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Phase noise caused by an inhomogeneous, time-variable water vapordistribution in our atmosphere reduces the angular resolution, visibilityamplitude and coherence time of millimeter and submillimeter wavelengthinterferometers. We present early results from our total power radiometry phasecorrection experiment carried out with the Submillimeter Array on Mauna Kea.  From accurate measurements of the atmospheric emission along the lines ofsight of two elements of the array, we estimated the differential atmosphericelectrical path between them. In one test, presented here, the phase correctiontechnique reduced the rms phase noise at 230 GHz from 72$\degr$ to 27$\degr$over a 20 minute period with a 2.5 second integration time. This corresponds toa residual differential electrical path of 98 $\mu$m, or 15 $\mu$m ofprecipitable water vapor, and raises the coherence in the 20 minute period from0.45 to 0.9.Comment: Accepted for publication in the SMA Special Volume of the ApJ Letters  (9 pages of text, 3 figures

Atmospheric Phase Correction Using Total Power Radiometry at the Submillimeter Array