Distortion Analysis for NSFCam2
   Abstract:  The distortion in NSFCam2 images was measured on the night of April 11, 2006, using two well populated star fields: NGC 5466 and a field just north of the galactic center.  All together, 265 stellar positions were used, and
 the 2MASS catalog was used for the reference coordinates of the stars.  The analysis shows what appears to be a distortion of 0.12" at a distance of 45" from field center.  
   In order for the mapping of large areas to be successful, the distortion of the camera/telescope optics should be smaller than the image resolution.  Distortion is a change in platescale with field angle.  A plot of difference between the distances from the center if the field of view to the star on the sky and this distance on the detector versus field angle will show curvature if there is distortion (a slope merely shows that the adopted plate scale is incorrect).  Thus, on the first night of the engineering run, we made observations with which the measurement of the distortion could be made.  60s K band images of the loose globular cluster NGC 5466 were taken, using beam switching and a 9 pt dither pattern.  Later in the night, the galactic center was observerd using the same parameters.  While the galactic center is too crowded to get good 2MASS astrometry, the B-beam field to the north was well populated with field stars but not too crowded, and thus was also used for this analysis.  For each field, a sky frame was made from the data and subtracted from the data.  The images were rotated to have north up and east left, but NOT coadded.  Should there be significant distortion, coadding aligned images would blur the distortion and potentially ruin the measurement.
   As such, the position of the stars in each of the individual images was measured using the imexam tool in IRAF.  The reference celestial coordinates for these stars was retrieved from the 2MASS catalog.  Since the 2MASS images typically have a resoltion of ~1", this is believed to be the dominant source of the scatter in the plot.  Confusion in these fields reduced the number of stars that could be used for this experiment.  The cloudy weather during the observations also reduced the number of stars that could be seen in some of the images.  Having the detector and sky positions of the stars in each image, the RA and dec of the center of the detector was calculated for each image with offsets from 4 of the field stars.  This was done after it was found that determining the field center with one star was not accurate enough.  Knowing the center of the detector in both sky and detector coordinates, the distance to each star from field center was calculated, both on the sky and on the detector.  The difference between these two measurements was plotted versus the distance of the star from the field center.  This was done for each star in each image, for a total of 265 measurements. The average values of the distortion measurement are:
Field Angle Distortion
0" to 10" -0.0170+-0.1117
10" to 20" -0.0126+-0.1034
20" to 30" 0.0169+-0.1043
30" to 40" 0.0245+-0.1190
40" to 50" 0.1264+-0.1094
Figure 1 :distortion.ps
   The resulting plot as shown includes the data from both fields overlaid.  For each 10" wide bin, I found the average and standard deviation of the data points, and these are shown as the red crosses.  The typical standard deviation of each bin is ~0.1".   The green line marks the trend in the average values of each bin.  Overall, there appears to be a small amount of distortion, which gradually increases to 0.12" at a field angle of 45".  The data do show that there is a trend, but it is statistically consistent with no trend.  As mentioned above, I believe that the dominant source of the scatter in the plot is the accuracy of the 2MASS photometry (especially in fields as crowded as these), with a secondary source being the inaccuracy of the sky coordinates of the center of the field of view.