It is known that birefringent coatings are a powerful experimental technique for the determination of surface strains of metals or other opaque bodies. In this paper the complete state of strain in such a coating is determined for an arbitrary one-dimensional variation of the displacement at the metal surface. It is shown that strain gradients or curvature of the surface have a pronounced effect on the observed birefringence, and must be taken into consideration. This can be done by means of two correction factors derived in the paper which take into account the elastic properties of the coating and its thickness. An experimental procedure is outlined for determining an unknown distribution of strain at the metal surface on the basis of the observed photoelastic pattern.