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We have developed a high-resolution imaging radar at 580 GHz. Coherent illumination in the 576-589 GHz range and phase-sensitive detection are implemented in an all-solid-state design based on Schottky diode sensors and sources. By employing the frequency-modulated continuous wave (FMCW) radar technique, we achieve centimeter-scale range resolution while utilizing fractional bandwidths of less than 3%. Our high operating frequencies also permit centimeter-scale cross-range resolution at several-meter standoff distances without large apertures. Scanning of a single-pixel transceiver enables targets to be rapidly mapped in three dimensions, and here we apply this technology to the detection of concealed objects on persons.