<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="">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><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="">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; text-transform: none; 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 lang="EN-US" style="color: rgb(31, 73, 125);" class="">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 lang="EN-US" style="color: rgb(31, 73, 125);" class="">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 lang="EN-US" style="color: rgb(31, 73, 125);" class="">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 lang="EN-US" style="color: rgb(31, 73, 125);" class="">(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 lang="EN-US" style="color: rgb(31, 73, 125);" class="">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 lang="EN-US" 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 lang="EN-US" style="color: rgb(31, 73, 125);" class="">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 lang="EN-US" 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 lang="EN-US" style="color: rgb(31, 73, 125);" class="">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 lang="EN-US" style="color: rgb(31, 73, 125);" class=""><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;">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;">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 lang="EN-US" class="">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 lang="EN-US" class="">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 lang="EN-US" class=""> </span><o:p class=""></o:p></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-US" class="">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 lang="EN-US" class="">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 lang="EN-US" class="">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 lang="EN-US" class=""> </span><o:p class=""></o:p></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-US" class="">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 lang="EN-US" class=""> </span><o:p class=""></o:p></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-US" class="">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 lang="EN-US" class=""> </span><o:p class=""></o:p></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-US" class="">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 lang="EN-US" class=""> </span><o:p class=""></o:p></div><div style="margin: 0cm 0cm 0.0001pt; font-size: 11pt; font-family: Calibri, sans-serif;" class=""><span lang="EN-US" class="">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><pre style="margin: 0cm 0cm 0.0001pt; font-size: 10pt; font-family: 'Courier New';" class="">_______________________________________________<o:p class=""></o:p></pre><pre style="margin: 0cm 0cm 0.0001pt; 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font-family: 'Courier New';" class="">_______________________________________________
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</pre></blockquote><p style="margin-right: 0cm; margin-left: 0cm; font-size: 11pt; font-family: Calibri, sans-serif; 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);" class=""><br class=""></p><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><span 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); float: none; display: inline !important;" class="">_______________________________________________</span><br 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);" class=""><span 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); float: none; display: inline !important;" class="">3dem mailing list</span><br 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);" class=""><a href="mailto:3dem@ncmir.ucsd.edu" style="color: purple; text-decoration: underline; 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; text-transform: none; 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="">3dem@ncmir.ucsd.edu</a><br 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);" class=""><a href="https://mail.ncmir.ucsd.edu/mailman/listinfo/3dem" style="color: purple; text-decoration: underline; 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; text-transform: none; 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="">https://mail.ncmir.ucsd.edu/mailman/listinfo/3dem</a><br 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);" class=""></div></blockquote></div><br class=""></div></body></html>