We present initial results from the investigation of a surface field phase perturbation method for the calculation of the wave field scattered by a rough surface. This technique is based on the extinction theorem and uses a perturbation expansion of a function closely related to the complex phase of the surface field. This approach was suggested earlier, but we use the expansion in a different way. In the present work we consider only deterministic periodic surfaces, rough in one dimension, on which the total field is zero. We find that, for surfaces with modest slope and curvature, this technique can be used to calculate scattered fields even when surface relief is significant compared to the wavelength of the incident radiation.