  Lucky Imaging is now an established observing procedure that delivers near
diffraction-limited images in the visible on ground-based telescopes up to ~2.5
m in diameter. Combined with low order adaptive optics it can deliver
resolution several times better than that of the Hubble Space Telescope. Many
images are taken at high speed as atmospheric turbulent effects appear static
on these short timescales. The sharpest images are selected, shifted and added
to give a much higher resolution than is normally possible in ground-based long
exposure time observations. The method is relatively inefficient as a
significant fraction of the frames are discarded because of their relatively
poor quality. This paper shows that a new Lucky Imaging processing method
involving selection in Fourier space can substantially improve the selection
percentages. The results show that high resolution images with a large
isoplanatic patch size may be obtained routinely both with conventional Lucky
Imaging and with the new Lucky Fourier method. Other methods of improving the
sensitivity of the method to faint reference stars are also described.
