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Re: Calculation of mag errors



Many thanks to Michael for going through this analysis.  Now we know.

The alternative would be to eliminate the flattening stage.  I have always
used only the linear correction. I don't want to remove this flattening
stage since it results in much better looking images, but will if you all
tell me I should. It is much easier to find a star in images that have had
this correction when one is just lookig at them.

Michael writes:
------------------------------
  A very easy, simple thing to do is to run a few examples of
ensembles of real Mark IV data, look at a few graphs, and make
up a simple table somewhat like this:

         if mag is      uncertainty is
           V = 7          0.02
           V = 8          0.03
           V = 9          0.04
                   etc.

Place the calculations and the table into a Tech Note.  Refer to the
Tech Note somewhere on the Mark IV database web pages.
--------------------------------------
Michael, "we" have already done something like this (well just all the
data not ensembles) and published it in S&T10 whose authors are T. Droege
and M. Richmond. OK the curve in S&T10 is for all the (then) MarkIV data. 
Seems to me that this is an upper limit on the error which I am comortable
to claim.

I would be quite happy for Michael S. to just report a value from this
curve as the uncertainty for the engineering data.  I don't see how to get
anything better.

Tom Droege

>
>   I have figured out the reason that the database values for
> uncertainty in each measurement do not agree with Andrew's
> calculations.  The difference is .... sky-subtraction.
>
>   Andrew (and I, in a followup) went through the calculations
> of photon noise due to the star+background, and compared it to
> the signal in the star.  We measured the sky background value
> from a Mark IV image, and measured star signal from the same
> Mark IV image.   We found the uncertainty in the instrumental
> magnitude for a V=12 star should be close to 0.06 or 0.07 mag.
>
>   I took advantage of Tom's data storage to look in detail
> at one particular V-band image which matches one particular
> V-band measurement in the database.  The database shows
> V=11.927 with uncertainty 0.020 mag.  The processed image
> I grabbed from Tom's disks has had
>
>              - dark subtracted (good)
>              - flatfield divided out (good)
>              - sky background fitted and subtracted (uh-oh)
>
>   Tom found that a number of the Mark IV images had large-scale
> variations, even after flatfielding, so I put into the pipeline
> an option to fit a low-order polynomial (order 1 = linear or
> 2 = quadratic) to the background sky, then subtract that model
> from the image, before searching for stars.  I believe
> that Tom does use the sky-subtraction in his normal
> processing.
>
>   Now, this means that the mean sky level in the processed
> Mark IV images is close to zero.  That means that the
> program which extracts instrumental magnitudes from the image
> calculates a very small background noise level -- since it
> believes that the mean sky level in an annulus surrounding
> the star will indicate the noise level.  The trouble here
> is that we've basically subtracted a big fixed number from
> all sky values, so the extraction routine ends up with
> a background noise value much lower than is proper.
>
>   I went through the calculations for this one particular
> star in this one particular sky-subtracted image.  If I
> use the sky-subtracted pixel values, I end up with an
> uncertainty of about 0.018 mag in my calculations by
> hand (using square apertures -- don't ask, but it's close
> enough for these purposes).  If I instead put back something
> like the original sky value into the pixels, and repeat
> the calculations, I end up with an uncertainty of 0.052 mag.
>
>   The value of 0.052 mag is pretty close to the typical
> uncertainty for a V=12 star which Andrew derived for
> one particular image on his own.  I think this means we
> have found the discrepancy.
>
>   Consequences?
>
>      - the values for instrumental magnitude uncertainty
>            in the Mark IV database are big underestimates;
>            we knew that already, since they don't take into
>            account systematic errors in flatfielding,
>            but now we see that the databased values don't
>            even provide accurate measurements of uncertainty
>            in the relative magnitude across a single frame.
>
>   Hmmm.  Before this week, I would have told someone to ignore
> the uncertainty values for _most_ purposes.  Now, I would tell
> someone to ignore them for _all_ purposes.
>
>   Fixes?
>
>      - I can imagine several ways to propagate the information
>            about actual sky levels into the calculation of
>            uncertainty in instrumental magnitude.  It would
>            mean modifying the TCL scripting code which runs
>            the pipeline and _possibly_ the C code of the
>            "phot" program within the XVista package.
>
>      - we can make available to users of the database some
>            better measure of the actual uncertainty in each
>            measurement.  There are several possibilities:
>
>              a. based on ensemble solution to all stars within
>                 a small local area (i.e. based on Mark IV data)
>
>              b. based on "theoretical" calculations of the
>                 sky brightness, star signal, etc., of the
>                 Mark IV systems
>
>              c. a simple table of values, based on some
>                 real data and/or theoretical calculations
>
>            I imagine these would all be _random_ uncertainties.
>            One could also try to calculate
>
>              d. the uncertainty in the actual V or I magnitude,
>                 combining random uncertainties with systematic ones
>
>   A very easy, simple thing to do is to run a few examples of
> ensembles of real Mark IV data, look at a few graphs, and make
> up a simple table somewhat like this:
>
>          if mag is      uncertainty is
>            V = 7          0.02
>            V = 8          0.03
>            V = 9          0.04
>                    etc.
>
> Place the calculations and the table into a Tech Note.  Refer to the
> Tech Note somewhere on the Mark IV database web pages.
>
>   _If_ we desire, we could modify the Mark IV database scripts
> (I say, "we", but Michael S. would have to do it, of course)
> to use the simple table to look up a value on the fly
> and place that value into the "uncertainty" column of the
> output.  In other words, we _could_, if desired, leave the
> Mark IV database as it is, not changing any values in
> the stored records, but add a bit of code to the
> access scripts so that they use a table value for the
> quoted uncertainty instead of the value stored in the database.
>
>   See, that is relatively quick, painless, and easy to do.
>
>   Making changes to the pipeline so that future extracted
> magnitude values have proper _instrumental_ uncertainties
> would be nice, I suppose.  I suspect that we will always
> pay little attention to these uncertainties....
>
>   Comments?
>
>                                     Michael Richmond
>
>
>
>