12.3 Bias and Dark Noise
171
To obtain this figure, a large number of calibration frames need to be generated and
compiled into a three-dimensional FITS cube (FITS files can be multidimensional)
with axial directions x and y being the horizontal direction and vertical direction of
the individual frames, and axis z being the individual calibration frames. By taking
the standard deviation through the z-axis, you obtain a two-dimensional collapsed
FITS frame. There are several methods you may use to determine the noise within
the calibration frame set. The author normally takes the mean value of the collapsed
frame as the noise value for the set.
To find the noise within the bias and dark calibration frames, we cannot just find
the standard deviation between our frames, as these include hot, cold, dead, and
stuck pixels. The variability of pixel sensitivity is addressed by the application of a
flat field frame and will be part of the flat field noise. As hot, cold, dead, and stuck
pixels always give the same value, they do not generate significant noise in time
series differential photometry, as we are looking at the change in brightness, and
these pixels do not change in value. This comes, however, with the proviso that the
target and check stars have not drifted in the image, a problem that is discussed later
in the chapter.
Typically, a dark or bias frame should have a low mean pixel count, as we are
detecting only read noise and thermal electrons. This means that pixels stuck at a
low value (often zero) or high value (often the saturation limit) will report a cross
frame standard deviation of zero. This, in turn, will falsely reduce the calibration
noise figure we are trying to find. We therefore have to remove the bad pixels before
calculating our final uncertainty.
There are two points in the process at which we can do this. Either we can address
the problem at the individual frame level or we can address it at the final, collapsed,
frame level. Computationally, the second method is easiest, and we have to perform
the processes only once. In both cases, you will need to perform some kind of
clipping, whereby values outside of a given range are discarded or replaced with
another value, normally the mean. This might be sigma clipping, whereby data with
values outside a specified number of multiples of the standard deviation are moved
or replaced. Sigma clipping can be dual-tailed, where the top and bottom ranges are
removed, or single-tailed, where only one end is removed. An alternative method
is a numerical clip, where values outside a specified range are clipped. This range
is normally determined from a frequency plot of the pixel values and, like sigma
clipping, can be at either end or both ends of the pixel value range.
Clipping the collapsed frame has the advantage of being faster, but pixels that are
inherently low noise might be excluded, as they will have a low standard deviation
(as will most bad pixels, although for different reasons).
Another alternative is to identify the bad pixels at the single-frame level using a
reverse sigma clip, whereby only bad pixels are left, and then use this as a mask to
apply to the collapsed frame.
Whichever method you choose, there is, at the time of writing, no single application that can perform all the steps needed. However, it is relatively straightforward
to produce a Python script using AstroPy and Numpy to achieve this process, and it
171
To obtain this figure, a large number of calibration frames need to be generated and
compiled into a three-dimensional FITS cube (FITS files can be multidimensional)
with axial directions x and y being the horizontal direction and vertical direction of
the individual frames, and axis z being the individual calibration frames. By taking
the standard deviation through the z-axis, you obtain a two-dimensional collapsed
FITS frame. There are several methods you may use to determine the noise within
the calibration frame set. The author normally takes the mean value of the collapsed
frame as the noise value for the set.
To find the noise within the bias and dark calibration frames, we cannot just find
the standard deviation between our frames, as these include hot, cold, dead, and
stuck pixels. The variability of pixel sensitivity is addressed by the application of a
flat field frame and will be part of the flat field noise. As hot, cold, dead, and stuck
pixels always give the same value, they do not generate significant noise in time
series differential photometry, as we are looking at the change in brightness, and
these pixels do not change in value. This comes, however, with the proviso that the
target and check stars have not drifted in the image, a problem that is discussed later
in the chapter.
Typically, a dark or bias frame should have a low mean pixel count, as we are
detecting only read noise and thermal electrons. This means that pixels stuck at a
low value (often zero) or high value (often the saturation limit) will report a cross
frame standard deviation of zero. This, in turn, will falsely reduce the calibration
noise figure we are trying to find. We therefore have to remove the bad pixels before
calculating our final uncertainty.
There are two points in the process at which we can do this. Either we can address
the problem at the individual frame level or we can address it at the final, collapsed,
frame level. Computationally, the second method is easiest, and we have to perform
the processes only once. In both cases, you will need to perform some kind of
clipping, whereby values outside of a given range are discarded or replaced with
another value, normally the mean. This might be sigma clipping, whereby data with
values outside a specified number of multiples of the standard deviation are moved
or replaced. Sigma clipping can be dual-tailed, where the top and bottom ranges are
removed, or single-tailed, where only one end is removed. An alternative method
is a numerical clip, where values outside a specified range are clipped. This range
is normally determined from a frequency plot of the pixel values and, like sigma
clipping, can be at either end or both ends of the pixel value range.
Clipping the collapsed frame has the advantage of being faster, but pixels that are
inherently low noise might be excluded, as they will have a low standard deviation
(as will most bad pixels, although for different reasons).
Another alternative is to identify the bad pixels at the single-frame level using a
reverse sigma clip, whereby only bad pixels are left, and then use this as a mask to
apply to the collapsed frame.
Whichever method you choose, there is, at the time of writing, no single application that can perform all the steps needed. However, it is relatively straightforward
to produce a Python script using AstroPy and Numpy to achieve this process, and it