Scheuer has suggested restoration of the brightness distribution across a source, as observed with a fan beam of given beam width fl , by convolving a restoring function with the observed diffraction pattern. The method is investigated in detail, and formulae are given for the r.m.s. errors of position, diameter, and flux density. Resolution is limited by noise and by band width. The noise limit is P = 52/(q12B), and the band-width limit is P = 0.51Y(BX), where p = restoring beam width in seconds of arc, X = wavelength in meter, B = band width in per cent of frequency, and qi = signal-to-noise ratio normalized to B = 1 per cent and to an integration time corresponding to t (about 3 sec). Resolution is highest, Po = 2.39 X' , if the optimum band width is chosen as B0 = 21.7 X ' . Even if a source has oniy qi = 5 at X = 1 m, it can be restored down to Po = 0.83 if the optimum band width of 7.6 Mc has been used; the positional accuracy of a point source, then, is +01" and the smallest resolvable diameter is 0.5". With qi = 20, diameters of 0.2" could be resolved. The optimum frequency for highest resolution depends on antenna size and receiver noise and lies between 250 and 900 Mc. Instrumental requirements are calculated. With parametric amplifiers, dishes of 60 feet in diameter are sufficient for resolving practically all sources where predictions of occultations are provided. For cosmological investigations, a diameter of 270 feet is needed; this would yield a resolution of 0.6" for over 200 sources/year, 2" for over 500, and 10" for almost 2000 sources/year. A set of fourteen restoring functions has been calculated and can be ordered in form of punched cards, together with the restoring program in FORTRAN.