Single beam spectrum, Fourier

Figure 1.2 Interferogram recorded by a d.c.-coupled detector in which the signal counts can vary from 0 to 16384 (top). Fourier transformation of the recorded interferogram profile yields a single-beam spectrum (middle). Single-beam spectra from a sample can be ratioed point-by-point in the spectral domain to single-beam spectra acquired without a sample in the beam path, yielding absorbance spectra (bottom). The absorbance features in a spectrum can be correlated to the molecular properties of the sample (dark profile), while a featureless spectrum (light profile) denotes the lack of sample in the beam path.

Figure 2. Interferogram (top) and resulting single beam spectrum after Fourier...

The encoded spectral information in the interferogram (I (<5)) is stored in a computer and transformed into the more familiar form of a single-beam spectrum (Fig. 3) by means of a fast Fourier transform. 

Fig. 3. Single-beam spectrum resulting from the Fourier transformation of the interferogram in Fig. 2 b.

The interferogram is actually a series of data points (retardation, intensity) collected during the smooth movement of the mirror. Using a mathematical function known as a Fourier transform, the spectrometer computer is able to deconvolute ( Fourier transform ) all the individual cosine waves that contribute to the interferogram, and so produce a plot of intensity against wavelength, or more usually the frequency in cm that is, the infrared single beam spectrum. All the... 

Fourier transform of such an interferogram produces a mid-IR single-beam spectrum. 

The Michelson interferometer does not measure the infrared spectrum directly. Rather, an interfero-gram is measured, and converted to a single-beam spectrum via Fourier transformation. Because of the critical role of this transformation, the method is generally referred to as Fourier-transform infrared spectroscopy, or FT-IR . Instruments using this... 

FIGURE 2.14 When an interferogram is Fourier transformed it produces a single beam spectrum. 

Typically, once the measurement of the background spectrum is complete, the sample is placed in the infrared beam. Interferograms are measured with the sample present, are added together, and then Fourier transformed to obtain the sample single beam spectrum, an example of which is shown in Figure 2.17. A sample single beam spectrum contains contributions from the environment, instrument, and sample. Note... 

Single Beam Spectrum The spectrum that is obtained after Fourier transforming an interferogram. A single beam spectrum is a plot of arbitrary infrared intensity versus wavenumber. 

Figure 10.11—Optical arrangement of a Fourier transform IR spectrometer, a) A 90c Michelson interferometer including the details of the beam splitter (expanded view) b) optical diagram of a single beam spectrometer (based on a Nicolet model). A weak intensity HeNe laser (632.8 nm) is used as an internal standard to measure precisely the position of the moving mirror using an interference method (a simple sinusoidal interferogram caused by the laser is produced within the device). According to the Nyquist theorem, at least two points per period are needed to calculate the wavelength within the given spectrum.

The molecules in the sample absorb at their characteristic frequencies, and hence the radiation intensity / (x) that reaches the detector is modified by the presence of the sample. The Fourier transform of /a(x) is the absorption spectrum of the sample, and this transform yields percent transmission versus wavenumber (cm ). This type of spectroscopy is single-beam, so a background spectrum is required in most cases. Also it requires the use of a digital computer to calculate the Fourier transform of /a(x). 

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