The influence of atmospheric turbulence on holographic ghost imaging using orbital angular momentum entanglement: Simulation and experimental studies

Optics Communications 294 (2013) 223–228

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The influence of atmospheric turbulence on holographic ghost imaging using orbital angular momentum entanglement: Simulation and experimental studies Shengmei Zhao a,b, Hua Yang a, Yongqiang Li a, Fei Cao a, Yubo Sheng a, Weiwen Cheng a, Longyan Gong a,c,n a b c

Institute of Signal Processing and Transmission, Nanjing University of Posts and Telecommunications (NUPT), Nanjing 210003, China Key Lab of Broadband Wireless Communication and Sensor Network Technology, NUPT, Ministry of Education, Nanjing 210003, China Department of Applied Physics, Nanjing University of Posts and Telecommunications, Nanjing 210003, China

a r t i c l e i n f o

abstract

Article history: Received 18 June 2012 Received in revised form 25 November 2012 Accepted 3 December 2012 Available online 8 January 2013

The holographic ghost imaging is a novel ghost imaging scheme, where orbital angular momentum (OAM) entanglement is used to encode object information. OAM state is associated with the spatial distribution of the wave-functions. Hence, atmosphere turbulence (AT), in principle, will reduce the corresponding image resolutions. In this paper, we quantitatively investigate the influences of AT on such imaging scheme with a two-gray-scale and a eight-gray-scale phase object by both numerical simulations and experiments, where the AT-induced phase perturbations are introduced by simulated random phase screens inserting propagation paths. The numerical simulation and experimental results show that with the increase of the constant of index refraction, the peak signal-to-noise ratio (PSNR) of the reconstructed image goes down quickly. For a two-gray-scale ‘NUPT’ character, PSNR degrades from 102 at A2n ¼ 1  1016 m2=3 weak turbulence to 20 at A2n ¼ 1  1012 m2=3 strong turbulence by simulations, while the PSNR decreases from 20 at A2n ¼ 1  1016 m2=3 to 12 at A2n ¼ 1  1012 m2=3 by experiment. When the object is turned to eight-gray-scale ‘Lena’ image, the PSNR values show that AT has the degraded effects on HGI, even at A2n ¼ 5  1016 m2=3 weak turbulence. All these results show that the holographic ghost imaging is influenced by atmospheric turbulence, the methods to mitigate the influence should be developed in the implementation of ghost imaging using OAM states. & 2012 Elsevier B.V. All rights reserved.

Keywords: Quantum ghost imaging Orbital angular momentum Atmosphere turbulence

1. Introduction In recent years, an intriguing optical technique, ghost imaging (GI), also known as two-photon imaging and correlated image, has attracted much attention in the field of quantum optics [1–4]. There are two optical beams in the system. One beam that crossed the object is detected by a bucket detector without any spatial resolution, the other beam is detected by a spatially resolving detector in the reference arm. The image is retrieved when the bucket detector signal is correlated with that signal in the reference arm, whose noise is spatially correlated to the signal beam [1]. In other words, the image was formed without directly obtaining any spatially resolved image information from the object itself [2], therefore it is called GI.

n Corresponding author at: Institute of Signal Processing and Transmission, Nanjing University of Posts and Telecommunications, Nanjing 210003, China E-mail addresses: [email protected], [email protected] (L. Gong).

0030-4018/$ - see front matter & 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2012.12.027

In 1995, Pittman et al. [5] demonstrated the GI using a source which produced quantum entangled photons by a spontaneous parametric down-conversion (SPDC) process. It was also supposed that GI could be implemented using a classical source with the proper statistical properties. For examples, in 2002, Bennink et al. [6] reported an experiment in which a demonstrably classstate source yielded a ghost image. Using pseudothermal light source, Valencia et al. [7] demonstrated GI. Based on this, Ferri et al. [8] further studied the high-resolution ghost image and ghost diffraction. Comparing with the thermal GI (based on classical source), quantum GI (based on quantum entanglement) offers much higher image contrast and a modest spatialresolution advantage [9]. For many optical applications, imaging through atmospheric turbulence (AT) is unavoidable [11]. In principle, AT will perturb the wavefront phase and amplitude of photon wave functions [12], and subsequently will affect the resolution and visibility of the imaging. The properties of quantum GI using positionmomentum entangled photons have been extensively investigated both in theory [13–15] and experiment [11] through AT.

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For examples, Refs. [13,14] showed that the images will be significantly degraded with strong turbulence and large propagation distance. Refs. [11,15] found that the influence of the AT can be mitigated under certain conditions. GI system allows the imaging of objects located in optically harsh (difficult to be reached) or noisy environment [10]. Therefore, it is a good candidate for distributed image processing, distributed sensing and communication schemes due to its distributed nature. Currently, a novel holographic GI (HGI) scheme based on orbital angular momentum (OAM) entangled states was proposed and demonstrated by experiments [16]. It has some advantages comparing with the quantum GI schemes without OAM [5,11,13–15]. For examples, it provides a convenient method to GI system with phase objects; it can enhance edge contrast of image; the use of single-mode detectors and hologram to select OAM state supports the high contrast images without need for background subtraction. OAM state of one photon may carry more than one bit information, so the quantum GI system using OAM state provides the potential to implement GI for multiple gray-scale object [17]. However, OAM state is encoded in the spatial profile of light beams, which leads to the purity of the mode theoretically more susceptible to turbulence aberrations in free space [18–20]. How AT quantitatively reduces the image resolutions in HGI system has so far less been discussed and analyzed. In this paper, we will give detailed studies of the influence of AT on HGI by simulation and experiment. We use a set of simulated phase screens to match the fluctuations in the index of refraction of atmosphere turbulence. Meanwhile, we employ a spatial light modulation (SLM) to control the random phase distributions of AT on the beams. This paper is organized as follows. In Section 2, we present the experimental setup of HGI system through AT, the thin sheet phase screen model of AT, and the theoretical deduction of the influence of AT on HGI. In Section 3, we give the numerical and experimental results of HGI through AT. Finally, we draw a conclusion in Section 4.

Phase filter φf (r,θ) 2π 0

SLM

Idler arm f=50cm f=1.5mm Di f=30cm

Pump

f=30cm

φa(r,θ)

Coincidence 2π

counter

BBO

0

SLM

Phase object φo(r,θ)

f=50cm f=1.5mm Ds 2π

or

0 2π 0

Signal arm Fig. 1. The schematic diagram of the implementation of HGI through atmosphere turbulence (AT). The object is encoded by the 0,1 symbol (different gray-scale), and represented by different special phase holograms. The special phase hologram is modulated by spatial light modulator (SLM). Coincidence measurements are made for the different object gray-scale. AT is introduced by a random phase screen. Di,s denote the detector in signal arm and idler arm, respectively.

given by [20,21] XX ‘ , ‘ cðr, yÞ ¼ C pss ,pii ½LG‘pss ðr, yÞ½LG‘pii ðr, yÞ:

ð1Þ

‘s ,ps ‘i ,pi

Here LG‘p ðr, yÞ ¼

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2p! 1 pð9‘9 þ pÞ! w0

! pffiffiffi !9‘9 2 2r 9‘9 2r Lp w0 w20

expðr 2 =w20 Þ expði‘yÞ ¼ R‘p ðrÞ expði‘yÞ

ð2Þ

and p X

ð9‘9 þ pÞ! wm , ðpmÞ!ð9‘9 þ mÞ!m!

2. Experimental setup and holographic ghost imaging through atmosphere turbulence

Lp ðwÞ ¼

In this section, we first describe the experimental setup, and we discuss the influence of AT on HGI theoretically on the setup.

where w0 is the beam waist, ps(pi) is the number of nonaxial radial nodes of the mode, ð‘s ,ps Þ and ð‘i ,pi Þ correspond to the signal and idler modes, respectively, with ‘s þ ‘i ¼ ‘p , and ‘p is the OAM of the pump. In our application, we only use a subspace of the complete Hilbert space, i.e., modes with ps ¼ pi ¼ 0. Hence, the probability amplitude is Z s , ‘i p r dr dy Fðr, yÞ½LG‘s ðr, yÞn ½LG‘i ðr, yÞn , ð4Þ C ‘0,0

2.1. Experimental setup Fig. 1 is the experimental schematic diagram of HGI through AT using entangled OAM states. A mode-locked (100 MHz) 355 nm laser is selected as the pump source. It is focused into a BBO crystal (type I, non-collinear down conversion, 5  5  3 mm) and two beams are produced by spontaneous parametric down-conversion (SPDC) source. The two beams are separated as signal arm and idler arm. The phase object is stepped across the signal beam and imaged onto a single-mode fiber (5 mm). Both phase object and phase filter are implemented by two SLMs (Hamamatsu Photonics). The entangled photons are collected via single mode fiber (SMF) to single-photon counter modules (Perkin Elmer), and the outputs from the modules are fed to a coincidence counter (made by ourselves).

2.2. HGI through atmosphere turbulence By SPDC in Fig. 1, a pump photon gets down-converted to a pair of signal and idler photons from the beta barium borate (BBO) crystal. The two-photon entangled states in the LG basis are

9‘9

ð1Þm

m¼0

ð3Þ

where Fðr, yÞ is the transverse spatial profile with OAM ¼ ‘p of the pump beam at the input face of the crystal (z ¼0). For simplicity, we assume that AT is only at the signal side with a single phase screen fa ðr, yÞ. Actually, the spatial variation by AT should be modeled by using several equally spaced phase screens between the transmitter and the receiver. As shown in Fig. 1, the signal mode propagates in the turbulent atmosphere fa ðr, yÞ, and the phase object fo ðr, yÞ, while the idler mode propagates the phase filter ff ðr, yÞ. Here, the phase aberration fa ðr, yÞ, the phase object fo ðr, yÞ and the phase filter ff ðr, yÞ are realized by SLMs, respectively [16]. The probability amplitude in Eq. (4) becomes Z ‘s , ‘i C~ 0,0 p r dr dy Fðr, yÞ½LG‘s ðr, yÞn ½LG‘i ðr, yÞn exp½ifo ðr, yÞ exp½ifa ðr, yÞ exp½iff ðr, yÞ:

ð5Þ

S. Zhao et al. / Optics Communications 294 (2013) 223–228

Substituting Eq. (2) into Eq. (4), the probability amplitude changes to Z ‘s , ‘i ~ ðrÞ exp½ið‘s þ ‘ ‘p Þy exp½if ðr, yÞ C~ 0,0 p r dr dy C i o exp½ifa ðr, yÞ exp½iff ðr, yÞ,

ð6Þ

‘p

~ ðrÞ ¼ R ðrÞ½R‘s ðrÞn ½R‘i ðrÞn . The coincidence counting is where C 0 0 0 then defined as [20] ‘s , ‘ i 2 C ¼ Pðls ,li Þ ¼ /9C~ 0,0 9 S ZZZ Z ~ ðrÞei½fo ðr, yÞfo ðr0 , y0 Þ ~ ðr 0 ÞC C p 0

0

0

and

s2 ðkx ,ky Þ ¼



 2p 2 Fn ðkx ,ky Þ, N Dx

0

0

2

0

0

exp½ið‘i þ ‘s ‘p Þðy yÞr drr dr dy dy :

ð7Þ

The quantity fw ðr, yÞ can be expanded in an azimuthal Fourier series as [16,18] X eifw ðr, yÞ ¼ G‘w ðrÞei‘w y , ð8Þ ‘w

where the expansion coefficients G‘w ðrÞ are given by Z G‘w ðrÞ ¼ dy eifw ðr, yÞ ei‘w y :

ð9Þ

Substituting Eq. (8) into Eq. (7), the coincidence counting is estimated as Z Z Z Z 1 X ~ ðrÞei½fo ðr, yÞfo ðr0 , y0 Þ ~ ðr 0 ÞC C Cp

ð12Þ

where FFT is the Fast Fourier Transform, A is an N  N array of complex random numbers with zero mean and variance one, and Dx is the grid spacing. Here we use Dx ¼ Dy. The spectrum of the fluctuations Fn ðkx ,ky Þ in the index of refraction is given as vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 3 ! u 2 2 2 7=12 ukx þ k2y kx þ ky 24 t 5 0:254 Fn ðkx ,ky Þ ¼ 0:033An 1 þ 1:802 2 2 kl kl

ei½ff ðr, yÞff ðr , y Þ /ei½fa ðr, yÞfa ðr , y Þ S 0

225

exp

2

kx þky 2

kl

! 2

2

kx þ ky þ

1

!11=6

L20

,

ð13Þ

where kx and ky are the wave-numbers in x and y direction, respectively. A2n is the structure constant of the index of refraction, which represents of the strength of turbulence. L20 is outer scale of turbulence that is the largest eddy size formed by injection of turbulent energy. kl ¼ 3:3=l0 with l0 equals to inner scale of turbulence. Fig. 2 shows a typical thin sheets phase screen model for atmosphere turbulence on LG transverse mode ð‘ ¼ 5Þ, where the refractive index structure parameter A2n ¼ 5  1013 m2=3 , L0 ¼ 50 m, l0 ¼ 0:0002 m, Dx ¼ 0:0003 m, and the propagating distance is 50 m. It is obviously shown that the thin sheets phase model illustrate perfectly the damage effect of atmosphere turbulence on the propagating beam.

‘a , ‘0a ¼ 1 0

0

0

0

ei½ff ðr, yÞff ðr , y Þ /G‘a ðrÞG‘0a ðr 0 ÞSei‘a y ei‘a y 0

0

0

0

exp½ið‘i þ ‘s ‘p Þðy yÞr drr dr dy dy :

ð10Þ

It is sure that the coincidence counting will be affected by the AT. For example, a phase object is made up of a single mode with ‘o ¼ 1 for the object, and a single mode with ‘f ¼ 0 is chosen for the idler beam. The coincidence counting is determined by the coefficient of G‘a , and then result in the influence on ghost imaging resolutions. 2.3. Thin sheet phase screen model Next, we will describe the thin sheet phase screen model (see Fig. 2) to simulate the phase aberration fa ðr, yÞ introduced in Fig. 1. For convenience, we denote the phase aberration of AT by fa ðx,yÞ, where x ¼ r cosðyÞ, and y ¼ r sinðyÞ. As a beam propagates through AT, the beam will be scattered by refractive index inhomogeneities of AT. The spatial variation in atmospheric aberration can be approximated by several thin sheets that modify the phase profile of the propagating beam. The phase aberration fa ðx,yÞ, which matches the fluctuations of the index of refraction [12], can be described by [22,23]

fa ðx,yÞ ¼ FFTðAsðkx ,ky ÞÞ

Fig. 2. The thin sheets phase screen model for atmosphere turbulence.

ð11Þ

3. Simulations and experimental results In the section, we will discuss the influence of atmosphere turbulence on HGI by simulations and experiments. We use the phase f0 from 0 to p to encode the object spatial information on the signal beam [17]. For example, if the object has K grey-scales, f0 ðkÞ ¼ ðp=ðK1ÞÞk, where k ¼ 0,1, . . . ,K1. We use one random phase screen fa ðx,yÞ discussed in Section 2 to model the effect of AT on beams, which can be modulated by a SLM [24]. On the idler arm, we change the phase of the reference beam so as to obtain the maximum coincidence rate in the coincidence counter. We could get each pixel matched phase of the object in the idler arm by analyzing the coincidence rate. We load each pixel information of the object to the beam and obtain its imaging in the idler arm according to the coincidence rate change. In our simulations and experiments, the pump source is a LG beam, which emits onephoton with zero orbital angular momentum, i.e., ‘0 ¼ 0. With SMFs, only ‘1 ¼ 0, p1 ¼ 0 and ‘2 ¼ 0, p2 ¼ 0 modes are selected. We give two examples to illustrate the effect of AT on HGI in the followings. The first one is for two-gray-scale object ‘NUPT’. Fig. 3 shows the corresponding simulation and experimental ghost imaging of characters ‘NUPT’ through AT. In order to illustrate the effect of the strength of turbulent aberration on HGI, we set the refractive index structure constant A2n at A2n ¼ 5  1016 m2=3 , 5  1015 m2=3 , and 5  1014 m2=3 , respectively. The other parameters for the phase screen are the following: the inner scales l0 ¼ 0:0002 m, the outer scales L0 ¼ 50 m, the transmission distance DZ ¼ 1 km, and Dx ¼ 0:0003 m. From Fig. 3, both simulations and experiments show that the quality of the imaging goes down as the strength of turbulent aberration increases. The figure shows that the AT will damage the imaging when the refractive index structure constant A2n is greater than 5  1016 m2=3 in experiment. At the same time, under the same turbulence aberration environment, the results in simulations are better than those in experiments. In order to describe the reconstructed image quantitatively, we adopt the peak signal-to-noise (PSNR) as an objective evaluation for

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S. Zhao et al. / Optics Communications 294 (2013) 223–228

Fig. 3. The effect of turbulent aberration on HGI of characters object ‘NUPT’ (a) simulation results and (b) experimental results.

the imaging [25], which is defined as MSEða,bÞ ¼

N 1 M 1 X X

1 ðaðx,yÞbðx,yÞÞ2 N  Mx¼0y¼0

110

ð14Þ

" PSNR ¼ 10 log10

2

PSNR

and #

maxVal : MSEða,bÞ

ð15Þ

where aðx,yÞ and bðx,yÞ are the intensity values of the original and the reconstructed image at position (x,y), and maxVal is the maximum difference gray scales for the original image object. Generally, the higher PSNR is, the better quality the reconstructed image has. We analyze the image quality varying with the strength of atmosphere turbulence by simulation and experiment. There exist the noise, aberrations and dark counting in experimental environment. For this, we simultaneously present the simulation results with updated noise model. The updated noise model comes from two aspects. One aspect is the Gaussian noise in the beam propagation. We simulatepffiffiffiffiffiffiffi the Gaussian noise using FG ðx,yÞ ¼ aðx,yÞ þibðx,yÞ, where i ¼ 1, aðx,yÞ and bðx,yÞ are zero mean Gaussian random numbers with standard variance s0 . For example, let us assume the amplitude of electric field is Uðx,yÞ, then the electric field passing through the Gaussian noise will turn to U 0 ðx,yÞ ¼ Uðx,yÞ expðiFG ðx,yÞÞ. The other aspect is from the fact that both the signal and idler beams in experiment will be disturbed by Gaussian noise and AT. The effect of AT on beam propagation is normally simulated by a series of random phase screens. Here, we assume each phase screen is a thin sheet and the beam undergoes free-space propagation between phase screens. If U 0 ðx,yÞ is the amplitude of the electric field just prior to the second phase screen, the field would be U 00 ðx,yÞ ¼ U 0 ðx,yÞ expðif0a ðx,yÞÞ after the beam pass through the second phase screen f0a ðx,yÞ. For a series of random phase screens, this procedure will be repeated until the last phase screen is reached. Considering above, in the simulation, we add Gaussian noise and phase screens caused by AT both at the signal and idler beam, and increase the number of phase screens caused by AT to the beam propagation. Fig. 4 shows the PSNR values of the reconstructed image vary with the strength of atmosphere turbulence for the two-grayscale object ‘NUPT’. According to the atmosphere turbulence model, the random phase screen caused by atmosphere turbulence is mainly determined by the constant of the index of refraction. In order to investigate the damaged effect of turbulent aberration, we calculate the PSNR for various strength of the turbulent aberration. We let the index of refraction change while

90

Experiment σ’=0, S, N=1 σ’=0.1,S,N=1 σ’=0.1, Β,N=2

70

σ’=0.2, B,N=3

50 30 10 1E-16

1E-15 1E-14 1E-13 strength of turbulence

1E-12

Fig. 4. The image quality varies with the strength of atmosphere turbulence for two-gray-scale object ‘NUPT’, where s0 is the standard variance of Gaussian noise, S represents AT only at signal beam, B stands for AT both at signal and idler beams, N represents the number of phase screens used in beam propagation.

keeping the other simulation parameters be constant during the simulations and experiments. At the same time, phase screen obtained from the simulation is different from time to time, even with the same simulation parameters, because the phase screen caused by AT is random. We give the average value of the PSNR in each case over 20 times. The figure indicates that the image quality decreases with the strength of turbulent aberration. Due to the noise, aberrations and dark counting in experimental environment, the PSNR in experiment is much lower than that in simulations at the same conditions. However, by adding Gaussian noise, the PSNR of the recovery image goes down quickly. For example, the highest PSNR value is 102 originally, while the PSNR of the recovery image goes down to 20 by adding s0 ¼ 0:1 Gaussian noise. With more phase screens, the decent of the PSNR curve goes down quickly and the simulation results are close to the experimental result. From Fig. 4, we could find that the two-gray-scale object can even be recovered at the middle turbulence without Gaussian noise, say A2n ¼ 1  1014 m2=3 because the PSNR value at this strength is high enough. The second example is for eight-gray-scale object ‘Lena’. Fig. 5 shows the corresponding simulation and experimental results for eight-gray-scale ‘Lena’ through AT. The parameters for the phase screen are, l0 ¼ 0:0001 m, L0 ¼ 5 m, DZ ¼ 10 km, and Dx ¼ 0:0003 m. The results show that the turbulent aberration has the bad effect on the GI system, and the simulation results are better than those in experiment at the same situations. For example, at A2n ¼ 5E 16 m2=3 , the imaging from HGI is almost indistinguishable in

S. Zhao et al. / Optics Communications 294 (2013) 223–228

227

Fig. 5. The effect of turbulent aberration on HGI of a common image object ‘Lena’ (a) simulation results and (b) experimental results.

the PSNR for the eight-gray-scale object is 20, while it is 64 for the two-gray-scale object. But in experiment, the two gray-scale objects have almost the same PSNR value owing to the environmental noise, aberration and the dark counting. The eight-grayscale object cannot be reconstructed at middle in simulation and at weak (A2n ¼ 5E16 m2=3 ) in experiment. Since we select K¼ 5 for the two-gray-scale ‘NUPT’ (the PSNR value will reach to infinity if we select K ¼2 for the two-gray-scale object even at the strong aberration condition, say A2n ¼ 1E12 m2=3 ), the Gaussian noise has more severely degraded effect on the two-gray-scale ‘NUPT’ character than on the eight-gray-scale ‘lena’. Both Figs. 3 and 6 also indicate that by adding Gaussian noise and with more phase screen in beams propagation, the simulation results are close to the experimental result.

Experiment

σ’=0, S, N=1 σ’=0.2,S,N=1 σ’=0.2, Β,N=2 σ’=0.4, B,N=3

26

PSNR

22 18 14 10 6 1E-16

1E-15

1E-14

1E-13

1E-12

strength of turbulence Fig. 6. The image quality varies with the strength of atmosphere turbulence for multiple gray-scale object ‘Lena’, where s0 is the standard variance of Gaussian noise, S represents AT only at signal beam, B stands for AT both at signal and idler beams, N represents the number of phase screens used in beam propagation.

experiment, while the imaging will be indistinguishable at A2n ¼ 5E14 m2=3 in simulation. With the increase of the refractive index structure constant, the imaging quality degrades quickly. Fig. 6 shows the PSNR values of the reconstructed ‘Lena’ vary with the strength of atmosphere turbulence. Similarly, we presents the simulation results with the updated noise model. We let the index of refraction change while keeping the other parameters be constant during the simulations and experiments. Meanwhile, we obtain the average value of the PSNR at any cases over 20 times. Both simulations and experimental results show that the value of PSNR decreases with the increase of A2n . Compared with the two-gray-scale object, the difference between the simulation result and the experimental results is relatively smaller for the eight-gray-scale object. The low value in grayscale is disturbed more seriously by the strength of turbulence aberration, which results in the object with larger gray-scale will be affected more seriously by AT under the same strength of turbulence aberration. The eight-gray-scale object has significantly lower quality to the two-gray-scale object in the simulation from Figs. 3 and 6. For example, at A2n ¼ 1E14 m2=3 ,

4. Conclusion In this paper, we have quantitatively investigated the influence of turbulent atmosphere on the holographic ghost imaging (HGI) with two different gray-scale phase objects, where the thin phase screen model is used and the turbulent aberration is simulated by a phase aberration distribution. In the HGI scheme, we encode the different object gray-scale information with different kinds of superposition of OAM states, and we introduce the phase aberration distribution to the propagation beam by spatial light modulators. We have studied the influence of turbulence on HGI both from simulations and experiments. In order to quantity the quality of imaging from HGI, we use PSNR as the objective evaluation. The simulation and experimental results show that atmosphere turbulence seriously affects the imaging resolution since the OAM state is associated with the spatial distribution. With the increase of the constant of index refraction, the PSNR of the reconstructed image goes down quickly. In the simulation, the image could be recovered at middle turbulence, and the two-gray-scale object has fully reconstructed quality. However, due to the environmental noise and the dark counting, the image will be affected by the turbulence even at the weak turbulence in experiment, the images are significantly degraded by the strong turbulence for the eightgray-scale object. By adding Gaussian noise and with more phase screen in beams propagation in the simulation, the simulation results could be close to the experimental result gradually. The methods to mitigate the influence should be developed in the implementation of ghost imaging using OAM.

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Acknowledgments The authors thank Optics group, School of Physics and Astronomy, Glasgow University for hosting S.M. as a visitor. Thanks to Dr. Leach for helping the setup of the experimental platform. S.M. is partially supported by NSFC (No. 61271238), SRFDPHEC (No. 20123223110003), UNSRF (No. 11KJA510002), JSHEI (No. NJ210002), PAPD, and ORF of KLBWC&SNT(MOE). L.Y. is supported by NSFC (No. 10904074).

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