Time domain measurements Fourier transform technique

Two main techniques are available to perform 2D-IRS, namely a pulsed-Jrequency-domain technique [88] and a time-domain-pulsed-Fourier transform technique [89]. A hybrid method using acousto-optic modulation has also been proposed recently [90]. In the pulsed-frequency-domain experiments, an intense broadband femtosecond pulse is split into a pump pulse, which passes a filter to reduce the band width to sections of typically 10 cm, and an unfiltered probe pulse. Both pulses are focused into the sample within an adjustable time delay. The probe pulse (full bandwidth) measures the spectral changes of the sample after the arrival of the pump pulse. For this purpose, the intensity of the probe light beam is recorded using a spectrometer equipped with a broadband array detector. 

Several comprehensive reviews on the BDS measurement technique and its application have been published recently [3,4,95,98], and the details of experimental tools, sample holders for solids, powders, thin films, and liquids were described there. Note that in the frequency range 10 6-3 x 1010 Hz the complex dielectric permittivity e (co) can be also evaluated from time-domain measurements of the dielectric relaxation function (t) which is related to ( ) by (14). In the frequency range 10-6-105 Hz the experimental approach is simple and less time-consuming than measurement in the frequency domain [3,99-102], However, the evaluation of complex dielectric permittivity in the frequency domain requires the Fourier transform. The details of this technique and different approaches including electrical modulus M oo) = 1/ ( ) measurements in the low-frequency range were presented recently in a very detailed review [3]. Here we will concentrate more on the time-domain measurements in the high-frequency range 105—3 x 1010, usually called time-domain reflectometry (TDR) methods. These will still be called TDS methods. 

The FT technique has been applied in a multitude of different areas. Starting at low frequencies, FT methods have been used for dielectric response spectroscopy of solids (sometimes called time domain reflectometry). A short picosecond voltage pulse is applied to a dielectric and the current response is measured. Fourier transformation of the current gives the dielectric response function, s v), which is typically interpreted as the Debye relaxation of dipoles. 

The methods used for expressing the data fall into two categories, time domain techniques and frequency domain techniques. The two methods are related because frequency and time are the reciprocals of each other. The analysis technique influences the data requirements. Reference 9 provides a brief overview of the various mathematical methods and a multitude of additional references. Specialized transforms (Fourier) can be used to transfer information between the two domains. Time domain measures include the normal statistical measures such as mean, variance, third moment, skewness, fourth moment, kurto-sis, standard deviation, coefficient of variance, and root mean squEire eis well as an additional parameter, the ratio of the standard deviation to the root mean square vtJue of the current (when measuring current noise) used in place of the coefficient of variance because the mean could be zero. An additional time domain measure that can describe the degree of randonmess is the autocorrelation function of the voltage or current signal. The main frequency domain... 

Impedance spectroscopy is frequently used to characterize unstable systems that change with time. One way to reduce the effects of system alteration during the measurement is to reduce the total measurement time by using a multisine technique, which is also frequently called time-domain or FFT (fast Fourier transform) technique [2]. 

The laser heating technique can be applied to perform temperature jumps by irradiating short laser pulses at the sample container. Ernst et al. (54) used such a temperature jump protocol to perform stop-and-go experiments. After the start of the laser pulse, the temperature inside the sample volume is raised to the reaction temperature, the conversion of the adsorbed reactants proceeds, and the H MAS NMR measurement is performed. After the laser pulse is stopped, the temperature inside the sample volume decreases to ambient temperature, and the C MAS NMR measurement is made. Subsequently, the next laser pulse is started and, in this way, the reaction is recorded as a function of the reaction time. By use of the free-induction decay and the reaction time as time domains and respectively, a two-dimensional Fourier transformation leads to a two-dimensional spectrum, which contains the NMR spectrum in the Ej-dimension and the reaction rate information in the Ts-dimension (54,55). 

It is possible that a skin, which is moist and cool gives exactly the same electrical response to measurements made at a single frequency as a skin, which is dry and warm. To separate and specify potentially confounding influences such as water content, temperature change, and sweat gland activity, it is necessary to use some form of electrical spectroscopic technique, that is, stimulation at three or more different frequencies, or a time-domain approach followed by Fourier transformation.44-46... 

We shall conclude this chapter with a few speculative remarks on possible future developments of nonlinear IR spectroscopy on peptides and proteins. Up to now, we have demonstrated a detailed relationship between the known structure of a few model peptides and the excitonic system of coupled amide I vibrations and have proven the correctness of the excitonic coupling model (at least in principle). We have demonstrated two realizations of 2D-IR spectroscopy a frequency domain (incoherent) technique (Section IV.C) and a form of semi-impulsive method (Section IV.E), which from the experimental viewpoint is extremely simple. Other 2D methods, proposed recently by Mukamel and coworkers (47), would not pose any additional experimental difficulty. In the case of NMR, time domain Fourier transform (FT) methods have proven to be more sensitive by far as a result of the multiplex advantage, which compensates for the small population differences of spin transitions at room temperature. It was recently demonstrated that FT methods are just as advantageous in the infrared regime, although one has to measure electric fields rather than intensities, which cannot be done directly by an electric field detector but requires heterodyned echoes or spectral interferometry (146). Future work will have to explore which experimental technique is most powerful and reliable. 

In order to actually cover 19 decades in frequency, dielectric spectroscopy makes use of different measurement techniques each working at its optimum in a particular frequency range. The techniques most commonly applied include time-domain spectroscopy, frequency response analysis, coaxial reflection and transmission methods, and at the highest frequencies quasi-optical and Fourier transform infrared spectroscopy (cf. Fig. 2). A detailed review of these techniques can be found in Kremer and Schonhals [37] and in Lunkenheimer [45], so that in the present context only a few aspects will be summarized. 

Measurements on monosaccharides, by Tait et oA, using time-domain techniques, have extended over the wide frequency range 10 - 10 Hz. Using both the original direct time conversion of the data and the full Fourier transform analysis, three separate relaxation times were found. Their values at 278 K and the activation energies are as follows ... 

Interferometric Raman spectroscopy Interferometric Raman Spectroscopy is a measurement technique that utilizes time-domain or space-domain measurements of electromagnetic radiation or other type of radiation for collecting Raman spectra based on the coherence of a radiative source. An example is a Fourier transform (FT) Raman spectrometer. 

There are a great number of techniques for the experimental determination of viscoelastic functions. The techniques most frequently found in the literature are devoted to measuring the relaxation modulus, the creep compliance function, and the components of the complex modulus in either shear, elongational, or flexural mode (1-4). Although the relaxation modulus and creep compliance functions are defined in the time domain, whereas the complex viscoelastic functions are given in the frequency domain, it is possible, in principle, by using Fourier transform, to pass from the time domain to the frequency domain, or vice versa, as discussed earlier. 

Line broadening. Syn. Apodization (not strictly correct). Any process that increases the measured width of peaks in a spectrum. This can either be a natural process we observe with our instrument, or the post-acquisition processing technique of selectively weighting different portions of a digitized FID to Improve the slgnal-to-nolse ratio of the spectrum obtained following conversion of the time domain to the frequency domain with the Fourier transformation. 

One of the methods used to study emulsions has been the use of dielectric spectroscopy. The permittivity of the emulsion can be used to characterize an emulsion and assign a stability (1,42,48—54). The Sjoblom group has measured the dielectric spectra using time-domain spectroscopy (TDS) technique. A sample is placed at the end of a coaxial line to measure total reflection. Reflected pulses are observed in time windows of 20 ns, Fourier transformed in the frequency range from 50 MHz to 2 GHz, and the complex permittivity calculated. Water or air can be used as reference sample. The total complex permittivity at a frequency (co) is given by ... 

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