Focusing properties of solid ultrasonic cylindrical lenses

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Abstract
The sound velocity, thermal coefficient of sound velocity, and attenuation coefficients of 20 common plastics were measured and used as a basis for the design of several lenses. Materials selected were polyethylene, nylon, polystyrene, polyphenylene oxide, and a low-sound-velocity silicone rubber compound. Using common geometrical optical techniques, lenses were designed to minimize off-axis aberrations for focal-length-to-aperture ratios ranging from 1 to 3 and aperture-to-wavelength ratios up to 150. Using methods analogous to chromatic aberration correction in optics, lenses were designed for constant focal length over a temperature range of 0° to 30°C. Two- and four-element lens systems with apertures up to 30 cm were fabricated from the selected materials. Measurements were made in the frequency range 600 kHz to 1.2 MHz and good agreement with theoretical predictions of focal length and directional response was observed. The effects of shear waves were not evident. The theoretical model used to evaluate lens performance was based on the numerical evaluation of the Fresnel-Kirchhoff diffraction integral. This work shows that it is possible, using established optical design methods and commonly available solid materials, to fabricate athermal acoustic lenses with good performance characteristics at aperture-to-wavelength ratios up to 150.

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