Fourier Transform Spectrometer

The core element of a FTIR spectrometer is the Michelson interferometer. In most of the cases, a classical two beam Michelson interferometer is used. As shown in Fig. 4.4, the FTIR spectrometer consists of an IR light source, two perpendicular plane mirrors, the beam splitter, and a detector.

The IR source is usually a globar, which is a silicon carbide rod. The globar is

electrically heated to temperatures in the range of 1, 000 to 1, 650◦C and shows

approximately a spectrum of a black body radiator. The detector is usually a

deuterated triglycine sulfate (DTGS) or mercury cadmium telluride (MCT) detector. The DTGS detector, which is often used for standard requirements, consists of a deuterium triglycine sulfate crystal and two electrodes enclosed in a temperature resistive encapsulation for example an alkali halide window. The DTGS detector uses the pyroelectric effect. The electromagnetic wave gets absorbed and the produced

Figure 4.4: Sketch of a simple FTIR spectrometer. The spectrometer is based on a Michel- son interferometer. The light gets divided into two parts where each beam takes a different path. When the beams recombine interference occurs which is measured at the detector.

heat causes a change in the polarization of the crystal leading to a detectable electric signal. The MCT detector on the other hand uses a mercury cadmium telluride blend which acts as a direct bandgap semiconductor. Incoming infrared photons get absorbed and produce electron hole pairs which again precipitates an electric signal. The MCT detector needs to be cooled, in order to suppress thermal noise. This is typically done by the usage of liquid nitrogen. The beam splitters for the mid- and near-infrared spectroscopy are usually germanium or iron oxide coated potassium bromide or cesium iodide glass prisms.

As shown in Fig. 4.4, the IR light emitted by the globar gets divided by the beam splitter. One of the beams get reflected by a fixed mirror R1 positioned at a distance of l to the beam splitter, while the other beam gets reflected at a second movable

mirror R2 which is at a distance of l + 1

2∆x, where

1

2∆x is the displacement of

the mirror. The two beams recombine at the beam splitter, interfere, and induce a signal at the detector. Due to the fact that both beams travel twice the distance from the beam splitter to the corresponding mirror and back, the optical path length difference between the two beams is ∆x.

By measuring the intensity of the interfering beam over the displacement x of the second mirror, all the spectroscopic information of the IR beam can be obtained. This fact will be investigated in the following paragraphs. It is assumed that the IR beam is monochromatic. This is of course not true when a continuous infrared light source is used, but this fact will be correct later. In the monochromatic case the wavenumber is a fixed value:

σ0 =

1

λ0

4.3 The FTIR Measurement Setup 49

The electric field at the position x and time t of the IR beam is given by:

E(σ0, x, t) = E · ei(2πσ0x−ωt)_{. (4.4)}

The electric fields of the two interfering beams at the detector, where one of them has a relative shift of ∆x is given by:

Etot(σ0, x, t) = E1· ei(2πσ0x−ωt)+ E2· ei(2πσ0(x+∆x)−ωt). (4.5)

The intensity of the two interfering beams is given by the square of the electric field. Therefore, one gets the following equation:

I(σ0, x) ∝ Etot· Etot∗ = E12+ E22+ 2 · E1· E2· cos(2πσ0∆x)

= I1 + I2+ 2 · p I1· p I2· cos(2πσ0∆x). (4.6)

Assuming an ideal beam splitter, I1 and I2 are equal and equation 4.6 simplifies

to:

I(σ0, x) = 2 · I0(1 + cos(2πσ0∆x)). (4.7)

In case of a continuous light source, which is the case for the globar in the FTIR spectrometer, one has to integrate over all wave numbers weighted by their spectral intensity B(σ): Itot(∆x) = Z ∞ 0 2 · B(σ)(1 + cos(2πσ0∆x))dσ = Z ∞ 0 2 · B(σ)dσ + Z ∞ 0 2 · B(σ) cos(2πσ0∆x)dσ. (4.8)

When the constant offset is neglected and the symmetry of cos(x) is used one gets:

IR(∆x) =

Z ∞

−∞

B(σ) cos(2πσ0∆x)dσ. (4.9)

Looking at Eq. 4.9, one can see that Itot(∆x) and B(σ) are actually Fourier pairs:

IR(∆x) = Z ∞ −∞ B(σ) cos(2πσ0∆x)dσ = F {B(σ)} B(σ) = Z ∞ −∞ IR(∆x) cos(2πσ0∆x)d∆x = F−1{IR(∆x)} (4.10)

The fact that Itot(∆x) and B(σ) are Fourier pairs makes it possible to gain

of the signal intensity over the mirror displacement Itot(∆x). In Fig. 4.5(a) and Fig. 4.5(b), the interferogram and the corresponding IR spectrum of N,N,N’,N’- tetrakis(4-methoxyphenyl)benzidine (MeO-TPD) is shown. Due to the fact that the mirror displacement is not infinite, the interferogram B(σ) is effectively multi- plied by a boxcar function. This multiplication leads to the fact that the obtained spectrum now consists out of a convolution of the correct spectrum and the Fourier transform of the boxcar function. This effect has to be considered when FTIR data is analyzed. One can weaken this effect by using a Gaussian shaped apodization functions.

Figure 4.5: (a) Interferogram of an IR spectrum of a MeO-TPD thin film measured with a Thermo Fisher Nicolet iS10 IR-Spectrometer. (b) The resulting IR spectrum of the MeO-TPD thin film by applying the Fourier transformation to the interferogram.

FTIR spectroscopy has significant advantages. Due to the fact that all wave- lengths are measured at the same time, one gains spectra in a shorter period of time. This fact also comprises a second effect. Because the full spectrum is abundant at the detector, a higher signal is received, compared to spectrometers measuring the

4.3 The FTIR Measurement Setup 51

spectrum via a monochromator. The signal to noise ratio per unit time is propor- tional to the square root of the number of resolution elements being monitored, in this case the intensity. Therefore, the signal to noise ratio is significantly increased. This effect is also called Jacquinot’s advantage.