Multiple oscillations in tilt/trefoil plot

Hi,

In a recent refinement, I have a fair bit of beam tilt - around 1.4mrad.

This manifests in the tilt/trefoil plot like this:

Is the second oscillation (where it goes from blue to red and then back to blue again) expected? This does not seem to be modeled, even if I select a resolution range in which it is included in the data:

Cheers
Oli

1 Like

For comparison, these are the observations and fits from Relion:

1 Like

I’ve recently run into this exact situation-- were you ever able to get an answer? Or was relion better able to handle it?

Hi @olibclarke and @dgoetschius,

We’d like to take a look into this phenomenon, and it would help if we had data that can reproduce this. If either of you are willing to confidentially share data with the CryoSPARC team (and still have access to the data causing the phenomenon!), please let me know in this thread or via DM, and I can follow-up with further instructions.

Best,
Michael

1 Like

Happy to provide data! I think one of ours may be on EMPIAR - will double check and update

I believe it was this one:

The micrographs are on EMPIAR, the particles are not on my GPU presently but I can retrieve them from backup if that’s more convenient?

EDIT: confirmed, this is the one! I have the particle stack, just let me know the easiest way to send and I’ll transfer it over

1 Like

Hi @mmclean, an exported refinement job showing this behavior with all links dereferenced is being uploaded to cryoem3; file name is J311.tar.gz.

Let me know if you received the file, and if you need any more info!

Cheers
Oli

1 Like

Hi @olibclarke,

Thanks for the speedy reply and for uploading the data! File received alright, just extracting now and will let you know if any questions/issues come up. Thanks again!

Best,
Michael

1 Like

Hi @olibclarke,

After looking more closely at the data, I believe this is a benign plotting artefact. The “data for odd terms” plots (where the multiple oscillations show) hold the per-pixel estimated phase residual in radians. So it’s the per-pixel independent estimate of the phase residual modulo 2pi, because phases are only uniquely determined up to additions of 2*pi. So where the second band of blue/red values start, that’s actually the phase wrapping around from pi to -pi (discontinuously).

The “fit” plots show the regression results of the phase residual (regressing across all pixels in the image) as per Zivanov et al. Here they vary continuously over frequency (by construction of the regression, because the phase is expressed as a linear combination of continuous zernicke polynomials) and aren’t limited to [-pi, pi], so no wrapping happens when they exceed this range.

Here’s a scatterplot of the raw data (“data for odd terms”) vs. the predicted phase (“fit”) and this confirms that they are the same +/- 2pi, so still indicating a strong agreement between data and fit.

We may be able to alter the plotted quantities slightly to make it clear that the effective difference between these two quantities is actually ~0 for all frequencies.

Best,
Michael

3 Likes

Gotcha, that is a helpful explanation, thanks Michael!

1 Like