Results of exposure selection

Observations undertaken using a CCD65 detector on the night of 2001 July 6 are listed in Table 5.2. All the data were taken through the HiRac I-band filter based at the NOT. The observational data was reduced using the approach described by the flow diagram of Figure 5.8.

An example image generated by applying the Lucky Exposures method to $110$ $s$ of data taken on M15 (field 1) on 2001 July 26 is shown in Figure 5.12. The $I=13$ star which was used as the reference for selection of the best $1\%$ of exposures and for exposure re-centring has been circled in the figure. The full frame of the CCD was read out in these observations. With the $3.4$ $MHz$ pixel rate of the CCD controller the frame rate for these observations was limited to $18$ $Hz$, allowing image motion to slightly blur the exposures. Despite this, other stars in the field have FWHM as small as $160$ $mas$, a substantial improvement over $500$ $mas$ for the seeing limited image shown in Figure 5.13. There was no evidence for gradual drift in the stellar positions during this run, indicative of telescope tracking errors which would blur the seeing-limited image.

Figure 5.12: Selected exposures from $110$ $s$ of data on M15. The $I=13.1$ reference star used for calculating the Strehl ratio and for re-centring the short exposures has been circled.

Figure 5.13: Seeing limited image generated by adding all the exposures from one run on M15 without re-centring them.

As only $1\%$ of the observing time was used for the image shown in Figure 5.12, the signal-to-noise ratio for detection of a star is expected to be lower than for the average image in Figure 5.13. If we assume that the images are sky-background limited, we can estimate the fractional decrease in signal-to-noise ratio relatively straightforwardly. We need to take into account the change in the size and shape of the PSF , but the image FWHM provides a good estimate for this effect. A good estimate for the fractional change $f$ in signal-to-noise ratio for detection of a star of flux $S$ will be:

$$f=\frac{S t_{le}}{\sqrt{B t_{le} d_{le}^{2}}} \times \frac{\sqrt{B t_{c}d_{c}^{2}}}{S t_{c}}$$ (5.2)

where $t_{le}$ is the total observing time in the Lucky Exposures , $d_{le}$ is the diameter of the PSF for Lucky Exposures observations in $as$, $t_{c}$ is the total observing time for the conventional (long exposure) image, $d_{c}$ is the diameter of the PSF for the conventional observation in $as$, and $B$ is the sky background flux per $as^{2}$. For the data presented in Figures 5.12 and 5.13, the fractional decrease in signal-to-noise ratio for using the Lucky Exposures method is:

$$f=0.31$$ (5.3)

In practice an astronomer must weigh this decrease in signal-to-noise against the benefits of higher image resolution.