Point source atom interferometry (PSI) uses the velocity distribution in a cold atom cloud to simultaneously measure one axis of acceleration and two axes of rotation from the phase, orientation, and period of atomic interference fringe images. For practical applications in inertial sensing and precision measurement, it is important to be able to measure a wide range of system rotation rates, corresponding to interferograms with far less than one full interference fringe to very many fringes. The interferogram analysis techniques used previously for PSI are not sensitive to low rotation rates, which generates less one full interference fringe across the cloud, limiting the dynamic range of the instrument. We introduce an experimental method, new to atom interferometry and closely related to optical phase-shifting interferometry, that is effective in extracting rotation values from signals consisting of fractional fringes as well as many fringes without prior knowledge of the rotation rate. Our method uses four interferograms, each with a controlled Raman laser phase shift, to reconstruct the underlying atomic interferometer phase map.
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