The crystal orientation matrices are defined in reference to a particular coordinate system, which is different in Mosflm, Denzo and XDS. This document tries to summarize the necessary informations to convert matrices from one coordinate system to the other. Note: Mosflm and Denzo are using to distinct coordinate systems for the gogniosta and the detector (the X and Y axis of the detector are not the same that defines the crystal orientation).
The crystal orientation matrix is defined relative to the camera (goniosta) coordinate frame. See the complete definition at http://www.mrc-lmb.cam.ac.uk/harry/mosflm/mosflm_user_guide.html#a3.
Z is parallel to the incident radiation beam. X is parallel to the spindle axis, from the crystal to the goniometer base. Y is the so-called "vertical" axis is perpendicular to the spindle and beam axes.
In terms of crystal orientation rotations: rotz would again denote rotations of the crystal around the beam axis, rotx would denote rotations of the crystal about the spindle axis and roty would denote rotations about the axis perpendicular to the beam and the spindle.
In XDS, the crystal orientation matrix, the detector cooordinates and the goniosta system are defined relative to a laboratory coordinate frame. This definition makes it possible to descibe any possible experimental setup. The complete description of this coordinate system is available here: http://www.mpimf-heidelberg.mpg.de/~kabsch/xds/coordinate_systems.html.
However, in the distributed XDS input files, the most common orientation for the beam is along the Z axis.
|
|
|
MOSFLM |
DENZO |
XDS |
|
|
Beam along |
X |
Z |
Z |
|
|
Rotation axis along |
Z |
X |
X if the rotation axis is horizontal (most
common on synchrotron) |
|
|
Third axis |
Y = Z × X |
Y = Z × X |
Y = Z × X |
[Q] are permutation matrices to go from one UB matrix to the other ([UBmos] = [Qdnz2mos] [UBdnz])
|
Qdnz2mos = |
0 |
0 |
1 |
Qmos2dnz = |
0 |
0 |
1 |
||||
|
1 |
0 |
0 |
1 |
0 |
0 |
||||||
|
0 |
1 |
0 |
0 |
1 |
0 |
||||||
|
Qdnz2xds(1) = |
0 |
1 |
0 |
Qxds2dnz(1) = |
0 |
1 |
0 |
||||
|
1 |
0 |
0 |
1 |
0 |
0 |
||||||
|
0 |
0 |
1 |
0 |
0 |
1 |
||||||
|
Qmos2xds(1) = |
0 |
0 |
1 |
Qxds2mos(1) = |
0 |
0 |
1 |
||||
|
0 |
1 |
0 |
0 |
1 |
0 |
||||||
|
1 |
0 |
0 |
1 |
0 |
0 |
||||||
|
(1) In the case that the rotation axis is horizontal and perpendicular to the beam direction. |
In all the data processing programs the crystal orientations matrices are written with a specific format in an ASCII file. These format are described bellow.
The REFIX format used by mosflm is the following:
Content |
Description |
Fortran Format |
UB11 UB12 UB13 |
UB = setting matrix |
3f12.7 |
UB21 UB22 UB23 |
3f12.7 |
|
UB31 UB32 UB33 |
3f12.7 |
|
dummy |
|
3f12.7 |
Ur11 Ur12 Ur13 |
Ur = reference orientation matrix |
3f12.7 |
Ur21 Ur22 Ur23 |
3f12.7 |
|
Ur31 Ur32 Ur33 |
3f12.7 |
|
cell |
cell parameters |
6f12.4 |
phixyzr |
(mis)setting angles |
3f12.4 |
Example:
-0.02097959 -0.00902253 0.00277554
0.01076026 -0.01447723 -0.00303052
0.01271281 -0.00263528 0.00714553
0.000 0.000 0.000
-0.78320117 -0.52269857 0.33672263
0.40169735 -0.83873395 -0.36764740
0.47458947 -0.15268128 0.86686404
36.5750 56.7600 118.8580 90.0000 90.0000 90.0000
0.000 0.000 0.000The *.x file contains in the first
lines the following informations: