Towards quantitative ultrasonic imaging

The acoustic wave equation with spatially varying wave number is used as the basis for setting up the ultrasonic inverse scattering problem in terms of the Porter-Bojarski integral equation, which relates measured data in terms of the holographic field with field-dependent secondary sources. Introducing the weak scattering or Born approximation, a solution of the inverse scattering problem is obtained by frequency integration, resulting in a time-domain-diffraction tomographic inversion scheme. For scatterers that do not satisfy the Born approximation, diffraction tomography is not quantitative, and, therefore, an extension is proposed, utilizing the exact quantum mechanical inversion theory in terms of the Newton-Marchenko equation