Recalculating Spatial scale for cross-dispersed modes, HIGH_MED and HIGH_LOW using header keywords

(correct) SLTH_PIX=                   65 / Slit height in pixels                          

(wrong) SLTH_ARC=               11.173 / Slit height in arcseconds     

The final pipeline products have these keywords, but the second one is wrong because of a misstep in the EXES_READHDR and EXES_TESTTORT routines. The past data archive is too large to correct without a concerted effort, but using Matt's email below, we can find the correct slit height in arcsec with just the information available in the headers of the pipeline products.

SLTH_PIX is correct. It is the average number of spatial pixels found on the orders of flat field, and adopted for the reduction. 

The other header keyword "ECHELLE" is the input angle, alpha and that lets us correctly calculate the slit height in arcsec, accounting for the anamorphic magnification

These lines of IDL will return a better value for the slit height

hdr=headfits("*SPC*") ; or "*WVM*

npix = sxpar(hdr,"SLTH_PIX")

alpha = sxpar(hdr,"ECHELLE")

pixscale0=0.201 ; arcsec

delta=5.43

slitheight=pixscale0 * cos((alpha + 5.43)*!dtor)/cos(alpha*!dtor)*npix

print, slitheight

Matt's email, Feb 3, 2021

"Hi Curtis (I added everyone else since anamorphic magnification is, I think, an interesting optical property of using gratings in plane diffraction (as opposed to Littrow)),

If you want to read all the details, it is in this post and its comments:  

http://codgermmck.blogspot.com/2016/08/hi-med-spatial-plate-scale-with-fcls_26.html

If you just want the formula, it is:

observed platescale = platescale * cos(beta)/cos(alpha) 

where 

platescale = 0.201"/pixel

alpha = input angle (from header)

beta = alpha + delta = output angle

delta = 5.43 degrees = difference between input and output beams.  

delta, remember,  was supposed to be, I thought, 2.715 degrees or half of the number required to fit the data.  I wonder if I got the half angle stuck in my head.  Curtis, do you remember how far apart the input and output beams are on the cross-disperser mirror?  

John's drawing of zemax beams on the acad components (optics+zemax.jpg in eE/optics is probably the best place to see it) makes it look like a little less than 2" between beam centers. With 40" as the distance from the echelle grating to the mirror, atan(2/40.) = 2.86 degrees which is close to my 2.715 degree number, so I'm still confused unless the input/output beams are more like 4" apart.

-matt"