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.

Figure 1

Simulation results: (a) original image, a modified head phantom image; (b) chosen probability density function curve; and reconstructions of (c) the positive image, (d) the negative image, and (e) their difference image.

Figure 2

Probability density function curves for the recovered pixel values, compared with the Gaussian theoretical curves. The probability density distributions and Gaussian theoretical curves of reconstructed pixel values falling in each pixel region where the gray value of the original image equals $d^{\left(k\right)}$ are shown for (a) positive and (b) negative images. The abscissa is the reconstructed pixel value and the ordinate indicates the probability of occurrence of these values.

Figure 3

Optical setup for CI. The thermal light emitted from a halogen lamp passes through an aperture diaphragm and a beam expander and illuminates a DMD. Then the modulated light is projected onto a black-and-white film (the object). The total intensity is recorded by a bucket detector.

Figure 4

Experimental results: (a) binarized image obtained by a camera and recovered (b) positive image, (c) negative image, and (d) their difference image.

Figure 5

Probability density function curves for the recovered pixel values, compared with theoretical Gaussian function curves. The probability density distributions and theoretical Gaussian curves of recovered pixel values falling in each pixel region where the original gray value equals 0 or 1 are shown for (a) positive and (b) negative images. Here the value of the pending term $\frac{D\left(e\right)}{a^2}$ is set equal to 120.

Figure 6

Schematic diagram of two Gaussian curves corresponding to two gray values.