A Data Reduction Proposal

[Tom Droege <tdroege2@earthlink.net>]

I will shortly send out Data Set 20a to Mark Pitts.  Here is a proposal as 
to what might be done with it.  This is just my proposal.  This is what I 
would do if I were up to speed on data analysis.  I might start it and 
instantly switch to something else as I started seeing results.  So if you 
start it there is no obligation to see it through to conclusion.  Here it is:

Hypothesis:  Things that affect the photometry also affect the astrometry.

Discussion:  Andrew has been seeing some affects due to things like 
bad/weak pixels and cosmic rays.  I would propose that weak pixels distort 
the light distribution around a detected star and thus the final position 
determined for the star.   A weak pixel should push the position determined 
away from the pixel.   Likewise a cosmic ray should pull the position 
towards the cosmic ray.  In either case, the position found will be moved 
from the position that would be found for a clean hit.  Of course, this is 
with statistics folded in.  It might not work for every star position 
found, but the hypothesis is that it makes an improvement for a group of 
measurements.  The astronomy for a group of clean measurements should be 
"tighter" than that of a group of "dirty" measurements.  I propose a test 
to see if this is true.

Procedure:

1) Use the Michael Richmond pipeline, or the pipeline of your choice to 
reduce the DS20a data to star lists.
2) Do not throw anything away (except for stars too near the image edges to 
be measured well).
3) In particular, do not require a V, I match to keep a measurement.
4) Sort the data by position.
5) Find stars.  (What?  I thought we found stars in 1?  Well, now we find 
stars by grouping.  We are now in x,y, number of hits space.  Previously we 
were in x, y, intensity space.  We now get a position that is the centroid 
of all the measurements that are clustered near one mean position.  First 
we find the centers of measurement clusters.  Then we extract all the 
measurements for a star at increasing radii from the center.  We will 
probably get position errors of one to two arc seconds from 1) above.  We 
might thus take radii of 1, 2, 3, 4, 5 arc seconds.  The larger the radii, 
the more measurements will be found for the star.  Note that this is not 
new software.  This is what one does to find stars in 1).  It is just that 
now the "intensity" axis is somewhat grainier.)
6) Now make plots of the data sets found for the various search 
radii.  Plot sigma of the measurements kept vs magnitude.  Compare this 
with the expected plot from the statistics as Michael and Andrew have been 
doing in their reduction.  Use this information to decide where to put the 
"cut".
7) Add in the VI pair requirement and compare again.   This is an extra cut 
that might (or might not) improve the result.

There should be hundreds of measurements of each star in each filter so the 
statistics should be pretty good.

I do not see any obvious bias that is introduced by this scheme.  Others 
might see something.  Comments are welcome.

Tom Droege