Spectral resolution domain

The selected extragalactic carbon stars have been observed with the VLT/UVES instrument in service mode. The spectral resolution was around 40000 over the domains 420-500 nm and 670-900 nm. We used carbon-rich MARCS model atmospheres and specific linelists in order to derive the abundances of metals,... 

The laser used to generate the pump and probe pulses must have appropriate characteristics in both the time and the frequency domains as well as suitable pulse power and repetition rates. The time and frequency domains are related through the Fourier transform relationship that hmits the shortness of the laser pulse time duration and the spectral resolution in reciprocal centimeters. The limitation has its basis in the Heisenberg uncertainty principle. The shorter pulse that has better time resolution has a broader band of wavelengths associated with it, and therefore a poorer spectral resolution. For a 1-ps, sech -shaped pulse, the minimum spectral width is 10.5 cm. The pulse width cannot be <10 ps for a spectral resolution of 1 cm . An optimal choice of time duration and spectral bandwidth are 3.2 ps and 3.5 cm. The pump pulse typically is in the UV region. The probe pulse may also be in the UV region if the signal/noise enhancements of resonance Raman... 

With 2D data sets non-decayed FIDs in both time domains (Fig. 5.13) are very common and a simple Fourier transformation would give rise to truncation effects in the final spectrum. To circumvent such unwanted effects 2D FIDs are usually rigorously damped, using stringent weighting functions to smoothly bring the last part of the FID close to zero. However this simple procedure severely impairs spectral resolution and should be replaced by LP, followed by suitable weighting, which both improves spectral resolution and excludes any truncation effects. 

A spectral resolution of the order of AEres requires a resolution in the time domain of the order of at least At h/AEres. 

The experimental techniques adopted to measure linear and nonlinear optical properties are quite different and must be discussed separately. In broad terms, linear properties can be measured using low intensity probes and high spectral resolution. They are usually understood in the frequency domain. Nonlinear responses on the contrary need very large intensities, typically achieved in short pulses, and are discussed in the time domain. In addition to these physical considerations, we have to remember that time-resolved spectroscopy and optical characterization usually require good optical quality samples, so our understanding of the physics of these materials is closely linked to their quality. 

Prior to Fourier transformation the time domain data may be modified by multiplication by a function q(t), a process commonly called digital filtering. By suitable choice of q(t), digital filtering may be used in NMR spectroscopy to enhance sensitivity, to improve spectral resolution, or to avoid truncation effects. Conceptually, there is very little difference between filtering of ID and 2D NMR spectra, so the treatment here may later be extended readily to the two-dimensional case. 

The most simple dispersive spectrometer (Fig. 12.2) comprises a source, a monochromator and a detector. The monochromator, made up of an entrance slit, an output slit and prisms or gratings, is u,sed to separate the light into its basic components. The role of the slit system is to enhance the spectral resolution and compensate for intensity variations. The transmission infrared spectrum of the sample is the recording of the light intensity transmitted as a function of the wave-numbers w hich are scanned in front of the monochromator output slit by rotating the dispersive element. In the infrared domain, the wave-numbers are always recorded sequentially, due to the single-channel nature of the detectors. This recording is compared to that of the reference or the source in order to deduce the absorption due to the sample. 

Figure 3. The 2D-IR spectra of a broad-band system (dialanine) recorded by means of (a) time-domain interferometry and (b) spectral interferometry. The spectra are the same with the signal to noise available, although the spectral resolution is slightly better for the spectral interferometry in our arrangement.

For such an experiment to work, we have to be able to distinguish the different domains during the evolution and the detection period of the two-dimensional experiment. Since proton spectral resolution in typical solids is very poor, we have to use homonuclear dipolar-decoupling methods to narrow the lines sufficiently to obtain spectral resolution. The 2D spin-diffusion CRAMPS spectrum was first recorded by Caravatti et al. [68] for blends of polystyrene (PS) and polyvinyl methyl-ether (PVME). There are other methods to generate an initial nonequilibrium polarization based on differences in linewidth or relaxation times. The reader is referred to the excellent book of Schmidt-Rohr and Spiess [67] for an overview. 

The digital spectral resolution is defined by the number of time domain data points for a given spectral width and is directly proportional to the length of the acquisition... 

The basic processing steps for ID NMR data can also be applied to the processing of 2D NMR data with similar effects. Of particular importance for the processing of 2D data matrices are zero filling and apodization. Usually 2D experiments are recorded with a relatively small number of time domain data points TD2, compared with a ID experiment, and small number of increments TDl in order to minimize data acquisition times. Typical time domain values are 512, Ik or 2k words. Small values of TD2 and TDl and the correspondingly short acquisition times cause poor spectral resolution and... 

Although a simple Fourier transform relationship can exist between a high spectral resolution frequency domain experiment and a time-domain quantum beat experiment, whenever the excitation and detection steps involve electromagnetic radiation of different spectral, spatial, or temporal characteristics, the intrinsic information content of time and frequency domain experiments needs not be identical. The format in which the information is presented may be more transparently interpretable in either the time or frequency domain. 

Three dimensional techniques should only be applied in case of overlap in optimally recorded 2D spectra. The basic principle of these experiments is simply to merge two 2D experiments. The addition of a third frequency domain increases the spectral resolution, and gives additional information. The 3D HMQC-COSY spectrum, for example, consists of a set of 2D H- H COSY maps separated according to the 13C chemical shift along the third frequency dimension. Thus moving across l3C, H and H, H planes makes unequivocal assignments possible [66]. 

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