Interferogram Fourier transform

Nowadays, most instruments use a FT-infrared (FT-IR) system, a mathematical operation used to translate a complex curve into its component curves. In an FT-IR instrument, the complex curve is an interferogram, or the sum of the constructive and destructive interferences generated by overlapping light waves, and the component curves are the IR spectrum. The standard IR spectrum is calculated from the Fourier-transformed interferogram, giving a spectrum in percent transmittance (%T) versus light frequency (cm ). 

The Fourier transformed interferograms provide IR spectra that can be recorded at will in normalized reflectance spectra (reflectance units R) (Fig. 17A), in quasi-absorbance units that are not proportional to concentration (-log/ ) (Fig. 17B), or in Kubelka-Munk units that are proportional to concentration (Fig. 17C). The substances can be localized on the TLC plate by using either spectral windows chosen at will (Fig. 18A and also dashed line in B) or the Gram-Schmidt technique (Fig. 18 dotted line in B). The first method can be used to increase selectivity (e.g., the spectral window can be chosen so as to detect only compounds with carbonyl groups), while the latter is universally applicable and independent of wave number. 

Figure 3.16(a) shows an interferogram resulting from the infrared absorption spectmm of air in the 400-3400 cm region. The Fourier transformed spectmm in Figure 3.16(b)... 

In FT-Raman spectroscopy the radiation emerging from the sample contains not only the Raman scattering but also the extremely intense laser radiation used to produce it. If this were allowed to contribute to the interferogram, before Fourier transformation, the corresponding cosine wave would overwhelm those due to the Raman scattering. To avoid this, a sharp cut-off (interference) filter is inserted after the sample cell to remove 1064 nm (and lower wavelength) radiation. 

The interferogram and the spectmm are related by the Fourier-transform pair ... 

The growth and decay of all other species (including O3) were monitored by Fourier transform infrared (FT-IR) spectroscopy at a total pathlength of 460 meters and a spectral resolution of 1 cm". At this pathlength, the intense absorptions of H2O and CO limit the usable IR spectral windows to the approximate regions 750-1300, 2000-2300, and 2400-3000 cm". Each spectrum (700-3000 cm" ) was adequately covered by the response of the Cu Ge detector. Approximately 40 seconds were required to collect the 32 interferograms co-added for each spectrum. 

In spectroscopy, for example, the Fourier transform of an interferogram, fix) is sampled at regular intervals, Ax. Equation (36) is then replaced by the summation... 

Figure 3.4 shows (i) a line spectrum (one-dimensional dispersive spec-trographic record), (ii) a spectrometric record, (iii) an interferogram obtained by a Fourier transform spectrometer, and (iv, v) two- and three-dimensional double dispersive spectra recorded e.g. by Echelle spectrometers. In principle, all forms may be obtained by OES. 

Transmission infrared spectra of species adsorbed on the catalyst were taken with a Digilab FTS-10M Fourier-transform infrared spectrometer, using a resolution of 4 cm-l. To improve the signal-to-noise ratio, between 10 and 100 interferograms were co-added. Spectra of the catalyst taken following reduction in H2 were subtracted from spectra taken in the presence of NO to eliminate the spectrum of the support. Because of the very short optical path through the gas in the reactor and the low NO partial pressures used in these studies, the spectrum of gas-phase NO was extremely weak and did not interfere with the observation of the spectrum of adsorbed species. 

The final step in obtaining the spectrum by the FTIR method is turning back the data obtained as a result of the repetitive interference action of the moving mirror into an intensity wavelength line. It is here that Fourier Transform mathematics is utilized. It is the signal intensity that is stored in a digital representation of the Interferogram. This information is then Fourier transformed by the computer into the frequency spectrum. 

In detector noise limited spectroscopies such as PAS it is advantageous to enhance the throughput of energy (Jacquinot s advantage) by utilizing a Michel son interferometer. One then Fourier transforms (FTs) the resulting interferogram to yield a PA spectrum that qualitatively resembles an absorption spectrum. 

In mathematical terms, the relationship between the interferogram in FTIR and the absorbance spectrum obtained by conventional IR is that the interferogram is the Fourier transform of the absorbance spectrum - hence the term FTIR. Application of an inverse Fourier transform to the interferogram, therefore, converts the output of the FTIR into a conventional display. 

A Fourier transform infrared spectroscopy spectrometer consists of an infrared source, an interference modulator (usually a scanning Michelson interferometer), a sample chamber and an infrared detector. Interference signals measured at the detector are usually amplified and then digitized. A digital computer initially records and then processes the interferogram and also allows the spectral data that results to be manipulated. Permanent records of spectral data are created using a plotter or other peripheral device. 

---