FTIR Data

Fourier Transform Infrared Spectroscopy

A form of infrared spectroscopy that is most widely used today is Fourier

Transform infrared spectroscopy. It differs from the conventional form of spectral

acquisition by using a polychromatic source of light to irradiate the sample and

manipulating the response with a mathematical process called Fourier transformation.

One finds in an FTIR spectrometer an interferometer that makes this method of

acquisition possible. Shown in Fig. 1 is an idealized Michelson-Morley interferometer.

M1

M2

B

S

D

Fig. 1. Schematic of a basic Michelson-Morley interferometer. S = source, M1 = fixed

mirror, M2 = moving mirror, Δx = displacement, D = detector, and B = beam splitter.

The infrared light coming from the source S is directed to a beam splitter B which

allows part of the light to pass through while the rest of the light is reflected back. The

reflected part of the beam travels to the fixed mirror M1, is reflected there and hits the

beam splitter again. The same happens to the light that passed through the beam splitter.

It hits the reflecting mirror M2 . However, this mirror is moving back and forth by a

distance Δx . When the beams coming from M1 and M2 recombine at the beam splitter,

they have a difference in path length so that they interfere. The beam leaving the

interferometer goes through the sample and finally reaches the detector. The signal that

emerges from the sample is called an interferogram and is given by:

S(x) = KΦνcos(4πxν) (1)

where K = a constant that includes detector response and geometrical factors,

x = mirror displacement, Δx in Fig. 1

ν = wavenumber of the signal

Fig. 2. Detector output against mirror displacement in a Michelson-Morley

interferometer both for (a) monochromatic light and (b) a broadband source. A spectrum

from its Fourier transform is shown in (c).

Since the radiation coming from the sample is made up of polychromatic light and since

the molecule absorbs and transmits light at different frequencies, the signal is the integral

over all frequencies:

dνν)πcos(4)( -

xxS ∫ ∞

∞ νΦ= (2)

or by doing a Fourier transform, the spectrum is obtained:

xxxS dν)πcos(4)( - ∫ ∞

∞ ν =Φ (3)

This method of spectroscopy provides various advantages: (1) wavenumber

accuracy; (2) a throughput advantage so that more light reaches the sample; and (3) all

the frequencies coming from the light source hit the detector simultaneously resulting in

an acquisition of a broad range of frequencies in a single measurement.