普遍声逆散射微扰论与形式参数展开法

GENERAL ACOUSTICAL INVERSE SCATTERING PERTURBATION THEORIES AND METHOD OF FORMAL PARAMETER EXPANSION

使用第一作者提出的形式参数展开法给出了在Ｂｏｒｎ 和Ｒｙｔｏｖ 变换下的有限形式声衍射层析成像理论算法．所给出的Ｂｏｒｎ 变换下的有限形式重建公式对散射体的要求比较松，适用于一类中强散射情况，而且计算量也不大．Ｒｙｔｏｖ 变换下的有限形式重建公式，因涉及广义散射，所以Ｓｏｍ ｍ ｅｒｆｅｌｄ 辐射条件不再成立，用它进行重建仍有很大困难．本文还给出了单频任意波阵面入射波情况下更普遍逆散射微扰论，包括Ｒｙｔｏｖ 变换下积分形式声逆散微扰理论．

This paper presents theoretical reconstruction algorithms of acoustical tomography in the finite analytic forms under Born and Rytov tranforms using the method of formal parameter expansion, which has been presented by Lu Zhenqiu. The Born transform reconstruction algorithm in the finite analytic form has no severe limitations to scatterers, i.e., it can be applied to moderately and strongly inverse scattering of some kind, and its calculation is not tedious either. The Rytov transform reconstruction algorithm in the finite analytic form has some difficulties resulted from the involved generalized scattering wave, in which case, the Sommerfeld radiation conditions are not applicable. This paper also presents general acoustical inverse scattering perturbation theories with a wave of single frequency and any wave front form as incident wave, including acoustical inverse scattering theory of integral form under Rytov transform.