Kirchhoff calculations of the coherent scatter from a series of very rough surfaces

Calculations are presented for the scattering of polarized light from a series of very rough one-dimensional gold-coated surfaces, as determined by the use of the Kirchhoff approximation with geometric shadowing. These surfaces have Gaussian autocorrelation functions with a 1/e width of 3.3 µm and Gaussian probability distributions of height with standard deviation varying between 0.25 and 1.73 µm. Calculations are performed for the scattering of light of wavelength 3.392 µm, so that the validity of the geometric-shadowing approximation and the Kirchhoff approximation itself are open questions. The values of the coherent (or specular) component of the scattered light for the four nonzero elements of the Mueller matrix (which fully describe the polarization properties of the scattered light) are calculated. Comparisons between the calculated results and experimental measurements on surfaces of the same parameters [Knotts and O'Donnell, J. Opt. Soc. Am. A 11, 697 (1994)] show good agreement up to approximately 70° incidence angle.