Instrument line shape function

Fig. 4. The functions a) I(Vt) and b) S(Vk), which are the instrument line shape functions for spectra computed using no apodization and triangular apodization, respectively.

It is proposed to recapitulate the basic physical and optical principles of spectroscopy in this review. For the comparison of different methods, we concentrate on the determination of wavelength as an essential part of spectroscopy. We also comment on the power of resolution of the various instruments and the instrument line-shape function. 

Having commented on the fundamentals, we now have to emphasize certain properties in more detail. We next discuss resolution, i.e. the minimum difference in the wave numbers of two narrow lines that can still be seen as separate lines by the spectrometer. This leads on to the instrument line-shape function of a spectrometer. 

Fig. 4. Instrument line-shape function for a diffraction grating (N = 8) and the smallest difference A A between two narrow lines which is clearly resolved by the grating...

This is the well-known formula that states that the resolution of a diffraction grating increases (and Jv decreases) with increasing order n of diffraction and number N of lines in the grating >. For the case of three lines, or for any other spectrum, the intensity is measured with a grating spectrometer as fimction of yd (for several orders of diffraction) (see Fig. 5). The data obtained in this way are then easily converted to / (A) or I ( ) and the problem of determining the spectral distribution I ( ) is solved. It should be noted that the linewidth obtained (see Fig. 5) is influenced by the limited resolution of the instrument and that the line-widths of the three laser lines are assumed to be actually much smaller. In other words, we have been discussing the properties of the instrument line-shape function of a diffraction grating. 

Fig. 10. Interferogram I (s) of a continuous spectrum versus path difference s (upper part), the corresponding spectrum I (f) versus wave number v, and the instrument line-shape function (for triangular apodization)...

Fig. 13. Sampling of an interferogram at equal increments As of the path difference (upper part) and the spectrum with instrument line-shape function (lower part)...

The first problem is that the integration cannot be performed for 0 g t < oo but only for a finite range 0 g t g T, for which the FID signal has been recorded (Tq = data acquisition time). This truncation of the FID signal leads to a finite resolution Av l/2To (cf. Vol. 58 Fig. 6, p. 86). The instrumental line shape function is of the type... 

S( ) is known as the instrument line shape function (ILS) and is illustrated in Figure 3. The effect of convolving the spectrum B(F)... 

Figure 2. The sine x function instrumental line shape function of a perfectly aligned Michelson interferometer with no apodization...

Depending on the measured bandwidth of the features (which themselves are dependent on the instrumental line-shape function, the real bandwidth, etc.), artifacts may be... 

Figure 8 Total instrumental line shape function Wlq(v) with three different 2-values.

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