Data reduction

Data from the L3Vision CCDs were analysed using a similar approach to that described in Chapter 3. However, a stronger emphasis was put on minimising sources of noise in order to extend the Lucky Exposures method to the faintest possible targets.

The observations in 2001 and 2002 were taken using a CCD65 detector with $20\times30$ $\mu m$ pixels. In order to obtain output images with square pixels and the correct aspect ratio, the sinc-resampling process applied to the short exposures was modified (panels c) and f) of Figure 3.13). In the modified scheme the images were resampled to have $4$ times as many pixels in the horizontal direction and $6$ times as many pixels in the vertical direction. The observations in 2003 were performed using a CCD87 detector with square pixels, so the images were resampled to have $4$ times as many pixels in both directions.

For many of the observations (particularly those near the centres of globular star clusters) it was necessary to select one star from a crowded field to act as a reference. In order to select light from the reference in each case, a rectangular region around the star was selected in the long-exposure average image (the image formed by summing all of the individual exposures without re-centring). This region was always chosen to include most of the flux from the reference star, but to exclude light from other nearby stars. The same region of each of the individual short exposures was then used in the calculation of the Strehl ratios and positions of the brightest speckles (as indicated in panels b)--d) of the flow chart in Figure 3.13).

Nieto & Thouvenot (1991) discuss the artificial sharpening (or ``over-resolution'') of the reference star image brought about by exposure selection and image re-centring at low signal-to-noise ratios. This results from coherent addition of noise in the re-centred exposures. An extreme example of this would be provided by a truly photon-counting detector used to image a field where there is never more than one photon per short exposure in the whole field of view. The exposures with a single photon in would be re-centred based upon the location of the photon, providing a $\delta$-function at the re-centring position regardless of the real sky brightness distribution.

For the data presented here, where many photons are received from the reference star in each exposure and the signal-to-noise ratio is determined by readout noise, the image quality obtained for other stars in the field in the final Lucky Exposures image can provide a reliable measure of the imaging PSF , as long as the readout noise is not distributed in a pattern which is coherent across the imaging area of the detector.