Ellipsometry was used for characterizing the thickness and overall film quality of BMMA films (poly(methyl methacrylate)) spin coated from solutions in chloroform. A new method for solving the equations and a new error minimization algorithm are developed for the determination of the thickness and refractive index of a transparent film from ellipsometry data at two angles of incidence. In the new algorithm, the error in the film parameters is minimized rather than the errors in Delta and Psi, which is conventionally done. It was found that both the magnitude of the residual and the relative data sensitivity are important when assessing the reliability of the inverted parameters and the quality of a thin film. The substrates were thermally oxidized silicon oxide films on 2 inch silicon wafers, and the oxide thicknesses were about 2500 Angstrom. Polymer (PMMA) film thicknesses, ranging from 0.08 to 2 mu m, were proportional to c(1.33)omega(-0.50), where c is the initial polymer concentration in solution (1.0-7.5 wt.%) and omega is the spin speed (1000-4000 rev/min) at which the films were coated. The absolute magnitude, rather than the relative magnitude, of the thickness variations influenced the determination of film quality from ellipsometry. Even though the relative film roughnesses were similar, the thinner films were of higher optical quality than the thicker films.