Contrast transfer function: Difference between revisions

Revision as of 18:35, 12 June 2015

Revision as of 18:39, 12 June 2015

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* The function exists in the spatial frequency ___domain, or k-space

* Whenever the function is equal to zero, that means there is no transmittance, or no phase signal is incorporated into the real space image

* The first time the function crosses the x-axis is called the '''point resolution'''

* To maximize phase signal, it is generally better to use imaging conditions that push the point resolution to higher spatial frequencies

* When the function is negative, that represents positive phase contrast, leading to a bright background, with dark atomic features

* Every time the CTF crosses the x-axis, there is an inversion in contrast

* Accordingly, past the point resolution of the microscope the phase information is not directly interpretable, and must be modeled via computer simulation

=== Scherzer Defocus ===

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== Linear Imaging Theory vs. Non-Linear Imaging Theory ==

The previous description of the contrast transfer function depends on linear imaging theory.  Linear imaging theory assumes that the transmitted beam is dominant, assumesthere is only weak phase scattering by the sample, assumesthere are no dynamical effects, and assumesthat athe verysample thinis sampleextremely 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>

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>