Both lucky imaging techniques and adaptive optics require natural guide stars, limiting sky-coverage, even when laser guide stars are used. Lucky imaging techniques become less successful on larger telescopes unless adaptive optics is used, as the fraction of images obtained with well-behaved turbulence across the whole telescope pupil becomes vanishingly small. Here, we introduce a technique combining lucky imaging techniques with tomographic laser guide star adaptive optics systems on large telescopes. This technique does not require any natural guide star for the adaptive optics, and hence offers full sky-coverage adaptive optics correction. In addition, we introduce a new method for lucky image selection based on residual wavefront phase measurements from the adaptive optics wavefront sensors. We perform Monte Carlo modelling of this technique, and demonstrate I-band Strehl ratios of up to 35 per cent in 0.7 arcsec mean seeing conditions with 0.5 m deformable mirror pitch and full adaptive optics sky-coverage. We show that this technique is suitable for use with lucky imaging reference stars as faint as magnitude 18, and fainter if more advanced image selection and centring techniques are used.
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