Formulas have been derived allowing the determination of the parameter ka (k = 2π/λ, a is the fiber radius) based on the approximate geometric theory for dielectric nonabsorbing unclad fibers of circular cross section from the course backscattered light intensity. The application of the method is restricted to fibers with the refractive indices within the interval (√2,2) and for ka > 100. In this region the method yields results with an accuracy of about 5%.
J. Holoubek, "Light scattering from unclad fibers: approximate ray theory of backscattered light," Appl. Opt. 15, 2751-2755 (1976)