We present the results of an experiment to image the interacting binary star beta Lyrae with data from the Navy Prototype Optical Interferometer (NPOI), using a differential phase technique to correct for the effects of the instrument and atmosphere on the interferometer phases. We take advantage of the fact that the visual primary of beta Lyrae and the visibility calibrator we used are both nearly unresolved and nearly centrally symmetric, and consequently have interferometric phases near zero. We used this property to detect and correct for the effects of the instrument and atmosphere on the phases of beta Lyrae and to obtain differential phases in the channel containing the Halpha emission line. Combining the Halpha-channel phases with information about the line strength, we recovered complex visibilities and imaged the Halpha emission using standard radio interferometry methods. We find that the results from our differential phase technique are consistent with those obtained from a more-standard analysis using squared visibilities (V^2s). Our images show the position of the Halpha emitting regions relative to the continuum photocenter as a function of orbital phase and indicate that the major axis of the orbit is oriented along p.a.=248.8+/-1.7 deg. The orbit is smaller than previously predicted, a discrepancy that can be alleviated if we assume that the system is at a larger distance from us, or that the contribution of the stellar continuum to the Halpha channel is larger than estimated. Finally, we also detected a differential phase signal in the channels containing HeI emission lines at 587.6 and 706.5nm, with orbital behavior different from that of the Halpha, indicating that it originates from a different part of this interacting system.
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