Far-field region

At sufficiently large distances from tlje origin (kr 1), in the far-field region, the scattered electric field E5 is approximately transverse (er E5 — 0) and has the asymptotic form (see, e.g., Jackson, 1975, p. 748)... 

Suppose that a detector is placed at a distance r from a particle in the far-field region, with its surface A A aligned normal to er (Fig. 3.4). If the detector is suitably collimated, and if er is not too near the forward direction ez, the detector will record a signal proportional to Ss erAA (AA is sufficiently small so that Ss does not vary greatly over the detector). The detector sees only the scattered light provided that it does not look at the source of incident light. From (3.10) and (3.13) it follows that... 

For convenience we take the incident electric field E, = Eex to be x-polarized. Because the medium is nonabsorbing, Wa is independent of the radius r of the imaginary sphere. Therefore, we may choose r sufficiently large such that we are in the far-field region where... 

Far-field region or radiation zone, defined by R > r7. At macroscopic distances, the longitudinal component of force is negligible, so that the radiation field is almost plane (i.e., perpendicular to the z-axis in Fig. 3). 

The emitted beam has both a specific intensity distribution profile and specific polarization properties. High-accuracy methods of computation of SR allow the calculation of the spectral flux and intensity distributions of emitted radiation in the near- and in the far-field regions.24 In Fig. 3.3(a) three distribution profiles... 

In general, the plume flow field is divided into the near-field, transition, and far-field regions [5]. The near-field region which is shown in Fig. 29.1 consists of a nearly inviscid jet core dominated by strong wave structures and a thin... 

In this limit, one can distinguish between the core region (p = 0(1)) and far field region (p = 0(1/e)), where the asymptotic expansions are different. 

Fig. 3. Schematic plots of the decay of the electrostatic potential if(r) near a polyelectrolyte chain of unspecified chain radius. The potential decay predicted by a nonlinear Poisson-Boltzmann analysis can be superimposed onto one predicted by a linearized Debye-Hiickel approximation in the far field region if the surface potential of the Debye-Hiickel is appropriately adjusted. However, in this case there remains strong deviation between the two approaches in the region nearer the chain.

Far-field region. This region is characterized by the independence of the relative angular distribution of the held with varying distance. The pattern is essentially independent of distance. 

The far-field region of the water-saturated transversely isotropic ground in a cylindrical coordinate system can be represented by this transmitting boundary. 

We can translate this equation into spatial frequency coordinates, such that u =kal2nf and v=kpl2nf, giving the Fourier transform relationship shown above for the far field region, with an added phase distortion due to the compression of R down to the focal plane/of the positive lens. 

Far field region = focal plane of a positive lens = FT(aperture function)... 

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