An ellipsometer measurement apparatus for determining the thickness of a film applied on a substrate, is described. The apparatus includes a light source emitting an incoming beam, a transmitting optical system conveying the polarized incoming beam to an incidence point on the substrate, and a receiving optical system that has an analyzer and conveys the reflected beam formed at the incidence point to a photodetector device, the polarization direction of the incoming beam and of the analyzer being modified in time relative to one another, and the intensity changes produced thereby being evaluated by way of an evaluation device in order to determine the film thickness. Easy handling and accurate measurement of the film thickness, even on difficult-to-access measured objects having differing curvatures, are achieved by the fact that an angle measurement device is provided with which the angle of the reflected beam relative to a tangential plane of the substrate at the incidence point can be sensed, and that the film thickness can be determined by way of the evaluation device as a function of the angle that is sensed.