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<div class="moz-cite-prefix">Hi All,<br>
<br>
Signing off or not, I am totally amazed at the level of
controversy/misunderstanding there is even among experts in our
field. This just shows how necessary this type of open discussion
is! <br>
<br>
There are TWO types of resolution in all fields where Fourier
Optics apply. The two type of resolution are currently probably
best defined in EM simply because in light optics the FRC-type of
criteria have just started its entry. In contrast to what Ed
suggests, light optics is actually lagging behind. The first type
of criterion, also the oldest type, is the INSTRUMENTAL
resolution. This probably first emerged in light-microscopy but is
in use everywhere, including astronomy and electron microscopy.
The second type of resolution criterion is related to the
STATISTICAL REPRODUCIBILITY of an experiment conducted with the
instrument.<br>
<br>
1) The instrumental or geometric resolution: that is, at which
resolution level does the transfer function of the instrument
drop to zero (independent of any object being present). Beyond
that level, no matter how long we measure, we will not collect any
higher resolution information about the object. The Raleigh/Abbe
formula relating numerical aperture and resolution fall in that
category. In 2D EM, once the Contrast Transfer function drops to
zero there is no further information transfer. In 3D,
reconstruction, the angular distribution of the projections
defines the maximum (isotropic) geometric resolution achievable.
Our contribution on this issue is: (van Heel and Harauz G:
Resolution criteria for three dimensional reconstructions, Optik
73 (1986) 119-122.
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<br>
But the instrumental/geometric resolution does not mean that you
will achieve that level of resolution in any one given experiment!
If one does not switch on the illumination in the light- or
electron microscope, the data collected in the experiment are
rubbish, no matter how good your geometric resolution is! Thus the
more practical statistical significant resolution achieved in one
3D reconstruction experiment was introduced. Our contribution here
was:<br>
<br>
2) Fourier Shell Correlation (Harauz G & van Heel M: Exact
filters for general geometry three dimensional reconstruction,
Optik 73 (1986) 146-156). More info in the Wikipedia page:
(<a class="moz-txt-link-freetext" href="https://en.wikipedia.org/wiki/Fourier_shell_correlation">https://en.wikipedia.org/wiki/Fourier_shell_correlation</a>). As is
the case with the 2014 paper Gabor is referring to, the 3D version
of the FSC was actually introduced to show how well 3D
reconstruction algorithms were performing comparing the
reconstruction results with the original, known test object. <br>
<br>
Still hope this helps, <br>
<br>
Marin<br>
<br>
================================================<br>
<br>
<br>
On 30/08/2015 16:27, Edward Egelman wrote:<br>
</div>
<blockquote cite="mid:55E35930.6060306@virginia.edu" type="cite">
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And I thought that you were "signing off"! In optics one uses a
test image and there is a well-defined definition of lines of
resolution. In crystallography one can look for holes in aromatic
rings, etc. as an indication of the true resolution. In both of
these cases one is starting with a known object and then looking
at the "transfer function" of the imaging system. In EM,
unfortunately, self-consistency or arguments about SNR (or
estimates of SNR) have substituted for a reality-based notion of
an instrumental transfer function. That is because such
reality-based tests were absent when one has 15, 20 or 30
Angstroms resolution. But we are no longer at that stage...<br>
Ed<br>
<br>
<div class="moz-cite-prefix">On 8/30/15 2:47 PM, Penczek, Pawel A
wrote:<br>
</div>
<blockquote
cite="mid:B8A7A8B2-6E80-437B-B048-C295DD654677@uth.tmc.edu"
type="cite">
<pre wrap="">Ed and Gabor, I have to respectfully disagree with your statements.
Ed - there is no “general” or “absolute” definition of resolution. What is called resolution differs from field to field
so when you say FSC is not a measure of resolution, what resolution do you have in mind? The one used in optics,
or the one used in X-ray crystallography? They are quite different from each other.
For better or worth, definition of FSC allows one to estimate level of SNR in the data and it does just that,
assuming that assumptions are fulfilled.
These assumptions call, among other things, for full independence of two realizations of the signal.
It is easy to see that it follows that thus defined FSC is not applicable to EM protocols as it would be always zero.
Simply, a chance that two truly independent refinement processes would magically end up with two structures
(or 2D averages) in the exact same orientation is infinitely small.
Therefore, in practice we compromise independence to certain degree to make the machinery of FSC applicable to EM.
I would submit that most of the confusion arises due to disagreements how much of independence one is allowed to compromise.
One kind of “abuse” is some kind of deterministic protocol that increases correlation, as Gabor points out.
In helical reconstruction, imposition of helical symmetry is such a step. However, fundamentally this cannot be avoided
if one is to apply FSC at all as pointed out above. So, we use various tricks to keep two structures in sync.
For example, a popular software package simply equates low frequency components between the two, which
of course introduces correlations beyond the cut-off point. How much nobody knows.
In closing, as often in life there is a mathematical definition and there is little argument about its meaning and applicability,
and then there is life. Normally there is full understanding that the two differ to a degree and one has to simply live with it.
We should keep in mind though that if FSC is applied to an outcome of an image processing protocol, its outcome becomes
as function of this protocol, as the ‘purity” of the original definition is compromised.
Regards,
-
Pawel Penczek
<a moz-do-not-send="true" class="moz-txt-link-abbreviated" href="mailto:pawel.a.penczek@uth.tmc.edu">pawel.a.penczek@uth.tmc.edu</a>
</pre>
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<p class="MsoNormal">Edward H. Egelman, Ph.D.<o:p></o:p></p>
<p class="MsoNormal">Professor<o:p></o:p></p>
<p class="MsoNormal">Dept. of Biochemistry and Molecular
Genetics<o:p></o:p></p>
<p class="MsoNormal">University of Virginia<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">President<o:p></o:p></p>
<p class="MsoNormal">Biophysical Society<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">phone: 434-924-8210<o:p></o:p></p>
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<pre wrap="">_______________________________________________
3dem mailing list
<a class="moz-txt-link-abbreviated" href="mailto:3dem@ncmir.ucsd.edu">3dem@ncmir.ucsd.edu</a>
<a class="moz-txt-link-freetext" href="https://mail.ncmir.ucsd.edu/mailman/listinfo/3dem">https://mail.ncmir.ucsd.edu/mailman/listinfo/3dem</a>
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