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<div class="moz-cite-prefix">Dear All<br>
To get a feeling for the type of fundamental issues at stake here,
search for: "Young's interference experiment" + "quantum eraser".<br>
<div id="gs_cit0" tabindex="0" class="gs_citr">Very visual and
accessible is: Rueckner, Wolfgang, and Joseph Peidle. "Young's
double-slit experiment with single photons and quantum eraser."
<i>American Journal of Physics</i> 81.12 (2013): 951-958.<br>
(A modern version of a classical experiment in physics)<br>
Have fun,<br>
Marin<br>
</div>
<br>
<br>
On 09/06/2017 23:59, David DeRosier wrote:<br>
</div>
<blockquote type="cite"
cite="mid:CA98564A-FA6B-48D7-BE4A-982A7AA5A950@brandeis.edu">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
I agree. Perhaps our two emails together will answer his question.
<div class=""><br class="">
</div>
<div class="">David</div>
<div class=""><br class="">
<div>
<blockquote type="cite" class="">
<div class="">On Jun 9, 2017, at 10:48 AM, Marin van Heel
<<a href="mailto:marin.vanheel@googlemail.com" class=""
moz-do-not-send="true">marin.vanheel@googlemail.com</a>>
wrote:</div>
<br class="Apple-interchange-newline">
<div class="">
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charset=utf-8" class="">
<div text="#000000" bgcolor="#FFFFFF" class="">
<div class="moz-cite-prefix"><br class="">
David, <br class="">
<br class="">
That would indeed be true in high-contrast images...
However since the phase contrast in cryo-EM is of the
order of a few percent at best (especially where it
concerns the high-resolution information), the Poisson
noise will be almost entirely determined by the "99%"
constant background (associated with the "zero-order
beam") . In other words:<br class="">
sqrt (99 + N(x,y)) ~ sqrt (99) {with sigma(N(x,y)) ~
1}<br class="">
<br class="">
Marin<br class="">
<br class="">
<br class="">
On 09/06/2017 18:14, David DeRosier wrote:<br class="">
</div>
<blockquote type="cite"
cite="mid:4E0B1DA0-6185-4F0F-9056-7A66E358CF37@brandeis.edu"
class="">
<meta http-equiv="Content-Type" content="text/html;
charset=utf-8" class="">
If the signal is N(x,y), then the expected error or
shot noise is sqrt(N(x,y)). The shot noise is
modulated if the signal is modulated. I think that is
what is being asked.
<div class=""><br class="">
</div>
<div class="">David</div>
<div class=""><br class="">
<div class="">
<blockquote type="cite" class="">
<div class="">On Jun 9, 2017, at 2:57 AM, Marin
van Heel <<a
href="mailto:marin.vanheel@googlemail.com"
class="" moz-do-not-send="true">marin.vanheel@googlemail.com</a>>
wrote:</div>
<br class="Apple-interchange-newline">
<div class="">
<div class="moz-cite-prefix"
style="font-family: ArialMT; font-size:
18px; font-style: normal; font-variant-caps:
normal; font-weight: normal; letter-spacing:
normal; text-align: start; text-indent: 0px;
text-transform: none; white-space: normal;
word-spacing: 0px;
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background-color: rgb(255, 255, 255);"><br
class="">
Hi Philip,<br class="">
<br class="">
Admittedly, the wave-particle duality of
nature is a confusing matter! All wave
functions and (complex) transmission
functions in the object plane and in
diffraction plane (back-focal plane of the
lens) are only probability functions. They
only become real entities when they are
measured in the image plane (the waves
squared, are actually measured). It is
there where we introduce the counting of the
arriving electrons (particles), a counting
which is subject to Poisson statistics.
Thus Poisson statistics is NOT subject to
the CTF. (See Alexis' post below)<br
class="">
<br class="">
Cheers<br class="">
<br class="">
Marin<br class="">
<br class="">
================================================<br class="">
<br class="">
<br class="">
On 09/06/2017 10:32, Philip Koeck wrote:<br
class="">
</div>
<blockquote type="cite"
cite="mid:C8D24D7E19AEE543942A826EE910B1C2018104AA6A@KIMSX02.user.ki.se"
style="font-family: ArialMT; font-size:
18px; font-style: normal; font-variant-caps:
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white-space: normal; widows: auto;
word-spacing: 0px; -webkit-text-size-adjust:
auto; -webkit-text-stroke-width: 0px;
background-color: rgb(255, 255, 255);"
class="">
<div class="WordSection1" style="page:
WordSection1;">
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span
style="color: rgb(31, 73, 125);"
class="">Hi again.<o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span
style="color: rgb(31, 73, 125);"
class=""><o:p class=""> </o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span
style="color: rgb(31, 73, 125);"
class="" lang="EN-US">Several people
have pointed out that shot-noise is
the main noise contribution and that
it isn’t modulated by the CTF.<o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span
style="color: rgb(31, 73, 125);"
class="" lang="EN-US">I’m having a
hard time understanding why it
wouldn’t be modulated by the CTF.<o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span
style="color: rgb(31, 73, 125);"
class="" lang="EN-US">All shot noise
that occurs before the imaging by the
objective lens should somehow affect
the exit wave, shouldn’t it?<o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span
style="color: rgb(31, 73, 125);"
class="" lang="EN-US">(I know I’m
switching from a particle to a wave
description here.)<br class="">
Since the whole exit wave (signal and
noise contributions) is multiplied by
the same phase factor containing the<br
class="">
lens aberration function, the noise in
it should be affected by the CTF just
as much as the signal.<br class="">
Now I’m thinking about shot noise
produced mainly during elastic
scattering in the specimen.<o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span
style="color: rgb(31, 73, 125);"
class="" lang="EN-US">I’m trying not
to think of inelastic scattering to
keep things simpler.<o:p class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span
style="color: rgb(31, 73, 125);"
class="" lang="EN-US"><o:p class=""> </o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span
style="color: rgb(31, 73, 125);"
class="" lang="EN-US">All the best,<o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span
style="color: rgb(31, 73, 125);"
class="" lang="EN-US"><o:p class=""> </o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span
style="color: rgb(31, 73, 125);"
class="" lang="EN-US">Philip<o:p
class=""></o:p></span></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span
style="color: rgb(31, 73, 125);"
class="" lang="EN-US"><o:p class=""> </o:p></span></div>
<div class="">
<div style="border-style: solid none
none; border-top-width: 1pt;
border-top-color: rgb(181, 196, 223);
padding: 3pt 0cm 0cm;" class="">
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family:
Calibri, sans-serif;" class=""><b
class=""><span style="font-size:
10pt; font-family: Tahoma,
sans-serif; color: windowtext;"
class="">Från:</span></b><span
style="font-size: 10pt;
font-family: Tahoma, sans-serif;
color: windowtext;" class=""><span
class="Apple-converted-space"> </span>3dem
[<a class="moz-txt-link-freetext"
href="mailto:3dem-bounces@ncmir.ucsd.edu" style="color: purple;
text-decoration: underline;"
moz-do-not-send="true">mailto:3dem-bounces@ncmir.ucsd.edu</a>]<span
class="Apple-converted-space"> </span><b
class="">För<span
class="Apple-converted-space"> </span></b>Alexis
Rohou<br class="">
<b class="">Skickat:</b><span
class="Apple-converted-space"> </span>den
7 juni 2017 15:25<br class="">
<b class="">Till:</b><span
class="Apple-converted-space"> </span><a
class="moz-txt-link-abbreviated"
href="mailto:3dem@ncmir.ucsd.edu" style="color: purple; text-decoration:
underline;"
moz-do-not-send="true">3dem@ncmir.ucsd.edu</a><br
class="">
<b class="">Ämne:</b><span
class="Apple-converted-space"> </span>Re:
[3dem] [TEM] CTF and SNR<o:p
class=""></o:p></span></div>
</div>
</div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><o:p class=""> </o:p></div>
<p style="margin-right: 0cm; margin-left:
0cm; font-size: 11pt; font-family:
Calibri, sans-serif;" class="">Hi
Philip,<o:p class=""></o:p></p>
<blockquote style="margin-top: 5pt;
margin-bottom: 5pt;" class="">
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span class=""
lang="EN-US">I’ll assume most of the
noise in an image of an ice-embedded
bio-molecule is due to variations in
the ice, so called structural noise.</span><o:p
class=""></o:p></div>
</blockquote>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class="">This is not a safe
assumption. In fact most of the noise is
shot noise, which is Poisson distributed
(so, Gaussian for our total exposures),
and not modulated by the CTF. Hence the
CTF does modulate the SSNR.<o:p class=""></o:p></div>
<p style="margin-right: 0cm; margin-left:
0cm; font-size: 11pt; font-family:
Calibri, sans-serif;" class="">A few
years ago, Joachim Frank and colleagues
attempted a quantification of this and
other sources of noise. You may find
this a good read. They come up with a
shot noise SNR of ~ 0.1, and a combined
shot+structural noise SNR of ~1, if I
read them correctly.<o:p class=""></o:p></p>
<p style="margin-right: 0cm; margin-left:
0cm; font-size: 11pt; font-family:
Calibri, sans-serif;" class="">Baxter,
W. T., Grassucci, R. A., Gao, H., &
Frank, J. (2009). Determination of
signal-to-noise ratios and spectral SNRs
in cryo-EM low-dose imaging of
molecules. Journal of Structural
Biology, 166(2), 126–32.<span
class="Apple-converted-space"> </span><a
href="https://doi.org/10.1016/j.jsb.2009.02.012" moz-do-not-send="true"
style="color: purple; text-decoration:
underline;" class="">https://doi.org/10.1016/j.jsb.2009.02.012</a><o:p
class=""></o:p></p>
<p style="margin-right: 0cm; margin-left:
0cm; font-size: 11pt; font-family:
Calibri, sans-serif;" class="">Cheers,<br
class="">
Alexis<o:p class=""></o:p></p>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><o:p class=""> </o:p></div>
<div class="">
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class="">On 06/07/2017
01:22 AM, Philip Koeck wrote:<o:p
class=""></o:p></div>
</div>
<blockquote style="margin-top: 5pt;
margin-bottom: 5pt;" class="">
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class="">Hi.<o:p class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""> <o:p class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span class=""
lang="EN-US">I’ve recently
encountered a bit of a conundrum:</span><o:p
class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span class=""
lang="EN-US"> </span><o:p class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span class=""
lang="EN-US">I’ll assume most of the
noise in an image of an ice-embedded
bio-molecule is due to variations in
the ice, so called structural noise.</span><o:p
class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span class=""
lang="EN-US">The CTF describes the
contrast transfer for both signal
and noise in the same way.</span><o:p
class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span class=""
lang="EN-US">So, what is the point
of changing the CTF by defocusing
and/or using a phase plate.<br
class="">
The SNR should be unchanged.</span><o:p
class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span class=""
lang="EN-US"> </span><o:p class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span class=""
lang="EN-US">I can think of one
explanation: If the signal spectrum
is very different from the noise
spectrum one could chose a CTF that
enhances the<br class="">
resolution bands where the
difference is big.</span><o:p
class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span class=""
lang="EN-US"> </span><o:p class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span class=""
lang="EN-US">Else: Is there some
other factor that affects visibility
of the molecule than SNR?</span><o:p
class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span class=""
lang="EN-US"> </span><o:p class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span class=""
lang="EN-US">All the best,</span><o:p
class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span class=""
lang="EN-US"> </span><o:p class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span class=""
lang="EN-US">Philip</span><o:p
class=""></o:p></div>
<div style="margin: 0cm 0cm 0.0001pt;
font-size: 11pt; font-family: Calibri,
sans-serif;" class=""><span
style="font-size: 12pt;" class=""><br
class="">
<br class="">
<br class="">
<o:p class=""></o:p></span></div>
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<pre class="moz-signature" cols="72" style="margin: 0cm 0cm 0.0001pt; font-size: 10pt; font-family: 'Courier New'; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; word-spacing: 0px; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255);">--
==============================================================
Prof Dr Ir Marin van Heel
Research Professor at:
Laboratório Nacional de Nanotecnologia - LNNano
CNPEM/ABTLuS, Campinas, Brazil
</pre>
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