Data items in the AXIS category record the information required
to describe the various goniometer, detector, source and other
axes needed to specify a data collection. The location of each
axis is specified by two vectors: the axis itself, given as a unit
vector, and an offset to the base of the unit vector. These vectors
are referenced to a right-handed laboratory coordinate system with
its origin in the sample or specimen:
| Y (to complete right-handed system)
/ principal goniometer axis
/Z (to source)
Axis 1 (X): The X-axis is aligned to the mechanical axis pointing from
the sample or specimen along the principal axis of the goniometer.
Axis 2 (Y): The Y-axis completes an orthogonal right-handed system
defined by the X-axis and the Z-axis (see below).
Axis 3 (Z): The Z-axis is derived from the source axis which goes from
the sample to the source. The Z-axis is the component of the source axis
in the direction of the source orthogonal to the X-axis in the plane
defined by the X-axis and the source axis.
These axes are based on the goniometer, not on the orientation of the
detector, gravity, etc. The vectors necessary to specify all other
axes are given by sets of three components in the order (X, Y, Z).
If the axis involved is a rotation axis, it is right handed, i.e. as
one views the object to be rotated from the origin (the tail) of the
unit vector, the rotation is clockwise. If a translation axis is
specified, the direction of the unit vector specifies the sense of
Note: This choice of coordinate system is similar to, but significantly
different from the choice in MOSFLM (Andrew G.W. Leslie, Harry Powell,
MRC Laboratory of Molecular Biology, Hills Road, Cambridge CB2 2QH, UK
http://www.dl.ac.uk/CCP/CCP4/dist/x-windows/Mosflm/). In MOSFLM,
X is along the X-ray beam (the CBF/imgCIF Z axis) and Z is along the
All rotations are given in degrees and all translations are given in mm.
Axes may be dependent on one another. The X-axis is the only goniometer
axis the direction of which is strictly connected to the hardware. All
other axes are specified by the positions they would assume when the
axes upon which they depend are at their zero points.
When specifying detector axes, the axis is given to the beam centre.
The location of the beam centre on the detector should be given in the
DIFFRN_DETECTOR category in distortion-corrected mm from the (0,0) corner
of the detector.
It should be noted that many different origins arise in the definition
of an experiment. In particular, as noted above, we need to specify the
location of the beam centre on the detector in terms of the origin of the
detector, which is, of course, not coincident with the centre of the
Example 1 -
This example shows the axis specification of the axes of a kappa
geometry goniometer (See "X-Ray Structure Determination, A Practical
Guide", 2nd ed. by G. H. Stout, L. H. Jensen, Wiley Interscience,
1989, 453 pp, p 134.).
There are three axes specified, and no offsets. The outermost axis,
omega, is pointed along the X-axis. The next innermost axis, kappa,
is at a 50 degree angle to the X-axis, pointed away from the source.
The innermost axis, phi, aligns with the X-axis when omega and
phi are at their zero-points. If T-omega, T-kappa and T-phi
are the transformation matrices derived from the axis settings,
the complete transformation would be:
x' = (T-omega) (T-kappa) (T-phi) x
_axis.vector _axis.vector _axis.vector
omega rotation goniometer . 1 0 0
kappa rotation goniometer omega -.64279 0 -.76604
phi rotation goniometer kappa 1 0 0
Example 2 -
This example show the axis specification of the axes of a
detector, source and gravity. We have juggled the order as a
reminder that the ordering of presentation of tokens is not
significant. We have taken the centre of rotation of the detector
to be 68 millimetres in the direction away from the source.
_axis.vector _axis.vector _axis.vector
_axis.offset _axis.offset _axis.offset
source . source . 0 0 1 . . .
gravity . gravity . 0 -1 0 . . .
tranz translation detector rotz 0 0 1 0 0 -68
twotheta rotation detector . 1 0 0 . . .
roty rotation detector twotheta 0 1 0 0 0 -68
rotz rotation detector roty 0 0 1 0 0 -68
Key Category Items
Items in Category axis