Re: Darks and Flats

["Tom & Lou Krajci" <krajcit@3lefties.com>]

From: "Tom Droege" <tdroege@veriomail.com>

> Jean-Claude Pelle hase recommended a large number of flat, dark, and bias
> frames in equal numbers.  It seems to me that the sigma of the signal is
> much smaller on the bias and dark frames than on the light.  So I would
> think that you need the largest number of flat frames, followed by fewer
> darks, and then still fewer bias frames to get equal noise levels.
>
> Lets say (roughly correct) the noise levels are:
> Frame   Counts       Sigma
> Bias     ?                   7 counts = 17.5 electrons
> Dark    ?                   20 counts
> Flat      20,000          175 counts  (at half full scale)
>
> With 20,000 counts and a scale of 2.5 e- per ADU one would expect a noise
> of 89 ADU just from the statistics.  (SQRT(20,000 x2.5))/2.5 We see more
as
> is expected from a flat that is not even and a CCD that has variations in
> sensitivity.  That is why we are taking a flat.  Experts might verify that
> these numbers are reasonable.
>
> Seems like I should then take 100 times as many Flats as Darks, and 4
times
> as many Darks as Bias frames.  This to get equal noise for the combined
> frames??  Of course, we must take enough bias frames to get rid of cosmic
> rays, so for practical purposes, one might take 5,10 and 50, or some such.

Some thoughts:

If your CCD system is reasonably well temperature regulated...your bias,
dark (thermal), and flat-dark (if you use them...they are darks of the same
exposure time as your flats) frames should not vary from night to night.
(Mine don't vary on my Cookbook CB245...I'll use the same set of master
calibration frames for a couple months after shooting them on a
cloudy/useless night.)  Your flats would vary only from dust accumulation on
the lens, window, etc. or movement of the lens w/respect to the CCD.
Perhaps after a camera is installed at a new site, most of the bugs worked
out...shoot master calibration frames (made from numerous bias, dark, and
flat-dark) on a lousy night for use for the rest of the season.  If there
are large seasonal temperature differences, you may have to shoot a series
of calibration frames in the beginning of the warm and cold seasons.

As for flats...since Tom D. is building each camera from scratch in his
shop...he could take instrumental flats for each CCD before it's put in the
camera housing/lens mount.  An instrumental flat has no vignetting...just
identifies the pixel-to-pixel variations on a chip, and does nothing to
characterize vignetting/scattering/etc of the overall optical system.
However, it can still come in handy if you team up an instrumental flat,
which should never change for each particular CCD chip, with sky flats.  The
sky/twilight flats can give you an idea of vignetting/gradients to correct
for (large scale variations) while the instrumental flat can fix the
pixel-to-pixel variations.  One easy way to make an instrumental flat is to
place the CCD in a dark/baffled enclosure, with a light source several feet
away...if the light source is too close...you will get too much illumination
variation across the chip since the corners are a bit farther from the light
source than the center of the chip.  Some algebra here will tell you how far
away you need the light source to keep the instrumental flat within x
percent of an 'ideal' instrumental flat.

Concerning the number of flats you need...no math proof given here (shame on
me!), but I shoot 36 flats to make a master flat...and I'm getting a
standard deviation of less than 0.01 mag. on my K-C data for time-series
photometry.  I may be able to get away with fewer flats, but it only takes
me 10 minutes to shoot these, so it's no big deal.  (My best night so far
has had std. dev. of 0.006 mag.  Not too shabby for a 12 bit camera.)

On the cloudy nights when I shoot bias frames I'll take 100 to 200 frames to
make a master bias, about 100 for a master flat dark, and I'll take several
hours worth of dark frames for median combining.  Probably overkill, but
this process is largely automated, so I get lots of sleep on those nights.
;-)

Bottom line:  If your system is regulated/constant/repeatable...shoot
calibration frames every several months or so (and instrumental flats only
once in Tom D's shop) ...on clear nights shoot lots of data, and derive sky
flats from the data.  Makes for a more productive night of imaging.  (I'll
spend six hours taking time-series photometry images, then only 10 minutes
taking flats.)

Hope this helps,
Tom Krajci