Frequency domains, time-resolved

Beyond imaging, the combination of CRS microscopy with spectroscopic techniques has been used to obtain the full wealth of the chemical and the physical structure information of submicron-sized samples. In the frequency domain, multiplex CRS microspectroscopy allows the chemical identification of molecules on the basis of their characteristic Raman spectra and the extraction of their physical properties, e.g., their thermodynamic state. In the time domain, time-resolved CRS microscopy allows the recording of the localized Raman free induction decay occurring on the femtosecond and picosecond time scales. CRS correlation spectroscopy can probe three-dimensional diffusion dynamics with chemical selectivity. 

The time-dependent methods, which are unaffected by or less sensitive to the complications that intensity measurements suffer, include the time domain (time-resolved) technique, in which the fluorescence decay lifetime x is measured, and the frequency domain technique, in which the frequency response of donor emission is used to obtain interprobe distances (distribution). Each requires highly specialized, high-cost, instruments, often custom-built for nanosecond lifetime measurement before the lanthanide probes were developed. In the time-resolved method, E = 1 - Tda/ d, where Tda and Td are donor fluorescence lifetime in the presence and absence of an acceptor, respectively. For the purpose of studying structure-function relations of macromolecules, the accurate measure of absolute distance is of less importance and interest than the changes in distance in response to condition changes. 

FT is essentially a mathematical treatment of harmonic signals that resolved the information gathered in the time domain into a representation of the measured material property in the frequency domain, as a spectrum of harmonic components. If the response of the material was strictly linear, then the torque signal would be a simple sinusoid and the torque spectrum reduced to a single peak at the applied frequency, for instance 1 Hz, in the case of the experiments displayed in the figure. A nonlinear response is thus characterized by a number of additional peaks at odd multiples of the... 

The most sophisticated techniques require time-resolved measurements (lifetime, anisotropy, spectra) either in the time or frequency domain ([6-10] for a focused journal issue on the subject see [11]). Thus, the significance of new, versatile, commercially available light... 

In order to better quantify the absolute value of chromophore concentrations, time of flight (TOF) must be measured in addition to light attenuation. This may be achieved using time-resolved or frequency domain methods. Time-resolved spectroscopy (TRS) was first pioneered by Delpy et. al. [19], Patterson et. al. [85] and Chance et al. [12, 13]. 

To summarize, current state of NIR research consists of two major groups of instrumentation (f) continuous wave and (2) time-resolved and frequency domain and two major groups of parameters assessed (f) slow responding hemodynamic (HbO and Hb) parameters and (2) fast response neuronal parameter. Assessing the fast response parameter requires high temporal resolution provided by NIR equipment. Such temporal resolutions are currently not possible using fMRI modality. Thus, a natural complementary relationship exists between fMRI and NIR methods, where fMRI can provide better spatial localization and NIR better temporal resolution. 

In addition, there is a large number of studies involving aromatic alcohols such as phenol [166] or naphthol, which have in part been reviewed before [21], These include time-resolved studies [21], proton transfer models [181], and intermolecular vibrations via dispersed fluorescence [182]. Such doubleresonance and more recently even triple-resonance studies [183] provide important frequency- and time-domain insights into the dynamics of aromatic alcohols, which are not yet possible for aliphatic alcohols. 

The value of fEdetermines all other variables in the equations above. In turn, fE is determined by the temporal resolution of interest of the system studied. To resolve an average excited state lifetime t, the required data sampling rate, in frequency domain techniques is at least an order ofmagnitude slower than it is in the time domain as stated by the following relation (when Np > 32 and Nw= 1) ... 

There are two widely used methods for measuring fluorescence lifetimes, the time-domain and frequency-domain or phase-modulation methods. The basic principles of time-domain fluorometry are described in Chapter 1, Vol.l of this series(34) and those of frequency-domain in Chapter 5, Vol. 1 of this series.<35) Good accounts of time-resolved measurements using these methods are also given elsewhere/36,37) It is common to represent intensity decays of varying complexity in terms of the multiexponential model... 

The elucidation of the intramolecular dynamics of tryptophan residues became possible due to anisotropy studies with nanosecond time resolution. Two approaches have been taken direct observation of the anisotropy kinetics on the nanosecond time scale using time-resolved(28) or frequency-domain fluorometry, and studies of steady-state anisotropy for xFvarying within wide ranges (lifetime-resolved anisotropy). The latter approach involves the application of collisional quenchers, oxygen(29,71) or acrylamide.(30) The shortening of xF by the quencher decreases the mean time available for rotations of aromatic groups prior to emission. 

At the present time, two methods are in common use for the determination of time-resolved anisotropy parameters—the single-photon counting or pulse method 55-56 and the frequency-domain or phase fluorometric methods. 57 59) These are described elsewhere in this series. Recently, both of these techniques have undergone considerable development, and there are a number of commercially available instruments which include analysis software. The question of which technique would be better for the study of membranes is therefore difficult to answer. Certainly, however, the multifrequency phase instruments are now fully comparable with the time-domain instruments, a situation which was not the case only a few years ago. Time-resolved measurements are generally rather more difficult to perform and may take considerably longer than the steady-state anisotropy measurements, and this should be borne in mind when samples are unstable or if information of kinetics is required. It is therefore important to evaluate the need to take such measurements in studies of membranes. Steady-state instruments are of course much less expensive, and considerable information can be extracted, although polarization optics are not usually supplied as standard. 

Stonehouse and Keeler developed an intriguing method for the accurate determination of scalar couplings even in multiplets with partially convoluted peaks (one- or two-dimensional). They recognized that the time domain signal is completely resolved and that convolution of the frequency domain spectrum is a consequence of the Fourier transform of the signal decay. The method requires that the multiplet be centred about zero frequency and this was achieved by the following method ... 

Fig. 8.11 (c), and there is not even one full relevant oscillation in the frequency domain. But the maximum entropy method enables useful information to be obtained even from such poorly resolved data as this, and in the time-interval domain in Fig. 8.11(d) the MEM transform ofln S (/) — In So(/) has a pronounced peak from which 2d/v for the cell at that point can be determined. The time separation is about 2 ns, corresponding to a thickness of less than 2 pm. This may be a world record for acoustic distance resolution in this way. 

Fig. 5. 19F/15N IMPEACH MBC spectrum of a mixture of 2- and 3-fluoropyridine. The accordion optimisation range was varied from 4 to 50 Hz the Fx frequency domain was digitised using 64 increments of the evolution time, ti. The Fi doublet splitting for the 2-fluoropyridine correlation of 70bs = 728 Hz (see text) is clearly visible while the smaller one for the 3-fluoropyridine correlation is no longer resolved. Reproduced from Ref. 27 by permission of J. Wiley Sons.

While in the frequency domain all the spectroscopic information regarding vibrational frequencies and relaxation processes is obtained from the positions and widths of the Raman resonances, in the time domain this information is obtained from coherent oscillations and the decay of the time-dependent CARS signal, respectively. In principle, time- and frequency-domain experiments are related to each other by Fourier transform and carry the same information. However, in contrast to the driven motion of molecular vibrations in frequency-multiplexed CARS detection, time-resolved CARS allows recording the Raman free induction decay (RFID) with the decay time T2, i.e., the free evolution of the molecular system is observed. While the non-resonant contribution dephases instantaneously, the resonant contribution of RFID decays within hundreds of femtoseconds in the condensed phase. Time-resolved CARS with femtosecond excitation, therefore, allows the separation of nonresonant and vibrationally resonant signals [151]. 

Patterson MS, Pogue BW. Mathematical model for time-resolved and frequency-domain fluorescence spectroscopy in biological tissue. Applied Optics 1994, 33, 1963-1974. 

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