Imaging reduction

There are various sources of systematic and random noise which are introduced into the data during this process. These sources and the necessary calibrations we apply will be discussed below.

Bias frames

When calibrating a science image we first of all need to take account of the zero offset of the pixels. In addition to any zero offset which may exist a bias is also introduced by the amplifier. This is done in order to properly sample the readout noise. Readout noise is mainly introduced by the amplifier itself when collecting the charges from the pixels and is random rather than systematic. The best method of accounting for the bias depends on how uniform the bias pattern is across the CCD and how variable the pattern is throughout the night. The overall bias image of the CCD can be measured by taking zero second exposures, so that the total time is equal to the readout time. Multiple bias frames are often taken and can then be combined to find the median of these exposures. A bias frame samples the whole of

the image and hence is useful to measure bias patterns which persist. However, bias images will often be taken before the night has begun and not during and hence not simultaneous with the the science image. Another option is to measure the mean offset for each row using an overscan region where, for each image, either the final columns are read out multiple times or a physical unexposed region is read out. This will look like additional columns on the produced image. The benefit of using the overscan region is that the bias level can be measured concurrently with the image. Typically, over the course of the night an averaged stack of the initial bias frames are suitable for correcting for the zero offset in the science data though the overscan region can be used instead. Subtraction of the bias from your science image accounts for the zero point offset.

As well as accounting for the zero offset, bias frames can also be used to measure the read noise. Subtraction of one bias frame from a second (or an average of a set of bias frames from an additional bias), removes the bias offset and any non-uniformity leaving only the random noise in the frame. Measuring the variance of this bias difference frame allows measurement of the readout noise (σ2_R=σ_{dif f}2 /2) noting that combining multiple bias frames increases the readout error by a factor of√N, whereN is the number of frames.

Flat field frames

We must also account for both the variability of sensitivity between pixels and non- uniform illumination of the CCD. This can be achieved by imaging a uniformly illuminated field. For optical data, the most often used flat field is the twilight sky just after sunset and just before sunrise. At low zenith angle (z ∼ 20◦) the twilight sky is relatively flat and by moving the telescope between exposures and combining the frames using a median method the stars can be eliminated. Flat field frames can also be taken within the telescope dome using an illuminated screen. These are called dome flats. Twilight flats are often used in preference to dome flats when possible since the dome screens cannot be made as uniform as the twilight sky. Finally flat fields can be taken of the night sky if there are large areas of sky within an image by dithering and median combining. However, these images are low signal-to-noise. Hence, these are more likely to be used in the infra-red where the sky background is brighter. It should also be noted that since any flat frames is still an image of a field the bias must be subtracted. The flat frames can then be used to scale the image.

Dark frames

Within a CCD, in addition to photoelectrons, there will also be thermally excited electrons, which provide an unwanted background. This is known as dark current and scales exponentially with temperature such thatn∝exp[−B/kT] where B is a constant (Birney et al., 2006). Though the current itself can be well modelled there is also a thermal noise component on top of this which scales as √n, hence it is beneficial to reduce this uncertainty as much as possible.

For the 8 m telescopes, in the optical regime the CCDs are cooled to around

−120◦C (for instance on the FOcal Reducer and low dispersion Spectrograph (FORS2) instrument on the VLT) whereas the near-infra red detectors are further cooled to around ∼ −200◦C. At these temperatures the dark current in the optical is typi- cally∼0.0006e−/px/s(Boffin, 2013, FORS User Manual) and in the near infra-red

∼0.10−0.15e−/px/s(Kissler-Patig et al. 2008; Carraro et al. 2011, HAWK-I User Manual). Hence dark current subtraction is important in the near infra-red region but for optical detectors it is negligible and attempting to remove it may add more noise to the data (Izzo et al., 2013, FORS2 Pipeline User Manual).

To correct for dark current a dark frame can be taken. Here the charge is allowed to accumulate for a duration equal to that of the science image but the CCD itself is never exposed. This dark frame can then be subtracted from the science image.

Background subtraction

The main reduction processes outlined above allow us to reduce the impact on our science images of error introduced by the CCD. However, there will also undoubtedly be a sky background level from scattered light within the camera, diffuse sources and the wings of bright objects. The background level and associated noise can be accounted for using sky apertures, as will be discussed in the next section. How- ever, if there is a variable sky background, with gradients across the image, then it may still be prudent to remove this directly from the image before photometry is performed.

The method chiefly employed in this thesis to subtract the background is through use of the source extractor program, SExtractor (Bertin and Arnouts, 1996). To measure the varying background level, a grid is constructed across the whole frame separated into a set of meshes. The background is estimated using the clipped mean, from iterative clipping of the background histogram to 3σ, unless the field is particularly crowded (defined by a change in the standard deviation >20%) in

which case the mode is used instead (Da Costa, 1992; Bertin and Arnouts, 1996). The background map, which can then be applied to the image, is a bi-cubic spline interpolation of the grid created1_{. A median filter can also be applied to help reduce} any overestimation on local scales due to bright sources. This is a sliding window of fixed width within which the median value is calculated for each window, smoothing out any unwanted extremes in the background map. The SExtractor program allows, amongst other things, the mesh and median filter sizes for background estimation to be specified and these values were chosen to best recreate the background seen in the processed images.