Ellipsometric view on reflection and scattering from optical blacks

The reflectance R(theta) and ellipsometric parameters for a black anodized aluminum sample were measured at wavelengths of 3.39 and 5.0 microm and at multiple incident angles. A three-phase model in which the dielectric constant for the rough layer is computed from Bruggeman's effective medium theory is used to reduce the ellipsometric data and to calculate the reference specular reflectance. Beckmann's scattering theory, modified for polarization effect, was used to reduce the reflectance data. A self-consistent solution was found in which the ellipsometric regressed effective thickness of the rough layer agrees with the reflectometric estimated roughness, and in which the measured reflectance data agree with Beckmann's scattering theory.