Piezoelectric ultrasonic radiators made in the form of a thin spherical shell radiate spherical sound waves which come to a focus at the center of curvature of the shell, thus enabling the production of much greater ultrasonic intensity in a small locality removed from the radiator than it is possible to obtain directly at the surface of a radiator. It is here shown by ultrasonic light diffraction pictures of the radiated sound field that the sharpness of focus is limited by wave diffraction in the manner well known in astronomical telescopes and may be calculated by optical diffraction formulas. By the same means the radiation efficiency of different areas of the curved surface is explored and the results compared with theory. The variation of efficiency is, of course, due to the variation of the effective elastic and piezoelectric constants of the differently oriented areas. Calculations are made of the radiation efficiency of a quartz radiator, and it is shown that a greatly improved focusing spherical radiator may be obtained by varying the thickness of the radiator to compensate for the varying frequency constant. Further, superior focusing cylindrical radiators may be obtained by special orientation or by thickness shaping or both.