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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
>
>
>
>