Integrated reflectance

The denominator (normalising constant) is the integrated reflectivity of the first crystal. Figure 2.13 shows the plane wave and the double-crystal rocking curve, again for Si 220 with CuK 1. We note the following ... 

The first summation is over nuclei A. Z are atomic numbers and Rap are distances between the nuclei and the point charge. The second pair of summations is over basis functions, ( ). P is the density matrix (equation 16 in Chapter 2), and the integrals reflect Coulombic interactions between the electrons and the point charge, where rp is the distance separating the electron and the point charge. 

Human color perception correlates with integrated reflectance (McCann et al. 1976). Other experiments have shown that the human visual system does not actually estimate the reflectance of objects (Helson 1938). What is known about the visual system is that color processing is done in an area denoted as V4 (visual area no. 4). In V4, cells have been found that respond to different colors irrespective of the type of illuminant (Zeki... 

Color Perception Correlates with Integrated Reflectances... 

McCann et al. (1976) demonstrated that human color perception correlates with integrated reflectance. We will give a definition for integrated reflectance in a moment. Basically, McCann et al. performed an experiment to show that human color perception correlates with the reflectance of objects as opposed to the amount of light reflected by the objects (see also Land (1974)). For their experiments, McCann et al. used a color Mondrian similar to the one used by Land. The Mondrian contained 17 colored areas. It was illuminated using three... 

If we have an arbitrary illuminant that is defined by the power distribution I AX), then the integrated reflectance Ri would be given by... 

The obtained results allow to study the electronic structure and optical properties of ZnO crystal on the basis of conceptually deeper and more detailed background, than it was previously available on integral reflectivity spectra, and to base theoretical calculations of the properties of zinc oxide upon new foundations. 

The overlap integral reflects the requirement of energy conservation in the ET process. Its value is uncertain because the homogeneous linewidth of solid-state spectra can be up to three orders of magnitude smaller than the inhomogeneous linewidth [359]. A value of 8xl021 J 1 has been adopted for the calculation of MD-MD ET in Cs2NaTmCl6 [360]. 

Figure 5.1 Integrated reflecting powers of various perfect crystals as a function of wavelength. The ordinate represents integration of the reflectivity in figure 5.2, in the range of —20 to +20 seconds of arc. From Kohra, Ando, Matsushita and Hashizume (1978) with permission.

Lorentzian line shape, with an intensity variation that decreases slowly away from the specular condition). Unfortunately, this method is also subject to systematic error. In addition to changes in peak shape, the sample orientation may drift with time (due to thermal stresses) resulting in a measured reflectivity that is systematically reduced with respect to the true integrated reflectivity. 

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