Ellipsometry as a technique for the measurement of the optical constants (n,k,d) of two layer films on substrates is presented in a tutorial fashion. The ideal two layer film model is described and departures from ideality that are likely to be encounterd in a real sample are discussed. The ellipsometric measurement of the change in polarization state upon reflection as well as the determination of the optical reflection angles DELTA and PSI are reviewed. Extraction of the optical constants from the DELTA, PSI measurement is discussed at length. Examples are drawn from double film systems of interest to the semi-conductor industry but the principles and procedures of analysis illustrated by these examples have general application.