TRANSPORT OF LIGHT IN A SCATTERING MEDIUM THROUGH MULTIPLE SMALL-ANGLE SCATTERING

Scattering of light by relatively large and numerous particles suspended in a liquid with a nearly matched index of refraction results in deflection through very small angles. The cumulative effect of many scatterings can, however, be substantial. Taking advantage of this small-angle-scattering property, we derive a simple asymptotic expression for the Nth-order multiple-scattering term based on steepest-descents evaluation of the Nth-order multiple integrals. When the dominant contribution to the scattering is high order (large N), the path followed by photons can be described by analogy with a deformed elastic rod, for which a constrained variational principle or principle of least action is specified. Euler-Lagrange equations are obtained for this constrained-end-point problem.