Ghost imaging with a single detector

We experimentally demonstrate pseudothermal ghost imaging and ghost diffraction using only a single detector. We achieve this by replacing the high-resolution detector of the reference beam with a computation of the propagating field, following a recent proposal by Shapiro [ Phys. Rev. A 78, 061802(R) (2008)]. Since only a single detector is used, this provides experimental evidence that pseudothermal ghost imaging does not rely on nonlocal quantum correlations. In addition, we show the depth-resolving capability of this ghost imaging technique.

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Figure 1

(Color online) Experimental setups for ghost imaging. (a) The standard pseudothermal two-detector setup, where a ghost image of the object is obtained by correlating the pseudothermal field measured by a CCD with the intensity measured by a bucket detector. (b) The computational single-detector setup used in this work. A pseudothermal light beam is generated by applying controllable phase masks ${\phi }_r\left(x,y\right)$ with a spatial light modulator (SLM). The object image is obtained by correlating the intensity measured by the bucket detector with the calculated field at the object plane.

Figure 2

(Color online) Computational ghost image reconstruction of a $2\times 2{\text{cm}}^2$ transmission mask placed at $L=84\text{cm}$. (a) Reconstructed image at the object plane, obtained with $16000$ realizations. The inset shows the transmission mask. (b) A calculated intensity pattern of a single phase realization. The resolution of the reconstruction in (a) is dictated by the speckle size. (c) Reconstructed out-of-focus image, at a different $z$ plane $\left(L=15\text{cm}\right)$, demonstrating the depth-resolving capabilities of the computational method. (d) Measured signal-to-noise ratio (SNR) of the reconstructed image as a function of the number of realizations (blue dots). The theoretical line depicts $\sqrt{N}$ dependence.

Figure 3

(Color online) Simultaneous reconstruction of an object and its diffraction pattern, with 8000 realizations. (a) Reconstructed ghost image of a two-slit transmission plate placed at $L=11\text{cm}$. The width of each slit is $170\mu \text{m}$ and the separation is $460\mu \text{m}$. The resolution of the image is determined by the speckle size, $\delta x\sim 0.018\text{mm}$. Scale bars indicate $300\mu \text{m}$. (b) An out-of-focus image reconstructed at $L=5\text{cm}$. (c) Ghost diffraction pattern reconstructed using a pinhole detector. The resolution of the diffraction image is $\delta k\sim 1.4{\text{mm}}^{-1}$, considerably lower than the Fourier limit $\delta x\delta k<0.5$. (d) A cross section of the ghost diffraction pattern shown in (c) (dashed blue line), and the theoretical two-slit diffraction pattern calculated from the dimensions of the double slit (solid red line).