Spatially resolved phase reconstruction for atom interferometry

Atom interferometers are employed for numerous purposes such as inertial sensing. They measure forces by encoding their signal in phase shifts between matter waves. Signal extraction algorithms typically require the resulting interference patterns to feature a priori known spatial distributions of intensity and phase. Deviations from these assumed spatial distributions, such as those caused by inhomogeneous laser wave fronts, can lead to systematic errors. For long interrogation times, such as for space operation, these distributions can display highly complex structures. We present an extraction algorithm designed for interference patterns featuring arbitrary and unknown temporally stable spatial phase profiles utilizing Principal Component Analysis. It characterizes complex phase profiles and thereby turns effects into a measured quantity which caused systematic errors in previous algorithms. We verify the algorithm’s accuracy and assess the statistical reconstruction error in the presence of atom projection noise as a function of the number of atoms and images. Finally, we extract the spatial phase profiles from experimental data obtained by an atom gravimeter.