In principle the image reconstruction problem in TEM is the inverse scattering problem of the Helmholtz equation: Find the scattering potential from the scattered field under plane wave illumination. In conventional TEM this problem is reduced to the straight line paradigm of X-ray tomography by various approximations, such as high frequency, far field, and Born.
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In this talk we deal with the inverse Helmholtz problem directly, without any approximations and simplifications. We describe the image reconstruction methods that are used in related fields such as medical ultrasound tomography and seismic exploration. We discuss their application to TEM. We demonstrate their possibilities and limitations by means of synthetic data.