Contrast transfer function: Difference between revisions

Revision as of 19:31, 12 June 2015

Revision as of 19:34, 12 June 2015

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[[File:CTF Modified by Spatial and Temporal Envelope Functions.pdf|thumb|CTF Function of a CM300 Microscope damped by temporal and spatial envelope functions.]]

 <nowiki> </nowiki>The envelope function represents the effect of additional aberrations that damp the contrast transfer function, and in turn the phase. The envelope terms comprising the envelope function tend to suppress high spatial frequencies.  The exact form of the envelope functions can differ from source to source.  Generally, they are applied by multiplying the Contrast Transfer Function by an envelope term Et representing temporal aberrations, and an envelope term Es representing spatial aberrations.
This yields a modified, or effective Contrast Transfer Function:

<math>K_{eff}(k) = E_tE_s(sin[(2\pi/\lambda)W(k)]</math>

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Examples of temporal aberrations include chromatic aberrations, energy spread, focal spread, instabilities in the high voltage source, and instabilities in the objective lens current. An example of a spatial aberration includes the finite incident beam convergence.<ref>{{Cite web|title = Envelope Functions|url = http://www.maxsidorov.com/ctfexplorer/webhelp/envelope_functions.htm|website = www.maxsidorov.com|accessdate = 2015-06-12}}</ref>

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As shown in the figure, the most restrictive envelope term will dominate in damping the contrast transfer function. In this particular example, the temporal envelope term is the most restrictive. Becuase the envelope terms damp more strongly at higher spatial frequencies, there comes a point where no more phase signal can pass through. This is called the '''Information Limit''' of the microscope, and is one measure of the resolution.

Becuase the envelope terms damp more strongly at higher spatial frequencies, there comes a point where no more phase signal can pass through. This is called the '''Information Limit''' of the microscope, and is one measure of the resolution.

<br /> Modeling the envelope function can give insight into both TEM instrument design, and imaging parameters. By modeling the different aberrations via envelope terms, it is possible to see which aberrations are most limiting the phase signal.

Various [http://jiang.bio.purdue.edu/software/ctf/ctfapplet.html software] [http://www.maxsidorov.com/ctfexplorer/ packages] have been developed to model both the Contrast Transfer Function and Envelope Function for particular microscopes, and particular imaging parameters.