High-precision Astrometric Millimeter Very Long Baseline Interferometry
  Using a New Method for Multi-Frequency Calibration
  In this paper we describe a new approach for mm-VLBI calibration that
provides bona-fide astrometric alignment of the mm-wavelength images from a
single source, for the measurement of frequency dependent effects, such as
`core-shifts' near the black hole of AGN jets. We achieve our astrometric
alignment by solving firstly for the ionospheric (dispersive) contributions
using wide-band cm-wavelength observations. Secondly we solve for the
tropospheric (non-dispersive) contributions by using fast frequency-switching
at the target mm-wavelengths. These solutions can be scaled and transferred
from the low frequency to the high frequency. To complete the calibration chain
one additional step was required to remove a residual constant phase offset on
each antenna. The result is an astrometric calibration and the measurement of
the core-shift between 22 and 43 GHz for the jet in BL Lacertae to be -8$\pm$5,
20$\pm$6 $\mu$as, in RA and Declination, respectively. By comparison to
conventional phase referencing at cm-wavelengths we are able to show that this
core shift at mm-wavelengths is significantly less than what would be predicted
by extrapolating the low frequency result, which closely followed the
predictions of the Blandford \& K\"onigl conical jet model. As such it would be
the first demonstration for the association of the VLBI core with a
recollimation shock, normally hidden at low frequencies due to the optical
depth, which could be responsible for the $\gamma$-ray production in blazar
jets.
