This thesis describes the development and use for science of the Cambridge Lucky Imaging system LuckyCam, designed for astronomical imaging though Earth’s turbulent atmosphere. I demonstrate that in good conditions LuckyCam gives diffraction-limited images in I-band, matching the resolution of the Hubble Space Telescope from the ground. In poorer conditions, the system improves the imaging resolution by factors of 3-4. The system is shown to reliably achieve very-high-resolution output images which are useful for a wide variety of astronomical programmes. The L3CCD (EMCCD) detector allows noise-free photon counting at CCD quantum efficiencies; calibration methods developed for astronomy with this detector are presented. My design and implementation of both fast LuckyCam data acquisition software and an automated Lucky Imaging pipeline is discussed in detail. I also present several methods for the measurement of the parameters of close binary systems using LuckyCam data, as well as calibration methods for speckle imaging using L3CCD detectors.

In the second part of this thesis, I detail the LuckyCam Very Low Mass (VLM) binary survey, a search for close companions to nearby late-M-dwarf stars. 110 targets are imaged at 0.1 arcsec resolution in only 16 hours on-sky, a very fast rate compared to other high resolution imaging systems. 21 new VLM binaries are found, a ~25% increase in the known number. Several more exotic systems were discovered during the surveys, such as a possible substellar companion, and a wide triple system. The orbital radius distribution of the binaries is found to have an apparently sharp change at around the M5.0-M5.5 spectral type, with the earlier-type stars having a large population of binaries wider than 10AU.