Fourier transform sensitivity

Chemical Gas Detection. Spectral identification of gases in industrial processing and atmospheric contamination is becoming an important tool for process control and monitoring of air quaUty. The present optical method uses the ftir (Fourier transform infrared) interference spectrometer having high resolution (<1 cm ) capabiUty and excellent sensitivity (few ppb) with the use of cooled MCT (mercury—cadmium—teUuride) (2) detectors. 

Fourier Transform Infrared (ftir) Spectroscopy. Ftir is a sensitive tool for... 

FT NMR Fourier transform NMR, the newer and more sensitive, less time consuming basic technique of NMR detection, almost exclusively used... 

Here Pyj is the structure factor for the (hkl) diffiaction peak and is related to the atomic arrangements in the material. Specifically, Fjjj is the Fourier transform of the positions of the atoms in one unit cell. Each atom is weighted by its form factor, which is equal to its atomic number Z for small 26, but which decreases as 2d increases. Thus, XRD is more sensitive to high-Z materials, and for low-Z materials, neutron or electron diffraction may be more suitable. The faaor e (called the Debye-Waller factor) accounts for the reduction in intensity due to the disorder in the crystal, and the diffracting volume V depends on p and on the film thickness. For epitaxial thin films and films with preferred orientations, the integrated intensity depends on the orientation of the specimen. 

M. Wilhelm, P. Reinheimer, and M. Ortseifer, High sensitivity Fourier-transform rheology, Rheol. Acta, 38, 349-356, 1999. 

Greatly enhanced sensitivity with very short measuring time is the major advantage of PFT (pulse Fourier transform) experiments. In the CW (continuous wave) experiment, the radiofrequency sweep excites nuclei of different Larmor frequencies, one by one. For example, 500 s may be required for excitation over a 1-KHz range, while in a PFT experiment a single pulse can simultaneously excite the nuclei over 1-KHz range in only 250 jits. The PFT experiment therefore requires much less time than the CW NMR experiment, due to the short time required for acquisition of FID signals. Short-lived unstable molecules can only be studied by PFT NMR. 

At the end of the 2D experiment, we will have acquired a set of N FIDs composed of quadrature data points, with N /2 points from channel A and points from channel B, acquired with sequential (alternate) sampling. How the data are processed is critical for a successful outcome. The data processing involves (a) dc (direct current) correction (performed automatically by the instrument software), (b) apodization (window multiplication) of the <2 time-domain data, (c) Fourier transformation and phase correction, (d) window multiplication of the t domain data and phase correction (unless it is a magnitude or a power-mode spectrum, in which case phase correction is not required), (e) complex Fourier transformation in Fu (f) coaddition of real and imaginary data (if phase-sensitive representation is required) to give a magnitude (M) or a power-mode (P) spectrum. Additional steps may be tilting, symmetrization, and calculation of projections. A schematic representation of the steps involved is presented in Fig. 3.5. 

Fourier transformation in (Fti), spectra are obtained with real (R) and imaginary (/) data points. For detection in the quadrature mode with simultaneous sampling, a complex Fourier transformation is performed, with a phase correction being applied in F. (c) A normal phase-sensitive transform P— RR and I- RI. (d) Complex FT is applied to pairs of columns, which produces four quadrants, of which only the RR quadrant is plotted. 

Figure 3.6 The first set of Fourier transformations across <2 yields signals in V2, with absorption and dispersion compronents corresponding to real and imaginary parts. The second FT across /, yields signals in V, with absorption (i.e., real) and dispersion (i.e., imaginary) components quadrants (a), (b), (c), and (d) represent four different combinations of real and imaginary components and four different line shapes. These line shaptes normally are visible in phase-sensitive 2D plots.

Recent work in our laboratory has shown that Fourier Transform Infrared Reflection Absorption Spectroscopy (FT-IRRAS) can be used routinely to measure vibrational spectra of a monolayer on a low area metal surface. To achieve sensitivity and resolution, a pseudo-double beam, polarization modulation technique was integrated into the FT-IR experiment. We have shown applicability of FT-IRRAS to spectral measurements of surface adsorbates in the presence of a surrounding infrared absorbing gas or liquid as well as measurements in the UHV. We now show progress toward situ measurement of thermal and hydration induced conformational changes of adsorbate structure. The design of the cell and some preliminary measurements will be discussed. 

In recent years, infrared spectroscopy has been enhanced by the possibility of applying Fourier transform techniques to it. This improved spectroscopic technique, known as Fourier transform infrared spectroscopy (FTIR), is of much greater sensitivity than conventional dispersive IR spectroscopy (Skoog West, 1980). Moreover, use of the Fourier transform technique enables spectra to be recorded extremely rapidly, with scan times of only 0-2 s. Thus it is possible to record spectra of AB cements as they set. By comparison, conventional dispersive IR spectroscopy requires long scan times for each spectrum, and hence is essentially restricted to examining fully-set cements. 

The time resolution of the instrument determines the wavenumber-dependent sensitivity of the Fourier-transformed, frequency-domain spectrum. A typical response of our spectrometer is 23 fs, and a Gaussian function having a half width... 

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