I am working on a small project which requires me to obtain the proper orientation of a crystal lattice with respect to the gonistat and source. I have until now successfully used the matrices from Mosflm and DENZO, which are consistent with each other and define the orientation of the reciprocal lattice in the lab space when the spindle is at 0deg.

I am trying to use the orientation computed by XDS, but this seems to not be consistent with the others. Here is an example:

mosflm .mat file:
 -0.00458796 -0.01054146 -0.01052990
  0.00600652  0.01617284 -0.00696834
  0.02352343 -0.00618559 -0.00027442
       0.000       0.000       0.000
  -0.1856881  -0.5200068  -0.8337343
   0.2431015   0.7978011  -0.5517381
   0.9520617  -0.3051332  -0.0217278
     39.6412     48.3160     77.5507     90.0000     90.0000     90.0000
       0.000       0.000       0.000
SYMM P222     

(top part is reciprocal matrix in the format:
 a*x  b*x  c*x
 a*y  b*y  c*y
 a*z  b*z  c*z
where x is the x-ray beam axis and z is the spindle axis)

DENZO (HKL2000) gives an equivalent matrix.

XDS orientation parameters:
CORRECT.LP
...
 REFINED VALUES OF DIFFRACTION PARAMETERS DERIVED FROM  30955 INDEXED SPOTS
 REFINED PARAMETERS:   DISTANCE BEAM ORIENTATION CELL AXIS
 STANDARD DEVIATION OF SPOT    POSITION (PIXELS)     0.70
 STANDARD DEVIATION OF SPINDLE POSITION (DEGREES)    0.08
 SPACE GROUP NUMBER     16
 UNIT CELL PARAMETERS     39.528    48.153    77.542  90.000  90.000  90.000
 E.S.D. OF CELL PARAMETERS  4.0E-02 3.3E-02 3.8E-02 0.0E+00 0.0E+00 0.0E+00
 REC. CELL PARAMETERS   0.025299  0.020767  0.012896  90.000  90.000  90.000
 COORDINATES OF UNIT CELL A-AXIS   -37.650    11.269    -4.236
 COORDINATES OF UNIT CELL B-AXIS    14.624    41.546   -19.461
 COORDINATES OF UNIT CELL C-AXIS    -1.764   -32.374   -70.439
 CRYSTAL MOSAICITY (DEGREES)     0.211
 LAB COORDINATES OF ROTATION AXIS  0.999962  0.007232 -0.004834
 DIRECT BEAM COORDINATES (REC. ANGSTROEM)   0.003134  0.005401  1.020962
 DETECTOR COORDINATES (PIXELS) OF DIRECT BEAM    1230.87   1260.93
 DETECTOR ORIGIN (PIXELS) AT                     1226.25   1252.96
 CRYSTAL TO DETECTOR DISTANCE (mm)       259.04
 LAB COORDINATES OF DETECTOR X-AXIS  1.000000  0.000000  0.000000
 LAB COORDINATES OF DETECTOR Y-AXIS  0.000000  1.000000  0.000000
...

(XDS defines spindle as X and beam as Z)

Converted to reciprocal lattice orientation matrix in mosflm axis conventions:
(output from xds2mos; manual calculation is consistent with this output)
 -0.00273114 -0.00809777 -0.01150308
 -0.00724876 -0.01754758  0.00521075
 -0.02353677  0.00634416 -0.00027012
       0.000       0.000       0.000
 -0.11022162 -0.39811300 -0.91068616
 -0.29254071 -0.86269689  0.41252918
 -0.94988163  0.31189970 -0.02138535
     39.5280     48.1530     77.5420     90.0000     90.0000     90.0000
       0.000       0.000       0.000


As you can see they are different. You can note that the component of each vector along the mosflm-Z (spindle) axis is consistent, suggesting that it is only the angle of rotation around the spindle axis that is inconsistent between the two. I know that for mosflm and DENZO the orientation matrix defines the orientation of the reciprocal lattice when the spindle is at 0 deg. XDS seems to be using a different reference point. Why is this and what is the proper way to obtain the absolute reciprocal orientation at 0 deg from XDS?

(If anyone wants to test this on their own, I can provide the frames I used to obtain these files.)