A free-path-length distribution function (FPDF) of multiply backscattered light is theoretically derived for a fractal aggregate of particles. An effective mean-free path-length l D is newly introduced as a measure of randomness analogous with a homogeneously random medium. We confirm the validity of the FPDF by demonstrating agreement between the dimensions designed for a particle distribution generated by a random walk based on the derived FPDF and estimated by the radius of gyration method. The FPDF is applied to Monte Carlo simulations for copolarized multiply backscattered light from the fractal aggregate of particles. It is shown that a copolarized intensity peak of enhanced backscattering in the far field decreases in accordance with θ2-D and has an angular width of λ/l D . This spatial feature of the backscattering enhancement corresponds to that of the copolarized intensity peak produced from a homogeneously random medium with a dimension of D = 3. As a result, the validity of the model for the fractal structure of particle aggregates and the applicability of the derived FPDF are confirmed by the numerical results.
© 1998 Optical Society of America
Original Manuscript: June 30, 1997
Revised Manuscript: February 24, 1998
Published: July 20, 1998
Katsuhiro Ishii, Toshiaki Iwai, Jun Uozumi, and Toshimitsu Asakura, "Optical free-path-length distribution in a fractal aggregate and its effect on enhanced backscattering," Appl. Opt. 37, 5014-5018 (1998)