Convert aniso Mag to motion_corr2

CTF Refinement
1

Dear all,
I have refined the anisotropic mag parameters for the data collected from a microscope using global CTF refinement. I obtained the parameters like this:
Anisotropic Mag: [[-0.00571369 -0.00932393] [-0.01013075 0.00451204]]
Anisotropic Mag Determinant: 0.99867812
I am wondering if there is a way to convert these parameters to Motioncorr2 format, so I can correct the aniso Mag during motion correction.
In Motioncorr2, three inputs are needed including magnifications along major and minor axes and the angle of the major axis relative to the image x-axis in degree.
Thanks,
Lei

2

Hi @rainfieldcn,

This isn’t a full answer, but to point you to a recent discussion about interpreting the anisomag matrix, its worthwhile to checkout this post: Help interpreting the anisotropic magnification matrix - #2 by mmclean.

After adding the identity and taking the singular-value decomposition (SVD), I believe the singular values would give you the magnifications along two orthogonal axes (major and minor). The angle relative to the image x-axis would probably be derivable from the rotation matrices (U or V) but I am not entirely sure if it would correspond to the angle relative to the x or y axes of the image.

Best,
Michael

1 Like
3

Hi Michael,

Could you clarify what the Anisotropic Mag parameter represents? Does it indicate the anisotropy present in the image, or is it the parameter used to correct anisotropy back to circular?

Thanks,
Lei

4

Hi @rainfieldcn,

Discerning between the two is somewhat nuanced as it depends on which representation you’re interested in (Real or Fourier), and the distinction also must be made between active or passive transformations.

In CS: If the anisomag matrix given in the event log (or in the particle cs file) is M, then the matrix I + M specifies a passive transformation on coordinates in Fourier space, where I is the 2-by-2 identity matrix. In other words, the anisomag matrix indicates how coordinates in the fourier pixels (x and y values) should be transformed in order to take “stretched” coordinates to “true” coordinates.

If primes (‘) represent coordinate values in the original basis (i.e. what is present in the micrograph), and subscript 0 represents coordinate values in an undistorted basis, then the relation between the two is:

Screenshot 2025-12-15 at 5.15.11 PM
Screenshot 2025-12-15 at 5.15.11 PM714×208 4.83 KB

Does this help clarify their meaning?

Michael

5

Hi Michael，

Yes. Your explanation is very clear.

Thank you very much!

Lei