Mid-Field Forward Scattering

Abstract

Experimental and theoretical results are given for forward scattering by spheres with radius large compared to wavelength, and with index of refraction η near unity. Both the intensity and phase of the scattered field (relative to that incident) are measured and computed for several spheres as functions of the separations of transmitter and receiver from the scatterer (say T and R). The scattering function of primary interest is that which reduces to the usual scattering amplitude in the limit of transmitter and receiver essentially at infinity—say, the function F such that F→f0 as T and R→∞. Differences between F and f0 arise from ``quadratic phase error'' terms involving not only the apertures of the horns, but also the size and dielectric properties of the scatterer. In the ``mid-field region,'' where the sphericity of the wavefronts is significant, the magnitude of the corrections introduced in F is of the order of Imf0, and Imf0 itself is an order of magnitude smaller than Ref0; consequently, although the ``finite geometry'' has only a second-order effect on the forward intensity |F|2, it has a first-order effect on the forward scattered phase arc tan[ImF/ReF]. In addition, since Imf0 is proportional to the total scattering cross section, the sphericity of the wavefronts has a first-order effect on the intensity integrated over all angles. Differences of a hundred percent in the phases of F and f0 may be encountered even in measurements for which T and R fulfill the usual ``far-field criterion.'' However, approximations for the far-field phase may be obtained by extrapolating measurements for several values of T and R in the usual laboratory geometry.