Abstract

We propose an interferometric method for the direct measurement of the moments of the transverse spatial variables of an optical field. The key elements are spatial light modulators, used to imprint a transverse phase on the field. We show that our measurement scheme can be used to measure the spatial correlation functions of a two-photon state directly, which allows for the identification of spatial entanglement without the need for partial state reconstruction. Our method can also be extended to N-photon states. We show that the method is more efficient than the measurement of marginal probability distributions, and that it can be made resilient to small alignment errors.