Diffraction of bounded wave beams

A theoretical solution is obtained for the problem of diffraction of bounded wave beams with aperture functions constructed assuming that, on the one hand, they provide uniform or cosinusoidal distributions of the field on a circle (ellipse) in the far-field zone (focal plane) and, on the other, they ensure the attainment of an extremal value of the field in the far-field zone. It is shown that the angular width of the intensity distributions measured at the half maximum power on these circles (ellipses) may be less than the axial angular width of an ideal radiator with the same temperature and power, and the ideal radiator itself is a special case of the aperture functions which are derived.