Coherence area

Reactions belonging to the same reaction type are projected into coherent areas on the Kohonen map this shows that the assignment of reaction types by a chemist is also perceived by the Kohonen network on the basis of the electronic descriptors. This attests to the power of this approach. 

Consider one resolution cell xm of the spectrum. The number of df, zm, is defined as the number of independent volumes that exist over the volume swept out by photons leaving the entrance slit during one exposure time t (see Fig. 3). An independent volume is the three-dimensional space over which a photon is coherent. Hence, if it has a coherence length c Arm, with c the speed of light and Arm the coherence time, and if it has a coherence area cTm, the coherence volume is simply their product, or c Arm om. On the other hand, the total volume swept out by a wave front of photons all leaving the aperture of area A during exposure time t is ctA. Hence the number of coherence volumes is... 

The coherence area om is measured at the entrance slit, because this is where the object is imagined to exist. From Fig. 1, this slit is distance R from the spectral source, which is incoherent and of area w2. Then the Van Cittert-Zernike theorem (Born and Wolf, 1959) gives... 

The concept of the coherence area may also be described as follows. Suppose one of the sample dimensions in the plane perpendicular to the sample-detector line is a. Then, the angular range of light accepted in that direction Aa must be on the order of... 

The use of clipping has a profound effect on the observed correlation function and its relation to the relaxation function. Because clipping is a nonlocal operation, the numerical factor/which relates Ck(t) to [Pg.135]

Existence of the long-range order in the packing with the lower limit of the coherence area from 0.5h > 400 A indicates that the packing shown in Figure 10 only is possible for these intermolecular distances. 

A, which defines the coherence area, clearly increases as the size of the source is decreased. 

As already indicated, the degree of coherence of the electron beam can have an important influence on the nature of electron diffraction patterns. However, in Chapters 3 and 4, which deal with the theories of electron diffraction, we assume, as we did earlier in this chapter, that the diameter of the coherence area is large compared with the [Pg.36]

The various research agendas engaging questions of fitness and fine-tuning applied to the cosmos stress that important future opportunities exist for continued and expanded inquiry into areas where the sciences touch on wider, deeper issues of human interest. It is important to note that the preliminary discussion recorded here represents relatively early-stage exploration into what may in time become a much larger and more coherent area of research. 

A brief description of some of the important features of optical mixing experiments is given in this appendix. We include discussions of the concepts of coherence and coherence area, their application to the calculation of predetection signal to noise ratios in optical mixing experiments, and a brief discussion of digital (photon counting) methods. 

The concept of coherence area is central in considerations of the signal-to-noise ratio in optical mixing experiments. When light from an extended source impinges on a screen, a diffraction pattern is produced which depends among other things, on the extent of the source that is, the intensity maxima and minima depend on the source dimensions. Figure 4.B.1 illustrates this for a one-dimensional case. Assume that each... 

If the source were three-dimensional and the observation plane a flat surface such as the cathode of a photomultiplier tube, then one could define an area around the point A such that the signals at all points within this area are partially coherent with those at A. This area would be called the coherence area. 

Estimates of the coherence area for typical light-scattering experiments have been given by several authors (Forrester, et al., 1955 Degiorgio and Lastovka, 1971). A useful estimate is... 

What happpens when the illuminated area of the photocathode is less than one coherence area In this case the fluctuating part of is proportional to ift (the... 

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