The techniques of image deconvolution can increase your effective telescope aperture by 40% without decreasing the astrometric precision or introducing artificial bias. Some studies also show that appreciable gain in astrometric accuracy can be obtained.
Theory of deconvolution
The imaging equation
In several parts of this book it has been pointed out that astrometry, as par t of astronomy, is an observational science in which the unknown physical basis is, in our observations, convolved with the structure of the source, the emission process, the atmosphere, the telescope detector interaction, etc. In a typical exposure of the sky taken from the ground this convolution makes our point-like stars appear as pixelized extended spots of light of about one arcsecond (or more) in size. The light in the star images shows, in general, a Gaussian-like pattern but it can vary across the frame. I n all types of observations (optical imaging from the ground or space, optical and radio interferometry, etc.), the process can be mathematically described as an imaging equation which is a relationship (with an integral operator) between the distribution of the source and the distribution of the observational data.