The Radiation Pattern on an Ultrasonic Focusing Radiator

Abstract

A focusing quartz radiator made in the form of a concave-convex lens of constant thickness (and being X-cut on the axis) should radiate spherical sound waves which focus at the center of curvature of the radiator surfaces. Because of wave diffraction, the focus should deviate from infinitely sharp in the same manner as is well known in the optical telescope. If R is the radius of curvature of the radiator, D the effective diameter of the radiator, and λ = v/f the ultrasonic wave-length, then the diameter of the central beam is δ1 = λR/D, of the first ring, δ2 = 2λR/D, of the second ring, δ3 = 3λR/D, etc. Using a 5-megacycle radiator (D = 29 mm, R = 63.5 mm) and radiating into water on the concave side, the pattern was studied by means of its light diffraction effects (of which slides will be shown). The radiation focused at the center of curvature and the diffraction at this point was as described above (δ2 = 1.5 mm). This is in agreement with the expectations and partial findings of J. G. Lynn, R. L. Zwemmer, A. J. Chick, and A. E. Miller, and is in disagreement with findings of L. W. Labaw. Variations of radiation efficiency about the periphery of the radiator are related to variations of the off-x-axis crystal constants, but do not affect the spatial distribution of the beam in the focal region.