The complex reflection coefficients of p-and s-polarized light and ellipsometric parameters of a transparent substrate of refractive index n(2), which is coated by a transparent thin film whose refractive index n(1) = root n(2) satisfies the anti-reflection condition at normal incidence, are considered as functions of film thickness d and angle of incidence phi. A unique coated surface, with n(1) = root n(2) and film thickness d equal to half of the film-thickness period D-phi at angle phi and wavelength lambda, reflects light of the same wavelength without change of polarization for all incident polarization states. (The reflection Jones matrix of such coated surface is the 2 x 2 identity matrix pre-multiplied by a scalar, hence tan psi = 1, Delta = 0.) To monitor the deposition of an antireflection coating, the normalized Stokes parameters of obliquely reflected light (e.g. at phi = 70 degrees) are measured until predetermined target values of those parameters are detected. This provides a more accurate means of film thickness control than is possible using a micro-balance technique or an intensity reflectance method. (C) 2016 Elsevier B.V. All rights reserved.