Linear and nonlinear inversion algorithms applied in nondestructive evaluation

Convenient tools for nondestructive evaluation of solids can be electromagnetic and/or elastodynamic waves; since their governing equations, including acoustics, exhibit strong structural similarities, the same inversion concepts apply. In particular, the heuristic SAFT algorithm (synthetic aperture focusing technique) can be—and has been—utilized for all kinds of waves, once a scalar approximation can be justified. Relating SAFT to inverse scattering in terms of diffraction tomography, it turns out that linearization is the most stringent inherent approximation. Hence, the results of nonlinear inversion schemes such as contrast source inversion are compared to the output of SAFT for a carefully designed ultrasonic experiment. In addition, it will be shown via synthetic as well as experimental data that SAFT can be extended to electromagnetic vector fields and to an inhomogeneous and/or anisotropic background material.

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