A synchronous measurement technique for the evaluation of atmospheric extinction coefficient and refractive index structure constant

Optics Communications 311 (2013) 288–293

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A synchronous measurement technique for the evaluation of atmospheric extinction coefficient and refractive index structure constant Dagang Jiang a,n, Ke Deng a, Peng Zhang a, Zhoushi Yao b, Xiaofeng Li a, Kaiyu Qin a a b

School of Astronautics & Aeronautic, University of Electronic Science and Technology of China, Chengdu 611731, Sichuan, China Research & Development Center, China Academy of Space Technology (Xi′an Branch), Xi′an 710036, Shanxi, China

art ic l e i nf o

a b s t r a c t

Article history: Received 3 May 2013 Received in revised form 19 August 2013 Accepted 24 August 2013 Available online 7 September 2013

Atmospheric extinction coefficient and refractive index structure constant (C 2n ) are important parameters to represent laser beam propagation in the atmosphere. However, to best of our knowledge, the typical measurement methods for these two parameters have not been integrated into a system. Therefore, a synchronous measurement technique for the evaluation of atmospheric extinction coefficient and C 2n is proposed, which is applicable from weak to strong fluctuation. This technique employs projector image optics with larger aperture Fresnel lens to receive atmosphere modulated speckle. The extinction coefficient is evaluated by speckle irradiance and C 2n is evaluated by speckle wander effect. The receiving aperture constrain condition is also discussed to ensure the speckle can be received in the long term beam wander effect under the strong fluctuation. The theory and experiment demonstration indicate that this technique provides a feasible way to simultaneously measurement extinction coefficient and C 2n . & 2013 Elsevier B.V. All rights reserved.

Keywords: Atmospheric propagation Atmospheric turbulence Space optics Free-space optical communications

1. Introduction Atmospheric extinction coefficient and refractive index structure constant (C 2n ) are important parameters to represent laser beam propagation in the atmosphere. The extinction coefficient describes transmittance (attenuation) effects and the C 2n describes turbulence effects, which are commonly researched in the application areas of free space optical communications (FSO) [1], laser radar [2], remote sensing [3] and so on. The extinction coefficient is typically measured by lidar or visibility sensor. The lidar is basing on the backscatter measurement with the assumption that the atmospheric extinction to backscatter ratio is certain and then the extinction can be indirectly retrieved by inversion algorithms [4,5]. However, the extinction to backscatter ratio is highly variable [6]. The visibility sensor is basing on the laser transmission measurement with the condition that the distance between transmitter and receiver is short (about half meter) and then the beam propagation effects (diffraction and beam wander) can be ignored [7]. The visibility sensor measurement result is then inferred to be homogeneous within a several mile radius around the sensor [8,9]. It only performs accurately when the climatic conditions are relatively stable.

n

Corresponding author. Tel.: þ 86 18030892950; fax: þ86 2861831857. E-mail address: [email protected] (D. Jiang).

0030-4018/$ - see front matter & 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.optcom.2013.08.076

Another approach to assess the atmospheric visibility is using digital photography [10,11]. The CCD camera is calibrated as an irradiance meter and measures the extinction coefficient through transmission characteristics of target and background irradiance, which is validated by the contrast experiment with lidar [11]. The C 2n measurement methods are varied. The measurement techniques include two main categories. One is to measure the C 2n by testing a certain turbulence effect, such as measuring the beam wander effect to evaluate C 2n [12–15], measuring the scintillation effect to evaluate C 2n [16,17], and measuring the angel-of-arrival fluctuation effect to evaluate C 2n [18,19]. Those methods depend on a basic assumption that the laser beam approximately horizontally propagates thought a quasi uniform landscape (whole terrestrial surface or water surface). The other technique is to measure the C 2n by a specific sensor on the local test point, such as using a thermometer [20] or a sonic anemometer [21]. Beam wander represents the movement of the beam center, which is initially received and measured by a large homogenous reflectance board [12,13]. However, the receiving irradiance decreases greatly by the reflect board. Some improved measurement methods come out, such as measured with large aperture receiving optics [14] and measured with three photo-detectors in a triangle-shaped array placed on the receiver plane [15]. It is worth noting that those C 2n evaluation methods are based on the relationship of C 2n and beam wander in the weak fluctuations, which is a simple analytic form with some estimation error in the strong fluctuations. Furthermore, the appropriate receiving aperture

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for the beam wander measurement has not been investigated in those researches. Scintillation represents the received irradiance fluctuations, which is described by a fourth-order statistic named scintillation index. The behavior of irradiance fluctuations is actually a combination of atmospherically induced scintillation and that caused by appreciable beam wander [22,23] p. 274. For the purpose of measurement simplification, the typical measurement of C 2n from scintillation usually neglects beam wander influence. Angle-ofarrival fluctuations represent the average wave-front fluctuations, which is associated with beam phase distortion in the atmosphere. The thermometer or a sonic anemometer is easily influenced by the heat source or wind field on the local test point. In sum, to best of our knowledge, the typical measurement methods for the extinction coefficient and C 2n have not been integrated into a system. In fact, simultaneously measurement of extinction coefficient and C 2n will be conducive to comprehensive understanding the behavior of laser beam propagation in the atmosphere. Especially for the application of FSO, atmospheric extinction coefficient and C 2n are important channel parameters, which respectively influence the availability and bit error-rate (BER) [24,25]. In this paper, inspired by the Fresnel lenses rear projection displays [26], we present a synchronous measurement technique with receiving aperture constraint condition, which employs large aperture projection optics to receive atmosphere modulated laser speckle images and evaluate extinction coefficient and C 2n from speckle images. The paper is organized in the following way. Section 2 presents the synchronous measurement principle and discusses the constraint condition of the receiving aperture. In Section 3, the experiment demonstration for this technique is carried out. Measurement device and experiment results are described. Section 4 discusses the measurement achieved and sketches some future suggestions. Section 5 makes a conclusion for this measurement technique.

2. Measurement principles When a collimated laser propagates in atmosphere, it is modulated by atmospheric molecules. The ideal Gaussian beam from the transmitter turns into speckle at the receiving aperture (see Fig. 1). The projector optics images the small size of speckle irradiance on the CCD. According to the geometric mapping relationship, the variance of the random displacement of the beam center at the receiving aperture can be obtained by series CCD images. Therefore, the C 2n can be measured through beam wander effect. Meanwhile, based on the linear relationship between the CCD pixel gray value and the incident irradiance, the receiving speckle power can be evaluated by the sum of CCD image gray value.

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Combined with the transmitting power and the propagation distance, the extinction coefficient is available. Furthermore, the receiving aperture should be large enough to ensure the speckle can be received under the long term beam wander effect. Otherwise, the partial speckle receiving will increase measured C 2n and extinction coefficient. 2.1. Projection optics design The projection optics is composed by two lenses. The focal length of lens 1 is F 1 and the focal length of lens 2 is F 2 . The distance between lens 1 and lens 2 is L1 and the distance between lens 2 and CCD is L2 . When L1 ¼ F 1 þ F 2 and L2 ¼ L1 F 2 =F 1 , the ABCD matrix is: ! 0 F 2 =F 1 ð1Þ 0 F 1 =F 2 The beam radius W′ at receiving aperture becomes W′F 2 =F 1 at CCD plane. The phase front radius of curvature F′ at receiving aperture becomes F′F 22 =F 21 at CCD plane. 2.2. Measurement C 2n from speckle images The C 2n can be treated as a constant in a horizontal path that traverses a uniform topography. Using the extended Huygens– Fresnel principle, under the assumption of the Kolmogorov power law spectrum and an infinite outer scale, the relationship of variance of beam wander and C 2n for a collimated beam can be expressed as following [23] p. 250: Z 1 h i1=6  2 1=3 ξ2 1 þ 1:63sR12=5 Λ0 ð1ξÞ16=5 dξ ð2Þ r C ¼ 7:25C 2n L3 W 0 0

where W 0 is the beam radius at the transmitter and Λ0 ¼ 2L=kW 20 . L is the propagation distance. s2R is Rytov variance and s2R ¼ 7=6 1:23C 2n k L11=6 . o r 2C 4 is the variance of the random radial displacement of the beam center at the receiving aperture and r 2C ¼ x2C þ y2C . The random axial displacement xc and yc can be obtained as following: , M

N

xC ¼ β ∑ ∑ xhðx; yÞ x¼1y¼1 M

N

yC ¼ β ∑ ∑ yhðx; yÞ x¼1y¼1

M

N

∑ ∑ hðx; yÞ

x¼1y¼1

,

M

N

∑ ∑ hðx; yÞ

x¼1y¼1

ð3Þ

where xc and yc are the speckle centroid at receiving aperture. M and N are axial pixel number of CCD. hðx; yÞ is the gray value in position ðx; yÞ on CCD plane. β ¼ F 1 =F 2 is the geometric amplification

Fig. 1. Illustration of laser propagation from laser source to CCD plane.

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coefficient of the projection optics, which is the ratio of speckle size at the receiving aperture to the speckle size at CCD plane. Eq. (2) is applicable from weak (s2R o 1) to strong (s2R 4 1) fluctuation, but it is difficult to express the C 2n and or 2C 4 in a simple analytic form. So C 2n is evaluated from the numerical simulation curves in Fig. 2 given by Eq. (2). Additionally, in order to ensure the speckle can be received in the long term beam wander effect under the strong fluctuation (see Fig. 3(a)), the receiving aperture should satisfy the constraint conditions: D Z 2ðW ST þ o r 2C 4 1=2 Þ ¼ 2

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  W 2LT  or 2C 4 þ o r 2C 4 1=2

ð4Þ

where W 2LT ¼ W 2ST þ o r 2C 4, and W 2ST is short term beam spread. According to Ref. [23] p. 238 the long-term beam radius defined by: W LT ¼ W

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 12=5 1 þ 1:63sR Λ

ð5Þ

where W is beam radius at distance L. For a collimated beam, 2 W ¼ W 0 ð1 þ Λ0 Þ1=2 and Λ ¼ 2L=kW 2 . Combined with Eq. (2), (4) and (5), the minimum receiving aperture is numerical simulated in Fig. 3(b). The measurement range of C 2n is depended on the manufactured aperture D.

2.3. Measurement extinction coefficient from speckle image As a Gaussian beam propagates through a random medium, the mean irradiance profile remains approximately Gaussian in the weak fluctuation [23] p. 189 and the mean irradiance is exactly Gaussian function in the strong fluctuation ignoring outer scale effects [23] p. 237. So the mean irradiance from weak to strong fluctuation can be written as: !   W2 2r 2 Iðr; LÞ ffi 20 expðαLÞexp  2 ð6Þ W LT W LT where W LT is defined as Eq. (5). The atmospheric extinction coefficient α with units of km  1 can be expressed as [27]: α ¼ aer mol mol aer aer aaer sca þ aabs þ asca þaabs , where asca is aerosol scattering. aabs is the mol absorption of aerosol. amol is molecular scattering. a is molecular sca abs absorption. Therefore, the power PðD; LÞ incident on the circular aperture D can be expressed as: " !# Z D 2 D2 PðD; LÞ ¼ 2π o Iðr; LÞ 4 rdr  P 0 expðαLÞ 1exp  2W 2LT 0 ð7Þ where P 0 is output power at transmitter. Because W 2LT is unpredictable, the item exp ðD2 =2W 2LT Þ should be ignored at certain condition. Once the manufactured aperture D is defined, the maximum measurable C 2n is given. Meanwhile the maximum W 2LT and the maximum power estimation error is confirmed. For example, if D ¼ 400 mm and L¼ 1940 m, the maximum 2 13 2=3 measurable (see Fig. 2(c)). The W 2LT ¼ 0:1486 m  C n is 10  m 2 2 estimation and exp D =2W LT r 0:0267. That means the power   error is less than 2.67% by ignoring the item exp D2 =2W 2LT . So Eq. (7) can be simplified at certain error level without aperture diameter:

α ¼ ln P 0  ln PðLÞ =L ð8Þ In the ideal condition, all the CCD pixels are uniform and there is no dark signal. The background irradiance is blocked by optical filter. The single pixel gray value can be described as following [28]: hðx; yÞ ¼ Apix RCCD t int G  Iðx; yÞ ¼ K  Iðx; yÞ

Fig. 2. Numerical simulation curves for o r 2C 4 with the change of C 2n .

rC2

ð9Þ

where I(x,y) is the laser irradiance on the pixel. Apix is the pixel area. RCCD is the response of CCD. tint is the integration time. G is

12

WST WLT

D

Fig. 3. The relationship between long-term spot size WLT, Shot term beam spread WST, beam wander o r 2C 4 1/2 and required aperture D (a). The minimum receiving aperture with change of C 2n (b).

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the circuit gain. K is a constant, which should be calibrated before measurement. Ignoring the optics loss in the receiver, the total irradiance on the CCD plane equals the incident power on the receiving aperture: M

N

PðLÞ ¼ ∑ ∑ Iðx; yÞ ¼ x¼1y¼1

1 M N H ∑ ∑ hðx; yÞ ¼ K x¼1y¼1 K

ð10Þ

where H is total gray value on the CCD plane. Therefore, the extinction coefficient can be further written as:

α ¼ ln P 0  ln H þ ln K =L ð11Þ 3. Experiment demonstrations 3.1. Experimental scene and device The distance between transmitter and receiver is about 2.0 km shown in Fig. 4. The landscape is quasi uniform. The transmitter is placed in the 7th floor of residential building. The receiver is arranged in the 5th floor of research building in campus. The propagation direction is from North to South to avoid the strong background light interference at the time of sunrise or sunset. The experimental device is shown in Fig. 5. The equipment is composed of a transmitter, a receiver and a processor. Both the transmitter and the receiver are set on the vibration isolation optical platform with type of HB401 from BOCIS Ltd. The transmitter emits collimated Gauss beam with a single-mode fiber laser source. The wavelength is 850 nm. The optical power is 50 mW. The transmitter antenna is cassegrain style with a diameter of

Fig. 4. Experiment scene (maps from Baidu map).

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100 mm. The divergence angle is 100 μrad. Guaranteed by the control circuit, the output optical power stability is better than 5‰. The measurement of both atmospheric extinction coefficient and C 2n is obtained by the CCD A, which is behind the projection optics of the receiver. The camera B beside the large aperture projector is used to coarse aim at the transmitter. The large aperture lens is the low-cost Fresnel lens with the 400 mm diameter, the 500 mm focal length and the 0.125 mm ring distance. The second lens focal length is 6 mm. The receiver field of view is 0.5 degree. The CCD A is Basler A602f with 100 fps of frame rate, 9.9 μm of pixel size, 656  491 of resolution, and 20 μs of minimal exposure time. The camera automatic gain control is off. The optical filter is 850 710 nm with cut-off depth OD3. The data processor collects the CCD output speckle images, and calculated atmospheric extinction coefficient and C 2n coefficient. During measurement, the gray value of images should not be saturated, which will under estimate extinction coefficient. Therefore the output power of transmitter should be properly adjusted before measurement. The calibration is adopted before measurement, which includes image geometric distortion correction and CCD irradiance response function calibration. 3.2. Experiment result The tested transmitter irradiance pattern in the lab is shown in Fig. 6(a). The typical speckle irradiance pattern at receiver is shown in Fig. 7(b). The background light at the pixels is weak with gray value between 0 and 3 even at noon. That confirms the Fresnel lens is practicable for the large aperture projector optics and the background light filtering algorithm is not necessary in this scene. The experiment is carried out in March 11, 2013. The weather is mild haze. Fig. 7 shows the measured atmospheric extinction coefficient and C 2n during a day. The X coordinate axis represents the whole day measurement time, which starts at 0:00 a.m. and ends at 23:59 p.m. The date output period is 1 min and the date is operated by 5 points smoothing. The minimal extinction coefficient is 0.31 dB/km at 19:16 and the maximum extinction coefficient is 2.24 dB/km at 5:07. The minimal C 2n is 10  15.27 m  2/3 at 18:05 and the maximum C 2n is 10  13.66 m  2/3 at 12:51. The extinction coefficient measurement result follows the typical haze conditions (with α E1.0 dB/km) [29]. The C 2n measurement result follows the classic variation trend (with the C 2n is strong at noon,  10  13 m  2/3, and is weak at night,  10  15 m  2/3) [29,30]. In addition, the required receiving aperture is discussed on the assumption that beam divergence is approximately diffraction limit according to Eq. (2), (4) and (5). In fact, the beam divergence is very difficult to achieve approximately diffraction limit. As far as the actual beam divergence is concerned, the actual beam radius W at 2000 m is 0.15 m. In this case, the beam radius W ¼ 2 W 0 ð1 þ Λ0 Þ1=2 in Eq. (5) should be replaced as: W ¼ 0:5  ðd þ θdiv LÞ ¼ 0:15 m

Fig. 5. Experiment device.

ð12Þ

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D. Jiang et al. / Optics Communications 311 (2013) 288–293

Fig. 6. The tested transmitter irradiance pattern (a) and the typical received speckle irradiance pattern at noon (b).

Fig. 7. The measured extinction coefficient (a) and C 2n (b). Table 1 The measurement parameters revisions for the actual beam radius. Parameter Beam radius W (L ¼ 2000 m)

Maximum measurable C 2n (D¼ 400 mm)

Power estimation error (D ¼ 400 mm)

Theoretical 0.052(m) Actual 0.147(m)

10  13.00 m  2/3 10  13.53 m  2/3

Less than 2.67 % Less than 5.29 %

where d is the transmitting aperture. θdiv is the actual beam divergence. Combined with Eq. (2), (4) and (12), when the receiving aperture D¼400 mm, the maximum measurable C 2n is 10  13.53 m  2/3 at 2000 m. Fortunately, the C 2n measurement result has not exceeded this value. Meanwhile, according to Eq. (14), the power estimation error is less than 5.29% when W¼0.15 m.

4. Discussions Fig. 8. The measured average gray value of background light.

This section is consisted of three parts. First, some important influence factors (such as: beam divergence, receiving aperture, background light and the transmitting optical power stability) are discussed. Second, the operation condition is discussed. Finally, some future suggestions are discussed. The receiving aperture is a key parameter in the measurement. In order to estimate C 2n through beam wander effect, the receiving aperture should be large enough to ensure the speckle can be received in the long term beam wander effect under the strong fluctuation (see Eq. (4)). And the receiving aperture also defines

the receiving power estimation error (see Eq. (7)). The receiving aperture constraint condition is discussed according to the relevant theory on the assumption that beam divergence is approximately diffraction limit. However, the actual beam divergence is very difficult to achieve approximately diffraction limit and the actual beam radius at distance L is differ from the theoretical beam radius. The measurement parameter revisions are necessary according to the actual beam radius. In this demonstration, the revisions are listed in Table 1.

D. Jiang et al. / Optics Communications 311 (2013) 288–293

Furthermore, on the assumption that the background light is uniformly distributed on the CCD, the mean gray value of background light is estimated by the eight points′ gray value on the receiving edge (see Fig. 8). In this demonstration, the background light is ignored because it is weak with gray value between 0 and 3 even at noon. In some special condition, if the background light cannot be ignored, Eq. (11) should be rewritten as:

α ¼ ln P 0  lnðHHB Þ þ ln K =L ð13Þ where H B is the total background light gray value, which is estimated by the gray value on the CCD edge. And: H B ¼ N total  ∑ hðx; yÞ=N edge x;y A A

ð14Þ

where A represent the edge area on CCD image. N edge is the number of calculated pixels in the edge area. N is the number of pixels on the CCD. Considering the mean gray value of beam illuminated pixels is above 200 and the mean grey value of background light is below 3, therefore the ratio of total background light and total beam irradiance is less than 3/200 ¼0.015. According to Eq. (13), the estimation error by ignoring background light is less than: lnð0:985Þ=L ¼ 0:0076 dB/km. That means it is appropriate by ignoring the background light in the demonstration. In addition to the beam divergence, receiving aperture and background light, the transmitting optical power stability is also influent the robustness of this method. The transmitting optical power fluctuation will cause total grey value fluctuation and influence the power estimation result. Fortunately, it does not influences beam center calculation. According to Eq. (11), if the power stability is less than 1%, the estimation error of extinction is less than lnð0:01Þ=L ¼ 0:005 dB/km. As far as the operation condition is concerned, the proposed method is suitable for estimating the C 2n on a quasi uniform landscape (whole terrestrial surface or water surface) and with approximately horizontally propagation path, which is similar with typical C 2n measurement method. And then, C 2n can be treated as a constant in this case. If the landscape is not quasi uniform (consisted by terrestrial surface and water surface) or not approximately horizontal, the C 2n will vary with the path [31,32]. The measurement error induced by considering the C 2n is a constant on the complicated landscape should be investigated in the future research, which is still a common problem for the typical measurement method. Furthermore, the receiving aperture constraint condition is also influenced by the maximum C 2n and distance in the measurement area. If the speckle moves out of the aperture, the measurement distance will be shorten. In order to improve this technique, the further researches are suggested as following: 1 More accurate mathematic model of C 2n and variance of beam wander could be developed. This technique evaluates C 2n from weak to strong fluctuation under the assumption of the Kolmogorov power law spectrum and an infinite outer scale. The theory assumption on modified atmospheric spectrum (see Ref. [23] p 68) and a finite outer scale would make the measurement more accurate for actual atmosphere. 2 Dynamic adjustment of transmit optical power could enlarge measurement range of extinction coefficient. In the experiment demonstration, transmit optical power is fixed before measurement and the measurement range of extinction coefficient depends on the CCD dynamic range. If the transmit optical power could be dynamic adjusted and recorded according to the receiving images, the measurement range of extinction coefficient could be enlarged.

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5. Conclusions A synchronous measurement technique for the evaluation of atmospheric extinction coefficient and C 2n is proposed, which is applicable from weak to strong fluctuation. This technique using larger aperture projector optics to receive atmosphere modulated speckle. The extinction coefficient is evaluated by speckle irradiance and C 2n is evaluated by speckle wander effect. The receiving aperture constrain condition is discussed to ensure the speckle can be received in the long term beam wander effect under the strong fluctuation regime. The theory and experiment demonstration indicate that this technique provides a feasible way to simultaneously measurement extinction coefficient and C 2n , which will be helpful to comprehensive understanding the behavior of laser beam propagation in the atmosphere. References [1] S. Bloom, Journal of Optical Networking (2003) 178. [2] M. Lei, H. Li, Z. Lei, X. Liu, Research on detection performance in laser ranging system, in: International Conference on Computer Science and Information Technology ICCSIT 2011, pp. 786–791. [3] R. Rao, Journal of Atmospheric and Environmental Optics 1 (1) (2006) 1. [4] A. Cohen, Applied Optics 14 (12) (1975) 2878. [5] M. Esselborn, M. Wirth, A. Fix, M. Tesche, Applied Optics 47 (3) (2008) 346. [6] H.G. Hughes, J.A. Ferguson, D.H. Stedphens, Applied Optics 24 (11) (1985) 1609. [7] T.I. Wang, Weather Identifier and Visibility Sensor, US Patent 5444530 1995. [8] O. Fiser, J. Svoboda, Z. Chladova, V. Schejbal, J. Pesek, FSO link attenuation measurement and modeling on Milesovka Hill, in: Proceedings of the Fifth European Conference 2011, pp. 2518–2522. [9] V. Brazda, O. Fiser, P. Pesice, J. Pesek, Combination of two visibility sensors to predict fog attenuation on FSO links, in: 11th International Conference on Telecommunications, 2011, pp. 199–202. [10] F.M Janeiro, F. Wagner, P.M. Ramos, A.M. Silva, Automated atmospheric visibility measurements using a digital camera and image registration, in: First Symposium on Environmental Instrumentation and Measurements, 2007. [11] X. xingsheng, T. shanchang, L. Yifeng, Optical Technique 26 (5) (2000) 403. [12] R.L. Phillips, L.C. Andrews, J. Stryjewski, B. Griffis, M. Borbath, D. Galus, G. Burdge, K. Green, C. Kim, D. Stack, C. Harkrider, D. Wayne, D. Hand, J. Kiriazes, Proceedings of SPIE 6303 (2006) 6303061. [13] Z. Wentao, Z. baohua, Journal of University of Electronic Science and Technology of China 36 (4) (2007) 784. [14] J. dagang, D. ke, Q. kaiyu, L. Xiaofeng, Laser beam wander monitoring with large aperture for terrestrial free space optical communication, in: ICEMI, 10th International Conference, 2011, pp. 308–311. [15] V.N.H. Silva, A.P.L. Barbero, R.M. Ribeiro, Journal of Lightwave Technology 29 (24) (2011)3603. [16] Y. Jiang, J. Ma, L. Tan, S. Yu, W. Du, Optics Express 16 (10) (2008) 6963. [17] M. xiaoshan, Z. wenyue, R. ruizhong, High Power Laser and Particle Beams 19 (4) (2007) 538. [18] W. Du, L. Tan, J. Ma, S. Yu, Y. Jiang, Laser and Particle Beams 28 (2010) 91. [19] C. chunyi, Y. huamin, T. shoufeng, L. yunqing, H. cheng, L. peng, Infrared and Laser Engineering Supplement 35 (2006) 423. [20] M. haiping, R. ruizhong, W.u xiaoqing, Z. wenyue, High Power Laser and Particle Beams 15 (12) (2003) 1155. [21] J. Svoboda, Z. Chladova, P. Pesice, O. Fiser, FSO link attenuation and structure index derived from 3D sonic anemometer measurement, in: 11th International Conference on Telecommunications, 2011, pp. 219–221. [22] R. Esposito, Proceedings of the IEEE 55 (1967) 1533. [23] L.C. Andrews, R.L. Phillips, Laser Beam Propagation through Random Media, second ed., SPIE, 2005. [24] H. Henniger, O. Wilfert, Radioengineering 19 (2) (2010) 203. [25] A. Prokes, Optical Engineering 48 (6) (2009) 066001. [26] A. Davis, R.C. Bush, J.C. Harvey, M.F. Foley, Fresnel Lenses in Rear Projection Displays SID 01 DIGEST (2001) (937–934). [27] A.K. Majumdar, J.C. Ricklin, Proceedings of SPIE 5892 (2005) 1. [28] R. jian wei, W. zhi, L. xiangsheng, R. jianyue, Optics and Precision Engineering 15 (8) (2007) 1186. [29] J.C. Ricklin, S.M. Hammel, F.D. Eaton, S.L. Lachinova, Journal of Optical and Fiber Communications Reports 3 (2006) 111. [30] W. ningquan, Z. zongyong, M. chengshen, X. liming, Chinese Journal of Quantum Electronics 15 (4) (1998) 423. [31] N. Qun, W. xiaoqing, High Power Laser and Particle Beams 19 (7) (2007) 1112–1116. [32] S. Gang, W. Ningquan, X. liming, M. chengsheng, High Power Laser and Particle Beams 17 (4) (2005) 485.