In many interferometric applications the variation of the reflected light intensity due to the separation distance change between two optical systems is the raw signal from which some unknown parameters must be determined. We consider the general situation in which the signal offset and amplification, the initial separation, and the optical properties of one of the systems are unknown. Using some major results from the complex analysis we derive closed-form expressions that give the exact solution of the above inverse problem in terms of the signal's Fourier coefficients. It is shown that the absolute reflectivity can be found unambiguously, while the initial separation and the reflectance phase are mutually correlated and one of these parameters can be found only if the other one is known.