Reflection Rayleigh

Fig. 8.6. Time-resolved measurements S(t, z) separating specular (geometrical) from Rayleigh reflections horizontal axis is time t vertical axis is defocus z the value of S(t, z) is indicated by the intensity, with mid-grey as zero and dark and light as negative and positive values of S (Weaver et al. 1989).

Equations (12.5) and (12.6) can be regarded as constituting a Green function, relating the Rayleigh reflected field to the incident field... 

Then the incident and Rayleigh reflected fields in the spatial frequency domain are related by... 

Since ky is conserved the Rayleigh reflected field can be separated into the product of a term in x and a simple exponential term in y, i.e. pn(x, y) = pR(x) exp(ikyy). Rewriting (12.15) in this form gives... 

Fig. 12.10. Time-resolved S(f, y) along a line perpendicular to a crack in glass, scanning across the crack (a) some distance from the end of the crack (b) 75 //m from the end of the crack. As in Fig. 9.3(b), the horizontal axis is time t the vertical axis is y, and the value of S(t, y) is indicated by the intensity, with mid-grey as zero and dark and light as negative and positive values of S. In both figures, the first echo (seen as the first stripy vertical bar) is the geometric reflection from the surface of the specimen, and the second echo (seen as the second stripy vertical bar) is the Rayleigh reflection ( 7.2). The patterns forming a x are the reflections from the near and the far sides of the crack, which cross over when the lens is directly above the crack. In (b), where the scan passes quite near to the tip of the crack, the hyperbolic pattern is due to the crack-tip-diffracted wave (Weaver et al. 1989).

The bottom loss, BL, is calculated from the Rayleigh reflection coefficient... 

Figure 4.7. Internal reflection of a shock wave from a free surface, (a) Reflection of a shock wave from a free surface causes a reflected rarefaction wave. As indicated in (b), this increases the velocity of the shocked material from u, to Uf. The path upon shocking is Rayleigh line 0-1, whereas unloading occurs along release isentrope curve I -O, (c) Release isentrope path in P- V plane is indicated.

The pressure waves when reflected from the top wall interact with the flame again and cause a destabilizing effect on the flame front. The flame is accelerated toward a denser medium and the growth of the perturbations thus turbulizes the flame front via Rayleigh-Markstein instability mechanism. 

Similar work was performed by Shaw et al.3 in 1999 when they used FT-Raman, equipped with a charge coupled device (CCD) detector (for rapid measurements) as an on-line monitor for the yeast biotransformation of glucose to ethanol. An ATR (attenuated total reflectance) cell was used to interface the instrument to the fermentation tank. An Nd YAG laser (1064 nm) was used to lower fluorescence interference and a holographic notch filter was employed to reduce Rayleigh scatter interference. Various chemometric approaches were explored and are explained in detail in their paper. The solution was pumped continuously through a bypass, used as a window in which measurements were taken. 

Figure 8. Calcium values in vertebrate bone and soft tissue samples versus 6 Ca in dietary source (Skulan and DePaolo 1999). Bone values are systematically about 1.3%o lower than source values. Soft tissue values are more variable. All of the values are hypothesized to reflect the balance between Ca dietary intake and exchange with bone calcium (Fig. 9). The soft tissue values are variable largely because the residence time of Ca in the tissues is short. The high value of the egg white reflects Rayleigh-type distillation the egg white loses light Ca to the shell as the shell forms. The small amount of Ca left in the egg white is highly fractionated. The low 6 Ca value of the seal muscle is interpreted as a sign of distress the seal may have had a dietary Ca deficiency for several days or longer before it died, and hence was deriving most of its Ca from bone dissolution.

Figure 10. Fe isotope compositions for total aqueous Fe (Fe,(,T) and ferrihydrite (FH) precipitate and aqueous Fe-ferrihydrite fractionations from the batch oxidation and precipitation experiment of Bullen et al. (2001). (A) Measured S Fe values from Bullen et al. (2001), compared to simple Rayleigh fractionation (short-dashed lines, noted with R ) using 10 1naFe.,-FH = 0.9%o, as well as the two-step re-equilibration model discussed in the text (i.e., Eqn. 12), shown in solid gray lines for the aqueous Fe and ferrihydrite components the predicted 5 Fe value for Fe(III), is shown in the heavy dashed line, which reflects continual isotopic equilibrium between Fe(II), and Fe(III),(. Note that in the experiment of Bullen et al. (2001), aqueous Fe existed almost entirely as Fe(II),(,. (B) Measured fractionation between total aqueous Fe and ferrihydrite precipitate, as measured, and as predicted from simple Rayleigh fractionation (black dashed line) and the two-step model where isotopic equilibrium is maintained between aqueous Fe(II),q and Fe(III),q (solid gray line).

The data of Croal et al. (2004) may also be interpreted to reflect a two-step proeess, where a -2.9%o fractionation occurs between Fe(ll)aq and Fe(lll)aq, accompanied by a +1.4%o fractionation between Fe(lll)aq and ferrihydrite upon precipitation, produces a net fractionation of-1.5%0. When cast in terms of common mechanistic models for separation of solid and liquid phases such as Rayleigh fractionation, it becomes clear that the two-step model produces essentially the same fractionation trend as a single -1.5%o fractionation step between Fe(ll)aq and ferrihydrite if the Fe(lll)aq/Fe(ll)aq ratio is low (Fig. 14). As the Fe(lll)aq/Fe(ll)aq ratio inereases, however, the calculated net Fe(ll)aq-ferrihydrite fractionation in the two-step model deviates from that of simple Rayleigh fractionation (Fig. 14). Unfortunately, the scatter in the data reported by Croal et al. (2004), which likely reflects minor contamination of Fe(ll)aq in the ferrihydrite precipitate, prevents distinguishing between these various models without eonsideration of additional factors. 

Fig. 6. Experimental arrangement for lifetime measurements by the phase-shift method, using laser excitation. The laser beam is amplitude-modulated by a Pockel cell with analysing Nicol prism and a small part of the beam is reflected by a beam splitter B into a water cell, causing Rayleigh scattering. This Rayleigh-scattered light and the fluorescence light from the absorption cell are both focused onto the multiplier cathode PMl, where the difference in their modulation phases is detected. (From Baumgartner, G., Demtroder, W., Stock, M., ref. 122)).

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