Restrictions on the Inversion of the Fresnel Reflectance Equations

The regions for which the Fresnel equations can be inverted to determine the optical constants, n and K, from polarized reflection measurements of a plane electromagnetic wave are presented for different angles of incidence. The surface upon which this wave is incident is assumed to be a large, smooth, planar surface of a conducting medium that is linear, homogeneous, and isotropic. The sensitivity of the inversion procedure to +/-1% error in the measured reflectances is presented graphically. Such a small error in reflectances could produce a large error, more than 20%, in the determined optical constants n and K with K being the more erroneous. Angles of incidence in the neighborhood of 10 degrees and 80 degrees produce the largest acceptable regions for inversion.