Abstract

Statistical solutions of the Khokhlov–Zabolotskaya–Kuznetsov equation were obtained to analyze mechanisms contributing to image quality enhancement in tissue harmonic imaging (THI). The focus is on suppression of image clutter due to phase aberration and reverberation. Tissue heterogeneity is modeled with a random phase screen characterized by its variance and spatial correlation length. Solutions for the mean intensities of the linear (fundamental mode) and second-harmonic fields were derived from a focused Gaussian beam that is transmitted through a phase screen located an arbitrary distance from the source. The random phase variations of the screen are assumed to be small and described by a Gaussian autocorrelation function. The solutions are validated by comparison with ensemble averages of direct numerical simulations. A benefit of the analytical approach is separation of the different contributions to deformation of the beam by the phase screen, and the statistical approach is convenient for quantifying the merits of THI. The degree to which THI reduces beam deformation is assessed using a measure based on signal-to-clutter ratios introduced previously for this purpose by C. E. Bradley [Proceedings of 17th International Symposium on Nonlinear Acoustics (AIP, New York, 2006)]. Statistical solutions will also be presented for backscattering. [Work supported by NIH DK070618.]

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