Formation mechanism of correspondence imaging with thermal light

Correspondence imaging can achieve positive-negative ghost images by just conditional averaging of partial patterns, without treating bucket intensities as weights. To explain its imaging mechanism, we develop a probability theory assuming the targets are of grayscale and the thermal reference speckles obey an arbitrary independent and identical distribution. By both simulation and experiments, we find that the recovered values in each region of the same original gray value conditionally obey a Gaussian distribution. A cross-point-to-standard-deviation ratio is used as the figure of merit to prove that the patterns with respect to larger bucket values generate a positive image with a higher quality and vice versa for a negative one. This work complements the theory of ghost imaging.