### 4 Basic principles of CCD data reduction

The primary aim of CCD data reduction is to remove any effects that are due to the nature of the detector and telescope – the ‘instrumental signature’. This is so that measurements (of intensity and possibly error) can be made that do not require any knowledge about how the data was taken. CCD data requires several corrections to attain this state. The most fundermental of these corrections is the ‘bias level’ subtraction.

The bias level is an electronic offset added to the signal from the CCD that makes sure that the Analogue-to-Digital Converter (ADC) always receives a positive value. The ADC is responsible for converting the signal representing the amount of charge accumulated in a CCD pixel to a digital value. A pixel is one of the discrete elements of the CCD where electrons accumulate during exposure to a light source (you see these as a picture element on your image display). The bias level has an intrinsic noise (induced by the signal amplification) known as the ‘readout noise’ (this one of the features which limits the usefulness of CCDs at very low light levels).

Usually the bias level is removed by the subtraction of specifically taken ‘bias-frames’ ($0$ second exposure readouts) or by using estimates derived from bias data that is added in regions around the real data. These regions are known as the bias strips or over/under-scan regions (see Figure §1).

After bias subtraction the data values are now directly related to the number of photons detected in each CCD pixel. The relation between the units of the data and the number of photons is a scale factor known as the gain. In this document the gain factor is referred to as the ADC factor. The units of CCD data before being multiplied by the ADC factor are known as ADUs (Analogue-to-Digital Units). CCD data when calibrated in electrons has a Poissonian noise distribution (if you exclude the readout noise).

Other corrections which are occasionally made to CCD data are dark count subtraction and pre-flash subtraction. These are only usual in older CCD data (but for IR array data the dark current correction is essential). Dark correction is the subtraction of the electron count which accumulates in each pixel due to thermal noise. Modern CCDs usually have dark counts of less than a few ADUs per pixel per hour, so this correction can generally be ignored. Pre-flashing of CCDs has been used to stop loss of signal in CCDs with poor across-chip charge transfer characteristics, the reasoning being that if signal is entered in a pixel before the main exposure, then subsequent losses are less likely to affect the data — note however that this also means that a higher signal to noise level is required for detection.

The final stage in the correction of CCD data for instrument signature is ‘flatfielding’. The sensitivity of CCDs varies from point to point (i.e. the recorded signal per unit of incident flux – photons – is not uniform), so if the data is to be relatively flux calibrated (so that comparison from point to point can be made) this sensitivity variation must be removed. To achieve this correction exposures of a photometrically flat source must be taken, these are known as flatfields. The basic idea of flatfield correction is then to divide the data by a ‘sensitivity map’ created from the calibrations, although in real life noise considerations, together with others (see appendix E), mean that particular care needs to be taken at this stage. After all these corrections have been made your data is usually1 ready for analysis.

Other processes which are frequently undertaken before analysis are registration, alignment, normalisation and combination. Registration is the process of determining the transformations which map the same positions on different datasets. This is essential if measurements, say with different filters, are to be made. In this case registration may be informal and just consists of identifying the same objects on different datasets. However, very accurate measures are often also required; certainly this is the case when data combination is to be performed. ‘Data combination’ is just when aligned datasets are combined by a process of taking the mean or some other estimator at each pixel, this is also frequently referred to as ‘mosaicing’. Aligning datasets means achieving pixel-to-pixel correspondence (in real data it is unlikely that this state is true, even if it was intended). Alignment uses the registering transforms to ‘resample’ the data onto a new pixel grid. If the exposure times, atmospheric transparency or sky brightness have varied, then data must be ‘normalised’ before combination. Normalisation is the determination of the zero points and scale factors which correct for these changes.

1Usually because another correction may also be necessary – the removal of fringing see appendix E.