[Aavso-photometry] Dark-subtracting flat frames

[Radu Corlan]

Greg,

You should definitely subtract darks from your flats. Failing to do this 
will introduce a maximum error of 


err = (Fh - Fl) (1 / F - 1 / (F + D))

where Fh is the highest value on the flat (that is not a bad pixel), Fl is 
the lowest value on the flat, F is the average value of the flat and D is 
the average value of the dark frame (this assumes the dark frame is pretty 
uniform; worse errors may apear in other cases).

As far as noise in concerned, the noise will be greatly dominated by the 
photon shot noise of the flat fields, so you don't need nearly as many 
darks as flats. Let's get an example:

Say you have an average flat value of 10000 electrons. This gives a noise 
level of 100 electrons. The expected noise of a short dark is much less, 
being close to the read noise of the camera, which can be around 20-30 
electrons.

To make best use of telescope time, you should take about 10 times more 
flats than darks in this case (100 / 30) ** 2 ~= 10. Only when the flats 
have a very low level you do need about the same number of darks.

It's not a good idea to use a single dark however, because there is no way 
of elliminating e.g. cosmic rays. better use at least 3.

You can safely use median for combining the darks in this case, as their
noise is not critical. But you may want to consider a more efficient
method of combining flats. Using median will improve noise less that using
the mead for instance. In this case, the factor is 0.65 - which means you
need to combine 2.36 times more frames to get the same noise reduction. Of
course, average doesn't give you any outlier rejection, so it's not always
recommended. However, some kappa-sigma cliping method will get good
outlier rejection and efficiency close to averaging.

I don't thing the order of the operations matters too much. you can make a 
master flat, a master dark and subtract them, create a master dark, 
subtract it from every flat then combine them, or subtract darks from each 
flat - it's going to give pretty much the same result.

Whoever is still reading at this point may have wondered how do you know 
when you've averaged enough flat frames. A quick estimate of the error 
introduced by flat-fielding is:

err = 1 / ( 0.886 * FWHM * sqrt(Nflat) * E)

where Nflat is the total number of electons in all the flat frames 
averaged, E is the combining method efficiency (0.65 for median, 1 for 
average).

This formula assumes that:

1. flatfield noise is photon shot noise limited (true if the flat fields 
   have a relatively large average value - a lot more that the square of 
   the read noise)

2. The flux from each star is considered uniform inside a FWHM-sized 
   circular area (0.886 is sqrt(PI/4)).

Just for fun, to get 0.001 noise contribution from the flat on a 
critically-sampled image, you need to combine flats containing a total 
level of roughly 500000 electrons.

Hope this helps more than it confuses.

Radu




> On Jan 11, 2005, at 8:48 AM, Greg Crawford wrote:
> 
> > In the world of pretty picture imaging there is some discussion about 
> > not
> > needing to dark-subtract flat frames. I wonder how well this applies to
> > photometric imaging?
> >
> > I normally operate an ST9E at -20C and take flats frames of 2 seconds 
> > duration
> > for V,R & I; and 15 seconds for B. My normal routine is to do 32 flat 
> > frames per
> > filter and median combine each filter's flat frames, then dark 
> > subtract a master
> > flat-dark made from either 32 x 2 second dark frames (for V,R, & I), 
> > or 32 x 15
> > second dark frames (for B).
> >
> > Am I adding noise to the master flats, wasting my time, or improving 
> > the quality
> > of my photometry?
> 
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-- 

-------------
Radu Corlan       Snail Mail: Bucuresti sect. 1, 
rcorlan at pcnet.ro  str. Argentina nr. 28, Romania

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