 cos(27rv2 6), where 6 is the optical path difference between the paths in the interferometer. A Fourier
transform relationship exists between the spectrum in wavenumber space and the ampli—
tude interference pattern in optical path difference space. A light source consists of two waves with wavenumbers v1 = 1000 cm‘1 and v2 = 1100 cm‘1 and equal amplitudes (A1 = A2). This spectrum is shown in the upper left
of the ﬁgure. The corresponding interferogram A(6) as given by the above equation for
0 < 6 < 16/ 121 is shown in the upper right of the ﬁgure. For the same FTIR instrument in a second case, the source is changed and now
consists of two narrow linewidth wavelengths such that v1 = 1000 cm"1 and v3 =
1200 cm‘1 and amplitude A3 = A1/2 where A1 is the same as in the ﬁrst case. The
spectrum for this second case is shown in the lower left of the ﬁgure. For this second
case, calculate and plot the resulting interferogram for 0 < 6 < 16/ v1. Include a sufﬁ
cient number of points such that all oscillations in the interferogram are clearly shown.
Please supply your plot on a separate page. However, for comparison with the ﬁrst inter
ferogram, also please sketch the interferogram in the box provided at the lower right of
the ﬁgure using the same a: and y scales as in the interferogram in the upper right ﬁgure. AMPLITUDE AMPLITUDE V1 V2 V1 V3
WAVENUMBER AMPLITUDE AMPLITUDE o 16/v1 o 161v1
OPTICAL PATH DIFFERENCE AMPLITUDE AMPLITUDE V1 V2 V1 V3
WAVENUMBER AMPLITUDE AMPLITUDE o 1cm1
l 1
I j
w
o 16/v1 OPTICAL PATH DIFFERENCE ...
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 Spring '08
 Gaylord

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