Wavenumber resolution

Ifourth(fd, 2 Q) was multiplied with a window function and then converted to a frequency-domain spectrum via Fourier transformation. The window function determined the wavenumber resolution of the transformed spectrum. Figure 6.3c presents the spectrum transformed with a resolution of 6cm as the fwhm. Negative, symmetrically shaped bands are present at 534, 558, 594, 620, and 683 cm in the real part, together with dispersive shaped bands in the imaginary part at the corresponding wavenumbers. The band shapes indicate the phase of the fourth-order field c() to be n. Cosine-like coherence was generated in the five vibrational modes by an impulsive stimulated Raman transition resonant to an electronic excitation. 

The wavenumber resolution was set at 6 cm-1 and 16 scans were coadded for each spectrum. UHCA was performed on the 1800-950 cm-1 region on second-derivative vector normalized spectra. The brown cluster and resultant mean extracted brown spectrum in Fig. 10.7(c) are representative of the dispersion artifact from... 

FTIR spectra were obtained with four wavenumber resolution using either a Nicolet 60-SX or a Mattson Cygnus spectrometer. Specimens were cast as thin films on sodium chloride discs, and the solvent was removed under vacuum at 60 C. The spectrometers were purged with dry, carbon dioxide-free, air. To explore the effect of exposure to moisture, selected specimens were left in the laboratory environment at about 25"C and 40% humidity for several days before being re-examined by FTIR spectroscopy. 

Paul Wilks has always been a proponent of the WIF. His most recent addition to his product line is the variable Alter array (VFA) spectrometer. It is a new-concept instrument that enables the user to obtain NIR spectra on a variety of materials wherever they occur, in the production plant or in the Aeld. It consists of an ATR sample plate with an elongated pulseable source mounted close to one end and a linear variable Alter attached to a detector array mounted close to the other (Fig. 4.1.8). The net result is a very compact spectrometer with no moving parts and no optical path exposed to air and capable of producing NIR spectra of powders. Alms, liquids, slurries, semisolids, and solid surfaces. The array has 64 elements giving an approximate 12 wavenumber resolution in the mid IR. Sample loading simply involves loading the ATR with a suitable thickness of material. Sample cups are not required. 

The monochromator generates a single-beam spectrum where the vertical coordinate is radiation energy as a function of wavelength or wavenumber reaching the detector. In double-beam spectrophotometers, the monochromator alternately measures source radiation intensity with an without sample absorption for each wavelength or wavenumber resolution element of the spectrum. From this, the instrument generates a percent transmission spectrum. 

Fourier Transform infrared system at four wavenumber resolution in double beam operation. Standard double precision computer software were used to present data properly scale expanded in absorbance form. 

Fourier transform infrared-attenuated total reflectance (FTIR, ATR-FTIR, Nicolet 8700, USA) spectroscopy was used to analyze the chemical structures of the specimens. All spectra were collected with 4 cm wavenumber resolution after 64 continuous scans at a wavelength range of 4000—600 cm ... 

High Wavenumber Resolution over a Wide Spectrai Range... 

In infrared spectra, two or more bands are often located in close proximity. To resolve these bands, the spectral measurement should be performed at an appropriately high enough wavenumber resolution. In this book, the term wavenumber resolution is used to express resolution in wavenumber in an observed spectmm, in order to differentiate it from spatial resolution used in microscope and imaging measurements (Chapters 16 and 17) and time resolution used in the time-resolved measurements (Chapter 20). 

In any spectral region, the wavenumber resolution obtained by an FT-IR spectrometer is given as the reciprocal of the maximum optical path difference between the fixed and movable mirrors in a Michelson interferometer. This wavenumber resolution applies to all the spectral range observable by an FT-IR spectrometer in use. The user of an FT-IR spectrometer can determine the wavenumber resolution by choosing the maximum distance of travel of the movable mirror. The wavenumber resolution (8v in cm ) is related to the maximum optical path difference (D in cm) as... 

The width of an infrared band is expressed by a half-band width, or more specifically, by a full width at half maximum (FWHM) (half the absorption maximum) which is shown in Figure 3.1. To measure a satisfactorily resolved infrared spectram, the wavenumber resolution of an FT-IR spectrometer must be set at a value (in cm ) smaller than the FWHM of the bands to be observed. An infrared absorption band of a sample in the condensed... 

As mentioned in Section 3.2.2, it is advisable to measure an FT-IR spectrum at a wavenumber resolution smaller than the FWHMs (in cm ) of bands in the spectmm. For solution samples, spectral measurements are usually performed at a wavenumber resolution of 4 or 2 cm . Even in such conditions, however, it is possible that the wavenumber of the peak of a band slightly differs from its true value. The reason for this small deviation is illustrated in Figure 3.6. The recorded digitized values of absorbance obtained from an FT-IR spectrometer are given discretely along the wavenumber axis they are usually given at intervals of 1 cm for a spectrum measured at 2 cm resolution and at intervals of 2 cm for that measured at 4 cm resolution. In the spectrum obtained in this way, the correct value of... 

Figure 3.6 Peak absorbances measured at two different wavenumber resolutions. Points measured at 2 cm resolution are indicated with both filled circles ( ) and open circles (oj, and those at 4 cm resolution are with filled circles ( ) only.

Since FT-IR spectrometry is based on the interference of waves of light (or radiation), first an account of this phenomenon is briefly given, before explaining the Fourier transform method by which an infrared spectrum is obtained from a measured interferogram. Some characteristics of FT-IR spectrometry, namely, wavenumber resolution, measurable wavenumber region, and accurate determination of wavenumbers are discussed. To facilitate the understanding of the description, which inevitably requires some mathematical formulations, many illustrations are provided. 

In this section, characteristics of FT-IR spectrometry, that is, wavenumber resolution, measurable spectral region, and accurate determination of wavenumbers, are discussed. As mentioned in Section 3.2.2, the term wavenumber resolution is used in this book instead of the commonly used terminology of just resolution. ... 

Although a brief introduction to the wavenumber resolution in FT-IR spectrometry was given in Section 3.2.2, this subject is discussed here in greater detail. 

Let us discuss in mathematical terms the relation between the wavenumber resolution and the maximum OPD in Equation (3.1). Before beginning the discussion, an explanation is given for the convolution theorem relating to Fourier transforms. This theorem is expressed by the following two equations. The bar above the function indicates the Fourier transform, and the symbols and indicate, respectively, ordinary multiplication and convolution. 

The convolution theorem described above is useM in deriving the relation between the wavenumber resolution and the maximum OPD in Equation (3.1). In Equation (4.12), the integration is performed for the entire OPD range from -oo to oo, but the maximum OPD is a finite value D in a real spectral measurement. Then, B (v) in Equation (4.12) should be replaced by 5 (v), which is given as... 

In the description of the Michelson interferometer in Section 4.3.1, it is postulated that the collimated beam travels parallel to the optical axes to impinge Mj and M2 perpendicularly. For considering the OPD, however, collimated beams traveling obliquely to the optical axes also need to be taken into account, because the source actually used is not a point but has a finite size. The existence of oblique beams results in a decrease in wavenumber resolution. 

To avoid a large decrease in wavenumber resolution arising from oblique rays, a circular aperture, called the Jacquinot stop (J-stop), is placed in the focal plane of the collimator as shown in Figure 4.12a. The optimal diameter of the J-stop is determined in order to make the wavenumber shift due to oblique rays smaller than the wavenumber resolution 8v determined by the OPD for the beam parallel to the optical axis. 

At the end of a spectral measurement, calibration of the spectral abscissa is needed to allow for the following two factors, namely, the size of the entrance aperture and the refractive index of air. The latter factor is disregarded in this chapter, because its effect is negligibly small at a wavenumber resolution employed for most practical analyses. The effect arising from the size of the entrance aperture is calibrated in the following way. 

Deconvolution in spectroscopy means a mathematical operation for enhancing apparent wavenumber resolution by narrowing bandwidths. Deconvolution is useful for separating overlapping bands and thereby determining the number of the overlapping bands and their peak wavenumbers. Although a few methods of deconvolution exist, only FSD, which is closely associated with FT-IR spectrometry, is described here. 

In the acmal process of performing FSD, it is necessary to specify the FWHM (2o-), the effective range of OPD (D), and an apodizing function that can suppress the side bands [A(x)]. If many bands with different bandwidths exist in the spectrum under smdy, the minimum bandwidth should be used to avoid excessive deconvolution, which will be accompanied by side bands. If a large value is chosen for D, the resultant bandwidth becomes narrow and the wavenumber resolution appears to be higher, but noise levels increase at the same time. As the S/N ratio depends on the apodizing function, it is advisable to test various apodizing functions. 

If the sample layer is too thick (in the case of a gas, if its pressure or concentration is too high), the wavenumber resolution may be reduced and the band shape may become distorted because of self-absorption. The emission spectra from a thin and a thick sample layer are compared in Figure 15.4, in which it can be seen that the spectrum from the thicker sample is distorted. 

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