The report is concerned with the properties of a parabolic antenna, focused in the near-field by axial displacement of the feed. A considerable improvement of the cross-range resolution will result, compared with the normal case of far-field focusing, in spite of emerging astigmatic, errors. The study is based on ray optics as well as field calculations using physical optics. According to the field calculations, a 30 cm diameter antenna gives a cross-range resolution of about 8 cm at 40 GHz, with the feed displaced by 0.5 cm, giving a focus at 4 m distance. The actual applications include looking through concealing material (walls, clothes, wrapping) for detection of human, weapons, explosives an the like. In such applications high cross-range resolution is essential e.g. for imaging.