Positive-Negative Ghost Imaging with Statistics of Realizations

We report a thermal-light “ghost” imaging without conventional intensity correlation calculation. Typically, ghost imaging is achieved with correlation calculation not only for entangled photons but also for thermal-light sources. In this paper, we set only thresholds for the bucket detector and the reference detector, and count the realizations when their signals are above or below the thresholds simultaneously. The distribution of the counts shows the image of our target. With proper threshold restrictions on the two detectors, we demonstrate both positive and negative images. Our work broadens the ghost-imaging reconstruction method, and provides a potential approach to ghost imaging with binary detectors in low-light or photon-counting regimes and a broader spectrum.

Figure 1

Experimental setup. A beam of pseudothermal light generated from the modulation of a laser beam by a ground glass (GG) enters a nonpolarizing beam splitter (BS) and is split into two beams. The transmitted beam passes through an object, and is recorded by a bucket detector ($D_2$). After a free propagation, the reflected beam is recorded by a space-resolved detector ($D_1$). The module $\mathrm{\&}$ is used for the logical conjunction measurement. $z_i$ and $z_s$ are the distances from the GG to the $D_1$ and the object, respectively.

Figure 2

Theoretical analysis results. All the blue curves represent the probabilities for the area of $T(x)=1$, and all the red curves represent the probabilities for the area of $T(x)=0$. $N$ is the number of units of $T(x)=1$. (a) The joint probabilities in the integral condition of $I_i(x)>\overline{I}$ and $B_i>\overline{B}$ simultaneously. (b) Probabilities in the integral condition of $I_i(x)>\overline{I}$ and $B_i<\overline{B}$. (c) Probabilities in the integral condition of $I_i(x)<\overline{I}$ and $B_i>\overline{B}$. (d) Probabilities in the integral condition of $I_i(x)<\overline{I}$ and $B_i<\overline{B}$.

Figure 3

Experimental generated positive and negative images with measurement of $50000$ realizations. (a) Distribution of realizations when $I_i(x)>\overline{I}$ and $B_i>\overline{B}$ simultaneously. (b) For $I_i(x)>\overline{I}$ and $B_i<\overline{B}$. (c) For $I_i(x)<\overline{I}$ and $B_i>\overline{B}$. (d) For $I_i(x)<\overline{I}$ and $B_i<\overline{B}$.

Figure 4

Experimental object and its images. (a) Binary mask of the object with 7206 transmitted pixels. (b) Normalized second-order correlation ghost imaging. (c) The difference between Figs. 3 and 3. (d) The difference between Figs. 3 and 3.