Given the read out noise in ADU, RON
the conversion factor in e-/ADU, CF, and the number of counts,
the uncertainty on
is given by
The Gunn r night 2+ flats (of which there are 11), where combined in one round. The combination was made using combine with the following parameters different from the default: lsigma = 2, hsigma = 2, scale = mean, weight = mean, nkeep = 1, grow = 2. The intention with scaling was, that the different flats, which have different levels, should be scaled to a common level, so that sigma rejection can be used, after which they should be scaled back, and then made into a weighted average. Unfortunately, it seems that combine does not scale back, leading to the output being just an unweighted mean. The uncertainty should not be much higher due to this, since the individual flat field images have similar levels (within a factor of less than 4 at worst). It also means, that the uncertainty on the combined image is very easy to calculate.
Table lists the
levels in ADU, Ni,
and the uncertainties on the individual flats,
is calculated from Eq. ()
(using N = Ni).
They also lists the scale factors, si, and the weights, ai,
but these quantities do not enter the uncertainty equations.
To calculate the uncertainty on the combined GR flat,
we apply Eq. () to the individual
(calculated from Eq. ),
The Johnson B and U night 2+ flats (of which there are 12 and 13, respectively), were combined in two rounds: first in 3 groups of 4 or 5 images, and then these 3 images were combined. The combination on both levels were made with combine using the same parameters as for Gunn r (the so-called scaled weighted mean). The two-level combination was used to make sure that no objects (stars) would make it to the final flat field, since there was not applied any offset of the telescope between the individual flats from night 6 (where only JB and JU flats were taken). Table and Table lists the levels in ADU, Nij, and the uncertainties on the individual flats, , with calculated from Eq. () (using N = Nij). They also lists the scale factors, tij, and the weights, bij, but these quantities do not enter the uncertainty equations.
To calculate the uncertainty the combined JB flat,
we apply Eq. () to the individual
in each of the 3 groups,
To calculate the uncertainty the combined JU flat,
we follow the same procedure as for JB:
The levels used
to calculate the relative uncertainties
(Eq. , , and ),
are the levels in the section
[25:800,25:925]. This section is in some sense ``normal'',
as opposed to the right and upper edge, which is more sensitive in the blue
than the rest of the chip.
The levels in the entire frames are
3733 ADU (GR), 4710 ADU (JB), and 4591 ADU (JU).
If these values are used for calculating the relative uncertainty,
we get 0.35% (GR), 0.30% (JB), and 0.30% (JU),
so there is only a small difference.
Even though the chip is more blue-sensitive in the right and upper side, it is still linear in that area. This was checked using 10 JU dome flats with levels of ADU (dfsc1649-1658, exptime 10 sec), and 10 with levels of ADU (dfsc1659-1663, exptime 5 sec; dfsc1664-1668, exptime 7 sec). The high and the low level images were separately combined, and the quotient of the 2 resulting images was made. This quotient images had a gradient in the x-direction of < 0.05%, and in the y-direction of < 0.1%, which is very small. The quoted numbers are (maximum - minimum)/2.
The relative uncertainties are summarized in Table (p. ).
Properties of E and S0 Galaxies in the Clusters HydraI and Coma
Master's Thesis, University of Copenhagen, July 1997
Bo Milvang-Jensen (email@example.com)