Frequency-dependent demodulation

Figure 6.10 Frequency-dependent phase shifts and demodulations (bottom panel) for IR-I44 (open symbols) and DOTCI (solid symbols), together with the best single exponential lit to each dataset. The residuals for the 1R-144 data set are depicted in the upper panel. Reproduced from Ref. 25 with permission.

The multiplicative property of the demodulation factors and the additive property of the individnal phase angles are the origin of a reversed frequency dependence of the apparent phase-shift and demodulation lifetimes and the inversion of apparent phase and moduISlion lifetimes when conpared to those of a heterogeneous sainpie. The apparent phase lifetime (x)i) calculated from the measured phase ( a) of the relaxed state is... 

Theory. If two or more fluorophores with different emission lifetimes contribute to the same broad, unresolved emission spectrum, their separate emission spectra often can be resolved by the technique of phase-resolved fluorometry. In this method the excitation light is modulated sinusoidally, usually in the radio-frequency range, and the emission is analyzed with a phase sensitive detector. The emission appears as a sinusoidally modulated signal, shifted in phase from the excitation modulation and partially demodulated by an amount dependent on the lifetime of the fluorophore excited state (5, Chapter 4). The detector phase can be adjusted to be exactly out-of-phase with the emission from any one fluorophore, so that the contribution to the total spectrum from that fluorophore is suppressed. For a sample with two fluorophores, suppressing the emission from one fluorophore leaves a spectrum caused only by the other, which then can be directly recorded. With more than two flurophores the problem is more complicated but a number of techniques for deconvoluting the complex emission curve have been developed making use of several modulation frequencies and measurement phase angles (79). 

A more complex but faster and more sensitive approach is polarization modulation (PM) IRLD. For such experiments, a photoelastic modulator is used to modulate the polarization state of the incident radiation at about 100 kHz. The detected signal is the sum of the low-frequency intensity modulation with a high-frequency modulation that depends on the orientation of the sample. After appropriate signal filtering, demodulation, and calibration [41], a dichroic difference spectrum can be directly obtained in a single scan. This improves the time resolution to 400 ms, prevents artifacts due to relaxation between measurements, and improves sensitivity for weakly oriented samples. However, structural information can be lost since individual polarized spectra are not recorded. Pezolet and coworkers have used this approach to study the deformation and relaxation in various homopolymers, copolymers, and polymer blends [15,42,43]. For instance, Figure 7 shows the relaxation curves determined in situ for miscible blends of PS and PVME [42]. The (P2) values were determined... 

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. 

In the frequency-domain, the experimentally measured quantities are the frequency- (w) and wavelength- (X) dependent phase shift (0m(X,a>)) and demodulation factor (MnXX, )). For any assumed decay model (equation 1), these values are calculated from the sine (S(X,o>)) and cosine (C(X,w)) Fourier transforms. If we assume the decay kinetics are described by a simple sum of exponential decay times we have (24) ... 

Equation (9.5) can be viewed as first a modulation of the window to frequency cq thus producing a bandpass filter w(n)eJ an followed by a filtering of x(n) through this bandpass filter. The output is then demodulated back down to baseband. The temporal output of the filter bank can be interpreted as discrete sine waves that are both amplitude- and phase-modulated by the time-dependent Fourier transform. 

When the signal is frequency modulated (Figure 3.11a) modulation sidebands still appear, but their phase is such that no signal results on demodulation by heterodyne detection. Only if the cavity or sample itself shows absorption dependent on the source frequency is some of the applied FM converted to amplitude modulation (Figure 3.11b) and a signal detected. 

The resulting time-dependent fluorescence (Em(t)) is equal in frequency to the exciting sinusoid (forced response), but is demodulated by a factor M and phase shifted by an angle ij> ... 

Examination of Hgure 4.2 reveals another effect of the lifetime, tiiis bang a decrease in the peak-to-peak bright of the emission relative to that of the modulated excitation. The modulation decreases because some of the fluoto-phores excited at the peak of the excitation continue to emit when the excitation it at a minimum. The extent to which diis occurs depends on the decay time and light modulation frequency. This effiect is called demodulation and can also be used tocalculate the decay time. At present, pulse and phase-modulation measurements ate both in widespread use. 

The phase shift and demodulation both depend on the fluorescence lifetimes and amplitudes and on the modulation frequency u according to (10)... 

Two widely used approaches are used for lifetime measurements, the time-domain approach and the frequency-domain approach. In time-domain measurements, a pulsed source is employed and the time-dependent decay of fluorescence is measured. In the frequency-domain method, a sinusoidally modulated source is used to excite the sample. The phase shift and demodulation of the fluorescence emission relative to the excitation waveform provide the lifetime information. Commercial instrumentation is available to implement both techniques. "... 

Fluorescence decay kinetics also can be measured by exciting the sample with continuous light whose intensity is modulated sinusoidally at a frequency (m) on the order of 1/t, where t again is the fluorescence lifetime. The fluorescence oscillates sinusoidally at the same frequency, but the amplitude and phase of its oscillatirais relative to the oscillations of the excitation light depend on the product of oo and t (Fig. 1.16 and Appendix A4). If mr is much less than 1, the fluorescence amplitude tracks the excitation intensity closely if an is larger, the oscillations are delayed in phase and damped (demodulated) relative to the excitation [28-30]. Fluorescence with multiexponential decay kinetics can be analyzed by measuring the fluorescence modulation amplitude or phase shift with several different frequencies of modulated excitation. 

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