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Narrow-angle interferometric astrometry offers the possibility of 10's of microarcsec per $\sqrt{\rm h}$ accuracy in the presence of atmospheric turbulence. The accuracy of a differential astrometric measurement depends on size of the star separation vs.\ the ``isokinetic angle''---the ratio of the instrument baseline to the atmospheric height. For typical narrow-angle measurements, the star separation is larger than the isokinetic angle, and the result is an accuracy which is only weakly dependent upon the separation and the baseline length. However, when the star separation is smaller than the isokinetic angle, there are now strong dependencies on both the baseline length and the separation. To exploit this behavior, optical interferometry can be used to provide long baselines which increase the isokinetic angle and reduce the atmospheric and photon-noise errors, while phase referencing at 2.2~$\mu$m is used to increase sensitivity in order to locate nearby reference stars. Recently, some measurements were made with the Mark~III Interferometer at Mt.~Wilson to validate the atmospheric theory. Simultaneous phase measurements of the two components of the 3" binary $\alpha$~Gem using a 12-m baseline have yielded results in good correspondence with the theory. The paper will discuss the atmospheric theory, these results, and the status of the NASA TOPS-O Interferometry Technology Testbed.
