Fourier imaging is an indirect imaging method which records the diffraction pattern of the object scene coherently in the focal plane of the imaging system and reconstructs the image using computational resources. The spatial resolution, which can be reached, depends on one hand on the wavelength of the radiation, but also on the capability to measure - in the focal plane - Fourier components with high spatial wave-vectors. This leads to a conflicting situation at THz frequencies, because choosing a shorter wavelength for better resolution usually comes at the cost of less radiation power, concomitant with a loss of dynamic range, which limits the detection of higher Fourier components. Here, aiming at maintaining a high dynamic range and limiting the system costs, we adopt heterodyne detection at the 2nd sub-harmonic, working with continuous-wave (CW) radiation for object illumination at 600 GHz and local-oscillator (LO) radiation at 300 GHz. The detector is a single-pixel broad-band Si CMOS TeraFET equipped with substrate lenses on both the front- and backside for separate in-coupling of the waves. The entire scene is illuminated by the object wave, and the Fourier spectrum is recorded by raster scanning of the single-detector unit through the focal plane. With only 56 µW of power of the 600-GHz radiation, a dynamic range of 60 dB is reached, sufficient to detect the entire accessible Fourier space spectrum in the test measurements. We present a detailed comparison between plane-to-plane imaging and Fourier imaging, and show that, with both, a lateral spatial resolution of better than 0.5 mm, at the diffraction limit, is reached.