The ratio rho-t = T(p)/T(s) of the complex amplitude transmission coefficients for the p and s polarizations of a transparent unbacked or embedded thin film is examined as a function of the film thickness-to-wavelength ratio d/lambda and the angle of incidence phi for a given film refractive index N. The maximum value of the differential transmission phase shift (or retardance), DELTA-t = arg-rho-t, is determined, for given N and phi, by a simple geometrical construction that involves the iso-phi circle locus of rho-t in the complex plane. The upper bound on this maximum equals arctan{[N - (1/N)]2} and is attained in the limit of grazing incidence. An analytical noniterative method is developed for determining N and d of the film from rho-t measured by transmission ellipsometry (TELL) at phi = 45-degrees. An explicit expression for DELTA-t of an ultrathin film, d/lambda << 1, is derived in product form that shows the dependence of DELTA-t on N, phi, and d/lambda separately. The angular dependence is given by an obliquity factor, f(o)(phi) = 2 1/2 sin-phi tan-phi, which is verified experimentally by TELL measurements on a stable planar soap film in air at lambda = 633 nm. The singularity of f(o) at phi = 90-degrees is resolved; DELTA-t is shown to have a maximum just short of grazing incidence and drops to 0 at phi = 90-degrees. Because N and d/lambda are inseparable for an ultrathin film, N is determined by a Brewster angle measurement and d/lambda is subsequently obtained from DELTA-t. Finally, the ellipsometric function in reflection rho-r is related to that in transmission rho-t.
