The effects of improving the accuracy of the angle of incidence on the ellipsometric determination of thickness and refractive index of oxide and nitride films on a silicon substrate are analyzed. It is found that the accuracy of a determination of a film's parameters, thickness and refractive index, depends as much or more on the accuracy of the angle of incidence measurement as on the accuracy of the measurement of the ellipsometric angles Δ and ψ. If measurements of Δ and ψ are made close to the principal angle of incidence, the accuracy of the determined film parameters can be improved by measuring the incident angle to an accuracy better than Δ and ψ. This is especially true for thin films of oxide less than a few tens of nanometers. Because of the higher refractive index of silicon nitride relative to silicon dioxide, a nitride film's thickness can be determined more accurately than an oxide film's thickness. Therefore, silicon nitride may make a good candidate film for a standard thickness sample.