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== Linear Imaging Theory vs. Non-Linear Imaging Theory ==
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The previous description of the contrast transfer function depends on linear imaging theory. Linear imaging theory assumes that the transmitted beam is dominant, there is only weak phase scattering by the sample, there are no dynamical effects, and that the sample is extremely thin. Few of these assumptions hold with real samples. In fact, even a single layer of Uranium atoms does not meet the Weak Phase Object Approximation.<ref>{{Cite book|title = Transmission Electron Microscopy:|last = Williams, Carter|first = |publisher = Springer|year = 2009|isbn = 978-0-387-76500-6|___location = |pages = }}</ref> One advantage of linear imaging theory is that the Fourier coefficients for the image plane wavefunction are separable. This greatly reduces computational complexity, allowing for faster computer simulations of HRTEM images.<ref>[http://www.numis.northwestern.edu/465/index.shtml Notes] prepared by Professor Laurie Marks at Northwestern University.</ref>
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In real samples, the specimens will be strong scatterers, and will include multiple scattering events. In order to account for these effects, non-linear imaging theory is required. This will incorporate second order diffraction intensity effects.<ref>This page was prepared in part for Northwestern University class MSE 465, taught by Professor Laurie Marks. </ref>
== See also ==
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