Polydisperse scattering theory and comparisons with data for red blood cells.

Recent results for low-frequency scattering by polydisperse distributions of correlated low-refracting particles averaged over orientation are analyzed numerically. The roles of shape and correlations (parameterized by c) and polydispersity (specified by the normalized variance d in size governed by the gamma probability density) are investigated. The key variable is the net volume fraction w occupied by the particles. The incoherent scattering is determined by delta = PS(c,d;w) with P as a particle population factor that is independent of w, and S as the fluctuation-correlation function of w. Earlier applications of monodisperse (d = 0) theory emphasized the influence of c on the peak delta = delta and its location w = w in order to invert ultrasonic scattering data of Shung and his associates for red blood cell suspensions under different flow conditions. For d greater than 0, comparable curves for delta (w) decrease more gradually with w increasing past w (because of additional scattering arising from polydispersity) and thereby provide better fits to data for the more controlled flows over broader ranges of hematocrit.

Inversion of ultrasonic scattering data for red blood cell suspensions under different flow conditions.

Recent results for low-frequency scattering by correlated random distributions of nonspherical particles averaged over orientation are applied to invert ultrasonic data for red blood cell suspensions under different flow conditions. The inversion procedure isolates a correlation parameter (c) representing a process in which the volume fraction (w) of particles increases linearly, and also a cell population parameter P. Reduced data records of scattering versus hematocrit are compared with S(c;w)P, where the generalized fluctuation function S is proportional to the variance in particle number, and P is proportional to the backscattering cross section of an isolated particle. The peak scattering for the different flow processes occurs at values of w ranging from about 0.15 for the most uniform to 0.25 for the least, corresponding to c values of about 2.1 to 0.4, as compared with w approximately equal to 0.13 and c = 3 for hard (repulsive at contact) spheres or aligned ellipsoids. The lower values of c suggest weaker repulsion between the deformable cells and effective interparticle attraction (aggregative trends), and c approximately equal to 2 may also involve flow alignment of the discoids.

Transparency of pair-correlated, random distributions of small scatterers, with applications to the cornea.

We consider transmission through pair-correlated random distributions of lossless dielectric (globular, cylindrical, or plate-like) scatterers with length parameter a and average spacing small compared to wavelength. Each optical particle is centered in a tough adherent transparent coating whose outer surface (sphere, cylinder, or slab) has radius b smaller than or equal to a. The corresponding attenuation coefficients beta varies directly as WM involve an integral of the appropriate radial-distribution function. Using the scaled-particle equations of state and statistical-mechanics theorems, we evaluate WM explicitly as a rational function of the volume fraction W of the fluid of rigid b particles. We obtain betaM = betaO WM with betaO as the uncorrelated value; W3(W) for spheres decreases more rapidly with increasing W than W2 for cylinders, and W2 decreases faster than W1, the result for slabs. We apply the results for cylinders in terms of W2 to the problem of the transparency of the cornea (whose collagen fibers are the scatters), as posed by Maurice. The value W APPROXIMATELY 0.6 GIVES GOOD ACCORD WITH THE ESSENTIALS OF THE Data for the transparency of the normal cornea, and the opacity that results from swelling is accounted for by corresponding smaller values of W. Thus, the normal cornea is modeled as a very densely packed two-dimensional gas, with gas-particle (mechanical) radius about 60% greater than the fiber (optical) radius.

Scattering by two-component random distributions of spheres.

Theory and prototype (at wavelength lambda = 5 mm) partial coherence scattering data for optical applications in diagnostic measurements on two component suspensions or gases are presented. Results are given for equal volume mixtures of two sizes of moving randomly distributed large spheres for all realizable values of the fractional volume w (the fraction of the slab region container filled by scattering material). The relative index of refraction of the spheres was about 1.017, and their diameters were 6.52lambda and 3.33lambda (so that we used about eight times as many small spheres as large ones for each value of w). The spheres were of lightweight Styrofoam, and their motion arose from turbulent air streams (flowing through grids that form the top and bottom of a Styrofoam container), and the data were obtained in real time by processing the instantaneous phase quadrature components of the scattered field with an electronic analog computer. We give results for the forward scattered coherent phase, for the coherent, incoherent, and total intensities, and for the covariant magnitude and phase which (together with the incoherent intensity) provide the variances and covariance of the instantaneous phase quadrature components. We also consider certain reduced data records (from which the major effects of scatterer size and material have been eliminated) to indicate the dependence of the scattering on the fractional volume and to facilitate comparison with earlier data for distributions of identical spheres.