This memo discusses the extent and characteristics of the band-to-band position shifts using data from the night of 970514. The night included a set of engineering test scans selected to exercise the telescope over a range of hour angles and zenith distances with relatively high density fields.
The band-to-band shifts first noted from the night of 970418 are confirmed, with the H-band, once more, responsible for the largest shifts. Furthermore, a sizable shift (1/3 pixel) was observed during a single scan. Large shifts during a scan will degrade the position reconstruction.
In order to analyze the band-to-band relationships a 2D (5 parameter) linear fit of J2-H2, J2-K2 and H2-K2 was was done for each scan. The translation (dx & dy), rotation (dtheta) and scale (dsx & dsy) parameters were solved for each of the three band-to-band relationships in each scan. For the dozen 6 degree scans, the same parameters were computed on a frame-by-frame basis within the scans.
Figure 1 contains plots of the dx and dy position differences between bands as a function of scan number. The lettering in the plot is too small to read easily, so here is the key. The top (bottom) panels is the difference between bands in the in-scan (cross-scan) direction. The leftmost panels are J-H, the middle panels are J-K, and the rightmost panels are H-K. The y-axis spans 2 pixels total in all plots.
One can deduce a fair amount from this figure. Since the range of the dependent variable (dx or dy) is the same for all 6 plots, it's obvious that H-band is, by far, the biggest contributor to the shift. Less obvious, but significant, is that J2-K2 differences, while much smaller, are well correlated with the other two band-pairs In one case the correlation is positive and the other negative. The correlations can be seen in Figure 2 which plots H2-K2 vs J2-H2, J2-K2 vs J2-H2 and J2-K2 vs H2-K2 (left to right) for both dx (upper panels) and dy (lower panels). Note that these plots are auto-scaled.
Figure 3 once more contains plots of the dx and dy position differences, but this time w.r.t. the hour angle at the start of scan. As with Figure 1, the dependent variable range is set to be the same for all 6 plots. The J2-K2 differences are more tightly grouped and show a small linear trend in dx with hour angle. The other two band-difference pairs show both a greater dependence on hour angle and more scatter. Figure 4 presents the same plots w.r.t. zenith distance.
All four figures to this point are consistent with flexure driven by telescope orientation but also dependent on it's last position. This is further illustrated by Figure 5 which plots a history of dx vs dy for each band-difference pair throughout the night. Dotted lines connect the points in scan order. These are auto-scaled to best show the history; so one must take care in comparing differences between the three plots. Note that for the H-band related plots (J2-H2 and H2-K2) the points fall into two groupings at opposite corners. In each case there is a single point which lies mid-way between the two groups. This point corresponds to scan 36 which is of considerable interest.
As mentioned previously, the five parameters which define the 2D linear transform between each band pair were computed on a frame-to-frame basis for each of the 6 degree scans. The five parameters are plotted as a function of frame number for a typical scan (033) in Figures 6, 7 and 8. Small linear trends in dx and dy can be seen as a function of frame number, much like those in scan 033, can be seen in all but one of the dozen scans fitted on a frame-by-frame basis. Scan 036 had much larger shifts over the scan, as can be seen in Figures 9, 10, and 11. It appears thatin most cases the large shifts occur during the slews between scans, but in this case much of the shift appears to have occurred during the scan, rather than the slew. Note that as with the scan-to-scan changes, H is the culprit, with a change of approximately a third of a pixel in both dx and dy.
Changes within a scan are much more troublesome to the position reconstruction algorithm than changes from scan-to-scan. The latter can be fitted out, the former cannot. The current model in PosFrm assumes a single 2D linear transformation defines the relationship between each band pair over a scan. To the extent that assumption is not true, errors will creep into the solution. The current algorithm has no way to remove them. I can't say that a shift the size observed in scan 036 would cause that scan to fail to meet the requirement, but depending on what else was going on in the scan it might. In any case, it makes me very nervous; it would certainly reduce the reconstruction accuracy significantly.
One has to wonder whether even larger shifts might occur over a single
scan. Remember that we have observed scan-to-scan changes of over
1.5 pixels (3 asec). It appears the prudent course would be to change
PosFrm to model the dx and dy between bands as a linear function of
frame number.
