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As a scientific and technological continuation of the X-band Synthetic Aperture Radar (X-SAR) and Shuttle Radar Topography Mission (SRTM) missions, the new X-SAR, namely, TerraSAR-X (TSX), was launched on June 15, 2007. Since then, it has provided numerous high-quality data over land and ocean operationally. In this paper, surface wave refraction and diffraction are investigated using TSX imagery acquired over the coast of Terceira island situated in the North Atlantic. Peak wavelength and wave direction are determined by SAR 2-D image spectra. They are compared to measurements of X-band marine radar and results of the WAve prediction Model (WAM). Significant wave height in the near-shore shallow water region is estimated from TSX Spotlight mode data following the wave refraction laws and using the developed XWAVE empirical algorithm. Image spectra of the TSX subscenes in the full-coverage region are given to investigate significant changes of wave direction and length. By analyzing another TSX image acquired in StripMap mode, a shadow zone in the lee side of Terceira island is identified. It is influenced jointly by wave refraction and diffraction. Furthermore, a cross-sea pattern revealed in the image spectra is investigated. The cross sea is generated by the diffracted wave rays from the northern and southern coasts of the island. Less wave directional spreading for the cross-sea situation is observed as well when compared to the image spectra at the origin of diffraction.