Acoustical Science and Technology 2015; 36(3): 208-215. DOI:10.1250/ast.36.208

The goal of the present study is to clarify the formation and behavior of sound pressure fields from a statistical point of view when the individual transducers constituting an array source have random performances or, alternatively, conversion efficiencies from electric to acoustic power that vary with the individual transducer. Linear and nonlinear fields are considered herein. Based on experimental data, we assume that the amplitudes and phases of pressure signals emitted from the transducers are random variables that obey Gaussian distributions. The phase changes are, however, not taken into consideration in our theory because of their small effects on the field formation. Spatial variation in pressure fields attributed to the random performance of transducers is large near the source, and fades with propagation in the farfield. Linear theory predicts that the mean value of the pressure amplitudes is the same as the value when the pressure on the array source is distributed uniformly. Interestingly, the standard deviation around the mean pressure is independent of the radial distance in the plane perpendicular to the beam axis, being inversely proportional to the square root of the number of transducers. For the second-harmonic components, both the mean value and standard deviation are dependent on the radial distance. The validity of these theoretical findings is verified by Monte Carlo simulation and experimental data.

This work was performed in the Kamakura Laboratory, The University of Electro-communications, Tokyo

pdf download

Copyright © 2015 The Acoustical Society of JapanThis article may be downloaded for personal use only. Any other use requires prior permission of the authors and the Acoustical Society of Japan.

**Clinic Ultrasound Laboratory (クレメント超音波研究室)**

Cleveland Clinic (クリーブランド・クリニック),

Lerner Research Institute

Case Western Reserve University

© 2013

* For a comprehensive listing see* PUBLICATIONS

**Clement GT**, Nomura H, Adachi H, Kamakura T, Feasibility of non-contact ultrasound for medical imaging, *Physics in Medicine and Biology* 2013; 58: 6263-6278

Tang SC, Jolesz FA,** Clement GT**. A Wireless Batteryless Implantable Ultrasonic Pulser-Receiver. *IEEE Trans Ultrason Ferroelectr Freq Control* 2011;58:1211-21.

Paltiel HJ, Padua HM, Gargollo PC, Cannon GM Jr, Alomari AI, Yu R, **Clement GT**. Volumetric ultrasound imaging of tissue perfusion: preliminary results in a rabbit model... *Phys Med Biol* 2011;56:2183-97.

McDannold N, **Clement GT**, Black P, Jolesz F, Hynynen K. Focused ultrasound surgery of brain tumors: Initial findings in three patients. *Neurosurgery* 2010;66:323-32; discussion 332.

**Clement GT**, Hynynen K. A non-invasive method for focusing ultrasound through the human skull. *Phys Med Biol* 2002;47(8):1219-36.