Howard, Ken, Gene, and Bill discussed alternate possible methods of implementing the Version 3 distortion correction on 18 September. This covers the main considerations and conclusions of that meeting, with some additional e-mail clarifications and expansions immediately afterwards. We considered the following possible solutions:

1. In BANDMERGE, adjust each star cross-scan co-ordinates x and in-scan co-ordinates y, based on Howard's curve of observed average position errors as a function of x only.

2. In PROPHOT, correct each of the (typically six) positions of the source candidate, both in x and y, at the point the frame dithers are applied, using Howard's distortion map for frame co-ordinates x & y.

3. In PROPHOT, after the source position has been determined from the chi-square minimization fit, apply a correction to both the fitted x and y co-ordinates of the source, just before writing the output .ps file. This would be an average of the frame corrections from Howard's distortion map, that would reflect the true number of frames actually available for the fit.

1. For fix at BANDMERGE, advantage is a fairly simple removal of the mean observed x and y effect. The big disadvantage is that the correction is only in the mean, as a function of x, as frame y co-ordinate of the sources are no longer known, so no correction based on y is possible. Only source positions are affected. John Fowler would be needed to make the changes to BANDMERGE, which are deemed fairly minor.

2. For the fix to the dithers in PROPHOT, the advantage is that improved registration of the six input frames would clearly benefit both positions and photometry to some unknown degree, probably small. Disadvantages are complexity and the possible need to modify the PSFs in some way. While modification of the pixels co-ordinates appears to be possible at a single point in PROPHOT, the situation with the PSFs and PSFMAKE is more complex.

   Ideally for this method, in PSFMAKE one would have to take each input star and correct its shape at the same time as it is centroided. The result would be a best-estimate of the on-axis, central PSF. Then both the position and shape of the PSF would be adjusted in PROPHOT as a function of frame x and y, in accordance with the distortion model. This could be done, eg, by a mathematical transformation of the central PSF, based on the distortion map. The question of whether to adjust only PSF position or also shape has not been investigated. On the one hand, the distortion information we have deals only with positions obtained from source locations. On the other, the shape of a star is known to have some dependence on x,y co-ordinates in the frame.

   One relatively simple, minimal alternative would be to not touch PSFMAKE, but only adjust PSFs in PROPHOT, by a translation (and conceivably an area-conserving shape transformation), of the unmodified input PSFs based on frame x and y and the distortion map. The input PSFs we have now tend to have the right centroid (just by being averages of many stars) and circular shape, being smeared by the average over uncorrected stars. Adjusting their positions in PROPHOT should help, but of course cannot undo the smearing. There would surely be some effect on the photometry, presumably an improvement, due to the improved registration of sources in the frames and somewhat more accurate PSFs. Nevertheless, this minimal method would still be non-trivial to implement and the results problematic to predict.

   However implemented, changes in this group would affect both positions and photometry. Considerable testing would clearly be required to verify the effects and insure that unforeseen problems are not introduced. Ken and or possibly Bill would have to make the changes, and both are heavily committed. Any changes to PSFMAKE would probably have to be done by Ken.

3. Advantage of this method of the correction to PROPHOT fitted positions is simplicity relative to (2) and improved position correction compared to (1), plus no need for John Fowler's time. Main disadvantage is that improved registration of the six frames obtained in method (2) would be lost. Only source positions would be affected, not photometry. Ken or probably Bill could make the changes, which appear to be fairly straightforward.

Based on the above, and considering our available resources before Version 3 must be operational, we four recommend (3) as the best solution.

27 September 2000, by Bill Wheaton