Instrumentation frequency domain measurements

This comparison between time and frequency domain measurements is performed at submegahertz frequencies in order to avoid the issue of deconvolution of time domain signals. At megahertz frequencies time domain measurements encounter an additional limitation, these signals must be deconvoluted to isolate the sensor response from the instrument response. The need for deconvolutions adds extra software and computation time, which limits the versatility of time domain techniques for real-time applications. No deconvolutions are necessary in the frequency domain as shown below. 

It is valuable to have fluorophores of known lifetimes for use as lifetime standards in time-domain oc frequency-domain measurements. Perhaps more inportaot than the actual lifetime is kno edge that the fluoroi icw disfda single-expcmential decays. Such fluoro c es are useful for testing the time-resolved instruments for systonatic errors. We have summarized the results on lifetime standards from several laboratm ies. Th e is no attempt to compare the values or to evaluate which values are more reliable. Much of the data is from our laboratory because it was readily available with all the exp imen-tal details. 

Figure 16 shows the experimental arrangement for the measurement of the surface pressure. The trough (200 mm long, 50 mm wide and 10 mm deep) was coated with Teflon. The subphase temperature was controlled within 0.1 C by means of a jacket connected to a thermostated water circulator, and the environmental air temperature was kept at 18 °C. The surface tension was measured with a Wilhelmy plate of platinum(24.5 x 10.0 x 0.15 mm). The surface pressure monitored by an electronic balance was successively stored in a micro- computer, and then Fourier transformed to a frequency domain. The surface area was changed successively in a sinusoidal manner, between 37.5 A2/molecule and 62.5 A2/molecule. We have chosen an unsaturated phospholipid(l,2-dioleoyl-3-sn-phosphatidyI-choline DOPC) as a curious sample to measure the dynamic surface tension with this novel instrument, as the unsaturated lipids play an important role in biomembranes and, moreover, such a "fluid" lipid was expected to exhibit marked dynamic, nonlinear characteristics. The spreading solution was 0.133 mM chloroform solution of DOPC. The chloroform was purified with three consecutive distillations. 

Ion detection is carried out using image current detection with subsequent Fourier transform of the time-domain signal in the same way as for the Fourier transform ion cyclotron resonance (FTICR) analyzer (see Section 2.2.6). Because frequency can be measured very precisely, high m/z separation can be attained. Here, the axial frequency is measured, since it is independent to the first order on energy and spatial spread of the ions. Since the orbitrap, contrary to the other mass analyzers described, is a recent invention, not many variations of the instrument exist. Apart from Thermo Fischer Scientific s commercial instrument, there is the earlier setup described in References 245 to 247. 

Prior to describing the possible applications of laser-diode fluorometry, it is important to understand the two methods now used to measure fluorescence lifetimes these being the time-domain (Tl)/4 5 24 and frequency-domain (FD) or phase-modulation methods.(25) In TD fluorometry, the sample is excited by a pulse of light followed by measurement of the time-dependent intensity. In FD fluorometry, the sample is excited with amplitude-modulated light. The lifetime can be found from the phase angle delay and demodulation of the emission relative to the modulated incident light. We do not wish to fuel the debate of TD versus FD methods, but it is clear that phase and modulation measurements can be performed with simple and low cost instrumentation, and can provide excellent accuracy with short data acquisition times. 

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. 

AutoFit Peaks III, Deconvolution method Deconvolution is a mathematical procedure that is used to remove the smearing or broadening of peaks arising because of the imperfection in an instrument s measuring system. Hidden peaks that display no maxima may do so once the data have been decon-voluted and filtered. This method requires a uniform x-spacing operated in the frequency domain. 

The application of FTIR in chemistry, its unique features, and the relevant instrumentation are well documented [34,35], In brief, an FUR spectrometer is based on a Michelson interferometer that provides a spectrum in the time domain which is Fourier-transformed by a computer to a spectrum in the frequency domain. The sample can be scanned repeatedly, and the accumulated spectra can be averaged, thus producing a representative IR spectrum of a very high signal to noise ratio. This enables the measurement of samples containing a very low concentra-... 

The statistical properties described above for frequency-domain stochastic errors are based on the equations for the instruments actually used for the measurement of complex quantities. While the statistical properties are developed here for electrochemical impedance spectroscopy, they are also valid for measurement of other complex quantities so long as the complex quantities are measured through similar physical principles. 

This part introduces methods used to measure impedance and other transfer functions. The chapters in this section are intended to provide an understanding of frequency-domain techniques and the approaches used by impedance instrumentation. This understanding provides a basis for evaluating and improving experimental design. The material covered in this section is integrated with the discussion of experimental errors and noise. The extension of impedance spectroscopy to other transfer-function techniques is developed in Part III. 

Impedance measurements can be made in either the frequency domain with a frequency response analyzer (FRA) or in the time domain using Fourier transformation with a spectrum analyzer. Commercial instrumentation and software is available for these measurements and the analysis of the data. 

Tvvo vidcl used approaches are used for lifetime measurcnienis. ilie lime-domain approach and the frt i/iu niy-domain approach. In tinte-domain measurements. a pulsed source is employed and the time-depcndcnr decay of fluorescence is measured. In the frequency-domain method, a sinusoidallv modulated source is used to excite the sample. The phase shift and demodulation of the fluorescence emission relative lo the excitation waveform provide the lifetime information. ( onimercial instrumentation is available to implement both techniques. ... 

A comprehensive overview of frequency-domain DOT techniques is given in [88]. Particular instraments are described in [166, 347, 410]. It is commonly believed that modulation techniques are less expensive and achieve shorter acquisition times, whereas TCSPC delivers a better absolute accuracy of optical tissue properties. It must be doubted that this general statement is correct for any particular instrument. Certainly, relatively inexpensive frequency-domain instruments can be built by using sine-wave-modulated LEDs, standard avalanche photodiodes, and radio or cellphone receiver chips. Instruments of this type usually have a considerable amplitude-phase crosstalk". Amplitude-phase crosstalk is a dependence of the measured phase on the amplitude of the signal. It results from nonlinearity in the detectors, amplifiers, and mixers, and from synchronous signal pickup [6]. This makes it difficult to obtain absolute optical tissue properties. A carefully designed system [382] reached a systematic phase error of 0.5° at 100 MHz. A system that compensates the amplitude-phase crosstalk via a reference channel reached an RMS phase error of 0.2° at 100 MHz [370]. These phase errors correspond to a time shift of 14 ps and 5.5 ps RMS, respectively. 

Measurement of the donor lifetime, which typically is 2-25 nsec, requires adequate time resolution. Two techniques, time-correlated singlephoton counting and frequency-domain fluorimetry modulation, can be used (see A. R. Holzwarth, this volume [14]). Excellent books have been written which include discussion of each technique, and Lakowicz and co-workers have discussed advances infrequency-domain instrumentation and applications to FRET. Donor lifetime measurements, unlike steady-state measurements, are capable of detecting multiple donor-acceptor transfer efficiencies in the sample. These lead to multiexponential decays. Donor lifetime measurements are also not affected by an inner-filter effect... 

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. 

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