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<div style="direction: ltr;font-family: Tahoma;color: #000000;font-size: 10pt;">In other words, the assumption made in Baxter et al. cited before (i.e., additive noise independent of CTF).<br>
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--Joachim<br>
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<div style="direction: ltr;" id="divRpF78782"><font face="Tahoma" color="#000000" size="2"><b>From:</b> 3dem [3dem-bounces@ncmir.ucsd.edu] on behalf of David DeRosier [derosier@brandeis.edu]<br>
<b>Sent:</b> Friday, June 09, 2017 6:59 PM<br>
<b>To:</b> Marin van Heel<br>
<b>Cc:</b> 3dem@ncmir.ucsd.edu; CCPEM@JISCMAIL.AC.UK<br>
<b>Subject:</b> Re: [3dem] [TEM] CTF and SNR<br>
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<div>I agree. Perhaps our two emails together will answer his question.
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<div class="">David</div>
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<div class="">On Jun 9, 2017, at 10:48 AM, Marin van Heel <<a href="mailto:marin.vanheel@googlemail.com" class="" target="_blank">marin.vanheel@googlemail.com</a>> wrote:</div>
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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="">
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<br class="">
On 09/06/2017 18:14, David DeRosier wrote:<br class="">
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<blockquote type="cite" 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.
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<div class="">David</div>
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<div class="">On Jun 9, 2017, at 2:57 AM, Marin van Heel <<a href="mailto:marin.vanheel@googlemail.com" class="" target="_blank">marin.vanheel@googlemail.com</a>> wrote:</div>
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Hi Philip,<br class="">
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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="">
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Cheers<br class="">
<br class="">
Marin<br class="">
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On 09/06/2017 10:32, Philip Koeck wrote:<br class="">
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<span class="" style="color:rgb(31,73,125)">Hi again.</span></div>
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<span class="" style="color:rgb(31,73,125)" 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.</span></div>
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<span class="" style="color:rgb(31,73,125)" lang="EN-US">I’m having a hard time understanding why it wouldn’t be modulated by the CTF.</span></div>
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<span class="" style="color:rgb(31,73,125)" lang="EN-US">All shot noise that occurs before the imaging by the objective lens should somehow affect the exit wave, shouldn’t it?</span></div>
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<span class="" style="color:rgb(31,73,125)" 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.</span></div>
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<span class="" style="color:rgb(31,73,125)" lang="EN-US">I’m trying not to think of inelastic scattering to keep things simpler.</span></div>
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<span class="" style="color:rgb(31,73,125)" lang="EN-US">All the best,</span></div>
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<span class="" style="color:rgb(31,73,125)" lang="EN-US">Philip</span></div>
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<b class=""><span class="" style="font-size:10pt; font-family:Tahoma,sans-serif; color:windowtext">Från:</span></b><span class="" style="font-size:10pt; font-family:Tahoma,sans-serif; color:windowtext"><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" target="_blank">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" target="_blank">3dem@ncmir.ucsd.edu</a><br class="">
<b class="">Ämne:</b><span class="Apple-converted-space"> </span>Re: [3dem] [TEM] CTF and SNR</span></div>
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Hi Philip,</p>
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<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></div>
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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.</div>
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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.</p>
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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" class="" style="color:purple; text-decoration:underline" target="_blank">https://doi.org/10.1016/j.jsb.2009.02.012</a></p>
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Cheers,<br class="">
Alexis</p>
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On 06/07/2017 01:22 AM, Philip Koeck wrote:</div>
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Hi.</div>
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<span class="" lang="EN-US">I’ve recently encountered a bit of a conundrum:</span></div>
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<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></div>
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<span class="" lang="EN-US">The CTF describes the contrast transfer for both signal and noise in the same way.</span></div>
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<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></div>
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<span class="" lang="EN-US"> </span></div>
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<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></div>
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<span class="" lang="EN-US"> </span></div>
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<span class="" lang="EN-US">Else: Is there some other factor that affects visibility of the molecule than SNR?</span></div>
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<span class="" lang="EN-US">All the best,</span></div>
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<span class="" lang="EN-US">Philip</span></div>
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==============================================================

    Prof Dr Ir Marin van Heel

    Research Professor at:

    Laboratório Nacional de Nanotecnologia - LNNano
    CNPEM/ABTLuS, Campinas, Brazil
 
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