⇦Chinese Physics Letters, 2019, Vol. 36, No. 4, Article code 044205 Multi-Path Ghost Imaging by Means of an Additional Time Correlation * Rui Liu (刘瑞)1, Ling-Jun Kong (孔令军)1, Yu Si (司宇)1, Zhou-Xiang Wang (王周祥)1, Wen-Rong Qi (齐文荣)1, Chenghou Tu (涂成厚)1, Yongnan Li (李勇男)1**, Hui-Tian Wang (王慧田)1,2,3** Affiliations 1Key Laboratory of Weak-Light Nonlinear Photonics and School of Physics, Nankai University, Tianjin 300071 2National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093 3Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093 Received 11 February 2019, online 23 March 2019 *Supported by the National Key R&D Program of China under Grant Nos 2017YFA0303800 and 2017YFA0303700, the National Natural Science Foundation of China under Grant Nos 11534006, 11774183 and 11674184, and the Collaborative Innovation Center of Extreme Optics.
**Corresponding author. Email: liyongnan@nankai.edu.cn; htwang@nju.edu.cn Citation Text: Liu R, Kong L J, Si Y, Wang Z X and Qi W R et al 2019 Chin. Phys. Lett. 36 044205    Abstract Ghost imaging functions achieved by means of the spatial correlations between two photons is a new modality in imaging systems. With a small number of photons, ghost imaging is usually realized based on the position correlation of photon pairs produced from the spontaneous parametric down-conversion process. Here we demonstrate a way to realize multi-path ghost imaging by introducing an additional time correlation. Different delays of paths will induce the shift of the coincidence peak, which carries the information about objects. By choosing the suitable coincidence window, we obtain images of three objects simultaneously, with a visibility of 87.2%. This method provides insights and techniques into multi-parameter ghost imaging. It can be applied to other correlated imaging systems, for example, quantum spiral imaging. DOI:10.1088/0256-307X/36/4/044205 PACS:42.30.Va, 42.30.-d, 42.65.Lm © 2019 Chinese Physics Society Article Text A traditional imaging system uses light, which is directly transmitted by, or scattered from, the object, to form an image. In the mid-1990s, a novel imaging method, ghost imaging, was presented using entangled photon pairs generated by the spontaneous parametric down-conversion (SPDC) process.[1] In ghost imaging, the object is illuminated by the signal light, which will be collected by a single-pixel (bucket) detector with no spatial resolution, while the idler light is recorded by a pixelated detector without interaction with the object; finally, the image of the object is obtained by only the coincidence measurement between the electrical signals from the two (single-pixel and pixelated) detectors. Unlike traditional imaging, ghost imaging is in fact a kind of indirect imaging technique. For ghost imaging, the correlation between the two (signal and idler or test and reference) photons/beams is indispensable, but the entanglement between them is unnecessary. Ghost imaging was demonstrated using various light sources including the entangled photons, thermal light sources, Gaussian Schell-model beam, partially coherent vector beam and x-ray.[2-15] Ghost imaging, as an important way of information transportation and acquisition, has attracted a great deal of attention[16-29] and has been a hot topic for a long time. Ghost imaging has been explored theoretically and experimentally using various degree-of-freedom photons, such as position or momentum correlations,[17,18,20,24] orbital angular momentum[30-32] and wavelength multiplexing.[33,34] Ghost imaging has its own unique features, e.g., it allows objects to be located in optically harsh or noisy environments without influencing the quality of the image.[35,36] Therefore, ghost imaging has potential applications, for instance, satellite and aircraft-to-ground-based distant imaging[37] and x-ray imaging.[38] The timing precision allows the system to trigger the detectors only at the instant of imaging.[20,39,40] If there is no such heralding signal, the camera cannot unambiguously detect the signal photons against the background noise. In this Letter, we demonstrate a way to realize multi-path ghost imaging by means of the time correlation of the photon pairs. Signal photons are divided into three optical paths with different objects. The signal photons passing through the objects are collected by a fixed fiber coupler and the idler photons are collected by a scannable multi-mode fiber, both of which are transferred to single photon detectors. The coincidence between these two detectors contains three peaks in different measurement windows and any peak carries the information of the different object in the certain path. By choosing the suitable coincidence window, we obtain the images of the three objects simultaneously, with a visibility of 87.2%. The experimental setup for performing multi-path ghost imaging by means of time correlation is shown in Fig. 1. A femtosecond (fs) pulsed laser at a central wavelength of 405 nm, with a pulse duration of $\sim$140 fs and a repetition rate of $\sim$80 MHz (which corresponds to the time interval between two neighbor pulses to be $\sim$12.5 ns), pumps a nonlinear crystal (BBO with a dimension 5$\times$5$\times$1 mm$^3$). Under the condition of type-I degenerate collinear phase matching, down-conversion photon pairs with the same polarization and wavelength of 810 nm are generated by the SPDC process. A dichroic mirror (DM1) removes the useless pump pulses (@405 nm) and reflects the down-conversion photon pairs (@810 nm). A beam splitter (BS1) divides the photon pairs into two paths (signal and idler photons). The signal beam is firstly divided into two paths by BS2, and the signal beam reflected by BS2 is further divided into two paths by a combination of a half wave plate (HWP) and a polarization beam splitter (PBS1). Finally, the signal beam is divided into three paths. To explore multi-path ghost imaging, three objects (O1, O2, and O3) are inserted into the three signal paths, respectively. L1 and L2 compose a $4f$ system. The BBO crystal is located on the front focal plane of L1 and all the three objects are located at the back focal plane of L2, i.e., the three objects are in the imaging plane of the BBO crystal.
cpl-36-4-044205-fig1.png
Fig. 1. Experimental setup of the multi-path ghost imaging. L1–L5 are lenses with the same focal length of $f=100$ mm. DM1–DM4 are dichroic mirrors, which allow the 405-nm light ($\sim$96%) to be transmitted and the 810-nm light ($\sim$97%) to be reflected. O1 (letter N), O2 (letter N rotated at $45^\circ$), and O3 (letter N rotated at $90^\circ$) are three objects, which are located in the focal planes of lens L2. BS1, BS2, and BS3 are beam splitters. PBS1 and PBS2 are polarization beam splitters. IF1 and IF2 are interference filters with a 3-nm bandwidth centered at 810 nm. MMF1 and MMF2 represent multi-mode fibers. The diameters of the fiber core are $\sim$200 µm for MMF1 and $\sim$50 µm for MMF2. D1 and D2 are single photon detectors. C.M. represents coincidence measurement.
In our experiment, the path Ps2 (BS2-O2-BS3-MMF1-D1) and the path Ps3 (BS2-O3-BS3-MMF1-D1) have the path differences of 1.2 m and 2.4 m with the path Ps1 (BS2-O1-BS3-MMF1-D1), which are used to change the delay time. Correspondingly, the paths Ps2 and Ps3 have the time delays of 4 ns and 8 ns with respect to the path Ps1, respectively. Then the photons passing through the objects are collected by the multi-mode fiber (MMF1) with a coupler and detected by a bucket signal-photon detector (D1). The idler photons without interacting with the objects are directly collected by another multi-mode fiber (MMF2) and recorded by another single-photon detector (D2). In the idler path, L1, L3, L4 and L5 compose two cascaded 4f systems, and the rear focal plane of L3 coincides with the front focal plane of L4. Thus, the two $4f$ systems image the plane of the BBO crystal onto the rear focal plane of L5, in which we will scan MMF2. In the front of MMF1 (MMF2), we insert an interference filter IF1 (IF2) centered at an 810-nm central wavelength with a 3-nm bandwidth to remove the unwanted light.
cpl-36-4-044205-fig2.png
Fig. 2. Examples of the coincidence measurement results with three coincidence windows. P1–P4 are four different positions in the scanning plane ($X$–$Y$) of MMF2. The peak in $\Delta t=0$ ($\Delta t=4, 8$ ns) shows the transmission of path Ps1 (Ps2, Ps3). The lack of peak in a certain coincidence window indicates that the corresponding path is blocked by an object. Images of three objects can be obtained from the three coincidence windows, respectively. The time window of the coincidence counter used in our experiment is $\sim$2.0 ns.
The coincidence measurement is sensitive to the time delay (or path difference) between signal and idler photons. By optimizing the path difference, we can obtain the coincidence of the three paths in three measurement windows. For example, in the idler path Pi (BS1-DM2-MMF2-D2), the photons will be detected by D2 at $t_{\rm i}$. In the signal path, there are three different paths for signal photons. For the path Ps1, the photons are detected by D1 at $t_{\rm s1}$. In our coincidence measurements, we set the two paths (Ps1 and Pi) to be of equal length to ensure $t_{\rm s1}=t_{\rm i}$, which means that there should be a peak of coincidence at the time delay of $\Delta t=t_{\rm s1}-t_{\rm i}=0$, as the coincidence measurement results shown in Fig. 2. When the two paths have different optical lengths, the peak will move away from $\Delta t=0$. As mentioned above, the other two signal paths Ps2 and Ps3 have the time delays of 4 ns and 8 ns with respect to the path Ps1 (or Pi), respectively. Thus, the signal photons can be detected with the corresponding time delays of $\Delta t=t_{\rm s2}-t_{\rm i}=4$ ns and $\Delta t=t_{\rm s3}-t_{\rm i}=8$ ns, respectively. There should be another two peaks at $\Delta t=4$ and 8 ns in the coincidence measurement results (as shown in Fig. 2). We can see that any peak of coincidence has the same full width of $\sim$2.0 ns, which is the same as the time window of the coincidence counter used in our experiment. The experimental data within the coincidence window is counted for extracting the information of objects in our experiment. Since there is an object in each signal path, the amplitude of each peak in the coincidence measurement results contains the information of the corresponding object. Correspondingly, to pick up the information of three objects, we set three coincidence windows centered at $\Delta t=0$, 4 and 8 ns, respectively. As shown in Fig. 2, four measurement results show the coincidence counts of four different positions (P1–P4) in the scanning plane of MMF2. A peak in coincidence window $\Delta t=0$ ($\Delta t=4$, 8 ns) indicates the transmission of the path Ps1 (Ps2, Ps3), while a lack of peak indicates that the corresponding path is blocked by an object.
cpl-36-4-044205-fig3.png
Fig. 3. Experimental results of multi-path ghost imaging, where (a), (b), and (c) are images of the three objects reconstructed from the coincidence measurement. Here $29 \times 29=841$ scanning steps are needed for each image. Each step covers an area with a diameter of 50 µm and has a coincidence time of $\sim$5 s. (d) A mixed image of the three objects achieved by extracting all information contained in the three peaks at each scanning step.
The information of each peak is extracted by recording the counts within each window only. To obtain the full two-dimensional information of the object and then reconstruct its image, we need to scan MMF2 connected to the single-pixel detector D2 in the $X$–$Y$ plane step by step. For each scanning step, D2 will cover an area with a diameter of 50 µm and the measurement time is $\sim$5 s. To reconstruct a frame image, D2 is scanned by $29\times29=841$ steps. The experimental results are shown in Figs. 3(a)–3(c). Clearly, the multi-path ghost imaging is realized. If the coincidence windows are too wide, coincidence counts from the three signal paths will be recorded simultaneously. Thus a clear image of the object cannot be obtained. If all the information contained in the three peaks is extracted together at each scanning step, the image will be a mixed image of the three objects, as shown in Fig. 3(d). To evaluate the quality of ghost imaging, the visibility is an important parameter. As an example, we extract the experimental data along the white horizontal line in Fig. 3(a) to plot them in Fig. 4 by the blue circles. The visibility of Fig. 4 has been calculated by[3,26,41] $$\begin{align} V=\dfrac{\langle I_{1} I_{2} \rangle_{\rm max}-\langle I_{1} I_{2} \rangle_{\rm min}}{\langle I_{1} I_{2} \rangle_{\rm max}},~~ \tag {1} \end{align} $$ where $\langle I_{1} I_{2} \rangle_{\rm max}$ and $\langle I_{1} I_{2} \rangle_{\rm min}$ are the maximum and minimum coincidence counts, respectively. The experimental data gives a visibility of 87.2%. The signal-to-noise ratio (SNR) is also an important parameter for evaluating the imaging quality and is defined as[42,43] $$ SNR=\dfrac{ \sum\limits_{x=1} ^{X} \sum\limits_{y=1} ^{Y} [f(x,y)-\overline{f(x,y)}]^2}{\sum\limits_{x=1} ^{X} \sum\limits_{y=1} ^{Y} [g (x,y)-f (x,y)]^2},~~ \tag {2} $$ where $f$ and $g$ represent the original and the retrieved images with the size of $X\times Y$ pixels, and $\overline{f(x,y)}= [\sum_{x,y=1} ^{X,Y} f(x,y) ]/(XY)$. We also calculate the SNR of image in Fig. 3(a) to be SNR = 2.62, which is larger than the result in Ref.  [43].
cpl-36-4-044205-fig4.png
Fig. 4. Data for calculating the visibility of the ghost image. The blue circles are the data corresponding to the white horizontal line in Fig. 3(a).
In conclusion, we have demonstrated multi-path ghost imaging by controlling the time delay between the paired photons. There are three peaks in the experimental results of the coincidence measurement in each scanning step. Each peak contains the information of one object. By transversely scanning the end of the multi-mode fiber in the idler path, the images of three objects can be reconstructed. The reconstructed images have a visibility of 87.2% and a signal-to-noise ratio of 2.62. For ghost imaging with a two-photon source, the visibility and the signal-to-noise ratio of the information are better than those with classical light sources.[24] In principle, more paths in the ghost imaging can be used together. However, the number of paths is limited by two factors including the pulse interval of the pulsed laser and the time window of the coincidence counter. To obtain the clear multi-path ghost images, the two adjacent coincidence peaks cannot be overlapped. Under our experimental conditions, the pulse interval is 12.5 ns and the time window of the coincidence counter is 2 ns, thus the upper limit of paths is up to six paths at most. The larger pulse interval of the pulsed laser and the narrower time window of the coincidence counter benefit to increase the number of path. References Optical imaging by means of two-photon quantum entanglementIdentifying Entanglement Using Quantum Ghost Interference and ImagingExperimental demonstration of ghost imaging with an electromagnetic Gaussian Schell-model beamGhost imaging with electromagnetic stochastic beamsErratum: Experimental X-Ray Ghost Imaging [Phys. Rev. Lett. 117 , 113902 (2016)]Fourier-Transform Ghost Imaging with Hard X Rays“Two-Photon” Coincidence Imaging with a Classical SourceLensless ghost imaging through the strongly scattering mediumTwo-Photon Imaging with Thermal LightCorrelated two-photon imaging with true thermal lightEncryption of ghost imagingCan Two-Photon Correlation of Chaotic Light Be Considered as Correlation of Intensity Fluctuations?Ghost-imaging experiment by measuring reflected photonsOptimization of speckle patterns in ghost imaging via sparse constraints by mutual coherence minimizationThermal light subwavelength diffraction using positive and negative correlationsSingle-pixel imaging via compressive samplingExperimental realization of sub-shot-noise quantum imagingQuantum-secured imagingSimultaneous Measurement of Complementary Observables with Compressive SensingImaging with a small number of photonsReal applications of quantum imagingSpatially resolved edge currents and guided-wave electronic states in grapheneCompressive samplingGhost Imaging with Thermal Light: Comparing Entanglement and ClassicalCorrelationPhase-conjugate mirror via two-photon thermal light imagingLongitudinal coherence in thermal ghost imagingRole of photon statistics of light source in ghost imagingHigh-resolution pseudo-inverse ghost imagingIncreasing the range accuracy of three-dimensional ghost imaging ladar using optimum slicing number methodHolographic Ghost Imaging and the Violation of a Bell InequalityGhost Imaging Using Orbital Angular MomentumObject Identification Using Correlated Orbital Angular Momentum StatesWavelength-multiplexing ghost imagingTwo-color ghost imagingPositive-negative turbulence-free ghost imagingStandoff two-color quantum ghost imaging through turbulenceRadar Coincidence Imaging: an Instantaneous Imaging Technique With Stochastic SignalsTabletop x-ray ghost imaging with ultra-low radiationReal-Time Imaging of Quantum EntanglementPhoton-sparse microscopy: visible light imaging using infrared illuminationCoherent imaging with pseudo-thermal incoherent lightTime-correspondence differential ghost imagingMultiple-object ghost imaging with a single-pixel detector
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