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As a novel imaging method, ghost imaging has been widely explored in various fields of research, such as lensless ghost imaging, computational ghost imaging, turbulence-free ghost imaging. Recently, ghost imaging in non-degenerated system with pseudo-thermal light has been discussed theoretically, however, to our best knowledge, no experimental evidence has been proven yet. In this paper, we propose a new approach to realize ghost imaging with different frequencies, which are generated through a non-degenerated four-wave mixing(FWM) process in Rb vapor. In our experiment, by employing pseudo-thermal light as the probe beam, we found that the generated FWM signal has a strong second-order correlation with the original thermal light. On basis of that, we successfully implement non-degenerate ghost imaging, and reconstruct highly similar images of objects.
© 2016 Optical Society of America
1. Introduction
Ghost imaging, first observed by Pittman et al. in 1995 [1] and extensively discussed in recent years, is a technique that reproduces the image of an object by making use of the nonlocal correlation feature of quantum imaging. It basically relies on two spatially correlated light fields and two respective photon-detectors: a bucket detector that collects the total intensity of a light field, by which the object is illuminated, and a high-resolution detector corresponding to a reference field without the object in it. Neither detector is capable of imaging the object independently. However, by combining the measurements of coincident photon detections, the imaging of the object can be achieved. In contrast to the classical optical imaging method, ghost imaging can remove the need of placing a spatially resolving detector near the objects when they are located in an optically harsh environment.
Initially, ghost imaging could only be realized with quantum entangled twin photons, for instance, two correlated photons generated by spontaneous parametric down conversion(SPDC) [2]. However, in 2002, it was found that with the classical pseudo-thermal light, the similar phenomena could be observed as with the quantum states [3–7].
On the basis of traditional ghost imaging, computational ghost imaging is presented [8]. It utilizes a programmable light field, which contains the whole spatial information of a speckle pattern and therefore removes the need of the spatially resolving detector. In particular, with multiple single-pixel devices and a set of suitable algorithms, computational ghost imaging can display full-color [9], and even three-dimensional [10] ghost imaging. Because of its great potential application, other state-of-the-art ghost imaging systems are ceaselessly come up with, such as lensless ghost imaging [11], turbulence-free ghost imaging [12], reflected ghost imaging [13] and so on.
In most cases, the object beam and the reference beam have the same wavelength. However, light with some specific frequencies cannot propagate for a long distance without loss no matter in free space or optical fibers. Such a loss would severely influence the quality of imaging. To overcome this defect, it is a reasonable way to use light with some other frequencies to assist the imaging process. It is called non-degenerate ghost imaging, and has some relevant achievements. Two color ghost imaging with both quantum and classical light source has been theoretically studied [14]. It shows that a high-quality reconstructed image can be obtained with two different wavelength beams. Meanwhile, non-degenerate ghost imaging [15, 16] and ghost interference [17, 18] with entangled photons have been realized experimentally. It can translate the image information from infrared to visible wavelengths. Yet, to our best knowledge, the experiment reported using thermal light with different frequencies has not been implemented. The difficulties are due to the fact that after passing through the ground glass diffuser beams with different wavelengths will obtain different phase shifts. Meanwhile, using spatial light modulators(SLMs) to load the same spatial intensity pattern onto each beam also needs some complex programming to overcome different phase shift. Different phase shift of two beams causes the degradation of coincidence, which affects the ghost imaging quality. However, pseudo-thermal light is much easier to generate and detect, thus it may have more potential application in optics imaging.
In this paper, we experimentally demonstrate the pseudo-thermal ghost imaging via a non-degenerated four-wave mixing(FWM) process. The different phase shift of two different wavelength beams are effectively avoided due to the phase match condition in FWM process. We attribute the probe beam to the pseudo-thermal light by a rotating ground glass. Then the second-order correlation between probe beam and generated signal beam through FWM process has been testified. Based on the strong second-order correlation between two beams, we successfully perform the ghost imaging experiment with different frequencies.
2. Experimental results and discussions
A typical FWM process in atomic medium is schematically shown in Fig. 1(a). The forward(F) and backward(B) pump beams have orthogonal linear polarization and counter-propagate to each other. The probe beam(P), which has the same polarization with B, is sent into an atomic vapor and intersects with the pump beams by a very small angle. On FWM condition, the FWM signal beam will be generated. The atomic medium used here is 85Rb vapor, which is enclosed inside a glass cell with the ambient temperature maintained around 70°C. The corresponding energy diagram of 85Rb and transitions involved in FWM process are depicted in Fig. 1(b). The frequencies of forward and backward pump beams, and probe beam (ωF, ωB, ωP) are tuned to resonant with |5S1/2, F = 3〉 → |5P3/2, F = 3〉, |5S1/2, F = 2〉 → |5P1/2, F = 2〉, and |5S1/2, F = 2〉 → |5P3/2, F = 3〉 transitions, respectively. The signal resonant with |5S1/2, F = 3〉 → |5P1/2, F = 2〉 can thus be generated. According to the phase matching condition, the signal beam counter-propagates with the probe beam, and has the same polarization as F.
Fig. 1 (Color online) (a)A typical FWM process. F, B, and P present the forward pump beam, the backward pump beam, and the probe beam, respectively. (b)The corresponding energy diagram and transition lines of 85Rb in the non-degenerate FWM process.
The experimental setup is schematically depicted in Fig. 2(a). Three external cavity diode lasers (TOPTICA DL-100) with the wavelength of 780nm or 795nm are utilized. Two of them are used as pump beams, while the third one serves as a probe beam. From the energy structure of 85Rb atom and transition lines, the wavelength of F and P is 780nm, while that of B and the signal beam is 795nm. Single-mode fibers are used here to optimize mode of lasers.
Fig. 2 The experimental setup of measuring (a)the second-order correlation and (b)implementing the ghost imaging in FWM. (a)Three external cavity diode lasers(not shown) are used to couple with three single mode optical fibers. The probe beam becomes pseudo-thermal light after passing through a rotating ground glass. Then the thermal light is separated into two parts by a PBS. The reflected part with vertical polarization is sent into a vapor cell as the probe beam and thus generates the signal by FWM, while the transmission part is directly reflected by a mirror. Both of these two beams are collected by a CCD camera with the same optical length. (b)An object is put in one of the beam paths, and the speckle patterns passing through it will be collected as the bucket detection for implementing the ghost imaging. SMF:single mode optical fiber; L:lens; Ms: mirrors; HWPs:half-wave plates; PBS:polarization beam splitter; BSs:beam splitters; CCD:charge coupled device camera.
After emitting out of the fiber, the probe beam is divided into two parts by a polarizing beam splitter(PBS). The reflected part with vertical polarization is sent into the vapor cell with a 1° angle of inclination to the pump beams. The transmitted part is directly collected by a charge coupled device(CCD) camera(INFINITY3). Meanwhile, the two pump beams propagate in the vapor cell with opposite direction to interact with probe beam. Under FWM condition, the generated signal beam which counter-propagates with probe beam will pass through the PBS, and then be collected by the CCD camera after being reflected by two BSs.
In our previous work, it has been proven that when the probe beam is Laguarre-Gaussian beam or Airy beam, the generated FWM signal has the same properties and phase distribution with them [19, 20]. It is a reasonable assumption that this conclusion will also work on psuedo-thermal light.
The pseudo-thermal light is obtained by sending a Gaussian mode beam through a rotating ground glass. Its coherence time can be controlled by adjusting the velocity of the motor, which drives the glass. The rotation speed is set at 20r/min, which corresponds to the coherence time of about 2.5ms for the pseudo-thermal light. Then it is divided into two parts by a polarizing beam splitter just as depicted before. The interaction between the pseudo-thermal probe beam with other two strong pump beams generates the FWM signal.
The power of the forward pump is 11mW, the backward pump is 10mW, the probe power is 500μW, and the FWM signal we obtained is 25μW. The FWM efficiency is 5% in our experiment, and it is influenced in many aspects. For instance, adjusting the detuning of these beams can largely suppress the absorption loss in FWM mixing. Furthermore, using different atomic level configuration, polarization of pump beams, and angle of probe beam and pump beams can also make a big difference in obtaining a higher efficiency.
To demonstrate ghost imaging, we use the probe beam and the generated signal beam as the two corresponding beams, namely the “object beam” and the “reference beam”, respectively. A CCD camera is used to synchronize them, and each of them is captured by only one half screen of the CCD camera. In particular, the optical lengths of these two beams should be equal by adjusting position of mirrors. The calculation starts at the position of the PBS where the thermal light splits into two parts, and ends at the CCD camera. Figure 3 shows two single shot images from the object beam and the reference beam, which exhibits random fluctuations in intensity as speckle patterns. Their correlation is examined by following two steps.
Firstly, we detect the photon statistics of the two beams by a photon-electron counting technique. The measurement consists in counting the number of photons arriving within a given observation time interval of duration T(T=100μs), and plotting the statistical distribution. The statistical histograms are presented in Figs. 4(a) and (b), comparing with that of a coherent beam with Gaussian profile directly emitted by the laser shown in Fig. 4(c). On the premise of having the same amount of photons, the curve in Gaussian beam is much more concentrating compared to the probe beam. The FWM signal, however, has more decentralized value of photon counting, and more similarity with the pseudo-thermal probe beam rather than Gaussian beam. From above measurements, we can draw a conclusion that the generated signal in FWM process is a pseudo-thermal field.
Fig. 4 The photoncount distribution of (a)the probe beam, (b)the FWM signal beam and (c)a Gaussian beam, respectively. The ordinate is the probability, while the abscissa is photon counts.
Secondly, we calculate the second-order correlation between the reference beam and the object beam on the basis of 500 shots of speckles patterns in Fig. 3. In addition, the time interval of sampling is 100μs, which is much shorter than the coherence time of the light source. Then we pick a random spot in the middle of Fig. 3(a), and calculate its second-order correlation with all the spots in Fig. 3(b) with formula
where, I(xi) is intensity of the spot in coordinate xi on each speckle pattern(i = a, b) and the brackets 〈...〉 denotes ensemble average. The calculation results are shown in Fig. 5. As we can see, there is a small area in the middle that has a maximum value that approaches to 1.7. The results show there is a strong correlation between the reference beam and the object beam.Fig. 5 The experiment results to test the second-order correlation. (a)The second-order correlated function of a random spot on one of the speckle patterns and all spots on the other one.(b)The corresponding cross-section of (a).
Bearing in mind the strong correlation, now let’s proceed the ghost imaging experiment. As shown in Fig. 2(b), a mask with a transparent double-slit(or a X-shape) is placed in the object beam path, just in front of the CCD camera. When the mask is illuminated by the thermal light, one half division of the CCD captures images shown in Figs. 6(a) and 6(d), while the other half division on CCD of the reference beam path still gets the speckle pattern. By using the bucket detection method, we sum up the total intensity of the beam passing through the mask, and calculate its second-order correlation with the reference beam in accordance with the following formula
where i = 1, 2, ..., N, N is the number of samples. denotes the integral of the light intensity passing through the object. r is pixel’s coordinate of speckle pattern in reference path and is the intensity of the pixel r.Fig. 6 The experimental results. (a) and (d) are images when a mask is illuminated by thermal light. (b) and (e) depict the reconstructed images of a double-slit and a X-shape transmission objects(insets), obtained by 10000 frames of two speckle patterns. (c) and (f) are results of complementary experiments we mentioned in text, also with 10000 frames of two speckle patterns.
This formula combines the intensity of these two beams, giving us the image that reveals the shape of transparent part on the mask. Averaged over 10000 shots, the results are presented in Figs. 6(b) and 6(e), showing the reconstructed images of two objects.
It is undeniable that, with the jagged and breezing edges, the visual effects of reconstructed images are less than satisfactory. One reason maybe due to the diffraction, which is severely influenced by object’s size and quality. To reduce the impact of diffraction, we carry out a complementary experiment. Instead of putting a real mask in front of CCD to generate the object speckle field, we directly capture two whole speckle patterns. Then we draw the outline of a double slit or a X-shape regions in one of the speckles. We sum up the whole intensity of the chosen regions, which is equivalent to the bucket detection. Figures 6(c) and 6(f) show the processing results. In contrast to former ones, the complementary experiment gives reconstructed images a little higher contrast and more smooth edges.
On the other hand, we realize the speckle size also significantly affects the imaging quality. In our recent experiment, we demonstrate the imaging contrast and visibility can be well enhanced with manipulating the speckle size. In such way, we believe our ghost imaging quality can also be improved with smaller speckle size.
Furthermore, we notice there exists a bright background for our reconstructed images. The bright background comes from the restricted interaction region and low efficiency of FWM. In our experiment, the thermal probe beam may not be totally included in the FWM interaction region. Thus the generated thermal signal beam only correlates to the part of probe beam. Meanwhile, the low efficiency degrades the whole spatial correlation of speckles between the probe beam and signal beam.
3. Conclusion
In conclusion, the main purpose of this paper is to experimentally verify that ghost imaging is feasible in a non-degenerated FWM process. By applying the pseudo-thermal light property to the probe beam, we collect the pseudo-thermal signal beam on FWM condition. The signal beam is verified to have the same statistical distribution of photon counts and the highly second-order correlation with the input thermal probe beam. With 10000 frames of transmission object’s speckle patterns, we get the realistic reconstructed images, which gives a potential method to achieve ghost imaging by beams with different frequencies.
Funding
National Natural Science Foundation of China (NSFC) (11374238, 11204235, 11534008).
References and links
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