  This paper presents a non-classic approach to narrow field astrometry that
offers a significant improvement over conventional techniques due to enhanced
reduction of atmospheric image motion. The method is based on two key elements:
apodization of the entrance pupil and the enhanced virtual symmetry of
reference stars. Symmetrization is implemented by setting special weights to
each reference star. Thus a reference field itself forms a virtual net filter
that effectively attenuates the image motion spectrum. Atmospheric positional
error was found to follow a power dependency ~ R^{K \mu /2} D^{-K/2+1/3} on
angular field size R and aperture D; here K is some optional even integer
2<=K<=sqrt{8N+1}-1 limited by a number N of reference stars, and \mu <= 1 is a
term dependent on K and the magnitude and sky star distribution in the field.
As compared to conventional techniques for which K=2, the improvement in
accuracy increases by some orders. Limitations to astrometric performance of
monopupil large ground-based telescopes are estimated. The total atmospheric
and photon noise for at a 10 m telescope at good 0.4" seeing was found to be,
depending on sky star density, 10 to 60 microarcsec per 10 min exposure in R
band. For a 100 m telescope and FWHM=0.1" (low-order adaptive optics
corrections) the potential accuracy is 0.2 to 2 microarcsec.
