Retrieval Method for Complex Refractivity from Reflection Measurements of Rough Surfaces

A method for the determination of complex refractivity based on reflection measurements of rough surfaces is proposed. The reflection spectra of a polished reflector and three different aluminum alloy rough surfaces are measured using a Fourier transform spectrometer. Using the Kirchhoff approximation, the relationship between the root mean square roughness and the natural logarithm of reflectance is deduced. Then, the numerical reflection spectra of a smooth surface, verified by the measured spectra of a polished reflector, are determined using the least squares method. The complex refractivity is subsequently extracted using the Kramers-Kronig relation, and the obtained results agree with the refractivity measured with an ellipsometer. The advantage of this scheme is that it immediately obtains complex refractivity from rough surfaces, which is more efficient for the fabrication of samples and the operation of retrieval systems.