The inverse scattering problem, whose goal is to reconstruct an unknown scattering object from its scattered wave, is essential in fundamental wave physics and its wide applications in imaging sciences. However, it remains challenging to invert multiple scattering accurately and efficiently. Here, we exploit the modified Born series to demonstrate an inverse problem solver that efficiently and directly computes inverse multiple scattering without making any assumptions. The inversion process is based on a physically intuitive approach and can be easily extended to other exact forward solvers. We utilised the proposed method in optical diffraction tomography and numerically and experimentally demonstrated three-dimensional reconstruction of optically thick specimens with higher fidelity than those obtained using conventional methods based on the weak scattering approximation.
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