Directional wave spectra calculated from digitized synthetic aperture radar (SAR) images of waves on Lake Michigan are compared to a wave directional spectrum determined from measurements taken at a tower and to a one-dimensional spectrum determined from a Waverider buoy. The comparision is within one frequency band for peak energy frequency and within 20 ¿ for direction, but the SAR image intensity spectrum does not have the same shape as a wave height spectrum. Wave refraction directions observed in the SAR spectra are within 10 ¿ of classical wave refraction calculations.