  Atom interferometers are sensitive to a wide range of forces by encoding
their signals in interference patterns of matter waves. To estimate the
magnitude of these forces, the underlying phase shifts they imprint on the
atoms must be extracted. Up until now, extraction algorithms typically rely on
a fixed model of the patterns' spatial structure, which if inaccurate can lead
to systematic errors caused by, for example, wavefront aberrations of the used
lasers. In this paper we employ an algorithm based on Principal Component
Analysis, which is capable of characterizing the spatial phase structure and
per image phase offsets of an atom interferometer from a set of images. The
algorithm does so without any prior knowledge about the specific spatial
pattern as long as this pattern is the same for all images in the set. On
simulated images with atom projection noise we show the algorithm's
reconstruction performance follows distinct scaling laws, i.e., it is
inversely-proportional to the square-root of the number atoms or the number of
images respectively, which allows a projection of its performance for
experiments. We also successfully extract the spatial phase patterns of two
experimental data sets from an atom gravimeter. This algorithm is a first step
towards a better understanding and complex spatial phase patterns, e.g., caused
by inhomogeneous laser fields in atom interferometry.
