A hydrodynamic theory is presented for the imaging of bottom topography and internal waves by X and K band radar. Central to this imaging is the energy spectrum of short surface waves. Here modulations of spectra by bottom topography or internal waves are calculated. A one-dimensional spectrum is used where wave numbers range from 50 to 1300 m-1. The effect of bottom topography or internal waves is described by a slowly varying surface current. Refraction, wind, nonlinear interactions, and dissipation are taken to govern the spectrum. For the first three effects, expressions are used which are derived from first principles. These already exist in the literature. Of the dissipation, little is known. By using two completely different parameterizations for the dissipation, it is shown here that this term is not essential to the modulation mechanism. In both cases it is found that for low wind speeds and k≥260 m-1 a small current change of about 20% can generate a change in energy level of a factor of 1000. The modulation is in antiphase with the current. Both magnitude and phase of the modulation agree qualitatively with measurements. This agreement is due to the inclusion in the present theory of nonlinear interactions between short surface waves. ¿ American Geophysical Union 1987