Near field and far field correlations of thermal light

We present theoretical analysis and experimental demonstration of near field and far field spatial correlations of thermal light. Similar to the inequality Δx−Δp+<1Δx−Δp+<1 for a two-photon entangled source, we obtain an inequality Δx−Δp−<1Δx−Δp−<1 which also concerns both photon position and transverse wavevector correlations of thermal light. To test this inequality, we carry out an experiment in which ghost diffraction and ghost imaging can be simultaneously observed without the aid of any lenses. Meanwhile, the inequality is examined experimentally.