Conclusions

The analyses presented here indicate that high resolution images can be obtained using the Lucky Exposures method even if the telescope used for the observations is not diffraction-limited. Mirror figuring errors which only vary slowly with position in the aperture plane can be corrected by the atmosphere during a Lucky Exposure as long as the figuring errors are sufficient small in amplitude. However, the probability of obtaining exposures with high Strehl ratios is reduced by such aberrations.

Using numerical simulations I found that accurate Strehl ratios could be calculated from pixellated short exposure images by sinc-resampling the images and then using the flux in the brightest pixel of the resampled image as an indication of the peak flux in the original speckle pattern. The images generated from the resampled, simulated exposures clearly showed a first Airy ring indicating that the pixel sampling was adequate for high resolution imaging. The calculated Strehl ratios were normalised using simulated data.

High frame-rate imaging data taken at the NOT in May 2000 were analysed in this chapter. The Strehl ratios measured for the short exposure images were found to be consistent with the atmospheric models presented in Chapters 1 and 2.

The temporal properties of the high frame-rate imaging data were investigated. The initial decorrelation in the recorded datasets was found to be determined by the telescope oscillation. Aside from the effects of telescope oscillation, the speckle patterns appeared to remain correlated for $\sim 65$ $ms$ for the data analysed on $\epsilon$ Aquilae (this was also consistent with the observations of $\gamma$ Leonis). This implies that exposure times of at least $30$ $ms$ should be adequate for high resolution imaging under atmospheric conditions similar to those experienced during our observing run. The brightest speckle was found to decay on similar timescales. The timescale relevant for the best $1\%$ of exposures appeared very slightly larger (but of a very similar magnitude).

Short exposures of $\epsilon$ Aquilae were binned together without re-centring in order to simulate longer camera exposure times. With effective exposure times of $27$ $ms$, the Strehl ratio for the Lucky Exposures image generated from the best $1\%$ of exposures is only $15\%$ lower than that obtained using $5.4$ $ms$ exposures. This reduction in Strehl ratio is probably predominantly due to the telescope oscillation. One $108$ $ms$ exposure generated from data taken when the telescope oscillation appeared to be at a minimum had a very high Strehl ratio of $0.24$. This implies that the atmospheric coherence timescale may have been longer than $65$ $ms$ at this instant. Studies of data from $\epsilon$ Aquilae suggest that much of the structure in the wings of the PSF for our imaging method results from the limited number of atmospheric realisations sampled. For deeper observations utilising longer periods of observing time (and using more selected exposures and hence more realisations of the atmosphere) the PSF should be much smoother. This is supported by results from $\zeta$ Boötis using a larger number of short exposures.

Observations of the binary star $\zeta$ Boötis showed a high degree of isoplanatism over the small separation of the binary ($0.8$ $as$). When one star was used as the reference for image selection, the imaging PSF for that star was not substantially different than that obtained for the companion. Profiles through one component of $\zeta$ Boötis indicated that the flux in the PSF dropped exponentially towards zero with increasing radial distance from the PSF core, with an $e$-folding distance of approximately $0.17$ $as$. This implies that high dynamic range observations should be possible using the Lucky Exposures method, as highlighted by the observations of $\alpha$ Herculis.

When larger fractions of exposures were selected, the image Strehl ratio decreased in a gradual way. When all the exposures are used, a conventional shift-and-add image is obtained.

The Strehl ratios measured for the two different components in $\zeta$ Boötis were found to agree in individual exposures to within $0.3\%$ RMS. No evidence was found for differential motion of the two stars in the short exposure imaging data.

Spatial autocorrelations of the individual short exposures and of the images generated using the Lucky Exposures method indicate that re-centring and co-adding the best $1\%$ of exposures does not produce a significant loss of high spatial frequency information. In contrast, re-centring and co-adding all the exposures does appear to produce a significant reduction in the highest spatial frequencies. Combined with the poorer intrinsic quality of typical exposures, this leads to substantially poorer image resolution.

Observations of the $4.4$ $as$ binary $\gamma$ Leonis showed evidence of atmospheric anisoplanatism, implying an isoplanatic angle of less than $10$ $as$. Simultaneous observations of objects separated by a larger angle on the sky are required in order to measure the isoplanatic angle accurately. The Strehl ratio obtained for one component of $\gamma$ Leonis was found to be most strongly correlated with the Strehl ratio for the other component $5$--$11$ $ms$ later, suggesting that the temporal decorrelation was at least partly related to an intermediate or high altitude layer which had a velocity component in the direction separating the stars in the plane of the sky.