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.