Thinking about CTF

[dustin.morado]

@Rasmus_Kock_Flygaard

So given my pixel size of 0.51 angpix and 800px box and 2.2 Å resolution (top panel in picture), particles with a defocus value of 2.4 um would be just at the limit of the CTF starting to alias?

Yes this is correct.

@Rasmus_Kock_Flygaard

But say I downsample particles to 1 angpix upon extraction (bottom panel in picture), I can either included particles with defocus values greater than 3.2 um without CTF aliasing or even reduce the box size to 540 px and still have no CTF aliasing?

Yes this is also correct because you didn’t change the box size to correspond with the down sampling. In the first graph you have a field of view of 400Å and then in the second graph the F.O.V. has now doubled to 800Å. So if you don’t have aliasing at 540 box size at 1Å, then correspondingly you wouldn’t have aliasing also at around a 1080 box size at your original sampling rate. This was explained here in the original post:

@dustin.morado

Putting what we know about the CTF frequencies and how the FFT is sampled we can now solve for the resolution at which the CTF will begin to alias for a given field of view (the box size in Angstrom units).

But in the application I changed the X-axis to box size at the selected sampling because that I feel is more practical in usage.

---

@Rasmus_Kock_Flygaard

But using Rado Danev’s rule-of-thumb equation, I could have particles with defocus value of 2.2 um contributing to 2.2 Å resolution.

So here Rado’s trick is just a quicker estimate whereas in the application you are using the full derivation from the CTF, it’s a little tricky because when you have aliasing you are still technically calculating the correct values of the CTF, there is just not sufficient sampling in the FFT to support it as the proper oscillation. Obviously the safest thing to do is avoid the aliasing, but even with some there is probably still room to recover the signal to a level so it safe to estimate in favor of allowing higher defocuses than to over estimate the cutoff and suggest lower defocuses.

@Rasmus_Kock_Flygaard

would there be any advantage of collecting data at lower mag, say 1 Å/px and then work with particles that are not downsampled upon extraction as compared to collecting at this very high mag and have to downsample particles for the sake of box size?

The advantage here is solely one of increasing the number of particles with the larger field of view. This requires another post that I will make now that you have raised it, but it is better to collect at a higher mag and then down-sample than to collect at the lower magnification and not down-sample because of the DQE of the camera. If you are not particle limited, in an image sampled at 0.51Å and then down-sampled to 1Å considering a resolution of 2.2Å you have the DQE dampening this signal much less here at half-Nyquist than if you consider that same resolution when sampled at 1Å and not down-sampled where you now have the DQE of the detector very near Nyquist where it is performing at its worst.

@Rasmus_Kock_Flygaard

Do you know if it makes a difference in Relion in terms of CTF refinements and polishing to have non-downsampled vs. downsampled particles?

There is no difference here that I am aware of.

Hope that helps and again let me know if anything didn’t make sense or needs clarification. I will work on a post on DQE in the coming weeks because I think you raise an interesting question that others have as well.

Best,
Dustin