Formation mechanism of correspondence imaging with thermal light

Abstract

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 gray-scale 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 crosspoint-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, vice versa for negative one. This work complements the theory of ghost imaging.

A probability theory for filtered ghost imaging

“…Recently, the joint probability density function (PDF) of two optical intensities in GI has been employed to explain some newly observed experimental phenomena. [31][32][33][34] As an alternative theoretical method, this has some advantages in handling certain problems compared with previous methods. Cao et al first derived the joint probability density function between the bucket and ref-erence signals to explain the correspondence imaging experiment by probability theory and further discussed some new phenomena in thermal GI by the fractional-order moments of intensity.…”

“…Cao et al first derived the joint probability density function between the bucket and ref-erence signals to explain the correspondence imaging experiment by probability theory and further discussed some new phenomena in thermal GI by the fractional-order moments of intensity. [31,32] Later, Yu et al gave a theoretical discussion of the formation mechanism of correspondence imaging with thermal light via probability theory in statistical optics, [33] and Hu et al investigated a Fourier-transform version by the joint probability density theory. [34] Recently, a new approach for reconstructing superresolution ghost images of targets in the FGI setup was experimentally demonstrated, [24][25][26][27] where the spatial resolution can exceed the Rayleigh diffraction limit by more than a factor of 10.…”

“…However, the reason why these enhancements can be realized is unclear, and the theoretical explanation is left untouched, so this requires further consideration. Inspired by the papers [24][25][26][27][31][32][33][34] mentioned above, we present here a theoretical investigation based on probability theory, where an analytical expression for the joint probability density function in the FGI scheme is provided. On this basis, analytical expressions for the normalized second-order intensity correlation functions for the three cases of low-pass, bandpass and high-pass filterings of the optical intensities of thermal light are also obtained.…”