The small‐amplitude, continuous wave reflected field produced by a spherical source placed at the focus of an ellipsoidal reflector

Ellipsoidal reflectors are widely used in electrohydraulic lithotripters. The small‐amplitude, continuous wave (cw) reflected field of a small spherical source that is placed at the first focus (f1) of an ellipsoidal reflector is investigated with both theory and experiment. This configuration is equivalent to a low‐amplitude (linear regime), cw‐driven lithotripter. To model the acoustic field reflected from an ellipsoidal reflector, geometrical acoustics is used to define a directivity function at the mouth of the reflector. An equivalent focused source with amplitude shading defined by the directivity function is then assumed as the boundary condition for the linear, lossless parabolic wave equation which is used to diffractively propagate the field outside the reflector. The spherical source is driven with a long tone burst at 470 kHz. The ellipsoidal reflector is made out of nickel and has a rhodium coating. The major and minor radii are 6.2 cm and 3.5 cm, respectively. Good agreement is found between experiment and theory. A useful property of ellipsoidal reflectors is that one can quickly and accurately position the source at f1 and the hydrophone at f2 by a simple iteration technique. [Work supported by NIH.]