What is our plate-scale and pixel-to-pixel spacing ?

We'd like to know the distance in arcminutes from the center of one
pixel to the center of an adjacent pixel.  The plate-scale at the
SPARO detector arrays is then obtained by dividing by the physical
separation of the pixels, which is 3.05 millimeters from the center of
one pixel to the center of the adjacent pixel.  Finally, the reimaging
in SPARO is 1:1, so the plate scale at the detectors should equal the
plate scale at SPARO's focal plane in the snout (e.g. at "field
lens").  This last quantity can be directly calculated from the Viper
ray tracing, providing a sanity check on SPARO's optics.

Also, we want to confirm the 22 degree "rotation" of the arrays on the
sky that is part of SPARO design.

We observed the SPASE absorber in Jan/Feb 2000, and
centered this source in each of SPARO pixels 2, 4, 5, 6, and 8.  (See
logbook 6, p. 22).  Thus we determined these pixels' "boresights" (e.g. found
pointing locations of each pixel).  The El center was not very well
determined, but the az center was accurately determined, by finding
the half-power points.  A quick analysis gives a pixel-to-pixel
spacing of 3.2 arcmin. A more careful analysis (see "boresight
analysis" below) takes advantage of the fact that the az positions are
well determined but the El positions are not, and gives:

->  pixel-to-pixel spacing = 3.5 arcmin

->  Inferred plate scale at the detectors = 1.16 arcmin/mm   

->  Rotation of array: 25 degrees

In Fall 2001, again using the SPASE source, we measured the following (log. 6, page 130):

->  pixel-to-pixel spacing = 3.28 arcmin

->  Inferred plate scale at the detectors = 1.08 arcmin/mm   

->  Rotation of array: 29.5 degrees

Compare these with:

->  Predicted plate scale (ray-tracing) = 0.98 arcmin/mm

->  Rotation of array (design): 22 degrees


Boresight analysis (using data from Jan/Feb 2000)

First, assume a 22 degree array rotation.

Based on the separation in azimuth of R4 (0.056 degrees) and R6 (0.053
deg.) to the average (from three scans) of R5, the plate scale is

R2 and R8 should then be 0.022 degrees away from R5 in azimuth.  In
actuality, R2 is 0.021 degrees off and R8 is 0.029 degrees off.  This
means R2 has a 21 degree rotation and R8 has a 29 degree rotation, which
averages to a 25 degree rotation (from normal Az-el axes).

Use this array rotation to determine a new plate scale from the R4-5-6
azimuth separations.  When this is done, you get 1.18'/mm for the plate

In the first case the focal length is 2.972m.  (In the second case the
focal length is 2.906m.)


Theoretical plate scale:

After checking out the plate scale on beam3, we get a ps = 0.98'/mm.  This
would give a 2.94' pixel spacing, with a focal length of 3.516m.