A unified treatment of dipole–dipole excitation transfer in disordered systems is presented for the cases of direct trapping (DT) in two-component systems and donor–donor transfer (DD) in one-component systems. Using the two-particle model proposed by Huber we calculate the configurational average of Gs(t), the probability of finding an initially excited molecule still excited at time t. For the isotropic three-dimensional case treated by Huber excellent correspondence is found with the previously reported infinite diagrammatic approximation. The anisotropy of the dipole–dipole interaction is included in the averaging procedure. Two regimes of orientational mobility are considered: the dynamic and static limit, rotations being much faster or slower, respectively, than the energy transfer. The following geometrical distributions are investigated: (a) Infinite systems of one, two, and three dimensions which lead to Förster-like decays. Two orientational distributions are considered for monolayers: dipoles confined to the plane or oriented isotropically. (b) Bilayers and multilayers. The averaging procedure for transfer from one layer to another is outlined in detail. The main parameters determining the decay of Gs(t) are the surface concentration and the ratio of the layer separation and the Förster radius. In a stack with a small number of layers, which is a finite system in one of the dimensions, an average over positions of the initially excited donor is included. At low surface concentration the decay gradually changes from two- to three-dimensional character as one increases the number of layers. This fractal-like behavior is solely due to the presence of excluded volumes and the finite nature of the system. Experimental observables are considered in detail. An analysis including a general formalism is presented to determine the loss of polarization memory if an excitation is transferred to a random distribution within the given geometrical constraints. It follows that after one transfer step, in the worst case, less than 10% of the initial anisotropy is conserved if the appropriate observation geometry is chosen. The anisotropy decay, which is manifested in a transient grating or fluorescence depolarization experiment, is
thus a useful observable for Gs(t) in DD transfer.
Phase-contrast imaging using conventional polychromatic x-ray sources and grating interferometers has been developed and demonstrated for x-ray energies up to 60 keV. Here, we conduct an analysis of possible grating configurations for this technique and present further geometrical arrangements not considered so far. An inverse interferometer geometry is investigated that offers significant advantages for grating fabrication and for the application of the method in computed tomography ͑CT͒ scanners. We derive and measure the interferometer's angular sensitivity for both the inverse and the conventional configuration as a function of the sample position. Thereby, we show that both arrangements are equally sensitive and that the highest sensitivity is obtained, when the investigated object is close to the interferometer's phase grating. We also discuss the question whether the sample should be placed in front of or behind the phase grating. For CT applications, we propose an inverse geometry with the sample position behind the phase grating.
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Summary
The influence of different physical parameters, such as the source size and the energy spectrum, on the functional capability of a grating interferometer applied for phase‐contrast imaging is discussed using numerical simulations based on Fresnel diffraction theory. The presented simulation results explain why the interferometer could be well combined with polychromatic laboratory x‐ray sources in recent experiments. Furthermore, it is shown that the distance between the two gratings of the interferometer is not in general limited by the width of the photon energy spectrum. This implies that interferometers that give a further improved image quality for phase measurements can be designed, because the primary measurement signal for phase measurements can be increased by enlargement of this distance. Finally, the mathematical background and practical instructions for the quantitative evaluation of measurement data acquired with a polychromatic x‐ray source are given.
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