Attaining the quantum limit of passive imaging

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The reason the direct-detection statistics is Poisson is that the total photon number in M ≫ 1 M\gg 1 statistically-independent modes each in a thermal state with mean photon number N 0 ≪ 1 N_{0}\ll 1 is close to Poisson with mean N = M ​ N 0 N=MN_{0} . The mean photon number per mode N 0 ≪ 1 N_{0}\ll 1 is true at optical frequencies

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