  Atmospheric propagation effects at millimeter wavelengths can significantly
alter the phases of radio signals and reduce the coherence time, putting tight
constraints on high frequency Very Long Baseline Interferometry (VLBI)
observations. In previous works, it has been shown that non-dispersive (e.g.
tropospheric) effects can be calibrated with the frequency phase transfer (FPT)
technique. The coherence time can thus be significantly extended. Ionospheric
effects, which can still be significant, remain however uncalibrated after FPT
as well as the instrumental effects. In this work, we implement a further phase
transfer between two FPT residuals (i.e. so-called FPT-square) to calibrate the
ionospheric effects based on their frequency dependence. We show that after
FPT-square, the coherence time at 3 mm can be further extended beyond 8~hours,
and the residual phase errors can be sufficiently canceled by applying the
calibration of another source, which can have a large angular separation from
the target (>20 deg) and significant temporal gaps. Calibrations for all-sky
distributed sources with a few calibrators are also possible after FPT-square.
One of the strengths and uniqueness of this calibration strategy is the
suitability for high-frequency all-sky survey observations including very weak
sources. We discuss the introduction of a pulse calibration system in the
future to calibrate the remaining instrumental effects and allowing the
possibility of imaging the source structure at high frequencies with
FPT-square, where all phases are fully calibrated without involving any
additional sources.
