[3dem] [TEM] amplitude contrast

Wed Aug 16 00:52:27 PDT 2017

Hi Rasmus.

Nice to hear from you.

Just one question: When you say "absorption" of the electron wave to describe the imaginary part of the atomic scattering factor, how would you picture this absorption?
What is actually happening when the wave amplitude decreases, (which should mean that the number of electrons decreases.)

All the best,

Philip

Från: Rasmus Schroeder [mailto:rasmus.schroeder at bioquant.uni-heidelberg.de]
Skickat: den 15 augusti 2017 17:27
Till: Philip Koeck
Kopia: Sacha De Carlo; 3dem at ncmir.ucsd.edu
Ämne: Re: [3dem] [TEM] amplitude contrast

Dear all,

may be I add my 5 cent .... as I am a bit responsible for "Angert et al. 2000" (and also hi Philip, we haven't seen each other for decades and now we talk about amplitude contrast ...).

The first two terms are the very conventional terms derived from the atomic scattering factors. The atomic scattering factors are complex entities, i.e. the phase part is real and thus results in a "phase factor", while the "amplitude" part results in a - as Steven pointed out rightly - exponential damping factor. In first order approximations (weak phase and amplitude objects = weak scatterer = weak interaction ...) this then leads in a vector diagram to an unscattered part of the wave, the scattered part (90 degrees phase shifted) and an "amplitude reducing" part.
@Philip: all this is still linear image formation, no 2nd order or so.
Just for the nature of the atomic scattering factor: the real part would be a simple "refractive index" contribution, while the imaginary part is really the effect of "absorption" of the electron wave.
It should also be noted, that the "spatial resolution" carried by the phase part is in general higher than that of the amplitude part ... Otherwise again Steve is right, the objective aperture is a simple frequency filter.

Now to the inelastic contribution: Using zero-loss filtering simply means removing electrons from the image. Contrary to earlier believes this is not just removing noise, as the inelastic events are not homogeneously distributed but depend on the difference between the interactions in the embedding ice vs. the actual protein or whatever. (A simple Gedanken experiment illustrates this: Of course if we could image a protein in vacuum, then inelastic scattering would only happen at the protein, and in zero-loss filtered images this protein would be dark on a bright background. And this is exactly what amplitude contrast looks like. Thus we modelled the zero-loss imaging with an additional "first order amplitude term" (actually inspired by the "Optical Theorem" of quantum mechanics ...). But one has to be cautious: Exactly as the normal amplitude contrast has a frequency dependence different form the phase contrast, the zero-loss contrast again is imaging more lower spatial frequencies. The reason is very simple: As we do see a dominant plasmon loss in ice and protein layers it is obvious that those interactions are delocalised to about a few nm. Only the inner shell inelastic core loss interaction volumes are localised to the atoms, but those events are rare and can be neglected ...

And to finish up the story: In 2000 we had to fit these three terms to very poor Thon ring patterns, as detectors were not too good ....
Still we had our "blind" student Endre who never knew what patterns Isabel would prepare for him to fit. But still, he did find patterns were a third term was needed (zero-loss) and others, which could be fit by the conventional two terms.

Anyway, it would be fun to repeat this experiment with modern DEDs ... maybe we ourselves should do it in the next few months.

And yes, sorry for writing such long contributions.

All the best,

Rasmus

On 15 Aug 2017, at 16:26, Philip Koeck <Philip.Koeck at ki.se<mailto:Philip.Koeck at ki.se>> wrote:

Hi again.

I've read a bit of Angert et al. 2000 now and I can rephrase my question.
In equation 2 there are 3 terms to the generalized phase shift: elastic phase contrast, elastic amplitude contrast and inelastic amplitude contrast.
The third is obviously due to removal of inelastically scattered electrons by the filter.

My question: What is the second term due to?

All the best,

Philip

Från: Sacha De Carlo [mailto:sacha.decarlo at dectris.com]
Skickat: den 15 augusti 2017 14:29
Till: Philip Koeck
Kopia: 3dem at ncmir.ucsd.edu<mailto:3dem at ncmir.ucsd.edu>
Ämne: Re: [3dem] [TEM] amplitude contrast

...thus my statement with a "may provide" instead of "will" (provide answers to...).

Alright, let's try this again, forward 8 years (2000), Angert et al, zero-loss (no inelastic scattering) and of course in a practical sense the ice thickness and size of the aperture DO influence the contrast (for the same defocus or in-focus image), but I do not recall other papers where it was quantified methodically (thoroughly)...

Cheers,
Sacha
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Rasmus R. Schroeder

CellNetworks-Cluster of Excellence (EXC81), BioQuant,
Heidelberg University
Im Neuenheimer Feld 267
69120 Heidelberg, Germany

Tel. +49-(0)6221-5451350
e-mail  rasmus.schroeder at bioquant.uni-heidelberg.de<mailto:rasmus.schroeder at bioquant.uni-heidelberg.de>

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