Demodulation factor

In the upper panel of Figure 13.6, the emission is drawn assuming a modulation frequency of 30 MHz and a lifetime of 9 nsec. Using the equations above, the phase angle is 59.5° and the demodulation factor is 0.5. (For further details, the reader is referred to Lakowicz(66)). Additionally, multifrequency phase and modulation instruments that operate over a range of frequencies have been described(67, flS) and simple instruments are possible if only one or several discrete frequencies are required (Figure 13.6, lower panel). 

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) ... 

The decay parameters [a (X) and rj are recovered from the experimentally measured phase shift and demodulation factor by the method of non-linear least squares (24,25). The goodness-of-fit between the assumed model (c subscript) and the experimentally measured (m subscript) data is determined by the chi-squared (x2) function ... 

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... 

Howeva, if the sample consists of a mixture of two fluoro-phores, or a single fluotophore that diqrlays two decay times, dien die fluorescence decay is doubly exponential. Multiexponentiai decays are fieqnendy encountered in biochemical fluorescence, and still more complex decays are found fen colUsional quenching cn in the pretence of spectral relaxation. Phase angles and demodulation factors may still be measured, but these values, when interpreted according to Eqs. [22.1] and [22.2], yield only apparent, and not actual, lifetimes. 

With reference to figure 1(a), the phase shift (O) and the demodulation factor (m) are related to the fluorescence lifetime x of single exponentially decaying fluorophores according to the relations ... 

In phase-modulation fluorometry, the pulsed light source typical of time-domain measurements is replaced with an intensity-modulated source (Figure 10.5). Because of the time lag between absorption and emission, the emission is delayed in time relative to the modulated excitation. At each modulation frequency (to = 2nf) this delay is described as the phase shift (0, ), which increases from 0 to 90° with increasing modulation frequency. The finite time response of the sample also results in demodulation to the emission by a factor m which decreases from 1.0 to 0.0 with increasing modulation frequency. The phase angle (Ow) and the modulation (m, ) are separate... 

The simplest approach for the redundant embedding of the information bits b into the host data x is the repeated embedding of each bit. Let p denote the repetition factor, thus the sequence of watermark letters d is p times longer than b. The watermark letters d are embedded, transmitted and demodulated as described in Sec. 2. However, instead of deciding for each demodulated value Un what transmitted watermark letter dn is most likely, the decoder can estimate directly the most likely transmitted watermark information bit bk from p different demodulated values in y. Without loss of generality, we assume that the fcth iirformationbit bk has been embedded into the data elements Xpk, Xpk+i,..., Xpk+p-i. For an AWGN attack, the demodulated... 

We can measure factor I as the threshold to arousal, as the amplitude of the spinal reflex or, because we want to know the intensity of internal stimulation, as the frequency of eye movement in the presence of complete somatomotor atonia. This measure is used as a proxy for putative PGO wave frequency. As such, it also constitutes an indirect estimate of cholinergic activity, which is, in turn, a measure of aminergic demodulation. This raises questions about the independence of Factor I and Factor M, the third dimension of the model. Neuromodulation (M) is the only dimension of the model that previous conceptualizations did not consider, even implicitly. This is because it cannot yet be measured in humans and... 

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> ... 

This exjnession shows that the emission is demodulated by a factor (1 + o> relative to the excitation. 

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