Wavefront Aberration Characterization and Correction for Laser Beam Propagating over Saline Water and Sands

6th IFAC Symposium on Mechatronic Systems The International Federation of Automatic Control April 10-12, 2013. Hangzhou, China

Wavefront Aberration Characterization and Correction for Laser Beam Propagating over Saline Water and Sands ⋆ Songsong Zhu1 , Hong Song1,2,∗ , Ping Yang3 , Hongbo Liu1 , Ruihong Lan4 , Yuan Liu1 , Haocai Huang1,4 Fengzhong Qu4,1 , Jianxing Leng1 , Ying Chen1,4 1

2

Ocean College, Zhejiang Univ., 310058, Hangzhou, China State Key Lab of Modern Optical Instrumentation, Zhejiang Univ., 310027, Hangzhou, China 3 Department of Digital Media, Hangzhou Dianzi Univ., 310018, Hangzhou, China 4 State Key Lab of Fluid Power Transmission and Control, Zhejiang Univ., 310027, Hangzhou, China ∗ Corresponding author: [email protected]

Abstract: Wireless laser communication is a promising method for communication in marine environment. However, as laser beam propagates through atmosphere, both wavefront and intensity of the laser beam can be influenced by the atmospheric turbulence. In this paper, wavefront aberration in the laser beam is characterized and corrected by an adaptive optics system while the laser propagates over saline water in a lab environment. Experiments have also been carried out when the laser beam propagates over sands for a comparison. With the correction by the closed-loop adaptive optics system, the variance of spots displacement in the Shack-Hartmann wavefront sensor has been reduced by 28% for saline water and 10% for sands. Keywords: adaptive optics, wavefront aberration correction, laser propagation over water, laser propagation over sands 1. INTRODUCTION Wireless laser communication systems use laser for data transmission in free space (Majumdar and Ricklin, 2008). Key features of wireless laser communication include: (1) a data transmission rate of Mb/s or even Gb/s, (2) no transmission media or spectrum license required, (3) portable and easy to deploy, (4) free of electromagnetic interference, etc. These make wireless laser communication a promising method for communication between islands or terminals over sea. However, as laser beam propagates through the atmosphere over sea, both the wavefront (i.e. phase) and the intensity of the laser beam can be influenced, due to absorption, scattering and refraction of the atmosphere (S.Hammel and D.Kichura, 2008). Because the refractive index of the atmosphere is changed by the atmospheric turbulence both spatially and temporally, the wavefront aberration in the laser beam also varies with space and time. In worst cases, wavefront aberration even leads to scintillation in the beam after propagating over long distance (Andrews et al., 1995). This adds to the noise in the receiver of the communication system, either degrading the reliability of the communication system or imposing a limit in the operation range or bandwidth (R.Tyson, 2002). ⋆ This work is supported by Cross Research Guide Funds for Ocean Subjects of Zhejiang University (project NO. 2012HY011B, 2012HY008B,2012HY005A), National Natural Science Fund of China (project NO. 41206079) and Program for Zhejiang Leading Team of S&T Innovation (project NO. 2010R50036).

978-3-902823-31-1/13/$20.00 © 2013 IFAC

Concerning the difference between marine and land environment for laser propagation, sea water plays a very important role. From one side, because the thermal capacity of sea water is higher than land (Sharqawy et al., 2010), the temperature difference between sea water and air is normally smaller than that between land and air under the same weather condition. From the other side, intense sea water evaporation and strong coastal wind in marine environment may even add to the wavefront aberration both spatially and temporarily. Research has been conducted to characterize the influence of atmospheric turbulence on laser beam propagating over sea. Most of work concentrates on estimating the refractive index structure parameter Cn2 by measuring the intensity fluctuation in the laser beam (X.Wu et al., 2007; F.S.Vetelino et al., 2007; S.Hammel and D.Kichura, 2008; A.V.Sergeyev and M.C.Roggemann, 2011), but investigation on wavefront aberration characterization and correction is still limited. Adaptive optics (AO) is an effective method for wavefront aberration characterization and real-time aberration correction (R.Tyson, 1998; F.Roddier, 1999; Zheng et al., 2011). Applications of AO can be found in astronomy (Hinnen et al., 2008; Petit et al., 2008; Cao et al., 2009; B. Cr´epy et al., 2010), retinal imaging (Christou et al., 2004; Gray et al., 2006), microscopy (Booth et al., 2002; Merino et al., 2006), laser beam shaping (U.Wittrock and H.M.Heuck, 2003; Aleksandrov et al., 2007; Yang et al., 2007). In this paper, we present the research on wavefront aberration characterization and correction using an AO system,

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IFAC Mechatronics '13 April 10-12, 2013. Hangzhou, China

for a laser beam propagating over saline water in a lab environment. The wavefront aberration is characterized in open-loop when only measurement takes place. Aberration corrections is achieved in closed-loop when the aberration is measured by a wavefront sensor and corrected by a wavefront manipulator in real-time. Comparison is also made with the case when the laser beam propagates over sands. By doing these, we want to characterize the difference in wavefront aberration between over-sands and over-salinewater laser propagation, and investigate the feasibility of using a closed-loop AO system for wavefront aberration correction in marine environment.

Optical table T1 Pin hole

Laser

L1 M1

Microscope objective

The paper is organized as follows. Section II describes the experimental setup for wavefront aberration characterization and correction. The control law for the closedloop AO system is presented in Section III. In Section IV, experiments are described and the experimental results are presented. Conclusions are drawn in Section V with future plans.

Saline water (or sands) + heater

2. EXPERIMENTAL SETUP

BS1

To characterize the wavefront aberration in the laser beam and evaluate the performance of the closed-loop AO system, an experimental setup has been built in the lab. The schematic of the experimental setup is depicted in Fig. 1, which mainly consists of a laser beam transmitter in optical table T1, an closed-loop AO system in optical table T2, basins filled with saline water (or sands) and a heater. The photo of the setup is shown in Fig. 2. Light from a HeNe laser (λ=632 nm, 2 mW) is filtered spatially by a microscope objective (20×) and a pin hole (φ=20 µm). The intensity of the laser beam is adjusted by a polarizer. The filtered light is collimated by lens L1, reflected by flat mirrors M1 and M2 successively and travels to the 37-actuator piezo-driven DM (PDM) through a beam splitter (BS1). The beam reflected by the PDM is reflected again by BS1 and flat mirror M3 to a Shack-Hartmann wavefront sensor (S-H WFS) via lenses L2 and L3. The collimated laser beam has a diameter of 1.2 cm. Saline water or sands is contained in four basins on the table between optical table T1 and T2, such that the center of the laser beam is about 4 cm above the saline water (or sands) surface. Each basin has a length of 40 cm and a width of 25 cm. A heater (400 W) is placed above the basins, radiating both the air and saline water (or sands) in the basins. Atmospheric turbulence is generated due to direct heating of the air, the air-water (or air-sands) temperature difference, and water evaporation. Wavefront of the laser beam is then distorted by the atmospheric turbulence. It’s worth noting that although the combination of basins and heater can’t simulate real marine (or land) environment completely (e.g., the propagation distance in the setup is shorter than in real marine environment and effect of costal wind is not considered), the difference between saline water and sands on laser propagation can still be observed and the effect of closed-loop AO system on wavefront aberration correction is clearly visible. The analysis method presented in this paper is also applicable to research in real marine (or land) environment. The wavefront of the beam is manipulated by the 37channel PDM. The resonant frequency of the PDM is 1 kHz. The PDM surface deformation is controlled by a control PC (Dell Precision T3500) via a digital-to-analog converter and a 40-channel high voltage amplifier (HVA). The digital-to-analog converter (DAC-40-USB, OKOTech,

M2 Control system

HVA PDM L2 C1

L3 M3

S-H WFS

Optical table T2

Fig. 1. Schematic of the experimental setup under investigation. Atmospheric turbulence is induced by the saline water (or sands) and the heater. Wavefront aberration is characterized and compensated by the closed-loop AO system.

Fig. 2. Photo of the experimental setup

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Incident beam

The residual wavefront aberration in the laser beam is then represented as ǫφ (k) = φ(k) − φm (k), (2) nf where ǫφ (k) ∈ R denotes the residual wavefront aberration.

Micro-lens Image sensor array

Aberrated wavefront

Fig. 3. Left: working principle of the S-H WFS; right: image captured by camera C1 behind the microlenses. ”+” :focal points of the micro-lenses; ”o”: spots focused by the micro-lenses. The Netherlands) has 40 output channels, interfacing with PC via a USB port. Each channel of the converter is able to generate output voltage between 0 and 5 V, with a resolution of 12-bit (i.e., 4096 discrete levels) and a bandwidth of 1 kHz. The voltage amplification of the HVA is about 80, with an output voltage range of 0 to 300 V and a bandwidth of 1 kHz. Referring to Fig. 3, the S-H WFS consists of an array of micro-lenses. Each micro-lens forms a sub-aperture for the incident beam, where the incident beam is focused on the image sensor of camera C1. Wavefront aberration in the beam leads to displacement of the spots from their nominal locations (i.e., focal points of the microlenes, marked by ”+” in Fig. 3). By calculating the spots displacement, the slopes of the wavefront aberration at the sampling points can be determined. The micro-lenses in the S-H WFS are distributed orthogonally. Pitch between neighboring micro-lenses is about 0.15 mm. The WFS images captured by C1 (ASI035MM, ZWOptical, China) are sent to the control PC via USB interface in real-time. Each image is processed by an image processing algorithm. The displacements of all spots are determined and used for feedback control. Camera C1 has a closed-loop sampling rate of 60 fps at a resolution of 400×400 pixels (each pixel has a size of 6 µm), 8-bit. The closed-loop sampling rate is limited by the maximum sampling rate of the camera itself (100 fps at 400×400 pixels) and the processing time of the image processing algorithm. The PDM, digital-to-analog converter, HVA and S-H WFS in the setup are generously supported by OKOTech, Delft, The Netherlands (OKO, 2008). 3. CONTROLLER OF THE CLOSED-LOOP AO SYSTEM Referring to the experimental setup as described in Section II, the block diagram of the closed-loop AO system is depicted in Fig. 4. The wavefront aberration in the incident laser beam at discrete time instant k is denoted by φ(k) ∈ Rnf , with nf the dimension of the discrete wavefront aberration. The wavefront manipulation by the PDM is denoted as φm (k) ∈ Rnf . Because the sampling rate of the closed-loop AO system (60 Hz) is much slower than the resonant frequency of the PDM (1 kHz), the PDM is considered quasi-static and φm (k) is approximated as φm (k) = Du(k) (1) na where u(k) ∈ R is the control signal to the PDM with na the dimension of u(k). na can be the number of actuators in the PDM in a zonal control mode, or the number of modes (e.g., Zernike modes) to be controlled in modal control. Matrix D ∈ Rnf ×na represents the linear transfer from control signal to the wavefront manipulation by the PDM.

When the laser beam enters the S-H WFS, images of spots are formed in the imaging sensor of camera C1. Coordinates of all spots are determined by the image processing algorithm, denoted as y(k) ∈ Rny . Vector y(k) contains both the vertical and horizontal coordinates of the spots. y(k) is related to the wavefront aberration ǫφ (k) as y(k) = z −d (W ǫφ (k) + η(k)) + y0 , (3) where z is the shift operator. Integer d is the number of sampling delays in wavefront measurement. Due to the inherent delay in digital control systems, d ≥ 1. Matrix W ∈ Rny ×nf , also called the geometry matrix of the S-H WFS, represents the linear conversion from the wavefront aberration to spots displacements. η(k) is the measurement noise. y0 ∈ Rny represents the nominal coordinates of the spots. If the noise term η(k) is omitted, then the spots displacement ye (k) is linearly related to the wavefront aberration as ye (k) = y(k) − y0 ≈ z −d W ǫφ (k). (4)

Incident aberration

Measurement noise

φ(k) φm (k)

η(k)

ǫφ (k)

D

W WFS

DM

y(k)

V (k) ye (k)

1 1−z −1

y0

F Projection

Integration Controller

Fig. 4. Block diagram of the closed-loop AO system. Combining Eq. (1), (2) and (4), the spots displacement ye (k) can be written as ye (k) ≈ z −d W (φ(k) − Du(k)). (5) In case φ(k) = 0, the open-loop transfer from the control signal u(k) to ye (k) can be represented as ye (k) ≈ −W D u(k)z −d , | {z }

(6)

M

which consists of a linear mapping M = W D ∈ Rny ×na and d sample delays. Based on the spots displacement ye , the control signal u to the PDM should be computed such that the variance of the wavefront aberration ǫφ is minimized. Because the variance of ye increases (or decreases) as the variance of the wavefront aberration ǫφ increase (or decreases), in our work the control objective in the closed-loop correction is set to minimize the variance of ye , i.e., min var(ye ), (7) u(k)

where var(ye ) is the variance of ye . The control signal u(k) is updated as

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IFAC Mechatronics '13 April 10-12, 2013. Hangzhou, China

ˆ T ye (k). ˆ + ρI)−1 M ˆ TM u(k) =u(k − 1) + µ(M {z } |

(8)

F

The matrix F ∈ Rna ×ny projects the spots displacement ye back to the space of the control signal u(k). Matrix ˆ ∈ Rny ×na is the estimate of M in Eq.(6), identified M ˆ , i.e., during system calibration. The pseudo inverse of M T ˆ −1 ˆ T ˆ (M M ) M , would give a least-square fitting from the residual spot displacement to the control signal. However, ˆ and M ˆ is illif there exist small singular values in M T ˆ ˆ conditioned, direct inversion of the matrix M M may lead to control signal of significantly large amplitude such that the closed-loop system gets saturated easily. In this case, a regularization factor ρ ∈ R is introduced to alleviate ˆ , such that the the influence of small singular values of M robustness of the closed-loop AO system can be improved. The value of ρ can be tuned by the user, normally ρ ≥ 0. I ∈ Rny ×ny is the identity matrix. Parameter µ ∈ R is a positive number defined by the user as well, to get a trade-off between performance and stability of the closedloop AO system. Substituting Eq. (6) into Eq. (8), the voltage update law changes to u(k) =u(k − 1) + F z −d W φ(k) − F z −d M u(k) = (I − z 1−d F M ) u(k − 1) + F z −d W φ(k). (9) | {z } Q

To ensure the stability of the closed-loop AO system, the eigenvalues of the matrix Q = I − z 1−d F M ∈ Rna ×na should be within the unit circle. Assume there only exists one sample delay in the WFS measurement (i.e., d = 1) ˆ is neglected (i.e., and the modeling uncertainty in M ˆ M = M ), then an analytical condition for closed-loop stability can be derived as follows.

By singular value decomposition (SVD) (G.H.Golub and Loan, 1996), matrix M ∈ Rny ×na can be decomposed as M = U SV T , (10) ny ×ny where U ∈ R and V ∈ Rna ×na are both unitary satisfying U U T = I and V V T = I. Matrix S ∈ Rny ×na is in the form of h iT S = diag(s1 , s2 , · · · sna ) 0Tny −na ×na (11)

with s1 ≥ s2 ≥ · · · ≥ sna > 0. Thus the matrix Q can be decomposed as Q = I − µ(M T M + ρI)−1 M T M = I − µ(V · diag(s21 + ρ, s22 + ρ, · · · s2na + ρ) · V T )−1 · V · diag(s21 , s22 , · · · s2na ) · V T

µs2na µs22 µs21 , 1 − , · · · , 1 − )·VT s21 + ρ s22 + ρ s2na + ρ (12) Eq. (12) is in the form of an eigenvalue decomposition. µs2i The eigenvalues of Q are just 1 − s2 +ρ , i = 1, 2, · · · , na . i To ensure all eigenvalues of Q are in the unit circle, i.e., 2 1 − µsi ≤ 1, (13) s2 + ρ = V · diag(1 −

i

parameter µ should satisfy   2ρ µ ∈ 0, 2 + 2 , si

(14)

for all i = 1, 2, · · · , na . In practice, modeling uncertainty ˆ . To get a good always exists in the identified matrix M compromise between the closed-loop stability and performance, µ and ρ are tuned such that the variance of spots displacement is minimized. 4. EXPERIMENTS AND RESULTS To characterize the wavefront aberration in the laser beam and investigate the effect of closed-loop AO system on wavefront aberration correction, experiments have been carried out in the setup shown in Fig. 1. The procedures for experiments are described as follows. 4.1 Identification of the matrix M Because the diameter of the laser beam is 40% of the faceplate of the PDM (12 mm with respect to 30 mm), only 19 actuators around the center of the PDM are selected for aberration correction, i.e., na = 19. 19 selected actuators are excited simultaneously by random control signals u(k), k = 1, 2, · · · , 500, and the S-H WFS spots coordinates y(k) are recorded at a rate of 60 fps. The random control signals are set before the experiments. Spots displacements ye (k) are calculated by ye (k) = y(k) − y0 , where y0 is the nominal coordinates of the spots (i.e.,when there is no disturbance in the air) and recorded beforehand. There are 127 illuminated spots in the WFS image, which is much more than the number of excited actuators. The AO system is over-determined. To reduce the computational complexity of the controller and the imaging processing algorithm, 38 output channels in ye on which the PDM has significant influence are selected (i.e., ny = 38) for matrix identification and for feedback control later on. During data acquisition, 500 samples are collected in total, among which 250 samples are used for matrix identification and the rest 250 samples for validation. Matrix M is estimated by least-square fitting between u(k) and ye (k) in the identification set, such that |ye (k) − ˆ u(k)| is minimized. M ˆ is evaluated by Accuracy of the estimated matrix M calculating the variance accounted for (VAF) of the matrix (Verhaegen and Verdult, 2007), which is defined as   var(ˆ ye − ye ) VAF(ˆ ye , ye ) = 1 − × 100%. (15) var(ye ) Here var(ye ) is the variance of ye . VAF(ˆ ye , ye ) ranges from ˆ −∞ to 100%. The VAF of the matrix M for the validation set is 81.5% as averaged over 38 output channels, indicatˆ is able to model the open-loop transfer ing the matrix M from u(k) to ye (k) accurately. 4.2 Wavefront aberration characterization With saline water (or sands) in basins, the heater is turned on. Wavefront aberration in the laser beam is measured by the S-H WFS in open-loop when the PDM is not active. Measurement started 30 minutes after the heater was switched on, when the temperature of the saline water and sands didn’t increase significantly any more. The room temperature, the temperature of the saline water and sands is about 15, 30 and 50 degrees centigrade, respectively. The sampling rate of the camera C1 is 60 fps and 1000 frames have been captured. Variance has been calculated for each output channel of ye over time.That is, vi = var(ye,i (k)) for i = 1, 2, · · · , ny

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IFAC Mechatronics '13 April 10-12, 2013. Hangzhou, China

10

PSD [px2/Hz]

10

10

10

10

ed by an AO system in a lab environment. The effectiveness of the closed-loop AO system for wavefront aberration correction has been evaluated.

−1

Experimental results show that the wavefront aberration induced by heated sands has stronger dynamics than by the heated saline water, because the sands-air temperature difference is more than that between saline water and air. However, it’s worth noting that only the effect of temperature gradient is simulated by the setup, while the effect of wind in a natural marine environment still needs to considered. With the closed-loop AO system running, the variance in the spots displacement has been reduced by 28% for saline water and 10% for sands.

−2

−3

−4

Water, AO off Sands, AO off Water, AO on Sands, AO on

In future work, a portable AO system will be developed and used for wavefront aberration characterization and correction in real marine environment.

−5

10

0

10

1

Frequency [Hz]

ACKNOWLEDGEMENTS

Fig. 5. Power spectrum density of the spots displacement for saline water and sands, with AO off and on and k = 1, 2, · · · , 1000, with vi the variance of ith output channel of ye . The averaged variance (denoted as va ) is calculated as ny 1 X va = vi . (16) ny i=1

The value of va is 0.9 µm2 and 1.7 µm2 for saline water and for sands, respectively.

The temporal characteristics of the wavefront aberration has been evaluated by computing the power spectrum density (PSD) of the spots displacement ye as well. Fig.5 shows the PSD averaged over ny = 38 output channels of ye . It can be seen that the PSD curve of the saline water is lower than sands in the whole frequency range under consideration, indicating that more dynamics is involved in the wavefront aberration as the laser propagates over sands than over saline water. 4.3 Wavefront aberration correction During wavefront aberration correction, the measurement provided by the S-H WFS is fed into the controller and control signal u(k) is updated as in Eq. (8) in realtime. The closed-loop sampling rate of camera C1 is 60 fps. Parameters µ and ρ are tuned to achieve minimum variance of spots displacement ye . The minimum variance is achieved when µ = 0.15, ρ = 20 for saline water and µ = 0.2, ρ = 20 for sands. The averaged variance va is 0.65 µm2 for saline water, reduced by 28% by the closed-loop AO system. In case of sands, the variance va is reduced by 12%, from 1.7 µm2 to 1.5 µm2 . The PSD in Fig.5 shows that the power density of ye has been reduced by about one order of magnitude for frequency lower than 1 Hz for both saline water and sands. As frequency increases, the correction becomes less significant. This indicates that the closed-loop AO system is able to correct the wavefront aberration at low frequency very effectively. To achieve effective aberration correction for high frequency, the sampling rate of the closed-loop AO system needs to be increased. 5. CONCLUSIONS AND FUTURE WORK Wavefront aberration in laser beam propagating over saline water and sands has been characterized and correct-

Authors would like to thank Dr. Vdovin, Dr. Soloviev and Dr. Loktev from OKOTech for their generous support in the AO system and Yaojiang Liu, Shenli Lin and Yu Huang for help in constructing the experimental setup. Authors also want to thank reviewers for their valuable comments on the paper. REFERENCES A.Aleksandrov, A.Kudryashov, A.Rukosuev, T.Cherezova, and Y.Sheldakova(2007). An adaptive optical system for controlling laser radiation. J. Opt. Technol., 74(8), 550– 554. L.C.Andrews, R.L.Phillips, and P.T.Yu (1995). Optical scintillations and fade statistics for a satellitecommunication system. Appl. Opt., 34(33), 7742–7751. A.V.Sergeyev and M.C.Roggemann (2011). Monitoring the statistics of turbulence: Fried parameter estimation from the wavefront sensor measurements. Appl. Opt, 50, 3519–3528. B. Cr´epy, S. Chaillot, J. -M . Conan, R. Cousty, C. Delrez, M. Dimmler, J.L. Dournaux, S. De Zotti, E. Gabriel, R. Gasmi, R. Grasser, N. Hubin, P. Jagourel, L. Jochum, F. Locre, P. Y. Madec, P. Morin, M. Mueller, G. Petit, D. Petitgas, J. J. Roland, J. C. Sinquin, and E. Vernet (2010). The M4 adaptive unit for the E-ELT. Proc. of 1st AO4ELT conference, 06001. M.Booth, M.Neil, R.Juskaitis and T.Wilson (2002). Adaptive aberration correction in a confocal microscope. Proc. Nat. Acad. Sci., 99(9), 5788–5792. Z.Cao, Q.Mu, L.Hu, D.Li, Z.Peng, Y.Liu and L.Xuan (2009). Preliminary use of nematic liquid crystal adaptive optics with a 2.16-meter reflecting telescope. Opt. Express, 17(4), 2530–2537. J.C.Christou, A.Roorda and D.R.Williams (2004). Deconvolution of adaptive optics retinal images. J. Opt. Soc. Am. A, 21(8), 1393–1401. F.Roddier (1999). Adaptive Optics in Astronomy. Cambridge University Press, Cambridge, UK. F.S.Vetelino, K.Grayshan and C.Y.Young (2007). Inferring path average cn2 values in the marine environment. J. Opt. Soc. Am. A, 24(10), 3198–3206. G.H.Golub and C.van Loan (1996). Matrix Computations (3rd Edition). The Johns Hopkins University Press, Baltimore, USA. D.C.Gray, W.Merigan, J.I.Wolfing, B.P.Gee, J.Porter, A.Dubra, T.H.Twietmeyer, K.Ahamd, R.Tumbar, F.Reinholz and D.R.Williams (2006). In vivo fluorescence imaging of primate retinal ganglion

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cells and retinal pigment epithelial cells. Opt. Express, 14(16), 7144–7158. K.Hinnen, M.Verhaegen and N.Doelman (2008). A datadriven H2 -optimal control approach for adaptive optics. IEEE Transactions on Control Systems Technology, 16, 381–395. A.Majumdar and J.Ricklin (2008). Free-space Laser Communications: Principles and Advances. Spinger, Germany. D.Merino, C.Dainty, A.Bradu and A.G.Podoleanu (2006). Adaptive optics enhanced simultaneous en-face optical coherence tomography and scanning laser ophthalmoscopy. Opt. Express, 14(8), 3345–3353. M.H.Sharqawy, J.H.Lienhard V and S.M.Zubair (2010). The thermophysical properties of seawater: A review of existing correlations and data. Desalination and Water Treatment, 16, 354C380. OKO Technologies (2008). Adaptive Optics Guide, available at: http://www.okotech.com. C.Petit, J.M.Conan, C.Kulcs´ar, H.F.Raynaud and T.Fusco (2008). First laboratory validation of vibration filtering with lqg control law for adaptive optics. Opt. Express, 16(1), 87–97. R.Tyson (1998). Principle of Adaptive Optics. Academic Press, Boston, USA. R.Tyson (2002). Bit-error rate for free-space adaptive optics laser communications. J. Opt. Soc. Am. A, 19, 753–758. S.Hammel and D.Kichura (2008). Turbulence effects on laser propagation in a marine environment. Proceeding of SPIE, 7090, 70900K–1–70900K–12. U.Wittrock, I.Buske and H.M.Heuck (2003). Adaptive aberration control in laser amplifiers and laser resonators. Proceeding of SPIE, 4969, 122–136. M.Verhaegen and V.Verdult (2007). Filtering and System Identification: A Least Squares Approach. Cambridge University Press, New York, USA. X.Wu, G.Sun and N.WENG (2007). Measurement and modeling of c2n at typical regions in china. Journal of Atmospheric and Environmental Optics, 2(6), 409–422. P.Yang, Y.Liu, W.Yang, M.Ao, S.Hu, B.Xu and W.Jiang (2007). Adaptive mode optimization of a continuouswave solid-state laser using an intracavity piezoelectric deformable mirror. Opt. Comm., 278(2), 377 – 381. Y.Zheng, X.Wang, L.Deng, F.Shen and X.Li (2011). Arbitrary phasing technique for two-dimensional coherent laser array based on an active segmented mirror. Appl. Opt., 50(15), 2239–2245.

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