Re: Everett and Howell Paper

[Stupendous Man <richmond@a188-l009.rit.edu>]

  As my previous message on this topic shows, I think that
the flatfielding is the major source of uncertainty in Mark IV
photometry.  Andrew is right that using the median of a bunch
of star-filled images is not as good as the median of a bunch
of images free of stars.  The best way to go is probably to
make a flatfield illuminator.

  However, one alternative which WILL improve the flatfielding
is to use twilight sky flats.  If one takes pictures of the sky
as the sun goes down, one will begin with saturated images.
As the sky darkens, the images will stop being saturated, yet
have very high signal levels in each pixel (in the case of the
Mark IV, just below saturation, about 60,000 electrons per pixel).
If one continues to take pictures, stars will begin to appear
as the sky level decreases.  Eventually, one ends up with 
ordinary night-sky images: a very low background sky level and
prominent stars.

  In that set of images, there will be a "sweet spot" in which
the sky level is still high enough to provide many electrons
and to overwhelm most stars, but low enough to avoid saturation.
By combining those twilight sky images with a median filter, one
will end up with a "flatfield" image of very high signal.  I believe
that such a "twilight sky flat" is probably superior(*) to a
purely "night sky flat", even though it is formed from fewer
images.

    (*) for some purposes -- see below

  Good references for twilight sky flats are available on-line: see

         Chromey and Hasselbacher, PASP 108, 944 (1996)
             http://adsbit.harvard.edu/cgi-bin/nph-iarticle_query?
                    bibcode=1996PASP..108..944C

         Tyson and Gal, PASP 105, 1206 (1993)
             http://adsabs.harvard.edu/cgi-bin/nph-bib_query?
                    bibcode=1993AJ....105.1206T&db_key=AST&high=3be715a47116845

  Tom brings up a good point:

> But It would 
> probably be flat in detail, not in the whole picture.  I.e. it would make a 
> flat that was good for fixing pixel to pixel variations, but not so good 
> for frame side to side.  What it more important?

  Indeed, since the Mark IV has a large (4x4 degree) field of view,
it will see a portion of the twilight sky which is NOT of uniform
brightness: the side of the field closer to the setting sun will be a
bit brighter than the other side of the field.  These variations 
(of size roughly 1% per degree) will lead to errors in the relative
measurements of stars on one side vs. stars on the other side of
the field -- it's true.  On the other hand, if one concentrates on
a small section of the entire image (as Andrew noted in his messages),
then this large-scale variation becomes very small.   AND, if one
is interested only in the CHANGE in brightness of a given star
relative to its neighbors, then such large-scale gradients can
be ignored completely.

  So, IF your goal is to measure changes in brightness very precisely,
then a high-signal flatfield image with some large-scale variations
is just fine -- and much better than a low-signal flatfield image
made from a combination of night-sky images.

  On the other hand, if your goal is to measure accurately the 
magnitudes of stars all the way across the frame, in order to make
a photometric catalog, then you should NOT use a twilight sky flat,
because it WILL introduce systematic errors of a few percent.
Instead, you might choose the low-signal night-sky flatfield image:
it will cause a larger (random) scatter, but a smaller (systematic)
error within each frame.

  It is even possible to combine a high-signal flat (twilight sky
or dome flat) together with a low-signal flat (from the night sky)
in order to get the best of both worlds: tiny fractional uncertainty
per pixel, and accurate corrections from one side of the field
to the other.  That's a complicated business, but it can be done.

  My approach here is going to be to try to make twilight sky
flats, and use them in ordinary reductions.  However, after I've
extracted magnitudes for stars in the cleaned images, I will then
look for systematic errors in photometry as a function of position
on the frame.  How?  I'll take a grid of images of a field,
shifting the telescope by, say, 1 degree up/down or left/right each
time.  With, say, a 5-by-5 grid of images of the same field, one 
can determine the systematic errors as a function of position ...
and therefore the CORRECTIONS which need to be made.  See
the paper

          Manfroid, A&AS 113, 587 (1995)
             http://adsbit.harvard.edu/cgi-bin/nph-iarticle_query?
                   bibcode=1995A%26AS..113..587M

  The most important thing is to figure out exactly what is the main
scientific goal of the Mark IV observations, and then make sure that
your reduction procedures will support that goal.

                                            Michael Richmond