User talk:Tnakane

This page is for drafting. DO NOT TRUST information on this page.

Orientations

Transformation by orientations and translations brings the reference into observations (i.e. particle image).

For developers, a good starting point for code reading is ObservationModel::predictObservation() in src/jaz/obs_model.cpp.

Coordinate system

In compliance with the Heymann, Chagoyen and Belnap (2005) standard RELION uses a right-handed coordinate system with orthogonal axes X, Y and Z. Right-handed rotations are called positive.

Image center

The center of rotation of a 2D image of dimensions xdim x ydim is defined by ((int)xdim/2, (int)(ydim/2)) (with the first pixel in the upper left being (0,0). Note that for both xdim=ydim=65 and for xdim=ydim=64, the center will be at (32,32). This is the same convention as used in SPIDER and XMIPP. Origin offsets reported for individual images translate the image to its center and are to be applied BEFORE rotations. This is confusing, because stored rlnOriginX/Y are from the reference to particles and applied AFTER projection...

Euler angle definitions

Euler angle definitions are according to the Heymann, Chagoyen and Belnap (2005) standard:

* The first rotation is denoted by phi or rot and is around the Z-axis.
* The second rotation is called theta or tilt and is around the new Y-axis.
* The third rotation is denoted by psi and is around the new Z axis

As such, RELION uses the same Euler angles as XMIPP, SPIDER and FREALIGN.

Contrast Transfer Function

CTF parameters are defined as in CTFFIND3, also see the publication by Mindell et al (2003).

Higher order aberrations

rlnOddZernike contains coefficients for asymmetric (antisymmetric) Zernike polynomials Z₁^-1, Z₁¹, Z₃^-3, Z₃^-1, Z₃¹, Z₃³, etc in this order. rlnEvenZernike contains coefficients for symmetric Zernike polynomials Z₀⁰, Z₂^-2, Z₂⁰, Z₂², Z₄^-4, Z₄^-2, Z₄⁰, Z₄², Z₄⁴, etc in this order. Thus, the 7-th item in the rlnEvenZernike, Z₄⁰, is related to an error in the spherical aberration coefficient.

Look at the table in Wikipedia https://en.wikipedia.org/wiki/Zernike_polynomials#Zernike_polynomials but ignore square root terms, as the coefficients are not normalised in RELION. For example, Z₃^-1 = (3r³ - 2r) sin θ = 3 (k_x² + k_y²) k_y - 2 k_y, where k_x and k_y are wave-numbers in the reciprocal space (1 / Å).

Anisotropic magnification corrections

Transformation by anisotropic magnification brings the reference into observations (i.e. particle images) in real space. Note that stretching in real space is shrinking in reciprocal space and vice versa.

rlnMagMatrix_00 to rlnMagMatrix_11 represent the matrix M in the section 2.4 of our preprint. The values become larger when the observed particle in the real space looks larger than the reference projection at the nominal pixel size. This also means that the true pixel size is actually smaller than the nominal pixel size.