Modulation ratio

Early laminates tended to be small because available presses were small, and their original uses were to replace small parts such as the natural mica insulator boards used in radio chasses. As decorative laminates evolved from industrial laminates and the size grew to serve markets such as tabletops, countertops, and wall paneling, laminate dimensions tended to fall into the typical building module ratio of about two length to one cross, such as 2 x 4s,... 

Using the modulation ratio M = m/mo and replacing u by t for clarity, we obtain... 

In practice, the phase shift and the modulation ratio M are measured as a function of co. Curve fitting of the relevant plots (Figure 6.6) is performed using the theoretical expressions of the sine and cosine Fourier transforms of the b-pulse response and Eqs (6.23) and (6.24). In contrast to pulse Jluorometry, no deconvolution is required. 

Fig. 6.9. Sim ulated variations of phase shift and modulation ratio versus frequency using Eqs (6.25) and (6.26).

Practically, the phase delay and the modulation ratio mR of the light emitted by the scattering solution (solution of glycogen or suspension of colloidal silica) are measured with respect to the signal detected by the reference photomultiplier. Then, after rotation of the turret, the phase delay r/ F and the modulation ratio mF for the sample fluorescence are measured with respect to the signal detected by the reference photomultiplier. The absolute phase shift and modulation ratio of the sample are then — [Pg.179]

The least-squares method is also widely applied to curve fitting in phase-modulation fluorometry the main difference with data analysis in pulse fluorometry is that no deconvolution is required curve fitting is indeed performed in the frequency domain, i.e. directly using the variations of the phase shift and the modulation ratio M as functions of the modulation frequency. Phase data and modulation data can be analyzed separately or simultaneously. In the latter case the reduced chi squared is given by... 

Instead of recording separately the decays of the two polarized components, we measure the differential polarized phase angle A (co) = — i between these two components and the polarized modulation ratio A (co) = mfm . It is interesting to define the frequency-dependent anisotropy as follows ... 

The well-defined statistics in single-photon counting is an advantage for data analysis. In phase fluorometry, the evaluation of the standard deviation of phase shift and modulation ratio may not be easy. 

The time of data collection depends on the complexity of the (5-pulse response. For a single exponential decay phase fluorometry is more rapid. For complex 5-pulse responses, the time of data collection is about the same for the two techniques in pulse fluorometry, a large number of photon events is necessary, and in phase fluorometry, a large number of frequencies has to be selected. It should be emphasized that the short acquisition time for phase shift and modulation ratio measurements at a given frequency is a distinct advantage in several situations, especially for lifetime-imaging spectroscopy. 

In the case of a single exponential decay, the lifetime can be rapidly calculated by either the phase shift [Pg.361]

TheAfc(co), MAo>), and are the measurable quantities in the frequency domain. Commonly the modulation ratio M(w) is used... 

Similarly, the overall observable phase delay and modulation ratio can be obtained from Eqs. (9. 64) and (9.65). 

The phase delay and the modulation ratio can be determined at each harmonic available for measurement. These harmonics can range from a few hertz to several gigahertz depending on the harmonic content of the excitation and the lifetime of the luminescent molecule/14,25,27 28) Although all this information is available from the light signals, the instrumentation may limit the number of harmonics that can be measured. 

The phase delay A(nwE) and modulation ratio M(na>E) information of the high-frequency signals is transferred to low-frequency signals by amplitude modulation (cross-correlation) of r.(t) and Iff) with a periodic train of pulses C(f) given by Ref. 29. 

PHASES AND MODULATIONS of at the most Npl2 harmonics of the reference and the response are derived. From this absolute values the phase delay and modulation ratio of multiple harmonics are simultaneously obtained according to Eqs. (9.96) and (9.97), respectively. 

NUMBER OF RUNS Each ofthe Np/2 phase delay and modulation ratio values is memory averaged over several runs to complete the experiment. 

The photoconductivity increases when the a-Si H is lightly doped with phosphorus (Anderson and Spear, 1977). However, phosphorus doping causes very slow decay of photoresponse. The photoresponse characteristic for the phototconductive sensor using undoped a-Si H is shown in Fig. 3. The illumination is the modulated light from a GaP LED. The modulation ratio is defined as M = (it — i2)/i2, where is the peak photocurrent and i2 is the bottom current just prior to the next pulse. Figure 4 shows the modulation ratio of a-Si H versus the pulse width T, compared to that of the CdS-CdSe photoconductive sensor. The CdS-CdSe sensor modulation ratio decreases as the repetition time becomes shorter. On the other hand, in the a-Si H photoconductive sensor, the modulation ratio does not decrease... 

Fig. 4. Modulation ratio for a-Si H photoconductive sensor [under 200- (O) and 50- (A) fiW cm-2 illumination] and CdS photoconductive sensor ( ) versus LED driving pulse width. [From Kagawa et al. (1982).]...

The modulation ratio M is another valuable parameter that describes the modulation of the fluorescence intensity relative to the excitation intensity ... 

In phase-modulation fluorometry, the sample is excited by a sinusoidally modulated light at high frequency. The fluorescence response, which is the convolution product (Eq. (7.6)) of the d-pulse response by the sinusoidal excitation function, is sinusoidally modulated at the same frequency but delayed in phase and partially demodulated with respect to the excitation. The phase shift and the modulation ratio M (equal to m/mo), that is the ratio of the modulation depth m (AC/DC ratio) of the fluorescence and the modulation depth of the excitation mg, characterize the harmonic response of the system. These parameters are measured as a function of the modulation frequency. No deconvolution is necessary because the data are directly analyzed in the frequency domain. 

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