We have measured the change in the optical reflection anisotropy of a clean Ge(001) surface upon exposure to molecular oxygen up to saturation coverage. Both phase and amplitude changes have been recorded with a normal-incidence ellipsometer. They have been found to be related by a Kramers-Kronig transformation. The change in the complex reflection ratio could be interpreted as an anisotropy of the clean Ge(001)2 × 1 surface dielectric function, using a three-layer McIntyre-Aspnes approach and neglecting the oxygen overlayer. The surface dielectric function anisotropy can be described fairly well by optical selection rules, based on symmetry arguments. This model was applied to the possible optical transitions at this surface between filled dimers, dangling bonds and back-bonds and the empty dangling bonds and dimers.