Photon Statistics Modal Reconstruction by Detected and Undetected Light

A novel technique is introduced for the reconstruction of multimode optical fields, based on simultaneously exploiting both the generalized Glauber's K-th-order correlation function g(K)$g<^>{(K)}$ and a recently proposed anti-correlation function (dubbed theta(K)$\theta <^>{(K)}$) which is resilient to Poissonian noise. It is experimentally demonstrated that this method yields mode reconstructions with higher fidelity with respect to those obtained with reconstruction methods based only on g(K)$g<^>{(K)}$'s, even requiring less "a priori" information. The reliability and versatility of this technique make it suitable for a widespread use in real applications of optical quantum measurement, from quantum information to quantum metrology, especially when one needs to characterize ensembles of single-photon emitters in the presence of background noise (due, for example, to residual excitation laser, stray light or unwanted fluorescence).