  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.
