A probability theory for filtered ghost imaging

Based on probability density functions, we present a theoretical model to explain filtered ghost imaging (FGI) we first proposed and experimentally demonstrated in 2017 Opt. Lett. 42 5290 (2017) . An analytic expression for the joint intensity probability density functions of filtered random speckle fields is derived according to their probability distributions. Moreover, the normalized second-order intensity correlation functions are calculated for the three cases of low-pass, bandpass and high-pass filterings to study the resolution and visibility in the FGI system. Numerical simulations show that the resolution and visibility predicted by our model agree well with the experimental results, which also explains why FGI can achieve a super-resolution image and better visibility than traditional ghost imaging.