Reduction

To obtain useful science data from a CCD image, several additional steps must first be taken:

De-biasing

This step refers to the removal of both the bias level offset and the readout noise, which usually has a fixed pattern component in addition to the stochastic element. A bias frame can be can be generated simply by taking an extremely short exposure with the shutter closed. Typically several 10s of bias frames are taken and combined in order to remove the Poisson noise.

Dark noise removal

In addition to electron-hole pairs generated by photons, the electrons can also be thermally excited, which provides an additional background noise source. The rate at which thermal electrons are generated decreases exponentially with decreasing temperature (Birney et al., 2006). In most professional astronomical observatories, the CCD’s are cooled by liquid nitrogen to cryogenic temperatures, drastically re- ducing the generation of thermal electrons. For these situations, dark currents are

negligible. For example, the AUXCAM detector in ACAM on the WHT has a dark current of<4 electrons an hour1, which is far below the sky brightness level.

In situations where the dark noise is an important contribution, a “dark frame” can be taken. Because different regions of the CCD will be at slightly different temperatures due to the precise layout of the electronics and airflow, the dark frame will contain a fixed pattern component, as well as a stochastic one. Similar to the bias correction, the shutter is closed, but the exposure length is set to be the same as the science data. Many dark frames are combined to average over the noise, and then the dark frame is subtracted from the science data. Since the dark frame will already contain the effect of the bias, one should only use one or the other correction, never both.

Flat fielding

CCD production is not perfect, and slight differences in the sensitivities and well depths of pixels can produce percent level variations in count rates from pixel to pixel. External factors such as vignetting in the instrument or dust settling on the chip or optics, also add to this effect. This obviously would wreak havoc high precision measurements if the star of interest travels across pixels.

Flat fielding is a method of attempting to remove these effects. The CCD is well exposed on a uniform intensity field, and the resulting image is bias/dark corrected, and then the science frame is divided by this flat frame to remove non- uniform responses.

An additional concern is the wavelength dependence of flat fields. This is a particular problem in thinned, back-illuminated CCD’s (such as the ones used by NGTS) due to slight variations in the etching of the surface layers. The flat-fielding strategy of NGTS is based around taking regular dawn and twilight flats (the sky is a convenient approximately flat illumination source). However, the sky is very blue, in contrast to the majority of NGTS targets which are quite red. Blue light is more sensitive to surface properties of CCD’s, leading to what is known as the “Blue Diamond effect” (Grange and Goad)2.

In some cases the importance of flat-fielding can be diminished, if the guiding is precise enough to keep the stars centered on the same pixels, or if the star is heavily defocussed, so that many hundreds of pixels are sampled (Southworth, 2010).

1_{http://www.ing.iac.es/PR/wht info/opticalCCDs.html, accessed 14/06/16}

2_{A conference poster on this topic can be found at http://www.mrao.cam.ac.uk/wp-}

Sky removal

The sky emits and scatters light, which is typically of no interest astronomically. This is mainly a problem for ground based observing, although geocoronal contam- ination can be a major limiting factor for space-based UV observations. Therefore it is necessary to estimate the sky contribution to the pixels containing the target and subtract this value. A larger number of non-target pixels used to estimate this background provides a better estimate, however if the sky background is spatially varying the pixels used must be kept close to the target.

When conducting high resolution spectroscopy and attempting to measure specific absorption lines, it is critical to separate out the absorption of the Earth’s atmosphere from that of the target, particularly if there are shared spectral lines (as is the case for sodium). Fortunately, for high resolution observations, the velocity signal of the Earths orbital motion makes it easy to separate out and remove this contribution. (This is what makes my measurement of the line profile of sodium in HD 189733b in Chapter 5 possible).

CCD equation

The total error on a pixel count value depends on several components, related to the different reduction steps mentioned so far, this is known as the CCD equation (Howell, 2006) S N = N_∗ r N_∗+npix 1 +npix nB NS+ND +N 2 R+G2σ2f (2.1)

Where N_∗ are the source counts, npix are the number of source pixels, nB

are the number of pixels used to estimate the background level,NS are the number

of sky countsper pixel ND is the dark current, NR is the readout noise (this term

is squared since it is a Gaussian component, not poisonian) G2 is the gain and σ_f2

is factor that depends on details of the ADC, typically about 0.29.

For the applications in this thesis, where the targets are relatively bright and well exposed, theN_∗ term is dominant, and the signal to noise ratio therefore scales roughly as√N_∗, but, it is worth being aware of other potential sources of error.