Optical interference fringe measurements of the thickness of weakly absorbing media can be rapid, accurate, and nondestructive. When the refractive indexnof the sample is known, it will give us the layer thicknessd. If, however,nis unknown, at least two independent spectrophotometric measurements are needed to obtain bothnandd. A statistically based scheme is proposed to analyze the interference pattern in order to determine the refractive index and the thickness of the sample. The absolute interference order is also determined with the proposed technique. The major approximation inherent in the method is that the layer must be weakly absorbing and nondispersive over the wavelength region of interest. The method is applied to determine the optical constants of a uniaxial medium with the optical axis parallel to the faces.