  Precise measurements of the geometrical thickness of a sample and its
refractive index are important for materials science, engineering, and medical
diagnosis. Among the possible non-contact evaluation methods, optical
interferometric techniques possess the potential of providing superior
resolution. However, in the optical frequency region, the ambiguity in the
absolute phase-shift makes it difficult to measure these parameters of
optically thick dispersive materials with sufficient resolution. Here, we
demonstrate that dual frequency-comb spectroscopy can be used to precisely
determine the absolute sample-induced phase-shift by analyzing the data
smoothness. This method enables simultaneous determination of the geometrical
thickness and the refractive index of a planar sample with a precision of five
and a half digits and an ultra-wide dynamic range. The thickness and the
refractive index at 193.414 THz of a silicon wafer determined by this method
are 0.52047(3) mm and 3.4756(3), respectively, without any prior knowledge of
the refractive index.
