P2B-15 Transient Acoustic Fields Produced by Rectangular Apertures and Linear Arrays in Viscous Media

The lossless impulse response approach models the transient effects of finite apertures, yet frequency-dependent attenuation is neglected, resulting in incorrect estimates of pulse broadening and beam spreading. An analytical time-domain expression that incorporates both loss and diffraction is needed for calculations of transient pressures generated by rectangular pistons in attenuating media. A causal Green´s function solution to the Stokes wave equation is decomposed into diffraction and loss factors, facilitating the calculation of the impulse response in lossy media obeying quadratic frequency dependence. The velocity potential produced by an impulsively excited, baffled, rectangular aperture is then solved analytically using this approach. Two separate expressions are derived: a nearfield solution, valid for all observation points, and a simplified farfield solution. The nearfield solution, based on a recently developed integral representation of the lossless impulse response for a rectangular aperture, consists of a sum of single-integrals involving the error function. The farfield solution generalizes the lossless trapezoidal solution to viscous media, yielding a closed-form solution in terms of the error function. Unlike the classical lossless impulse response, these proposed solutions are bandlimited, eliminating the need for artificially large sampling frequencies. The near and farfield impulse responses, as well as wideband pressure fields, are numerically evaluated and quantitatively compared. The proposed solutions combine the competing effects of loss and diffraction, thus providing an analytical reference for other numerical calculations. Applications to phased array ultrasonic imaging, including the calculation of point spread functions (PSF), are demonstrated. Results show that in the presence of loss, a reduction in both axial and lateral resolution in the PSF is observed.