Kramers-Kronig Analysis of Relative Reflectance Spectra Measured at an Oblique Angle

Ratio reflectance R is defined as R = R(p)/R(s) , where R(p) and R(s), are absolute specular reflectances of a material for electromagnetic waves linearly polarized with the electric field vector parallel and perpendicular to the plane of incidence, respectively. An algorithm was developed for computing both the index of refraction n and extinction coefficient k from an R spectrum obtained for radiant flux incident on a plane surface of the material at an oblique angle in the range 10 degrees less, similar theta </= 45 degrees . Kramers-Kronig (K-K) analysis of the R spectrum provides spectral values of Deltaø = ø(p) - ø(s), the difference between phase shifts due to reflection of the two separate polarization components. Real and imaginary parts of a Fresnel equation for the ratio reflectivity provide equations for computing n and k when R, theta and Deltaø are known quantities. A synthetic R spectrum for water was generated by Appropriate use of n and k values for that substance and the generalized Fresnel equation for ratio reflectance. The algorithm, when applied to the synthetic R spectrum, returned values of n and k for water in the 25,000-500-cm(-1) wevenumber interval that were primarily limited in their accuracy by the interval size used for Simpson's rule numerical approximation of the K-K integral.