30 May 2001 Investigation of focused and unfocused transducer beam patterns in moderately nonlinear absorbing media
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The novel solution of the KZK equation for acoustic pressure of the second harmonic in slightly focused beam of a circular transducer was obtained in a closed form for moderately nonlinear absorbing media (Gol'dberg numbers ~ 1). The solution is based on the method of slowly changing wave profile in combination with the method of successive approximations. Two pairs of transducers (Valpey-Fisher Corp.) Were compared to investigate the influence of focusing on the applicability of the moderate nonlinearity approach. The first pair was of 0.25' diameter and the second was of 0.5' diameter. Both pairs has one transducer with flat surface and the other geometrically focused at 4'. The central frequency for all transducers was 5 MHz. Measurements were undertaken in the blood-mimicking solution of water and glycerine. The results demonstrated that for slightly focused transducers with circular apertures, the moderate nonlinearity approach is still valid, as it was proved for flat sources with the same source level, despite the higher pressures in the focal region. The peak pressure for the weakly focused system occurs at a shorter range than focal length.
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Nikolay A. Kharin, Nikolay A. Kharin, } "Investigation of focused and unfocused transducer beam patterns in moderately nonlinear absorbing media", Proc. SPIE 4325, Medical Imaging 2001: Ultrasonic Imaging and Signal Processing, (30 May 2001); doi: 10.1117/12.428222; https://doi.org/10.1117/12.428222

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