Position Reconstruction Analysis (ORT3) plus Recommendations
Document number: WSDC D-T016

1. OVERVIEW

Analysis of the ORT3 position reconstruction reveals some problems. Presented herein are conclusions regarding the nature of those problems, followed by recommendations for improvement and finally the supporting analysis.

1.1 Background

Some definitions and background explanations are in order before proceeding. The term "20-parm" refers to a 20-parameter (2 translation, 1 rotation & 2 scale for each of the 4 bands) SFPRex fit which simultaneously ties the 4 bands to each other and to the 2MASS reference stars. The term "3-parm" refers to a scaled back fit where only 3 parameters (2 translation & 1 rotation of the shortest wavelength band only) are fitted for. Apriori knowledge of scale factors and band-to-band relationships are used to fill in the other 17 unfitted parameters. If the fit is done using apriori position knowledge refined only by the pattern matcher it is referred to as "1st pass". If the frameset has already been refined by a previous SFPRex fit it is referred to as "2nd pass". Thus the "2nd pass" fit has the advantage of a better starting point. Currently the pipeline does a 1st pass 3-parm fit which is passed on to downstream processors. A 2nd pass 20-parm fit is also done for every frameset with the results used for trending purposes only.

The SFPRex Merged Point (SFMP) file contains band-frame extractions which have had distortion removed, been bandmerged within SFPRex and mapped onto the sky using the final band-frame reconstructions, yielding RA:DEC positions. It is suitable for astrometric verification of the SFPRex solution. Note that although the SFMP includes single-band sources (needed for MFPRex) as well, normally only the multi-band merged sources are used for astrometric verification. For the 3-parm case, however, one is forced to use single band sources since that's all that's available. Herein "SFMP3p" will be used to refer to the SFMP files generated by the 1st pass 3-parm processing and "SFMP20p" to refer to those resulting from the 2nd pass 20-parm processing.

1.2 Conclusions

  • The 1st pass 3-parm SFPRex band-frame reconstructions currently used by the downstream pipe are far worse than the 2nd pass 20-parm reconstructions. This appears to result from:

    •       a) Sensitivity of SFPRex reconstruction accuracy to large apriori frame position errors

          b) Apriori scale and band-to-band errors which are not fitted for with the 3-parm solution

  • Systematic differences observed between the SFPRex solution (represented by SFMP) and the final positions (represented by MDEX) are also too large.

    1.3 Recommendations

    Obviously, the efforts to identify the source of the sensitivity of SFPRex reconstruction accuracy to large apriori frame position errors should be continued with high priority. In addition, the following actions are recommended:

  • Provide the capability to use 2nd pass 20-parm band-frame reconstructions to feed the downstream pipe. Even if not considered acceptable for generating data to be used in the catalog, having this capability would prove very useful for both testing purposes (as will be discussed in the analysis section) and during IOC when band-to-band relationships and scale factors are not as well known. This would provide a mechanism to remove the effect of errors in our apriori knowledge of scales and band-to-band on downstream pipeline processing until everything is properly calibrated. It would also show what the properly calibrated results should look like, thus giving us a target to aim for.

  • Reduce any position biases introduced post-SFPRex to negligible values. Failing that, fit them out. Assuming a test with the 20-parm solution passed downstream shows MDEX-SFMP20p differences similiar to the MDEX-SFMP3p differences from this test, the problem needs to be addressed. These systematic differences need to be reduced to negligible values. They are presumably caused by centroiding differences between single band-frame and coadd extractions. Unintended differences in how distortion is handled in SFPRex vs. elsewhere might also have some impact, as well as other as yet unidentified causes. On 2MASS we gave up the attempt and simply fitted out the differences in the PosPts processor; it worked fine. Of course in 2MASS we were using the equivalent of the current SFMP20p, so we were comparing bandmerged to bandmerged.

    • 2. ANALYSIS

    Both the mean SFMP-2MASS and the mean MDEX-SFMP differences averaged over a frame should be very small. Small SFMP-2MASS differences demonstrate that the SFPRex band-frame solutions are true to the 2MASS reference system. Small MDEX-SFMP differences demonstrate that unwanted biases have not been introduced downstream of SFPRex.

    2.1 SFMP vs. 2MASS

    As can be seem in Figure 1 where frame average RA differences are plotted as a function of frame number (3-parm in the top panel, 20-parm in bottom) there are problems with the 3-parm results. It is likely that both the order of processing and the fact that only the RA, DEC and rotation angle in band 1 are fitted for during 3-parm processing are significant. In Figure 2 the same pair of plots are presented for DEC. These look even worse. The relative merits of the 3-parm vs. 20-parm results are driven home by Figure 3 which compares histograms of SFMP-2MASS differences (dRA in the top panel and dDEC in the bottom). Figure 4 presents the RA population sigma values as a function of frame number (3-parm in the top panel, 20-parm in bottom). The fact that they become large for the 3-parm, but not the 20-parm, probably reflects apriori scale errors which aren't fitted for in the 3-parm. Figure 5, which looks very similar, presents the same plots for the DEC sigmas.

    If the SFPRex reconstruction accuracy is sensitive to apriori band-frame position errors then it should show up when the SFMP-2MASS differences are plotted as a function of apriori position error. At first glance Figure 6, which plots dRA (top panel) and dDEC (bottom panel) as a function of the overall RA correction determined, seems confusing. The reconstruction errors appear expanded with both large and small RA correction magnitudes and less so in between. They may even be worse at the small end. This will be explained shortly. Figure 7 presents the same plots as a function of DEC correction. This time the results for both dRA and dDEC are noticeably worse at large absolute values of DEC correction. To better understand the previous two figures, consider Figure 8 which plots the DEC corrections for ORT3 as a function of the RA correction. When the DEC corrections have their largest absolute values, the RA corrections have their smallest. It all makes sense if one assumes apriori DEC errors are the dominant driver for both dRA and dDEC reconstruction errors.

    2.2 MDEX vs. SFMP

    Figure 9 plots the MDEX-SFMP3p differences as a function of frame number with dRA in the top panel and dDEC in the bottom. The magnitude of the vertical range is the same in both, allowing a direct comparison. These differences trend out to 150 mas of dDEC, with individual points reaching as far as 200 mas in one direction. Although the SFMP3p-2MASS differences can become this large (in rare instances even larger) in either direction, a comparison of SFMP3p-2MASS and MDEX-SFMP3p difference histograms in Figure 10 shows the MDEX-SFMP3p differences are perhaps an even greater contributor to the systematic errors overall. In fact, it appears from the comparison of SFMP20p-2MASS and MDEX-SFMP3p difference histograms in Figure 11 that if the current 2nd pass 20-parm band-frame solutions were passed downstream, instead of the 1st pass 3-parm solutions, the post-SFPRex biases could become dominant.

    There may be some comparison of "apples and oranges" going on here since SFMP3p contains single-band sources and MDEX bandmerged sources. Some of the observed differences may stem from that. For the ORT3 runs SFPRex used in-house conversion routines rather than the WCS routines. Previous testing has shown negligible differences, but for consistency we should use the same WCS routines used elsewhere in the pipe. We need to run a test where the 20-parm band-frame solutions are passed to the downstream pipe. Then we can compare bandmerged SFMP20p positions to the bandmerged MDEX positions.

    Figure 12 presents population sigmas for dRA (top) and dDEC (bottom) as a function of frame number. Note that the sigmas are somewhat higher for DEC over most of the frame number range. It also shows marked variation with frame number whereas RA doesn't. Don't really know the cause of this behavior but suspect it has something to do with apriori scale and/or band-to-band errors. Again a test with the 20-parm results used downstream might shed some light. Finally Figure 13 presents dDEC as a function of dRA for the MDEX-SFMP differences, resulting in an image resembling a pair of earphones with cords attached. Am drawing a blank as to the cause of the dual populations with the connecting arcs in this figure, but suspect it's probably a clue as to what's causing the differences.

    Last update - 8 October 2009
    Howard McCallon - IPAC