[3dem] [TEM] CTF and SNR

Fri Jun 9 10:48:04 PDT 2017

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
>>> *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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>>>
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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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