High Resolution VLBI Astrometry with the $\theta-\theta$ Transform

The recent development of $\theta-\theta$ techniques in pulsar scintillometry has opened the door for new high resolution imaging techniques of the scattering medium. By solving the phase retrieval problem and recovering the wavefield from a pulsar dynamic spectrum, the Doppler shift, time delay, and phase offset of individual images can be determined. However, the results of phase retrieval from a single dish are only know up to a constant phase rotation, which prevents their use for astrometry using Very Long Baseline Interferometry. We present an extension to previous $\theta-\theta$ methods using the interferometric visibilities between multiple stations to calibrate the wavefields. When applied to existing data for PSR B0834+06 we measure the effective screen distance and lens orientation with five times greater precision than previous works.