Hi @team,

Wondering if I might have some clarification on the Ewald sphere correction approach, mainly because it seems I have been scooped on a little side project I was considering but thankfully hadn’t started. From the Tutorial:

“As of v3.3, cryoSPARC supports the correction of Ewald sphere curvature during refinement and CTF refinement. While the standard reconstruction of a 3D density is based upon maximizing the likelihood of the data given the image poses, the algorithm used for Ewald sphere correction is an improvement on the “simple insertion” method developed by [3]. This itself is an approximation to the maximum likelihood method, while accounting for the geometry of the Ewald sphere.”

Where reference [3] is M. Wolf, D. DeRosier and N. Grigorieff, “Ewald sphere correction for single-particle electron microscopy”, Ultramicroscopy, vol. 106, no. 4-5, pp. 376-382, 2006. Available: 10.1016/j.ultramic.2005.11.001.

My reading of this is that, unlike in relion, there is no splitting the images into different “sectors” in the single-sideband approach suggested by Russo and Henderson and the Fourier coefficients are added back to the two different (Freidel related) Ewald spheres with the CTF (e^{iχ(k)}) removed, ie. the “simple insertion” method. At the moment relion doesn’t do iterative alignment of 2D images with the 3D model using an Ewald sphere corrected forward model, but it appears that cryosparc now does? I assume iterative refinement of the 3D volume solves the “two Ewald sphere” ambiguity that Wolf et al. spend much of their paper addressing and that Russo and Henderson solve with the “single-sideband” approach?

Appreciate that some of this might be the subject of an upcoming publication but would welcome any extra detail you can give.

Cheers,

Hamish