Second-order spatial correlation in the far-field: Comparing entangled and classical light sources

•Second-order spatial correlation with entangled and classical light in the far-field is investigated.•The role of photon statistics and detection mode in the second-order spatial correlation are discussed.•The difference of second-order spatial correlation with entangled and classical light sources is deduced. We consider second-order spatial correlation with entangled and classical light in the far-field. The quantum theory of second-order spatial correlation is analyzed, and the role of photon statistics and detection mode in the second-order spatial correlation are discussed. Meanwhile, the difference of second-order spatial correlation with entangled and classical light sources is deduced.