Acoustic field of Gaussian and Bessel transducers

An explicit analytical form of the impulse response for circular transducer with truncated Gaussian distribution of vibrational velocity on its surface is developed. In an existing paper [J. Naze Tjotta and S. Tjotta, J. Acoust. Soc. Am. 71, 824 (1982)] the impulse response for Gaussian distribution was given [Eq. (17)]. This formula is valid only for the case of an ultrasonic transducer with infinite radius (a=+∞). In this paper an impulse response function for the case of truncated Gaussian profile is established. The formula [Eq. (3)] developed by the authors is valid for ultrasonic transducers of arbitrary radius a∈(0,+∞). Formula (17) from the above cited article by Naze Tjotta and Tjotta is a particular case of the more general formula [Eq. (3)] established in this paper. Employing the transfer function method, the acoustic field for truncated Gaussian distribution in the near and far zones is calculated. Similar calculations are performed for the circular transducer with truncated Bessel function distribution on its surface. The similarities and differences between these two kinds of acoustic fields are discussed.