The retrieval of ocean wave spectra from SAR images is a challenging problem because the imaging mechanism is nonlinear, the image spectrum contains contributions of speckle noise, and the interpretation of a SAR image as a single snapshot in time causes directional ambiguities. We present a new wave retrieval methodology that overcomes these problems to a significant extent by utilizing spotlight-mode SAR images from TerraSAR-X and COSMO-SkyMed in combination with advanced subaperture processing. The long integration times of spotlight-mode images enable us to derive time series of subaperture images for periods of up to a few seconds, which show the propagation directions and speeds of moving patterns. Then we can use Fourier analysis and a filter based on the known dispersion relation of ocean waves to separate actual ocean wave signatures in the data from other contributions. This process is phase-preserving and lets us reconstruct short "videos" of the spatio-temporal evolution of the ocean wave signatures during the SAR overpass, which are easier to invert into surface slope and elevation fields and the corresponding wave spectra than conventional SAR intensity images.