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<p></p> <p><b>New page</b></p><div>== Citation ==<br /> <br /> Fanelli, D. &amp; Öktem, O. Electron tomography: a short overview with an emphasis on the absorption potential model for the forward problem Inverse Problems, 2008, 24, 013001<br /> <br /> [http://scholar.google.com/scholar?cites=15589599254688959234&amp;hl=en Cited by]<br /> <br /> == Abstract ==<br /> <br /> This review of the development and current status of electron tomography<br /> deals mainly with the mathematical and algorithmic aspects. After a very<br /> brief description of the role of electron tomography in structural biology, we<br /> turn our attention to the derivation of the forward operator. Starting from<br /> the Schr¨odinger equation, the electron–specimen interaction is modelled as<br /> a diffraction tomography problem and the picture is completed by adding a<br /> description of the optical system of the transmission electron microscope. The<br /> first-order Born approximation enables one to explicitly express the intensity<br /> for any finite wavenumber in terms of the propagation operator acting on the<br /> specimen convolved with a point spread function, derived from the optics in the<br /> transmission electron microscope. Next, we focus on the difficulties that cause<br /> the reconstruction problem to be quite challenging. Special emphasis is put on<br /> explaining the extremely low signal-to-noise ratio in the data combined with<br /> the incomplete data problems, which lead to severe ill-posedness. The next step<br /> is to derive the standard phase contrast model used in the electron tomography<br /> community. The above-mentioned expression for the intensity generalizes<br /> the standard phase contrast model which can be obtained by replacing the<br /> propagation operator by its high-energy limit, the x-ray transform, as the<br /> wavenumber tends to infinity. The importance of more carefully including<br /> the wave nature of the electron–specimen interaction is supported by<br /> performing an asymptotic analysis of the intensity as the wavenumber tends<br /> to infinity. Next we provide an overview of the various reconstruction<br /> methods that have been employed in electron tomography and we conclude by<br /> mentioning a number of open problems. Besides providing an introduction to<br /> electron tomography written in the ‘language of inverse problems’, the authors<br /> hope to raise interest among experts in integral geometry and regularization<br /> theory for the mathematical and algorithmic difficulties that are encountered in<br /> electron tomography.<br /> <br /> == Keywords ==<br /> <br /> Image formation model, quantum physics, electron waves<br /> <br /> == Links ==<br /> <br /> Article http://www.ncbi.nlm.nih.gov/pubmed/18427122<br /> <br /> == Related software ==<br /> <br /> == Related methods ==<br /> <br /> == Comments ==</div>

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