The ultrasonic field in lossy media: some simulation and experimental results

The subject of the paper is simulation and measurements of an ultrasonic field in an isotropic homogeneous medium with attenuation. The complex problem of simultaneous influence of wave diffraction, attenuation, and velocity dispersion occurs. Only few publications can be mentioned on this subject. For example in [1] is presented an investigation of the complex problem of ultrasound field distribution in lossy media, taking into account both the radiation of the ultrasonic signal by finite aperture and attenuation in media having velocity dispersion. The solution in frequency domain is presented here. The method is based on the use of complex wavenumber k(ω), therefore analysis in space-spectra domain is called a “k-space” calculation of ultrasonic field distributions. In [1], the main conclusion states the following: for typical linear arrays and typical biological media, the image (B-scan) modification due to medium absorption is caused mainly by the magnitude modifications of different frequency components, but not by pulse modification due to phase velocity differences of those frequency components. Another calculation method for ultrasonic field in attenuating medium is presented in [2]. Therein, the radiation of aperture and field distribution is analysed on the basis of three-dimensional impulse response of aperture. According to Huygen’s principle, the spherical waves are emitted by elementary sources on the aperture. The attenuating medium modifies the propagation of spherical waves, which continuously depend on the distance from the aperture. The calculation of field is done in far-field (Fraunhofer) region, which does not reveal the main point of continuos modification of wave propagation. The mathematical expressions necessary for the simulation of transient or stationary ultrasonic fields in attenuating media has been summarised in [3], the minimum-phase filter approach was developed in [4]. Natural wave propagation in terms of linear acoustics is analysed. One of the basic assumptions is that speed of sound does not depend on the acoustic path length and remains constant c0 within all the media under investigation. The medium is described as homogeneously attenuating medium, where attenuation is caused by ultrasonic energy absorption only. In the present paper the one-dimensional problem of ultrasound attenuation and velocity dispersion is investigated theoretically and experimentally as a first step. Two models were applied, both having mutually related attenuation and velocity dispersion: 1) time-causal model; 2) minimum-phase filter model. Then the threedimensional situation was simulated; in this case the interference of waves in lossy media was concerned. Results are presented showing the simultaneous influence of attenuation and diffraction in the three-dimensional approach on the wave-front and zero-crossings of spacedistributed pulse signal. The comparison of simulations and experimental results are shown. Minimum-phase and time-causal models were applied in the calculations. The main goal of the paper is to simulate wave attenuation and velocity dispersion in space, taking into account the causality principle. Some simulation results obtained were compared with experimental measurements and the findings discussed. Must be pointed that present paper is the continuation of earlier one [3] which could help to clarify results presented herein.