[3dem] [External] Re: Cs question

Mon Feb 16 15:39:51 PST 2026

Hi,

If your pixel size is off, both defocus and Cs are refined to absorb the pixel size error.
This gives a very good CTF fit but the resulting values are non-physical.
Please see this:
https://urldefense.com/v3/__https://relion.readthedocs.io/en/release-3.1/Reference/PixelSizeIssues.html*cs-and-the-error-in-the-pixel-size__;Iw!!Mih3wA!FsTUSEahBrII222EDKqoF8yl3yDTXuEv4acHbTZs6iNxcUeVcnEIrQvLLVuClPKv_GJTEcTuc9W8UftXyAmk3V7XgCWFz-hcvPg$ 

Best regards,

Takanori Nakane

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From: 3dem <3dem-bounces at ncmir.ucsd.edu> on behalf of Morgan, David Gene via 3dem <3dem at ncmir.ucsd.edu>
Sent: 17 February 2026 8:31
To: zbyszek; Ruben Diaz Avalos
Cc: 3dem at ncmir.ucsd.edu
Subject: Re: [3dem] [External] Re:  Cs question

Hi,

Thanks for that information.  We have come up with a Cs value on a Thermo Arctica that is significantly different from what Thermo says it should be (our value is about 3.0 while Thermo says it should be 2.7) and so I wondered what others have found.

I was surprised that our refined value was so different (more than 10%).  However, I just looked at changes in calculated CTF curves for these very different values of Cs, and the changes are tiny.  Probably too small to have any impact on the structure...

I would still like to know whether others find refined values near manufacturers' suggestions, and whether our value is an outlier.

Again, thanks for the information.

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            David Gene Morgan
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             IU Bloomington
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Subject: [External] Re: [3dem] Cs question

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Hi Ruben and David,

I ran similar tests (refinement of Cs) on both Thermo and JEOL instruments. On the Thermo systems, I consistently obtained values close to 2.7 across at least 10 different instruments for high-resolution structures, with small deviations that are well explained by Ruben’s description. I also didn’t see any resolution improvement from refining the Cs value.

Best regards,

Zbyszek Otwinowski

On 2026-02-16 15:47, Ruben Diaz Avalos via 3dem wrote:

Hi David,

Nominal Cs is fundamentally a hardware property of the objective lens and pole piece geometry, and manufacturers determine it from the electromagnetic lens design. For a Krios, the stated value (~2.7 mm) is not empirical tuning but a well-characterized design parameter. In principle, it should not vary significantly between microscopes of the same configuration.

What we refine in image processing, however, is not a direct physical measurement of the lens geometry, but the coefficient of the k^4 term in the CTF phase function. In Zernike language, this corresponds primarily to the radially symmetric fourth-order component (the Z4^0 term of the wave aberration). In practice, that fitted coefficient can absorb small modeling imperfections — residual coma, higher-order aberrations not explicitly modeled, envelope inaccuracies, or subtle systematic phase errors. So the "refined Cs" should be interpreted as the best-fit fourth-order phase term under the assumptions of the refinement model.

In one of our datasets (TMV, refined to 1.8 Å), the refined Cs converged to 2.7 mm when processing the full dataset. Importantly, pixel size is extremely well calibrated in this case because TMV provides a very precise internal ruler via its layer-line spacing and helical repeat, so I am confident that pixel size error is not significantly contributing to the k^4 term.

Out of curiosity, I split the dataset into three arbitrary subsets and refined them independently. The refined Cs values were 2.75 mm, 2.69 mm, and 2.8 mm. When I recombined all particles, the final reconstruction was essentially identical to the original 1.8 Å map, with no meaningful change in resolution or map features.

So empirically, at least in this regime, a ~2–3% variation in the refined Cs did not have a noticeable impact on the outcome. That is not entirely surprising, since the phase error introduced by a small fractional change in Cs remains modest over the spatial frequency range that carries usable signal, especially compared to the dominant defocus term.

It would certainly be interesting to test the robustness more aggressively by starting from a deliberately incorrect Cs (for example 2.5 mm) and seeing whether refinement converges back to the nominal value and whether map quality degrades in the process. But based on this dataset, small deviations from the manufacturer value appear to be well tolerated at ~1.8 Å.

Ruben.

Ruben Diaz Avalos,

La Jolla Institute for Immunology.

On Mon, Feb 16, 2026 at 1:07 PM Morgan, David Gene via 3dem <3dem at ncmir.ucsd.edu<mailto:3dem at ncmir.ucsd.edu>> wrote:

Hi,

For those of you who have used any of the image processing programs to refine the Cs value for your microscope, how does the refined value compare to what the manufacturers claim?

As I understand it, the manufacturers simply calculate a Cs value for each microscope/pole piece model.  I guess I have always assumed that those values are relatively accurate, but I don't really have any data to support that.  Nor am I certain what would constitute "relatively accurate."

Any thoughts would be appreciated.  Thanks.

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NOTE:  my email has changed to dagmorga at iu.edu<mailto:dagmorga at iu.edu>.
             Email to dagmorga at indiana.edu<mailto:dagmorga at indiana.edu> will stop being
             forwarded later this year.

    politics is more difficult than physics.
                                             A. Einstein

            David Gene Morgan
        Electron Microscopy Center
             043E Simon Hall
             IU Bloomington
          812 856 1457 (office)
          812 856 3221 (3200)
      https://urldefense.com/v3/__http://iubemcenter.indiana.edu__;!!Mih3wA!FsTUSEahBrII222EDKqoF8yl3yDTXuEv4acHbTZs6iNxcUeVcnEIrQvLLVuClPKv_GJTEcTuc9W8UftXyAmk3V7XgCWFVFWjLz8$ <https://urldefense.com/v3/__http://iubemcenter.indiana.edu__;!!Mih3wA!GtPRGTEs6TwC_HvS-grWkxuNLZZrTPkNnxibfaqE1R2wuugqzQRLCXxNTJ6tcwkHZ9lKP0Ewa1fN0w9zI0Y$>
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