On the reflectivity of surfaces with thin transition or contaminated layers

The spatial profile of the dielectric pemittivity of any bulk sample is always to some extent smoothed or modified by various factors including interaction with atmospheric and environmental gases. This Fact hinders optical measurements and should be taken into account, in the interpretation of experimental data. The modification of the Fresnel reflectivity formula for the case where the spatial permittivity distribution deviates from an abrupt stepwise profile is considered. A correction in terms of the integral characteristics of this deviation is obtained and it is valid if a sin theta much less than lambda, where a is the dcl,th of the contaminated layer, and lambda and theta are the wavelength and grazing angle of the incident beam, respectively.