Full statistical mode reconstruction of a light field via a photon-number resolved measurement

We present a method to reconstruct the complete statistical mode structure and optical losses of multimode conjugated optical fields using an experimentally measured joint photon-number probability distribution. We demonstrate that this method evaluates classical and non-classical properties using a single measurement technique and is well-suited for quantum mesoscopic state characterization. We obtain a nearly-perfect reconstruction of a field comprised of up to 10 modes based on a minimal set of assumptions. To show the utility of this method, we use it to reconstruct the mode structure of an unknown bright parametric down-conversion source.