Interferogram sampling

Figure 7.1. Simulated interferogram sampled at equally spaced intervals (solid vertical lines) and unequally spaced intervals (dashed lines). The difference between the ordinate values of the correctly and incorrectly sampled interferograms is equivalent to noise superimposed on the true interferogram. The error is dependent on both the difference between the correct and actual sampling positions and the slope of the interferogram at each point.

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. 

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... 

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. 

Let the discrete spectrum, which consists of the coefficients of u(k) and v(k), be denoted by U(n) and V(n), respectively. The low-frequency spectral components U(n) are most often given by the most noise-free Fourier spectral components that have undergone inverse filtering. For these cases V(n) would then be the restored spectrum. However, for Fourier transform spectroscopy data, U(n) would be the finite number of samples that make up the interferogram. For these cases V(n) would then represent the interferogram extension. 

A very-low-frequency sinusoid was superimposed on these spectral lines owing to channeling. This comes about by reflections from the window surfaces that contain the sample gas. These often result in a spike on the interferogram, which produces a superimposed sinusoid on transforming. Rather than removing the sinusoid from the entire data set, we fitted a smooth curve to the base line of each isolated set of lines treated. 

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