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.

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