Possible Technique for Removing Distortion Prior to Martinizing

One approach would be to take each band-merged source, try to backtrack it's position into the component band-frame coordinates to make pseudo extractions, compensate for distortion at the band-frame level, and then generate a new band-merged position for the source. Although this is a feasible approach, there are difficulties associated with it. The positions obtained in band-frame coordinates will never exactly match the original positions. That information was lost when the band merging was done. It would also be difficult to recover the relative weighting factors needed to properly recombine the distortion-adjusted pseudo-extractions. Adding to the complexity would be the need to evaluate possible changes in distortion with time for all three bands.

A more direct, and simpler, approach is to work with the effective distortion of the band-merged positions themselves. These are, after all, the positions which drive the martinizing process. In order to accomplish this, final band-merged 2MASS positions are differenced from a large number of matched USNO-A2.0 positions. It has been previously demonstrated during band-frame distortion modeling, that with biases properly removed, using the higher-density lower-accuracy USNO-A2.0 gives comparable results to using Stone astrometric fields. Biases are removed at the scan level and resulting mean in-scan and x-scan differences are computed as a function of x-scan position. No attempt is made to model variations in the distortion with in-scan position, since these are smoothed out by the frame-to-frame in-scan offsets.

II. Results for Southern telescope:

In order to check for possible variation of distortion with time, the first 10, mid 10 and last 10 Southern nights from the Fall Release dataset were analyzed.

first10 = 980319s 980321s 980322s 980323s 980325s 980327s 980328s 980330s 980331s 980401s
mid10   = 981003s 981004s 981005s 981006s 981007s 981008s 981009s 981010s 981011s 981012s
last10  = 990209s 990210s 990211s 990212s 990214s 990215s 990216s 990218s 990219s 990220s

Mean x-scan difference is plotted as a function of x-scan position for each of the three time periods at the Southern telescope in Figure 1. The first10 set is plotted in red with the binned average values marked with "+" signs. The mid10 set is green marked with "x" signs and the last10 set is blue marked with large dots. Note that all three datasets show very consistent x-scan distortion. This suggests two things. First, that the approach yields repeatable results and second, that there appears to be little or no change in Southern x-scan distortion during the time period covered by the Fall Release. Note that while the x-scan distortion goes through a range of about 0.14 asec, the edge-to-edge difference is only about half that magnitude. It is the uncorrected edge-to-edge differences that are likely to introduce biases into the martinizing.

The plots are repeated in Figure 2 for the Southern in-scan distortion. As with the x-scan distortion, there is little change between time periods. Although the range is much less, the magnitude of the edge-to-edge difference is about the same. Figure 3 combines the data from all three time periods and presents mean in-scan (black line marked with "x" signs) and x-scan (red line marked with "o" signs) differences together.

III. Results for Northern telescope:

Figure 4 and Figure 5 repeat for the Northern telescope the same information presented previously for the Southern telescope in Figures 1 and 2, respectively.

first10 = 970607n 970608n 970609n 970610n 970614n 970615n 970616n 970617n 970622n 970623n
mid10   = 980511n 980512n 980515n 980516n 980520n 980522n 980523n 980524n 980526n 980527n
last10  = 990509n 990510n 990512n 990515n 990516n 990517n 990518n 990519n 990520n 990521n

This time, however, one of the three time periods appears to differ in each case. For the x-scan distortion (Figure 4) it is the first10 time period which differs and for the in-scan distortion (Figure 5) it is the last10.

To shed further light on this, two additional 10-night sets were selected and analyzed. The first additional dataset, "quart1", was taken 1/4 of the way through the Northern nights in the Fall Release and the second, "quart3" was taken at the 3/4 point.

quart1  = 971204n 971205n 971211n 971212n 971215n 971216n 971217n 971218n 980106n 980107n
quart3  = 981115n 981117n 981118n 981119n 981121n 981122n 981123n 981124n 981125n 981126n

Figure 6 and Figure 7 repeat Figures 4 and 5 with the new time periods added. The quart1 dataset is plotted orange marked with "*" signs and quart3 is cyan marked with solid triangles. Note that in both cases the additional data fall essentially on top of the previous consistent data, leaving, as before, only first10 differing in x-scan and last10 differing in in-scan.

Although more runs are needed to determine where the distortion changes in the North, I see no fundamental difficulty. A single night typically provides 25,000 to 30,000 differences, which should be adequate for a reasonably good determination of distortion. Assuming the change occurs at a discrete point in time, that point could be found via a binary search through the observation nights. That should minimize the number of nights which have to be processed to find the break point.