  Quantitative characterization of the spatial structure of single photons is
essential for free-space quantum communication and quantum imaging. We
introduce an interferometric technique that enables the complete
characterization of a two-dimensional probability amplitude of a single photon.
Importantly, in contrast to methods that use a reference photon for the phase
measurement, our technique relies on a single photon interfering with itself.
Our setup comprises of a heralded single-photon source with an unknown spatial
phase and a modified Mach-Zehnder interferometer with a spatial filter in one
of its arms. The spatial filter removes the unknown spatial phase and the
filtered beam interferes with the unaltered beam passing through the other arm
of the interferometer. We experimentally confirm the feasibility of our
technique by reconstructing the spatial phase of heralded single photons using
the lowest order interference fringes. This technique can be applied to the
characterization of arbitrary pure spatial states of single photons.
