Single-pass polarizer-surface-analyzer null ellipsometry (PSA-NE) can be used to characterize film-substrate systems, provided that the film thickness lies within one of a set of permissible-thickness bands (PTB). For a transparent film on a transparent or absorbing substrate, the PTB structure consists of a small number of finite-bandwidth bands followed by a continuum band that extends from a film thickness of about half the wavelength of light to infinity. It is shown that this band structure is a direct consequence of the periodicity of the ellipsometric function p (the ratio R//p/R//s of the complex amplitude-reflection coefficients for the p and s polarizations) with film thickness. The PTB for the SiO//2-Si film-substrate system at He-Ne laser and mercury spectral lines are calculated. The angles of incidence for PSA-NE on a film-substrate system with known film thickness are easily predicted with the help of a graphical construction in the angle of incidence-vs-thickness phi d plane. PSA-NE is generally applicable to the determination of both film thickness and optical properties of a film-substrate system. The procedure for its application to the special, but important, case of film-thickness measurement alone, when the optical properties are known, is given and is checked experimentally by the determination of the oxide-film thickness on Si wafers. In an automated form, PSA-NE can be a serious competitor for interferometric reflectance methods. 17 refs.