Computing Distortion Using USNO-A2.0

H.L. McCallon 10-30-98

Up until now distortion has been computed from special scans of Stone's astrometric fields. See descriptions of distortion calculations for the North and South using Stone fields. Keeping in mind that we are only interested in relative positions for the distortion analysis, it should be possible to use an inherently lower accuracy catalog such as the USNO-A2.0 to determine the distortions. Provided pertinent biases can be removed, the increased standard deviation of the USNO-A2.0 can be compensated for by using more points. Being able to use the USNO-A2.0 to compute distortion has some definite advantages. Since all calibration scans are reconstructed using the USNO-A2.0, there is no need to re-run PosFrm with a new set of reference stars before beginning the analysis. Any sufficiently large set of calibration scans can be used as input to the distortion analysis.

As a test of concept, I took the calibration scans from the night of 981005s, which happened to be on line, as input to the distortion analysis. After any remaining biases were removed a band at a time, the USNO-A2.0 sources used as reference stars by PosFrm were mapped into individual band-frame coordinates. These were matched to 2MASS extractions with high quality positions and position differences were computed. After some trimming, the x-scan (dx) and in-scan (dy) differences were fitted separately for each band to the following polynomial:

         del =c1*x^2 +c2*y*x^2 +c3*x*y +c4*x*y^2 +c5*y^2 +c6*x +c7*y +c8 +c9*x^3 +c10*y^3

Figure 1 plots the average x-scan distortion in J-band as a function of x-scan frame position in the upper-left panel and as a function of in-scan frame position position in the lower-left panel. Note that the units are pixels. The in-scan distortion is plotted in the two panels to the right. The same presentation is made for H-band in Figure 2 and for K-band in Figure 3. In each plot the solid black lines refer to the measured distortion distortion and the dotted red lines to the polynomial fit.

The average difference values from these plots show more variation than seen in the Stone South distortion analysis. The modeling, however, smooths out those variations and ends up quite close to the Stone results. This is illustrated by Figure 4, which compares J-band model distortion using the USNO-A2.0 (dotted red line) to that obtained using the Stone field (black line). The comparison is repeated for H-band in Figure 5 and K-band in Figure 6.

The matches are not bad and should get even better if more USNO-A2.0 differences were used. Given that the scatter from a USNO-A2.0 fit is about three times as large as that from a Stone fit, one would expect to need three squared (9) times as many sources to get the same model quality. Using all the calibrations from the night of 981005s falls far short of that criteria:

              Stone Count    USNO-A2.0 Count   Ratio USN/Stone

     J-band    15528           23591            1.52
     H-band    14826           20208            1.36
     K-band    14422           12259            0.85