- the spacecraft axes are defined with the
*Z*axis being the NFI pointing axis, the*Y*axis being parallel to the solar array, and the*X*perpendicular to it, as shown in the paylod accomodation figure. - the detector
*xy*mechanical axes are defined by its mechanical mount and are parallel to the strongback axes and to the detector electronic axes (i.e. linearised pixel coordinates) - the detector
*z*axis completes the triad, and is the axis along the gas cell and mirror unit axis. The DU and MU mounting is solidal because of the carbon fiber envelope, and the misalignments are due to its mounting on the spacecraft optical bench. - the first angle
*alpha*corresponds to a rotation around the*Z*axis (rotations must be applied in this order) - the second angle
*beta*corresponds to a rotation around the*y'*axis - the third angle
*gamma*corresponds to a rotation around the*x"*axis - the effect of the three rotations is shown in fig. 4.1.5-I
- the mechanical orientation of the three MECS detectors is such that unit M3
*xy*axes are grossly parallel w.r.t. the spacecraft*XY*axes, while unit M1 and M2 axes are flipped (see fig. 4.1.5-II)

Fig. 4.1.5-I : each panel shows the rotation from the thicker axis system to the thinner one. The first three panels give the individual rotations described above, while the last one gives the overall misalignments. The orientation and rotation relative magnitude corresponds to unit M3, but rotation angles are exaggerated by a factor 100

The relevant coefficients have been calibrated from raster scan observations of
a given celestial sources at known pointings. For all practical applications there is
no significant rotation (within a couple of degrees) around the *Z* axis, hence *alpha* has been fixed
to 0 ° for unit M3 or 180 ° for unit M1 and M2 (to give the same orientation as
the spacecraft axes), while angle *beta* corresponds to a shift of about 10 arcmin
along the *x* axis for all detectors, and *gamma* is smaller (between half
and 2.5 arcmin) with uncertainties of about a quarter of arcmin.

Fig. 4.1.5-II : orientation of MECS units with respect to the
spacecraft *XY* axes

The effect of this is that if the satellite is pointed with its *Z* axis on the
target, the latter will be positioned behind the strongback. This is visible in the
first light pointing.
The pointing strategy takes account of this, and compensates, placing the source close
to the MECS centre, as in the
second light pointing.

The coefficients are stored in files
`m{1,2,3}.misalignment`
and are used by software for
conversion
between image and sky coordinates.