Arrival time distribution profile

The majority of all work carried out to date makes use of arrival time analysis, and subsequently a wave velocity value for thickness measurement and for defect location. The wave velocity in a composite material is difficult to use precisely because of the anisotropic characteristics of a composite material. A typical wave or phase velocity profile in polar coordinates is illustrated in Figure 8, showing the nonspherical nature of the wave velocity distribution. The wave velocity distribution can even be more complex for a realistic composite material structure. Despite a possible weakness in the understanding of basic physics and wave propagation in a composite material, thickness measurement can still be carried out by using carefully selected calibration specimens and procedures. Calibration of a test instrument can therefore be carried out for subsequent thickness measurement and defect location analysis in a structure. 

In this section, we discuss methods that detect the time delay td between excitation of a fluorophore and arrival of a fluorescence photon. The distribution of times constitutes the fluorescence decay profile of the fluorophore. The average time lag between the excitation event and the emission is the fluorescence lifetime y of the fluorophore. The fluorescence decay contains information about dynamic processes that deplete the excited state (Fig. 2a). In time-resolved fluorescence experiments, the fluorescence decay is measured to gain information about these processes. 

The transit time for an arbitrary profile depends in general on both ray invariants, i.e. t = t(P, 1). Thus a group of rays, each ray having different values of j and T, can all have the same transit time t. In Fig. 4-11 (a) these rays lie along the contour t (]5,7) = t in the jS-Fplane. Rays with common transit time t + dt lie along the neighboring contour t( J) = t+dt. It then follows that the total power arriving at the end of the fiber between times t and t + d is carried by those rays in the shaded area between the two contours, denoted by dA. If we recall the normalized distribution function 7) for bound rays introduced in... 

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