[gnuastro-devel] [task #14124] Magnitude error in MakeCatalog

[Mohammad Akhlaghi]

URL:
  <http://savannah.gnu.org/task/?14124>

                 Summary: Magnitude error in MakeCatalog
                 Project: GNU Astronomy Utilities
            Submitted by: makhlaghi
            Submitted on: Thu 18 Aug 2016 06:30:09 PM JST
         Should Start On: Thu 18 Aug 2016 12:00:00 AM JST
   Should be Finished on: Thu 18 Aug 2016 12:00:00 AM JST
                Category: MakeCatalog
                Priority: 5 - Normal
              Item Group: Enhancement
                  Status: In Progress
                 Privacy: Public
        Percent Complete: 0%
             Assigned to: makhlaghi
             Open/Closed: Open
         Discussion Lock: Any
                  Effort: 0.00

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Details:

Currently MakeCatalog can output the magnitude of an object, but it doesn't
calculate the magnitude error. MakeCatalog does calculate the signal-to-noise
ratio (S/N) however. 

Converting from the S/N to the error in estimating the magnitude is an easy
operation (detailed below) which can be done with something like AWK, but it
is common enough to justify its inclusion as a column in MakeCatalog.

To derive the error in measuring the magnitude from the S/N, let's take `F' as
the flux, `Z' is the zeropoint, `M' is the magnitude, `S' is the S/N, and `D'
to stand for capital delta (or error in a value) then from

    `M = -2.5*log10(F) + Z'

we get the following equation after calculating the derivative with respect to
F.

    `dM/df = -2.5*( 1/(F*ln(10)) )'

>From the Tailor series <https://en.wikipedia.org/wiki/Taylor_series>, `DM' can
be written as:

    `DM = dM/dF * DF'

So 

    `DM = |-2.5/ln(10)| * DF/F'

But `DF/F' is just the inverse of the Signal to noise ratio, or `1/S'. So 

    `DM = 2.5 / ( S * ln(10) )'

Note that this is just the raw flux measurement S/N, it does not include
correlated noise, or aperture errors (which are also present in a realistic
situation). This will be noted in the manual.

Maybe later, we can find ways of including these extra error sources directly
in MakeCatalog (with the help of NoiseChisel in the form of FITS header
values, ofcourse).




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