Optimization of computational ghost imaging

We studied the second-order correlation function of computational ghost imaging, and we gave the expressions of second-order correlation function in the signal and background region. We found the total intensity of the modulated source influences the visibility of the reconstructed image. We discussed the positive-negative correlation phenomenon in a computational ghost imaging (CGI) system, and a protocol was given to distinguish the positive and negative correlations. This protocol allows us to determine the dividing line of positive and negative correlations before sampling, and it was verified by our simulations and experiments; the imaging quality of computational ghost imaging can be greatly improved by using this protocol.

Figure 1

Experimental setup of CGI. (1) Projector. (2) Transmissive object. (3) Collecting lens. (4) Bucket detector. (5) PC.

Figure 2

Theoretical results of the visibility of CGI with different $\alpha /M$. $\alpha /M$ is the proportion of the white pixels in the binary patterns. $M$ is the amount of pixels in every binary pattern. $\beta /M$ is the object's total transmission ratio, for (a) $\beta /M=0.2$, and for (b) $\beta /M=0.4$.

Figure 3

Experiment result of images reconstructed by CGI with different $\alpha /M$. From (a) to (h), the values of $\alpha /M$ are $0.125$, 0.1875, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, respectively.

Figure 4

The visibility of the reconstructed images in Figs. 3–3.

Figure 5

Comparison of the criterion to distinguish positive and/or negative correlations determined by PNFC protocol and our protocol. The criterion determined by our protocol is 29.25; the two dashed lines are 29 and 30, respectively.

Figure 6

Simulation results of positive-negative correlation in a CGI system. (a) The reconstructed image of CGI. (b) The reconstructed image when we reverse the negative correlation steps. (c) The positive image. (d) The negative image.

Figure 7

Experimental results of conventional CGI versus CGI reversing the negative image. (a)–(d) are the reconstructed images of normal CGI, and (e)–(h) are the reconstructed images of CGI reversing the grayscale of negative correlation steps. The numbers of total measurements of (a) and (e), (b) and (f), (c) and (g), (d) and (h) are 2000, 5000, $10000$, $20000$, respectively.