[fitswcs] I've got this FITS WCS matrix

[Malcolm J. Currie]

I've been given some Gemini NIRI data.  The WCS headers are listed
below.

CTYPE1  = 'RA---TAN'           / the coordinate type for the first axis
CRPIX1  =     1281.62863446163 / x-coordinate of reference pixel
CRVAL1  =    0.698405727933413 / first axis value at ref pixel
CTYPE2  = 'DEC--TAN'           / the coordinate type for the second axis
CRPIX2  =     433.151678256953 / y-coordinate of reference pixel
CRVAL2  =     35.8161778878783 / second axis value at ref pixel
CD1_1   = 6.02715759044019E-06 / partial of first axis coord w.r.t. x
CD1_2   = 1.27956486107373E-08 / partial of first axis coord w.r.t. y
CD2_1   = -1.6056794631393E-08 / partial of second axis coord w.r.t. x
CD2_2   = -5.96793770760736E-06 / partial of second axis coord w.r.t. y

Now for the purpose of registration in a pipeline I need to know the
rotation from this CD matrix to determine the approximate locations of
the source after dithering.  Using Equation 191 from WCS Paper II, I
find that rho_a is 179.84 degrees and rho_b is 0.12 degrees to two
decimal places.  What should one do in such cases?

Back in April I had recommended to the Gemini people that it excludes
shear from their model that fits to a grid, since the detector doesn't
have any.  They just need a rotation, and scaling matrix (I did also say
that using CDELTn and PC matrix would be clearer).  I believe that the
orientation is 180+/-small change, but I have data for one night where
the rotation came out as 89.3 for both rho_a and rho_b.  Only one of
three nights do the two values agree within the errors and lie near 180
degrees.

Malcolm Currie
Starlink Project