Physical Chemistry Third Edition

23.3 Rotational and Vibrational Spectra of Diatomic Molecules 969

Fourier Transform Infrared Spectroscopy

Most modern infrared spectrometers use Fourier transform techniques rather than dis-

persion techniques. In a Fourier transform infrared spectrometer a pulse of infrared

radiation is passed through aninterferometer, as depicted in Figure 23.10.^9 The beam

splitter divides the beam into two beams of equal intensity, which are recombined after

being reflected by separate mirrors, one of which is movable. As this mirror moves, the

detector responds to changes in the intensity as the two beams interfere constructively

or destructively. The intensity of the pulse as a function of time is called aninterfero-

gram. As depicted in the figure, a single frequency produces a sinusoidal interferogram.

A pulse can be thought of as containing many frequencies, and an interferogram can

have a complicated appearance depending on the intensities of the various frequencies.

An interferogram is taken without a sample in position and another is taken with

the sample in position. The difference between the interferograms is a function of time

and can be represented by aFourier transform:

I(t)

1

√

2 π

∞∫

−∞

c(ω)eiωtdω (23.3-14)

Appendix B contains a brief introduction to Fourier series and transforms. Equation

(23.3-14) is analogous to a linear combination of basis functions, but with an integration

instead of a sum. The variableωis sometimes called the “circular frequency” of the

Fixed-position mirror

Beamsplitter

Sample

position

Detector

Single-frequency

source ()

Movable

mirror

 5 0

I()

 5  2



2

0  3  

2

 5   532 

n 5~^1 

n

c(n)

Spectrum

Interferogram

~n 0

~

~

Figure 23.10 The Radiation Path in a Fourier Transform Infrared Spectrophotometer

(Schematic).If only one wavelength is present, the sinusoidal interferogram at the lower

right is observed as the movable mirror in the Michelson–Morley interferometer changes its

position. The Fourier transform of this signal is a single sharp line, as shown at the lower

left. From W. D. Perkins,J. Chem. Educ., 63 , A5 (1986).

(^9) W. D. Perkins,J. Chem. Educ., 63 , A5 (1986); and 64 , A296 (1987).