Multifrequency measurements

In order to implement frequency domain based sensing systems capable of monitoring the temporal luminescence of sensors, in few seconds, data must be collected at multiple frequencies simultaneously. Single-frequency techniques have been used to make frequency domain measurements of luminescent decays. 14, 23 28) This approach is unsuitable for real-time applications since data must be acquired at several frequencies in order to precisely and accurately determine the temporal variables of luminescent systems. 1 Each frequency requires a separate measurement, which makes the single frequency approach too slow to monitor the evolution 

Frequency domain measurements require the use of periodic excitation sources. The luminescent molecules respond to the periodic excitation exhibiting the same frequency of modulation. This luminescence exhibits a phase delay and a demodulation with respect to the excitation due to the inability of the sensor molecule to respond to the higher frequencies of the excitation. This inability of the sensor molecules roughly begins at modulation frequencies /modulation of the same order of magnitude or faster than the decay rate 

At very high frequencies the luminescence is completely demodulated and only an average intensity is obtained. The maximum frequency of modulation of the response is determined by kr + k f[Parameter]) of the sensor-carrier preparation. 

In the frequency domain, any periodic excitation, r.(t), can be described by a sum of sinusoidally modulated light waveforms at harmonics of the fundamental frequency of the excitation 

Sinusoidal excitation provides only one harmonic at the modulation frequency. In contrast, pulsed light provides a large number of harmonics of the excitation repetition frequency. The harmonic content, the number of harmonics and their amplitude, is determined by the pulse width and shape.(25) For example, a train of infinitely short pulses provides an infinite number of harmonics all with equal amplitude. A square wave provides only three modulation frequencies with sufficient amplitude to be usable. Equation (9.74) gives the harmonic content of a train of rectangular pulses R(t) of D duty cycle (pulse width divided by period) and RP peak value  

A2 = 6G, A3 = 36G lower trace) at X-(9.5GHz), Q-(34GHz) and W-(94GHz) band freq uencies. All field units given in Gauss. 

---

Amrani E. H., Ibrahim S., and Persaud K. C., Synthesis, chemical characterisation and multifrequency measurements of poly A-(2-pyridyl) pyrrole for sensing volatile chemicals, Mater. Sci. Eng., Cl, 17-22, 1993. 

A strong dependence of spectral shapes oceurs in multifrequency measurements when D /iv at a particular band, see Fig. 4.11 below. 

Hence, if one plots the data from multifrequency measurements on skin in vivo in the complex plane and uses a circular regression to derive, for example, the Cole parameters, one must be aware of the following SC alone does not necessarily produce a circular arc, and as described earlier in this chapter, the measured volume or skin layer is highly... 

The master curve in the form of stiffness versus frequency can be created by fitting the experimentally determined shift factors to a mathematical model. With a multifrequency measurement, frequencies beyond the measurable range of the DMA can be achieved by using the superposition method based on the Williams-Landel-Ferry (WLF) equation [60, 61]. For a temperature range above the T, it is generally... 

H. Engstrom and J. C. Wang [1980] Automatic Multifrequency Measurements of the Complex Impedance of Fast Ion Conductors, Solid State Ionics 1, 441-159. 

The GNSS measurements can be used vice versa for the determination of ionosphere parameters. When we use AtL-Ats=5(At), then such multifrequency measurements could be used with Equation (3) for the TEC computation. The more distant frequencies, the better results, because the value of 5(At) is then greater than the natural variations of the measured pseudorange caused by other factors. Measurements using GNSS signals become an important source of data for monitoring the ionosphere. 

Examination of Eqs. (2.9-2.11) suggests that having frequency domain lifetimes measured at a variety of frequencies is desirable, as it will allow a mixture of fluorophores to be determined. With this in mind, two approaches may be taken to obtain multifrequency results. The first of these is simply to make a series of FLIM measurements while stepping through a predetermined set of frequencies. In practice, this is of limited utility for biological systems because of photo-induced damage to the specimen. 

Spectral FLIM involves measuring the apparent lifetimes in a preparation at many wavelengths with the assistance of a spectrograph or a series of filters (see also Chapter 4, Figs. 4.7 and 4.8 depicting hyperspectral FLIM in the time domain). The goal of the measurement is similar to that of the multifrequency approach ... 

Hedstrom, J., Sedarous, S. and Prendergast, F. G. (1988). Measurements of fluorescence lifetimes by use of a hybrid time-correlated and multifrequency phase fluorometer. Biochemistry 27, 6203-8. 

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. 

Jameson, D. M., Gratton, E., and Hall, R. D. 1984. The measurement and analysis of heterogeneous emissions by multifrequency phase and modulation fluorometery. Appl. Spectrosc. Rev. 20 55-106. 

All fluorescence measurements were performed with an SLM 48000 MHF multifrequency cross-correlation phase and modulation fluorometer. The excitation... 

Three techniques are actually available for measuring the fluorescence lifetime Strobe, Time Correlated Single Photon Counting (TCSPC), and multifrequency and crosscorrelation spectroscopy. Strobe and TCSPC are based on measurement in the time domain, while multifrequency and cross-correlation spectroscopy measure fluorescence lifetimes in the frequency domain. The time domain allows direct observation of fluorescence decay, while the frequency domain is a more indirect approach in which the information regarding the fluorescence decay is implicit. 

Fluorescence lifetime measurements are an important aspect of photophysical research. In the past few months the phase-shift measurement technique has become more widely used. This is largely due to the successful achievement of a multifrequency modulation apparatus. An apparatus made from commercially available components has been described and shown to have an accuracy of 10 ps. The performance was checked using mixtures of acridine and quinine sulphate and least-squares-ht procedures. A series of papers from the Illinois group give very detailed account of the state of the art and show the power of the method. The colour delay error arising from the wavelength error in photodetectors can be determined and fluorescence decay times can be obtained with an accuracy of a few picoseconds. ... 

An important development in the phase-shift technique is the use of a radiofrequency synthesizer as the driver for the Pockels cell modulator. In this way, the excitation beam can be modulated at any frequency between 1 and 200 MHz [137-139]. This approach allows use of cw lasers such as the He-Cd laser and even mode-locked lasers [139] as the excitation source. If d and M are measured at six to ten suitably spaced frequencies, least-squares curve-fitting techniques can be employed to obtain lifetimes with greatly enhanced precision. Typical data obtained by this multifrequency technique make measurement of decay times as short as 10 ps possible. Gratton and coworkers have developed other curve-fitting procedures to analyze data obtained on a multifrequency phase-shift fluorimeter. These experiments include the construction of time-resolved spectra [140], measurements of ro-... 

Hollinger JP, and Mennela RA (1973) Oil spills Measurements of their distributions and volumes by multifrequency microwave radiometry. Science 181 54-56... 

The use of multifrequency cross correlation phase and modulation phosphorometry, based on a technology usually associated with fluorescence lifetime determination, has also now been applied to the measurement and analysis of triplet state decay times . ... 

TaUe 2.3 shows the values of the fluorescence lifetimes of the Tip residues of the sialylated ai-add glycoprotein measured with the multifrequency and TCSPC trathniques. 

---