Blackman Harris apodization

Figure 9.4. Interferogram (spectrum A) and its expansion (b) obtained from cyclohexane excited at 1064 nm. The Raman spectrum resulting from Blackman-Harris apodization (4-term), 2 x zero filling and Fourier transformation is shown as spectrum C, plotted against the absolute wavenumber rather than Raman shift.

Figure 9.5. FT-Raman spectra of solid nylon obtained with 1064 nm excitation (245 mW) and a Bruker IFS/66 FT-Raman spectrometer with a germanium detector. Resolution was 4 cm in all cases, and the number of scans and associated total measurement time are shown. Blackman-Harris apodization, 2 x zero filling.

Table 5.2. Coefficients of the Happ enzel and Blackman-Harris apodization functions.

Figure 5.3. Various apodization functions (left) and the instrumental lineshape produced by them (right) (a) boxcar truncation (b) triangular (c) trapezoidal (d) Norton-Beer weak, medium, and strong (e) Happ-Gen-zel (f) Blackman-Harris 3-term and 4-term. The maximum retardation is set to / = 1. In the Fourier transform the FWHH of the main lobe is indicated.

The choice of a particular apodization depends on what one is aiming at. If the optimum resolution of 0.605// is mandatory, the boxcar truncation (no apodization at all) should be chosen. If a loss of resolution of 50% compared to the boxcar can be tolerated, the Happ-Genzel, or even better, the Blackman-Harris three term apodization is recommended. Since the Blackman-Harris window shows the highest side lobe suppression and is furthermore nearly zero at the interval ends, it can be considered the top performer. 

The experimental sequence used for these analyses is as follows ions are formed by laser-induced ionization in the source cell (residual pressure 10 Pa). During the ionization event, the conductance limit plate between the two cells (source and analyze) is kept at the trap potential (typically +0.75 V) to confine positive ions to the source side. A variable delay period follows, during which ion/molecule reactions can occur. A frequency excitation chirp allows the ion excitation the resulting image current is finally detected, amplified, digitized, apodized (Blackman-Harris, three terms), and Fourier-transformed to produce a mass spectrum. 

The FWHH of the ILS function given by the Happ-Genzel function is close to that of the Norton-Beer strong apodization function. Another common function that strongly suppresses the sidelobe amplimde is the Blackman-Harris function,... 

There are other apodization functions in use besides the Norton-Beer and the Happ-Genzel. These functions have not been tested as thoroughly however, it has been noted by the authors that the Blackman-Harris and Blackman apodization functions (Section 2.4) are considerably broader than the Norton-Beer medium or Happ-Genzel apodization functions. It is expected that these functions will not adhere to Beer s law as well as the Norton-Beer medium function. 

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