We describe a new method which achieves high precision Very Long Baseline
Interferometry (VLBI) astrometry in observations at millimeter wavelengths. It
combines fast frequency-switching observations, to correct for the dominant
non-dispersive tropospheric fluctuations, with slow source-switching
observations, for the remaining ionospheric dispersive terms. We call this
method Source-Frequency Phase Referencing. Provided that the switching cycles
match the properties of the propagation media, one can recover the source
astrometry. We present an analytic description of the two-step calibration
strategy, along with an error analysis to characterize its performance. Also,
we provide observational demonstrations of a successful application with
observations using the Very Long Baseline Array at 86 GHz of the pairs of
sources 3C274 & 3C273 and 1308+326 & 1308+328, under various conditions. We
conclude that this method is widely applicable to millimeter VLBI observations
of many target sources, and unique in providing bona-fide astrometrically
registered images and high precision relative astrometric measurements in
mm-VLBI using existing and newly built instruments.Comment: Astronomical Journal, accepted for publicatio