Quantum differential ghost microscopy

Quantum correlations become formidable tools for beating classical capacities of measurement. Preserving these advantages in practical systems, where experimental imperfections are unavoidable, is a challenge of the utmost importance. Here we propose and realize a quantum ghost imaging protocol stemming from the differential ghost imaging, a scheme elaborated so far in the limit of bright thermal light, particularly suitable in the relevant case of faint or sparse objects. The extension toward the quantum regime represents an important step as quantum correlations allow low-brightness imaging, desirable for reducing the absorption dose. Furthermore, we optimize the protocol in terms of signal-to-noise ratio, to compensate for the detrimental effects of detection noise and losses. We perform the experiment using spontaneous parametric down conversion light in a microscope configuration. The image is reconstructed exploiting nonclassical intensity correlation in the low photon flux regime, rather than photon pairs detection coincidences. On the one side, we validate the theoretical model and on the other we show the applicability of this technique by imaging biological samples.

Figure 1

Scheme of GI and DGI protocols. Spatial correlations between two beams are exploited. The reference beam is detected by a spatial resolving detector, the probe beam, after interacting with the sample impinges on a detector without spatial resolution. Every pixel $x_j^{\left(2\right)}$ is in one-to-one correspondence with a resolution cell $x_j^{\left(1\right)}$ at the object plane. For the image reconstruction the number of photons detected by the bucket detector $N_1$ and the one detected by each pixel in the resolving detector, $n_2\left(x_j^{\left(2\right)}\right)$, are used in the data elaboration. In DGI protocol (dashed path) also the integrated signal $N_2$ is exploited.

Figure 2

Experimental GI reconstructions of a binary object ($t_{+}=1, t_{-}=0$) for $\mathcal{N}=952$ and $H=2000$, using SPDC light. The object consists in a totally absorbing deposition occupying a variable fraction $\epsilon$ of the reconstructed area. Different values of $\epsilon$ are considered and the corresponding SNR estimated; for small $\epsilon$, e.g., $\epsilon =0.18, \mathrm{SNR}<1$ and the deposition on the right side is almost hidden in the noise.

Figure 3

SNR, normalized per the number of frames $H$ and the number of pixels in the reconstructed area $\mathcal{N}$, as a function of the object occupation fraction $\epsilon$, for different values of the channel efficiency $\eta$ ($t_{+}=1, t_{-}=0, {\mathrm{\Delta }}_{\text{el}}=0$). (a) High-brightness regime. (b) Low- brightness regime, twin-beam case.

Figure 4

DGI and ODGI are compared in terms of SNR with GI, varying both the channel efficiency $\eta$ and the number of detected photons per mode $n_2/M$. The surfaces are obtained for the twin-beam case, considering a binary object ($t_{+}=1,t_{-}=0$) and $\epsilon =0.1$.

Figure 5

Scheme of the experimental setup. In the BBO crystal two beams with perfect correlation in the photon number (twin-beam state) are generated. The probe beam interacts with the sample and is detected by a half of a CCD camera chip, while the other beam goes directly to the second half of the chip. The equivalent bucket detector on both channels is simulated by integrating (summing pixels signal) over the two regions. Two different samples are used: A set of uniform depositions of different transmittance $t_{-}$ and a biological object, i.e,. a wasp wing.

Figure 6

SNR as a function of $\epsilon$, the fraction of the detection area occupied by the deposition, for (a) $t_{-}=0$ and (b) $t_{-}=0.52$. Green refers to GI, purple to DGI, and yellow to ODGI. The dots are the experimental data, obtained for $H\sim 3\times {10}^4$ frames and an area of $\mathcal{N}=952$ pixels. The dashed lines are obtained fitting the data with the theoretical model, considering $\eta$ as a free parameter. The confidence region at $1\sigma$ is also reported as colored bands around the curves.

Figure 7

SNR as a function of $t_{-}$, fixed $\epsilon =0.52$. Green refers to GI, purple to DGI, and yellow to ODGI. The dots are the experimental data, obtained for $H\sim 3\times {10}^4$ frames and an area of $\mathcal{N}=952$ pixels. The dashed lines are obtained fitting the data with the theoretical model, considering $\eta$ as a free parameter. The confidence region at $1\sigma$ is also reported as colored bands around the curves.

Figure 8

SNR as a function of $\epsilon$, for $\eta \sim 0.5$. Green refers to GI, purple to DGI, and yellow to ODGI. The dots are the experimental data, obtained acquiring $H\sim 3\times {10}^4$ frames and considering an area of $\mathcal{N}=952$ pixels. The dashed lines are obtained fitting the data with the theoretical model, considering $\eta$ as a free parameter. The confidence region at $1\sigma$ is also reported as colored bands around the curves.

Figure 9

SNR as a function of $\epsilon$, for $\eta \sim 0.3$. Green refers to GI, purple to DGI, and yellow to ODGI. The dots are the experimental data, obtained acquiring $H\sim 3.5\times {10}^4$ frames and considering an area of $\mathcal{N}=525$ pixels. The dashed lines are obtained fitting the data with the theoretical model, considering $\eta$ as a free parameter. The confidence region at $1\sigma$ is also reported as colored bands around the curves.

Figure 10

Images of a wasp wing with spatial resolution of ${\left(5\mu \mathrm{m}\right)}^2$. (a) Direct image, obtained averaging 5000 frames. (b), (c) Reconstruction using the GI and ODGI protocol, respectively. The total region is divided into nine subregions, the protocol is applied to each of them, and finally the complete image is recovered. Forty blocks of 5000 images acquired at 2 MHz are processed.

Figure 11

Images of a green bug wing with spatial resolution of ${\left(5\mu \mathrm{m}\right)}^2$. (a) Direct image, obtained averaging 5000 frames. (b) Reconstruction using the ODGI protocol. The total region is divided into nine subregions, the protocol is applied to each of them, and finally the complete image is recovered. Eight blocks of 5000 images acquired at 100 kHz are processed. (c) $S_{\text{GI}}$ and $S_{\text{ODGI}}$ reconstruction of the border detail squared in (a). (d) $S_{\text{GI}}$ and $S_{\text{ODGI}}$ reconstruction of the spot detail squared in (a). The reconstruction for different number of frames is reported.