Linear and nonlinear ultrasound fields formed by planar sources with random pressure distributions

Abstract

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 subject to 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.