This study represents an inverse problems approach to rough surface scattering, an objective being the inference of certain statistical characteristics of the rough surface directly from the coherently scattered pressure field. A combined theoretical and experimental approach is used. Eckart's physical-acoustic model is applied to derive relationships for the probability density function and correlation function of surface heights. The results are expressions which depend solely upon the scattered pressure field. Verification of the theory is accomplished through experiments conforming to the constraints outlined in the theory. Experimental measurements of the steady-state complex scattered pressure field from a pressure release model surface are made with use of a single-frequency small beamwidth source. Several signal processing techniques are used to obtain estimates of the probability density function and correlation function. Comparisons are then made between the inferred characteristics and the actual characteristics of the surface determined by direct measurement techniques. [Work supported by the Office of Naval Research.]