[3dem] [TEM] CTF and SNR

Fri Jun 9 18:11:58 PDT 2017

In other words, the assumption made in Baxter et al. cited before (i.e., additive noise independent of CTF).

--Joachim
________________________________
From: 3dem [3dem-bounces at ncmir.ucsd.edu] on behalf of David DeRosier [derosier at brandeis.edu]
Sent: Friday, June 09, 2017 6:59 PM
To: Marin van Heel
Cc: 3dem at ncmir.ucsd.edu; CCPEM at JISCMAIL.AC.UK
Subject: Re: [3dem] [TEM] CTF and SNR

I agree. Perhaps our two emails together will answer his question.

David

On Jun 9, 2017, at 10:48 AM, Marin van Heel <marin.vanheel at googlemail.com<mailto:marin.vanheel at googlemail.com>> wrote:

David,

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:
sqrt (99 + N(x,y)) ~ sqrt (99)  {with sigma(N(x,y)) ~ 1}

Marin

On 09/06/2017 18:14, David DeRosier wrote:
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.

David

On Jun 9, 2017, at 2:57 AM, Marin van Heel <marin.vanheel at googlemail.com<mailto:marin.vanheel at googlemail.com>> wrote:

Hi Philip,

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)

Cheers

Marin

================================================

On 09/06/2017 10:32, Philip Koeck wrote:
Hi again.

Several people have pointed out that shot-noise is the main noise contribution and that it isn’t modulated by the CTF.
I’m having a hard time understanding why it wouldn’t be modulated by the CTF.
All shot noise that occurs before the imaging by the objective lens should somehow affect the exit wave, shouldn’t it?
(I know I’m switching from a particle to a wave description here.)
Since the whole exit wave (signal and noise contributions) is multiplied by the same phase factor containing the
lens aberration function, the noise in it should be affected by the CTF just as much as the signal.
Now I’m thinking about shot noise produced mainly during elastic scattering in the specimen.
I’m trying not to think of inelastic scattering to keep things simpler.

All the best,

Philip

Från: 3dem [mailto:3dem-bounces at ncmir.ucsd.edu] För Alexis Rohou
Skickat: den 7 juni 2017 15:25
Till: 3dem at ncmir.ucsd.edu<mailto:3dem at ncmir.ucsd.edu>
Ämne: Re: [3dem] [TEM] CTF and SNR

Hi Philip,

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.
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.

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.

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. https://doi.org/10.1016/j.jsb.2009.02.012

Cheers,
Alexis

On 06/07/2017 01:22 AM, Philip Koeck wrote:
Hi.

I’ve recently encountered a bit of a conundrum:

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.
The CTF describes the contrast transfer for both signal and noise in the same way.
So, what is the point of changing the CTF by defocusing and/or using a phase plate.
The SNR should be unchanged.

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
resolution bands where the difference is big.

Else: Is there some other factor that affects visibility of the molecule than SNR?

All the best,

Philip

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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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