Frequency domain method

The second chapter by Peter Verveer and Quentin Hanley describes frequency domain FLIM and global analysis. While the frequency domain technique for fluorescence lifetime measurement is sometimes counterintuitive, the majority of the 10 most cited papers using FLIM have taken advantage of the frequency domain method as stated by these authors. The global analysis of lifetime data in the frequency domain, resolving both E and /d has contributed significantly to this advantage. 

While publications on fluorescence lifetime imaging microscopy (FLIM) have been relatively evenly divided between time and frequency domain methods, a majority of the 10 most highly cited papers using FLIM have taken advantage of the frequency domain method [1, 2-9]. Both techniques have confronted similar challenges as they have developed and, as such, common themes may be found in both approaches to FLIM. One of the most important criteria is to retrieve the maximum information out of a FLIM... 

At present, two main streams of techniques exist for the measurement of fluorescence lifetimes, time domain based methods, and frequency domain methods. In the frequency domain, the fluorescence lifetime is derived from the phase shift and demodulation of the fluorescent light with respect to the phase and the modulation depth of a modulated excitation source. Measurements in the time domain are generally performed by recording the fluorescence intensity decay after exciting the specimen with a short excitation pulse. 

Gratton, E., Breusegem, S., Sutin, J., Ruan, Q. and Barry, N. (2003). Fluorescence lifetime imaging for the two-photon microscope time-domain and frequency-domain methods. J. Biomed. Opt. 8, 381-90. 

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]. 

FLIM has been developed using either time-domain or frequency-domain methods (Herman et al., 1997). 

As shown in Section 11.2.1.1, more details can be obtained by confocal fluorescence microscopy than by conventional fluorescence microscopy. In principle, the extension of conventional FLIM to confocal FLIM using either time- or frequency-domain methods is possible. However, the time-domain method based on singlephoton timing requires expensive lasers with high repetition rates to acquire an image in a reasonable time, because each pixel requires many photon events to generate a decay curve. In contrast, the frequency-domain method using an inexpensive CW laser coupled with an acoustooptic modulator is well suited to confocal FLIM. 

Figure 9.7. Noise content of a fiberoptic oxygen sensor signal (a) in the time and (b) in the frequency domains. Time domain signals require broad frequency bandwidths. Frequency domain signals require very limited-frequency bandwidths. Noise is reduced by band limiting the signal, an advantage of frequency domain methods.

J. R. Lakowicz, Fluorescence studies of structural fluctuations in macromolecules as observed by the time, lifetime and frequency domains, Methods Enzymol. 131, 518-567 (1986). 

There are several methods for testing for stability in the Laplace domain. Some of the most useful are discussed below. Frequency-domain methods will be discussed in Chap. 13. 

To overcome these problems, we must learn another language Chinese. This is what we wilt call the frequency-domain methods. These methods are a little more removed from our mother tongue of English and a little more abstract. But they are extremely powerful and very useful in dealing with realistically complex processes. Basically this is because the manipulation of transfer functions becomes a problem of combining complex numbers numerically (addition, multiplication, etc.). This is easily done on a digital computer. 

In Chap. 12 we will learn this new Chinese language (including several dialects Bode, Nyquist, and Nichols plots). In Chap. 13 we will u.se frequency-domain methods to design closedloop feedback control systems. Finally, in Chap. 14, we will briefly discuss some frequency-domain and other methods for experimentally identifying a process. 

The design of feedback controllers in the frequency domain is the subject of this chapter. The Chinese language that we learned in Chap. 12 is now put to use to tune controllers. Frequency-domain methods are widely used because they have the significant advantage of being easier to use for high-order systems than the time- and Laplace-domain methods. 

S.G. Johnson and J.D. Joannopoulos, Block-iterative frequency-domain methods for Maxwell s equations in a planewave basis , Optics Express, 8, 173-190 (2001). 

Many interesting phenomena can arise in nonlinear periodic structures that possess the Kerr nonlinearity. For analytic description of such effects, the slowly varying amplitude (or envelope) approximation is usually applied. Alternatively, in order to avoid any approximation, we can use various numerical methods that solve Maxwell s equations or the wave equation directly. Examples of these rigorous methods that were applied to the modelling of nonlinear periodical structures are the finite-difference time-domain method, transmission-line modelling and the finite-element frequency-domain method." ... 

This chapter is organized as follows By reference to a signal model, time-scale and pitch-scale modifications are defined in the first part. The second part presents frequency-domain techniques while the third part describes time-domain techniques. In the fourth part, the limitations of time-domain and frequency-domain methods are discussed along with improvements proposed in the last few years. 

Historically, the first techniques designed to achieve independet control over pitch or duration were carried out in the time domain Fairbanks, Everitt and Jaeger s modified tape recorder [Fairbanks et al., 1954] probably is the first known automatic time-domain system for speech transposition. By contrast with frequency-domain methods, time-domain techniques for time or pitch scale modification manipulate short-duration time-segments extracted from the original signal, a mechanism usually called sampling or splicing As a result, they tend to require much fewer calculations and lend themselves quite well to real-time implementations. 

Lastly it should be noted that the time or scan rate issue equally plagues time as well as frequency domain methods for obtaining Rf, since in the time domain measurement, the triangle waveform is simply the Fourier synthesis of a series of sinusoidal signal functions. However, voltage sweep, potential step, and impedance methods should all yield the same value of Rf when all the scan... 

In conclusion, the rather straightforward one-color pump-probe scheme of the self-heterodyne method seems particularly appropriate for smaller coupled systems where the vibrational spectra are less congested. The main content of the present approach and the frequency domain method described in Section IV.C are the same, namely the existence and magnitudes of cross peaks and their relationship to couplings between... 

Fluorescence anisotropy decay can also be measured by frequency-domain methods. In this approach, the polarized fluorescence intensities 7 (oo) and 7j (oo) are measured as a function of the modulation frequency of the polarized excitation beam. Even more information about frequency-domain anisotropy measurement and analysis can be found in the monograph by Lakowicz (see Eurther Reading). 

Over a substantial number of years the phase-shift or frequency-domain method has been employed for the measurement of fluorescence lifetimes. The technique requires the continuous excitation of a fluorescent sample with a source of varying intensity. The fluorescence response would normally be expected to increase and decrease to reflect the changes in excitation intensity. However, in a frequency-domain experiment the excitation beam is modulated at a high frequency, (o = 2nf, to produce a sinusoidally changing intensity given by ... 

The third class of techniques include a frequency-domain method based on the identification of the sensitivity function S s)) and the complementary sensitivity function T s)) from plant data or CPM of multivariable systems [140]. Robust control system design methods seek to maximize closed-loop performance subject to specifications for bandwidth and peak... 

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