A general procedure to fit optical constants, using a transfer function model with temperature-and/or-composition-dependent coefficients, is presented. The model is further inverted by a simple algorithm to retrieve temperature and composition information from optical measurements obtained by spectroscopic ellipsometry. The method was applied to fit: (1) the complex index of refraction of the system AlXGa1-xAs at 600 degrees C, for values of X between 0 and 1. (2) Two data bases of complex dielectric constants, for near-lattice-matched InGaAs and InAlAs, and around temperatures of 500 degrees C. The parameters of the model are determined with a least squares algorithm with recursive "whitening" of the error, which shows fast convergence to a near-optimal solution, even when handling a large number of parameters. The level of accuracy achieved makes this method an adequate sensor for temperature, composition, and thickness control during molecular beam epitaxy growth.