<div dir="ltr"><div class="gmail_default" style="font-size:small">Hi Phillip,<br><br></div><div class="gmail_default" style="font-size:small">Based on your last post, I think the missing link here for you is a more fundamental description of what shot noise is. When you flip a fair coin you will get 50/50 heads/tails only in the long run, however you can not make a prediction about any given flip and in fact getting three heads in a row for example would not be so terribly unusual. While this is an example where the underlying process has a binomial distribution which in the limit of many experiments begins to look like a normal distribution, it illustrates what is going on here.<br><br></div><div class="gmail_default" style="font-size:small">In our case, the underlying process is best modeled by a Poisson distribution, but the end result is the same -<b> given a very few measurements, there is a randomness in our result that has nothing to do with the sample, and only to do with the quantum (discrete) nature of the electron.<br></b><br>While we talk about using, say 20 electrons/ angstrom squared , this is of course an average measurement. Where shot noise arises then is our inability to say whether the number of electrons we measure in a given pixel is due solely to the number scattered into that pixel by events in the sample, or if perhaps due to the fluctuations in probability of an electron even having a chance to interact with the specimen and thereby be measured. <br><br></div><div class="gmail_default" style="font-size:small">Hopefully I didn't muddle that too much, and forgive me if that is too basic a description.<br><br></div><div class="gmail_default" style="font-size:small">HTH<br><br></div><div class="gmail_default" style="font-size:small">Ben H.<br></div><div class="gmail_default" style="font-size:small"><br><br></div></div><div class="gmail_extra"><br clear="all"><div><div class="gmail_signature" data-smartmail="gmail_signature"><div dir="ltr"><div><div dir="ltr"><div dir="ltr"><div dir="ltr"><div style="text-align:justify"><span style="color:rgb(32,18,77);font-family:garamond,serif;font-size:small">*************************************</span><br></div><div><font size="2"><span style="color:rgb(32,18,77);font-family:garamond,serif;line-height:24px">Benjamin Himes</span><br></font></div><div><font size="2"><span style="text-align:justify;color:rgb(32,18,77);font-family:garamond,serif">D</span><span style="color:rgb(32,18,77);font-family:garamond,serif;text-align:justify">epartment of Structural Biology</span></font></div><div><font face="garamond, serif" size="2" color="#20124d" style="background-color:rgb(255,255,255)"><span style="text-align:justify">University of Pittsburgh School of Medicine</span><br style="text-align:justify"><span style="text-align:justify">2050 Biomedical Science Tower 3 (BST3).</span></font></div><div><span style="color:rgb(32,18,77);text-align:justify"><font face="garamond, serif" size="2">3501 5th Ave, Pittsburgh, PA 15260</font></span><font face="garamond, serif" size="2" color="#20124d" style="background-color:rgb(255,255,255)"><span style="text-align:justify"><br></span></font></div><div><font face="garamond, serif" size="2" color="#20124d" style="background-color:rgb(255,255,255)"><br></font></div><div><font face="garamond, serif" size="2" color="#20124d" style="background-color:rgb(255,255,255)"><b>(412) 648-7262 </b>(Office)</font></div><div><font size="2" color="#20124d" style="background-color:rgb(255,255,255)"><font face="garamond, serif"><strong style="text-align:justify">(412)648-8998</strong><span style="text-align:justify"> (Lab fax)</span></font></font></div><div><font size="2" color="#20124d" style="background-color:rgb(255,255,255)"><font face="garamond, serif"><span style="text-align:justify">*************************************</span></font></font></div><div><font color="#274e13" size="2" face="garamond, serif"><span style="line-height:24px"><div><br></div></span></font></div></div></div></div></div></div></div></div>
<br><div class="gmail_quote">On Fri, Jun 9, 2017 at 5:57 AM, <span dir="ltr"><<a href="mailto:3dem-request@ncmir.ucsd.edu" target="_blank">3dem-request@ncmir.ucsd.edu</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Send 3dem mailing list submissions to<br>
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Today's Topics:<br>
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1. Re: [TEM] CTF and SNR (Philip Koeck)<br>
2. Re: [TEM] CTF and SNR (Marin van Heel)<br>
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------------------------------<wbr>------------------------------<wbr>----------<br>
<br>
Message: 1<br>
Date: Fri, 9 Jun 2017 09:32:13 +0000<br>
From: Philip Koeck <<a href="mailto:Philip.Koeck@ki.se">Philip.Koeck@ki.se</a>><br>
To: "<a href="mailto:3dem@ncmir.ucsd.edu">3dem@ncmir.ucsd.edu</a>" <<a href="mailto:3dem@ncmir.ucsd.edu">3dem@ncmir.ucsd.edu</a>><br>
Subject: Re: [3dem] [TEM] CTF and SNR<br>
Message-ID:<br>
<<a href="mailto:C8D24D7E19AEE543942A826EE910B1C2018104AA6A@KIMSX02.user.ki.se">C8D24D7E19AEE543942A826EE910B<wbr>1C2018104AA6A@KIMSX02.user.ki.<wbr>se</a>><br>
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<br>
Hi again.<br>
<br>
Several people have pointed out that shot-noise is the main noise contribution and that it isn't modulated by the CTF.<br>
I'm having a hard time understanding why it wouldn't be modulated by the CTF.<br>
All shot noise that occurs before the imaging by the objective lens should somehow affect the exit wave, shouldn't it?<br>
(I know I'm switching from a particle to a wave description here.)<br>
Since the whole exit wave (signal and noise contributions) is multiplied by the same phase factor containing the<br>
lens aberration function, the noise in it should be affected by the CTF just as much as the signal.<br>
Now I'm thinking about shot noise produced mainly during elastic scattering in the specimen.<br>
I'm trying not to think of inelastic scattering to keep things simpler.<br>
<br>
All the best,<br>
<br>
Philip<br>
<br>
Fr?n: 3dem [mailto:<a href="mailto:3dem-bounces@ncmir.ucsd.edu">3dem-bounces@ncmir.<wbr>ucsd.edu</a>] F?r Alexis Rohou<br>
Skickat: den 7 juni 2017 15:25<br>
Till: <a href="mailto:3dem@ncmir.ucsd.edu">3dem@ncmir.ucsd.edu</a><br>
?mne: Re: [3dem] [TEM] CTF and SNR<br>
<br>
<br>
Hi Philip,<br>
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.<br>
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.<br>
<br>
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.<br>
<br>
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. <a href="https://doi.org/10.1016/j.jsb.2009.02.012" rel="noreferrer" target="_blank">https://doi.org/10.1016/j.jsb.<wbr>2009.02.012</a><br>
<br>
Cheers,<br>
Alexis<br>
<br>
On 06/07/2017 01:22 AM, Philip Koeck wrote:<br>
Hi.<br>
<br>
I've recently encountered a bit of a conundrum:<br>
<br>
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.<br>
The CTF describes the contrast transfer for both signal and noise in the same way.<br>
So, what is the point of changing the CTF by defocusing and/or using a phase plate.<br>
The SNR should be unchanged.<br>
<br>
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>
resolution bands where the difference is big.<br>
<br>
Else: Is there some other factor that affects visibility of the molecule than SNR?<br>
<br>
All the best,<br>
<br>
Philip<br>
<br>
<br>
<br>
<br>
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Message: 2<br>
Date: Fri, 9 Jun 2017 10:57:18 +0100<br>
From: Marin van Heel <<a href="mailto:marin.vanheel@googlemail.com">marin.vanheel@googlemail.com</a>><br>
To: Philip Koeck <<a href="mailto:Philip.Koeck@ki.se">Philip.Koeck@ki.se</a>>, "<a href="mailto:3dem@ncmir.ucsd.edu">3dem@ncmir.ucsd.edu</a>"<br>
<<a href="mailto:3dem@ncmir.ucsd.edu">3dem@ncmir.ucsd.edu</a>><br>
Cc: "<a href="mailto:CCPEM@JISCMAIL.AC.UK">CCPEM@JISCMAIL.AC.UK</a>" <<a href="mailto:CCPEM@JISCMAIL.AC.UK">CCPEM@JISCMAIL.AC.UK</a>><br>
Subject: Re: [3dem] [TEM] CTF and SNR<br>
Message-ID: <<a href="mailto:4f5587ae-e13d-e1c6-e287-a92b4885b7f0@googlemail.com">4f5587ae-e13d-e1c6-e287-<wbr>a92b4885b7f0@googlemail.com</a>><br>
Content-Type: text/plain; charset="windows-1252"; Format="flowed"<br>
<br>
<br>
Hi Philip,<br>
<br>
Admittedly, the wave-particle duality of nature is a confusing matter!<br>
All wave functions and (complex) transmission functions in the object<br>
plane and in diffraction plane (back-focal plane of the lens) are only<br>
probability functions. They only become real entities when they are<br>
measured in the image plane (the waves squared, are actually measured).<br>
It is there where we introduce the counting of the arriving electrons<br>
(particles), a counting which is subject to Poisson statistics. Thus<br>
Poisson statistics is NOT subject to the CTF. (See Alexis' post below)<br>
<br>
Cheers<br>
<br>
Marin<br>
<br>
==============================<wbr>==================<br>
<br>
<br>
On 09/06/2017 10:32, Philip Koeck wrote:<br>
><br>
> Hi again.<br>
><br>
> Several people have pointed out that shot-noise is the main noise<br>
> contribution and that it isn?t modulated by the CTF.<br>
><br>
> I?m having a hard time understanding why it wouldn?t be modulated by<br>
> the CTF.<br>
><br>
> All shot noise that occurs before the imaging by the objective lens<br>
> should somehow affect the exit wave, shouldn?t it?<br>
><br>
> (I know I?m switching from a particle to a wave description here.)<br>
> Since the whole exit wave (signal and noise contributions) is<br>
> multiplied by the same phase factor containing the<br>
> lens aberration function, the noise in it should be affected by the<br>
> CTF just as much as the signal.<br>
> Now I?m thinking about shot noise produced mainly during elastic<br>
> scattering in the specimen.<br>
><br>
> I?m trying not to think of inelastic scattering to keep things simpler.<br>
><br>
> All the best,<br>
><br>
> Philip<br>
><br>
> *Fr?n:*3dem [mailto:<a href="mailto:3dem-bounces@ncmir.ucsd.edu">3dem-bounces@ncmir.<wbr>ucsd.edu</a>] *F?r *Alexis Rohou<br>
> *Skickat:* den 7 juni 2017 15:25<br>
> *Till:* <a href="mailto:3dem@ncmir.ucsd.edu">3dem@ncmir.ucsd.edu</a><br>
> *?mne:* Re: [3dem] [TEM] CTF and SNR<br>
><br>
> Hi Philip,<br>
><br>
> I?ll assume most of the noise in an image of an ice-embedded<br>
> bio-molecule is due to variations in the ice, so called structural<br>
> noise.<br>
><br>
> This is not a safe assumption. In fact most of the noise is shot<br>
> noise, which is Poisson distributed (so, Gaussian for our total<br>
> exposures), and not modulated by the CTF. Hence the CTF does modulate<br>
> the SSNR.<br>
><br>
> A few years ago, Joachim Frank and colleagues attempted a<br>
> quantification of this and other sources of noise. You may find this a<br>
> good read. They come up with a shot noise SNR of ~ 0.1, and a combined<br>
> shot+structural noise SNR of ~1, if I read them correctly.<br>
><br>
> Baxter, W. T., Grassucci, R. A., Gao, H., & Frank, J. (2009).<br>
> Determination of signal-to-noise ratios and spectral SNRs in cryo-EM<br>
> low-dose imaging of molecules. Journal of Structural Biology, 166(2),<br>
> 126?32. <a href="https://doi.org/10.1016/j.jsb.2009.02.012" rel="noreferrer" target="_blank">https://doi.org/10.1016/j.jsb.<wbr>2009.02.012</a><br>
><br>
> Cheers,<br>
> Alexis<br>
><br>
> On 06/07/2017 01:22 AM, Philip Koeck wrote:<br>
><br>
> Hi.<br>
><br>
> I?ve recently encountered a bit of a conundrum:<br>
><br>
> I?ll assume most of the noise in an image of an ice-embedded<br>
> bio-molecule is due to variations in the ice, so called structural<br>
> noise.<br>
><br>
> The CTF describes the contrast transfer for both signal and noise<br>
> in the same way.<br>
><br>
> So, what is the point of changing the CTF by defocusing and/or<br>
> using a phase plate.<br>
> The SNR should be unchanged.<br>
><br>
> I can think of one explanation: If the signal spectrum is very<br>
> different from the noise spectrum one could chose a CTF that<br>
> enhances the<br>
> resolution bands where the difference is big.<br>
><br>
> Else: Is there some other factor that affects visibility of the<br>
> molecule than SNR?<br>
><br>
> All the best,<br>
><br>
> Philip<br>
><br>
><br>
><br>
><br>
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><br>
> 3dem mailing list<br>
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--<br>
==============================<wbr>==============================<wbr>==<br>
<br>
Prof Dr Ir Marin van Heel<br>
<br>
Research Professor at:<br>
<br>
Laborat?rio Nacional de Nanotecnologia - LNNano<br>
CNPEM/ABTLuS, Campinas, Brazil<br>
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