The coherent component of specularly scattered underwater sound is sensitive to the probability density function (PDF) of displacements of the rough surface. For the specular reflection of diverging waves, the coherent component and the PDF are shown to be related by the Fourier transformation. Laboratory measurements of sound scattered at a partially shadowed nearly Gaussian model sea surface show the coherent component is much larger than would be expected for a Gaussian PDF. Fourier transformations of the measured PDF, on inclusion of a shadowing correction, gave the coherent component. Fourier transformation of the coherent component yields a surface PDF similar to the measured PDF with shadowing correction.