Polarized bidirectional reflectance of optically thick sparse particulate layers: An efficient numerically exact radiative-transfer solution

- Polarized bidirectional reflectance of semi-infinite particulate layers is considered.
- An iterative numerical solution of Ambartsumian's integral equation is described.
- This solution is highly efficient and yields benchmark accuracy.
- The resulting computer program is publicly available online.
- The paper serves as a detailed user guide to the computer program.

We describe a simple yet efficient numerical algorithm for computing polarized bidirectional reflectance of an optically thick (semi-infinite), macroscopically flat layer composed of statistically isotropic and mirror symmetric random particles. The spatial distribution of the particles is assumed to be sparse, random, and statistically uniform. The 4×4 Stokes reflection matrix is calculated by iterating the Ambartsumian's vector nonlinear integral equation. The result is a numerically exact solution of the vector radiative transfer equation and as such fully satisfies the energy conservation law and the fundamental reciprocity relation. Since this technique bypasses the computation of the internal radiation field, it is very fast and highly accurate. The FORTRAN implementation of the technique is publicly available on the World Wide Web at http://www.giss.nasa.gov/staff/mmishchenko/brf. It can be combined with several existing computer programs providing the requisite single-scattering properties of spherical or morphologically complex particles and applied to a wide range of optical characterization problems. Benchmark results obtained with this program can be used for testing alternative solvers of the vector radiative transfer equation.