The FCLS coordinates are, according to Ted Dunham's email in Feb of 2013 and stated in a previous TAAS post, millimeters and the DAOF TAAS FCLS corresponds to a SOFIA platescale of 4.16" per mm. From the difference between top and bottom image locations, I calculate an EXES platescale of
17.96mm / 376.2 pixels = 0.04774 mm/ pixel
or
0.04774 mm / pixel * 4.16 " / mm = 0.199" / pixel
Our design number comes assuming we are F/10 and have 25 micron pixels and is:
2.06e5 arcsec * 25 microns/pixel / 2.5e6 microns / 10 = 0.206" arcsec/pixel
Looks like we are <4% off from the design number. Good enough.
For rotation, I first considered the angle between our slit long axis and our columns. This comes out to be 10.6 degrees (determined by using IDL ROT(image,angle) function and seeing what angle gives best alignment of top and bottom of the slit). Our slit is rotated -10.6 degrees clockwise from our columns
Comparing our slit to the FCLS x,z coordinates, I first plotted the FCLS coordinates for the spot and noted that the top of the slit ends up in the lower left corner of the plot. This means our slit is rotated
180 + atan(fcls_x / fcls_z) = 231.3 degrees
clockwise from the FCLS Z axis. Assuming the FCLS axes correspond to +elevation (+x) and +cross elevation (+z), this means we are rotated 231.3 degrees clockwise from the cross elevation axis.



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