吸收媒质中非线性有限衍射波的理论、实验和计算仿真研究

项目名称： 吸收媒质中非线性有限衍射波的理论、实验和计算仿真研究

项目编号： No.30800270

项目类型： 青年科学基金项目

立项/批准年度： 2009

项目学科： 金属学与金属工艺

项目作者： 杜宏伟

作者单位： 中国科学技术大学

项目金额： 22万元

中文摘要： 有限衍射波有很大的声场深度，用于超声成像可以获得很高的帧率，但在线性成像模式下图像空间分辨率相对于传统的聚焦成像有所下降。利用有限衍射波的高次谐波进行成像有望改善空间分辨率。Bessel波和X波是两类最典型的非衍射波，对其非线性特性的研究已有十几年历史，理论研究发现其高次谐波近似是非衍射的。但对于存在媒质吸收效应、换能器孔径有限等条件下的实际非线性有限衍射波仍需要进一步研究。 本项目以KZK方程为模型方程推导高次谐波的封闭解析解,对Bessel波、X波及Gauss聚焦波进行理论研究；采用空域分解和并行计算提高算法效率，得到非线性声场的数值解，进行声场仿真；构建了单阵元超声检测实验系统。研究了非线性、吸收和衍射三种效应综合作用下高次谐波的特性。 本项目研究的科学意义主要体现在以下两个方面：（1）原创性；（2）实现了对于实际非线性有限衍射波较为系统的描述。

中文关键词： 有限衍射波；高次谐波；KZK方程；数值计算仿真；空域分解

英文摘要： Limited diffraction beam(LDB) has large depth of field and may have important application in ultrasonic imaging to provide high frame rate (HFR), But the spatial resolution of the image with a linear imaging mode decreases as compared to conventional focused imaging. Nonlinear imaging with higher-order harmonics of LDB may improve the spatial resolution. Bessel beam and X-wave are two typical non-diffraction beams, and research about the nonlinear properties of them has been carried out for more than decade. The theoretical results indicate that their higher-order harmonics are nearly non-diffracting. But more studies are also necessary in the light of the realizable nonlinear LDB under the conditions of absorbing medium and finife aperture. In this project, a theoretical description of nonlinear Bessel beam、X-wave and focused Gaussian beam is implemented by solving the KZK equation with an analytical method. The nonlinear field is calculated and simulated with a spatial-domain decomposition numerical method and parallel computation to improve the algorithm efficiency. A single-element ultrasonic detection system is designed. Properties of higher-order harmonics are investigated under the comprehensive effects of nonlinearity、absorption and diffraction. The scientific significance of this project is embodied in the following two aspects: (1) originality (2) A systematic description is achieved about the realizable nonlinear LDB.

英文关键词： limited diffraction beam;higher-order harmonics;KZK equation;numerical calculation and simulation;spatial-domain decomposi- tion