Applying flat field and dark
frame corrections
Flat field frames
Flat fielding corresponds to correcting the combined optical-system and
CCD throughput at each pixel so that each pixel on the CCD would
respond equally to a source with the same photon flux. Flat
fielding removes the effect of the pixel-to-pixel sensitivity
variations across the array as well as the effect of dust or scratches
on the CCD window, and vignetting by the telescope or camera lens
optics. A flat field frame must be produced for each
filter/lens/telescope combination to obtain good results. The
flat-field frames are obtained by photographing an evenly illuminated
target at very close range (and therefore out of focus) or by shooting
the sky near dusk or dawn. The prior technique using a halogen
illuminated flat white target is preferrable because the light level is
more easily controlled and can be performed carefully at leisure rather
than hastily, in the field. If the CCD is cooled and the
exposures are reasonably short, then the dark (thermal) count may be
neglected. It is best to shoot several frames (at least ten) and
average these to reduce the noise. The more, brighter, frames the
better, however the CCD should be operated well away from saturation
where the response may be nonlinear. In the case of the Pyxis
camera, anything below 50,000 ADU is acceptable. The flat field
generation tool (see multiple file
processing) simplifies the process of creating the flat field
frames by first subtracting the offset level from each selected flat
field image, and averaging the images together.
Dark or thermal count frames
During long integrations at moderate cooling a significant amount of
charge can accumulate in the CCD pixels due to thermal
excitation. The purpose of producing dark or thermal count images
is to subtract the contribution from thermally generated charge in the
image. Professional astronomers overcome the problem of dark
charge by cooling their CCD's to temperatures near the boiling point of
liquid nitrogen (~77K). This of course is not practical for most
amateurs, so moderate cooling between -20 °C and -40 °C using a
thermo-electric cooler is usually employed. Inevitably, for
integrations longer than 5 minutes, the dark count will begin appearing
in certain pixels on the CCD which have particularly high dark
currents; these are referred to as "hot-pixels". It is the
hot-pixels that cause the greatest problem in the image degradation
because they are often as bright as some of the dim stars in the image,
so that simple thresholding to remove the hot-pixels often results in a
significant loss of image information. Median filtering is
helpful in removing the hot-pixels because these are often isolated,
however the median filter can significantly "soften" the image,
especially in cases when the PSF is less
than 2-3 pixels wide.
The dark count may be subtracted if a dark count image is available
that exhibits less noise than the
dark count contribution in the image being processed. This
last point is very important; if the dark count image to be subtracted
has more noise than the image to be processed, then subtraction will
actually lead to an increase in noise! This means that dark count
images must be obtained for much longer integration times (at the same
cooling temperature) as the original image to be processed.
Alternatively, many dark count images may be obtained and averaged,
however the noise will be higher when multiple images are averaged due
to the higher read noise compared to reading a single image with an
equivalent total integration time. The integration should not be
so long that the hot pixels approach saturation. Management of
the dark count frames is somewhat easier than for the flat field frames
because the same dark frame can be applied to all images, regardless of
what filters or optics were used to produce the image. A tool is
provided to create an average dark count-frame from the dark-count
images (see multiple image processing).
How are the photometric frames
created?
Internal to the Pyxis firmware is a routine that estimates the dark
count and offset level in each image acquired. The dark count is
obtained from a portion of 4 shielded CCD rows in the KAF-401/1602
sensors; this is saved as the image parameter
"BottomThermalCount". The offset (or bias) level is determined by
averaging 1000 "overscan" horizontal CCD pixels so that no thermal or
photo-electrons are measured. For the Pyxis KAF-401 camera, the
offset is typically 4000-6000 ADU; it is saved as the image parameter
"BiasLevel".
The procedure for creating the dark-count and flat-field frames is
identical. The "BiasLevel" is subtracted when the images used to
create the flat-field or dark frames are summed so that only the
contribution from thermally or photo-generated electrons remains.
The summed images are then scaled so that the maximum intensity in the
sum-image is 65535; the maximum value for a 16-bit unsigned
integer. The median value in the center of the image is computed
and assigned to the "BiasLevel" parameter of the image.
How are the photometric
corrections applied?
The dark count frame should always be subtracted first because the dark
count is not affected by the effective CCD pixel sensitivity nor the
number of photo-electrons collected at the pixel. If the
automatic routine is used in the multiple file processor, then the dark
frame intensity is weighted by the ratio of the "BottomThermalCount" in
the image to be processed to the "BiasLevel" in the dark count
image. The "BiasLevel" in the dark count image should
represent the median intensity in the image, if the "Create thermal
frame" function on the multiple image processing form was used.
The purpose of the prior subtraction of the bias and later scaling of
the dark count frame is to allow dark count frames obtained for
different integration times to be used. Otherwise, dark count
frames must be produced for each integration time used, which is rarely
practical.
The "flat-fielding" operation consists of dividing the intensities in
the image to be processed (minus the offset level of the image) by the
flat-field image. The resulting image is automatically scaled in
intensity so that the most is made of the dynamic range of a 16-bit
integer. An important point to remember is that the flat-fielding
produces an image whose pixel intensities more accurately reflect the
light intensity of the imaged object, however the connection of the
pixel intensities to the collected pixel photo-electrons is lost due to
the somewhat arbitrary scaling used in the flat-fielding
procedure.
Note that if the multiple image processing tool is employed, then three
options are available to determine the bias to subtract from the
images. The bias can be estimated from a histogram of a
rectangular region of the image, determined from the quoted value in
the image header or a fixed value can be selected. The first
method is not recommended because the bias estimate will also include
contribution from sky glow. If you are worried about a fixed
pattern in the image offset frame (that is a frame obtained in the dark
under conditions where the thermal count is negligible) then a series
of offset frames can be generated and subtracted from the images prior
to dark-frame and flat-field correction. During flat-field and
dark-frame correction the bias to subtract should then be set to
0. Note that no fixed pattern has been noticed in the Pyxis
KAF401e prototype camera offset frame - the spatial (meaning from pixel
to pixel in the same image) and temporal (meaning from frame to frame
looking at the same pixel) noise properties of the offset frames are
identical.