Fourier transform spectroscopy apodization

It is instructive to consider a specific example of the method outline above. The triangle fimction (l/l) a (x/l) was discussed in Section 11.1.2. It was pointed out there that it arises in dispersive spectroscopy as the slit function for a monochromator, while in Fourier-transform spectroscopy it is often used as an apodizing function. Its Fourier transform is the function sine2, as shown in Fig. (11-2). The eight points employed to construct the normalized triangle fimction define the matrix... 

It is found that multiplication of the Fourier transform of the data by a carefully chosen window function is very effective in removing the artifacts around peaked functions. This process is called apodization. Apodization with the triangular window function is often applied to Fourier transform spectroscopy interferograms to remove the ringing around the infrared... 

The Polytec FIR 30 provides the parabola fit and the Coderg FS 4000 a special electronic phase error correction. All instruments with the fast Fourier transform (FFT) correct phase errors in the interferogram mathematically according to a method first proposed by M. Forman 88,70) xhis correction procedure was outlined in detail in Section 5.3 (cf. Fig. 41). In addition to Fourier transform and phase error correction, it is advisable to use apodization in Fourier spectroscopy (cf. Sections 2.3 and 3.2). In all commercial instruments, the operator has the choice among a number of different apodization functions. 

Chapter 5 addresses the concept of the Fourier transform technique without going into mathematical details. The advantages of the technique and the artefacts connected with it are discussed. These include such issues as apodization function, zerofilling, phase correction, and acquisition mode, which are important for an understanding of the measuring process. For Raman spectroscopy, the rivalry between dispersive and FT techniques is also considered. 

---