FTIR spectroscopy

Fourier-transform infrared (FTIR) spectroscopy is the standard method for measuring infrared absorption spectra of solids, liquids and gases. Light from a broadband infrared source passes through a Michelson interferometer with one moving mirror, then through or off the sample, and onto a single detector. The detector signal as a function of optical path difference is the interferogram; its Fourier transform is the spectrum. A typical laboratory instrument covers the mid-infrared from 4000 to 400 cm⁻¹ (2.5 to 25 µm) at a resolution of 4 cm⁻¹ in well under a minute, and research instruments reach resolutions of 0.001 cm⁻¹ or finer for gas-phase work.

From interferogram to spectrum

For monochromatic light of wavenumber $\tilde\nu$, the detector sees a cosine as the optical path difference $x$ changes, with one fringe per wavelength of path. A broadband source produces the sum of all these cosines:

$$I(x) = \int_0^\infty B(\tilde\nu)\, \cos(2\pi\tilde\nu x)\,d\tilde\nu,$$

where $B(\tilde\nu)$ is the spectrum. All wavelengths add in phase at zero path difference, giving a sharp centreburst, and dephase away from it. The spectrum is recovered by a cosine (in practice, fast) Fourier transform of the sampled interferogram. Because the mirror moves at constant speed $v$, each wavenumber is encoded as an audio-frequency signal at $f = 2v\tilde\nu$: a mirror speed of 0.316 cm/s puts 1000 cm⁻¹ light at 632 Hz.

A transmission measurement takes a background single-beam spectrum without the sample and a sample spectrum, and their ratio gives transmittance; absorbance follows from the Beer-Lambert law.

Resolution

Truncating the interferogram at a maximum optical path difference $L$ limits the resolution. Using the common convention

$$\Delta\tilde\nu \approx \frac{1}{L},$$

1 cm⁻¹ resolution needs $L = 1$ cm, which the moving mirror provides with 0.5 cm of travel because the path difference is twice the mirror displacement; 4 cm⁻¹ needs only 0.25 cm of path difference. Conventions differ: the unapodized instrument line shape is a sinc function with full width at half maximum $0.603/L$, and apodization, which tapers the interferogram to suppress the sinc side lobes, broadens the line beyond that.

Sampling with a HeNe reference

The interferogram must be sampled at precisely equal steps of path difference. A helium-neon laser at 632.8 nm travels through the interferometer alongside the infrared beam, and its fringes trigger the analog-to-digital converter. Sampling once per HeNe fringe, every 632.8 nm of path difference, sets the Nyquist limit at $1/(2 \times 632.8\text{ nm}) \approx 7900$ cm⁻¹, comfortably above the mid-infrared. The laser also gives every spectrum an accurate wavenumber scale, often called the Connes advantage.

Fellgett and Jacquinot advantages

The multiplex (Fellgett) advantage arises because every spectral element is measured during the whole scan, so when detector noise dominates, as it usually does in the infrared, the signal-to-noise ratio improves by roughly the square root of the number of elements. A 4000–400 cm⁻¹ spectrum at 4 cm⁻¹ has 900 elements, a potential gain of about 30. The throughput (Jacquinot) advantage arises because the interferometer accepts a circular aperture much larger than the narrow slit a grating spectrometer needs at the same resolution, so far more light reaches the detector.

Detectors and sources

Sources are usually silicon carbide globars, heated to about 1000–1500 K. The two common detectors are deuterated triglycine sulfate (DTGS), a room-temperature pyroelectric detector with flat response but low speed and sensitivity, and mercury cadmium telluride (MCT), a photoconductor cooled with liquid nitrogen that is much faster and more sensitive but can respond nonlinearly at high photon flux and has a long-wavelength cutoff that depends on composition.

Sampling accessories: ATR

Attenuated total reflectance (ATR) is now the most common sampling method. The sample is pressed against a high-index crystal, usually diamond, germanium or ZnSe, and the infrared beam undergoes total internal reflection inside it. The evanescent wave penetrates a short distance into the sample:

$$d_p = \frac{\lambda}{2\pi n_1 \sqrt{\sin^2\theta - (n_2/n_1)^2}}.$$

For diamond ($n_1 = 2.4$), a sample of index 1.5 and $\theta = 45°$, $d_p \approx 2.0$ µm at 1000 cm⁻¹ (10 µm) and about 0.67 µm at 3000 cm⁻¹. ATR needs almost no sample preparation, but because $d_p$ grows with wavelength, low-wavenumber bands appear stronger than in a transmission spectrum unless an ATR correction is applied.

Common questions

What does FTIR measure?

It measures how much infrared light a sample absorbs at each wavenumber. The absorption bands correspond to molecular vibrations, so the spectrum identifies functional groups and, by comparison with libraries, specific compounds.

Why does an FTIR need a background scan?

The raw single-beam spectrum includes the source emission, beamsplitter and detector response, and absorption by water vapor and CO₂ in the beam path. Ratioing the sample spectrum against a recent background removes these. Water vapor and CO₂ levels drift between the background and sample scans, so purging the instrument with dry air or nitrogen improves stability.

What is the difference between FTIR and Raman?

Both are vibrational spectroscopies with complementary selection rules: infrared absorption requires a change in dipole moment, and Raman spectroscopy a change in polarizability. FTIR is strong for polar groups such as C=O and O–H; Raman is better for symmetric bonds and aqueous samples.

References: P. R. Griffiths, J. A. de Haseth, Fourier Transform Infrared Spectrometry, 2nd ed. (Wiley, 2007); B. E. A. Saleh, M. C. Teich, Fundamentals of Photonics, 3rd ed. (Wiley, 2019).