We describe the process of analysing a beam using spatial state tomography, a generalization of Stokes polarimetry to higher-dimensions. The process consists of measuring the intensity of spatial components in various spatial bases to construct a generalized Stokes vector and its corresponding density matrix. Just as for polarization, this matrix can describe coherent, partially coherent and completely incoherent states of light incoming from a telescope. As applied to the spatial properties of a beam, this density matrix quantifies the spatial amplitude and phase of each spatial state of which the beam is composed, giving the correlated wavefront phase information.
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