[3dem] [TEM] CTF and SNR
Marin van Heel
marin.vanheel at googlemail.com
Sat Jun 10 00:29:49 PDT 2017
Dear All
To get a feeling for the type of fundamental issues at stake here,
search for: "Young's interference experiment" + "quantum eraser".
Very visual and accessible is: Rueckner, Wolfgang, and Joseph Peidle.
"Young's double-slit experiment with single photons and quantum eraser."
/American Journal of Physics/ 81.12 (2013): 951-958.
(A modern version of a classical experiment in physics)
Have fun,
Marin
On 09/06/2017 23:59, David DeRosier wrote:
> 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
>>>>> *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
>>>>>
>>>>>
>>>>>
>>>>> _______________________________________________
>>>>>
>>>>> 3dem mailing list
>>>>>
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>>>>>
>>>>> https://mail.ncmir.ucsd.edu/mailman/listinfo/3dem
>>>>>
>>>>>
>>>>>
>>>>> _______________________________________________
>>>>> 3dem mailing list
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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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>>>
>>
>
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