<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space;" class="">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="">marin.vanheel@googlemail.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class="">
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<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;
-webkit-text-stroke-width: 0px; 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: normal;
font-weight: normal; letter-spacing: normal; orphans:
auto; text-align: start; text-indent: 0px;
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word-spacing: 0px; -webkit-text-size-adjust: auto;
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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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==============================================================
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CNPEM/ABTLuS, Campinas, Brazil
</pre>
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