Incoherent diffraction

To recognize island formation one takes advantage of the difference between coherent and incoherent diffraction from a set of N identical scatterers. If the waves scattered off the individual scatterers are incoherent in their phases, the observed intensity will be proportional to N (addition of intensities). If, however, these scattered waves are coherent, the intensity will be proportional to N (addition of amplitudes). Incoherence occurs either when the incident wave arrives with incoherent phases at different scatterers, which occurs in practice for scatterers separated by at least the coherence length of the incident beam, or when the scatterers themselves are located incoherently, i.e. are disordered. 

Coloration can be physical or chemical (pigmentary) or a combination, and biomimetic versions of the principles involved are contributing to textiles, plastics, and camouflage systems. There are several types of physical coloration, loosely classified as scattering (coherent and incoherent), diffraction, and interference. They can... 

Light Shaping in the LGP using Incoherent Diffraction Gratings... 

Due to diffraction effects of micron-sized mirrors in a regular array, commonly used techniques for surface characterization based on interferometry are inefficient. To overcome the diffraction effects we have developed a novel surface characterization method with an incoherent light source, based on the Foucault s knife-edge test (Zamkotsian and Dohlen, 1999). Since Leon Foucault introduced the knife-edge test in the last century (Foucault, 1859), it has been widely used for testing optical surfaces (see Ch. 3). The test offers a simple way of obtaining easily understandable, qualitative information of the surface shape. 

As an example, consider a planar wavefront from an incoherent source passing through an aberration-free circular lens. When the image is diffraction-limited, an Airy disc pattern is observed (Goodman, 1996). For an aperture of radius 1 / 2n) the pdf for photon arrival is given by... 

Figure 20. Diffraction of coherent and incoherent light from a grating pattern with a spatial frequency, p = (26 ) ...

A primary hydration number of 6 for Fe + in aqueous (or D2O) solution has been indicated by neutron diffraction with isotopic substitution (NDIS), XRD, 16,1017 EXAFS, and for Fe " " by NDIS and EXAFS. Fe—O bond distances in aqueous solution have been determined, since 1984, for Fe(H20)/+ by EXAFS and neutron diffraction, for ternary Fe " "-aqua-anion species by XRD (in sulfate and in chloride media, and in bromide media ), for Fe(H20)g by neutron diffraction, and for ternary Fe -aqua-anion species. The NDIS studies hint at the second solvation shell in D2O solution high energy-resolution incoherent quasi-elastic neutron scattering (IQENS) can give some idea of the half-lives of water-protons in the secondary hydration shell of ions such as Fe aq. This is believed to be less than 5 X I0 s, whereas t>5x10 s for the binding time of protons in the primary hydration shell. X-Ray absorption spectroscopy (XAS—EXAFS and XANES) has been used... 

See also, Bacon, G.E. "Thermal Neutron Diffraction", 3rd ed. Oxford University Press Oxford, 1976, for a discussion of spin-incoherent scattering as well as other aspects of the theory and practice of neutron scattering. 

The standard method for normalisation of diffracted intensity data into electron units, is to compute both the mean square atomic scattering factor and the mean incoherent scatter for the particular molecular repeat over a range of high two theta values (say 40°-60°) where their total value can be considered to be equivalent to the actual diffraction from the molecular system concerned. An appropriate normalisation factor is then applied to the experimental intensity data after geometrical correction and, finally, incoherent scatter is subtracted ( 1 ). 

Es is the electric field amplitude of the diffracted beam. Ec and Einc are the coherent and incoherent electric field amplitudes of the background intensity, respectively. 0 is the phase shift between the signal and the coherent background, and the phase of Ec is arbitrarily chosen to be zero. For convenience, the proportionality factor between E2 and / is set to unity. Sbom = E2 is the homodyne and Sbet = 2 ECES cos 0 the heterodyne signal. The total background is Jb=E2c + Efnc. 

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