  We use the Kramers-Kronig transform (KKT) with logarithmic kernel to obtain
the reflection phase and, subsequently, the complex refractive index of a bulk
mirror from reflectance. However, there remains some confusion regarding the
formulation for this analysis. Assuming the damped Drude model for the
dielectric constant and the oblique incidence case, we calculate the additional
terms: phase at zero frequency and Blashke factor and we propose a reformulated
KKT within this model. Absolute reflectance in the s-polarization case of a
gold film is measured between 40 and 350 eV for various glancing angles using
synchrotron radiation and its complex refractive index is deduced using the
reformulated KKT that we propose. The results are discussed with respect to the
data available in the literature.
