The beam forming properties of a concave spherical reflector with an on-axis receiver

A wave-theoretical formulation for the on-axis scattering of a concave, sph erical reflector with a pressure release surface is presented. Expressions for the reflector gain and half-power beam width are derived using a statio nary phase analysis of the radiation integral arising from the Kirchhoff; H elmholtz scalar diffraction theory. The gain is shown to scale with frequen cy and the beam width scales inversely with frequency. The results of the a nalysis compare well with data collected from a 3-m spherical dish in both air and underwater calibrations. (C) 1999 Acoustical Society of America. [S 0001-4966(99)04809-2].