Abstract

Simple asymptotic approximations are derived for the bulk coherent propagation coefficient (<i>K</i>) in pair-correlated distributions of obstacles with minimum separation (<i>b</i>) between particle centers large compared to wavelength (λ). The size of the scatterer (maximum diameter 2<i>a</i> ≤ <i>b</i>) is arbitrary compared to λ. The functional equation for <i>K</i> involves only the forward-scattered and backscattered amplitudes of an obstacle and simple integrals of the total correlation function (<i>F</i>). For large particles with small refractive contrast, the leading terms differ from the leading terms for small-spaced particles in that the scattering cross-section term involves a different packing factor (<i>W</i>). The present <i>W</i> depends on 2<i>a</i>/<i>b</i> and the zeroth moment of <i>F</i>, whereas for small spacing <i>W</i> is the limit of the structure factor for small <i>b</i>/λ. Higher-order terms involving the first and second moments of <i>F</i> are also derived, and the forms are applied to obtain explicit results for spheroids in terms of the volume fraction of statistical pa ticles. More generally, the initial functional equation can be evaluated in terms of existing tabulated values of <i>F</i>.

© 1983 Optical Society of America

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