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Application of adaptive optics to Free-Space Optical communications Noah Schwartz Université de Nice Sophia-Antipolis Ecole doctorale Sciences Fondamentales et Appliquées

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December 17, 2009 PhD Thesis Defense N. Schwartz 2 Free-Space Optical Communications Atmospheric turbulence Telescope Typical Free-Space Optical (FSO) system

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December 17, 2009 PhD Thesis Defense N. Schwartz 3 FSO advantages and uses Natural advantages of FSO Directivity (secure, free from interference) No frequency regulation High data throughput ( fiber optics) Easy to install (no civil engineering) … Applications Metropolitan area networks Fiber optics impractical Temporary networks installation (disaster recovery, …) … Drawback: strong sensitivity to atmospheric condition! Fog (absorption and diffusion) & atmospheric turbulence

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December 17, 2009 PhD Thesis Defense N. Schwartz 4 Presentation outline I. FSO and Atmospheric turbulence II. Comparison of different Adaptive Optics correction strategies wrt FSO performance III. Implementation of the dual-beam full-wave correction IV. Conclusion and perspectives

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December 17, 2009 PhD Thesis Defense N. Schwartz 5 Presentation outline I. FSO and Atmospheric turbulence I. Turbulence effects on FSO systems II. AO Precompensation: existing methods II. Comparison of different Adaptive Optics correction strategies wrt FSO performance III. Implementation of the dual-beam full-wave correction IV. Conclusion and perspectives

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December 17, 2009 PhD Thesis Defense N. Schwartz 6 Laser beam propagation and turbulence L = 10 km λ = 1.5 µm D pupil = 30 cm Wind speed = 5 m.s -1 C n 2 = m -2/3 Telescope Atmospheric turbulence Laser propagation through turbulence Context & existing methods – Correction comparison – Full-wave implementation – Conclusion

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December 17, 2009 PhD Thesis Defense N. Schwartz 7 Laser beam propagation and turbulence L = 10 km λ = 1.5 µm D pupil = 30 cm Wind speed = 5 m.s -1 C n 2 = m -2/3 Telescope Atmospheric turbulence Laser propagation through turbulence Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Power in the Bucket: I

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December 17, 2009 PhD Thesis Defense N. Schwartz 8 Histogram I Intensity Histogram Turbulence effects on FSO systems I D = 30 cm, L = 10 km, = 1.5 µm Wind speed = 5 m.s -1 C n 2 = , , m -2/3 Temporal evolution Time [s] Context & existing methods – Correction comparison – Full-wave implementation – Conclusion

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December 17, 2009 PhD Thesis Defense N. Schwartz 9 Goal Estimation of FSO link quality: Link quality estimation What are the existing AO correction methods? Detection noise Intensity probability density function (PDF) p I log-normal for weak perturbations p I for strong perturbations ? Mitigation: decrease fluctuations & increase M.A. Khalighi et al., Fading Reduction by Aperture Averaging and Spatial Diversity in Optical Wireless Systems, JOCN, 2009 Context & existing methods – Correction comparison – Full-wave implementation – Conclusion

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December 17, 2009 PhD Thesis Defense N. Schwartz 10 Conventional AO principle Correction: Wavefront (WF) measurement: back-propagating laser beacon Deformable Mirror (DM) controlled by WF measurement C.A. Primmerman et al., Compensation of atmospheric optical distortion using a synthetic beacon, Nature,1991 Telescope 2 Atmospheric turbulence Telescope 1 Laser WFS DM RTC Beacon Data Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Conventional AO

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December 17, 2009 PhD Thesis Defense N. Schwartz 11 Conventional AO limitation : strong perturbations regime Wave amplitude cancellation and phase discontinuity Branch points intensity phase Geometrical WFS (scintillation, WF discontinuity) not adapted Correction with continuous DM not adapted Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Conventional AO

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December 17, 2009 PhD Thesis Defense N. Schwartz 12 Direct phase control Implementation One or two DMs controlled by power in the bucket maximization Iterative process No wavefront sensor (WFS) Limitations Need of fast converging algorithms Need for fast AO loop M. A. Vorontsov, et al., Adaptive phase distortion correction based on parallel gradient-descent optimization, Optics letters, Telescope 2 Atmospheric turbulence Telescope 1 DM Data RTC Laser Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Direct control Feedback Receiver

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December 17, 2009 PhD Thesis Defense N. Schwartz 13 Dual-beam Full-wave correction Dual-beam full-wave correction (Barchers 1 ) Only conceptual proposition Weak turbulence study only Proof of correction convergence Proposed a dual-beam phase-only correction Pupil truncation Full-wave conjugation [1] J.D. Barchers and D.L. Fried, Optimal control of laser beams for propagation through a turbulent medium, J. Opt. Soc. Am. A, Telescope 2 Telescope 1 Full-wave conjugation Full-wave conjugation Laser Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Dual-beam

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December 17, 2009 PhD Thesis Defense N. Schwartz 14 Conclusion – part I Laser beam propagation through turbulence Creates intensity fluctuations at receiver Incompatible with FSO requirements in terms of FSO systems needs Increase mean intensity Decrease fluctuations below ( below ) Different AO correction concepts considered Phase-only: Conventional AO, Direct phase control, Dual-beam phase- only correction Full-wave: Dual-beam full-wave correction AO: a solution capable of reaching such a requirement? Context & existing methods – Correction comparison – Full-wave implementation – Conclusion

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December 17, 2009 PhD Thesis Defense N. Schwartz 15 Presentation outline I. FSO and Atmospheric turbulence II. Comparison of different Adaptive Optics correction strategies wrt FSO performance III. Implementation of the dual-beam full-wave correction IV. Conclusion and perspectives

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December 17, 2009 PhD Thesis Defense N. Schwartz 16 Presentation outline I. FSO and Atmospheric turbulence II. Comparison of different Adaptive Optics correction strategies wrt FSO performance I. Conventional AO II. Direct phase control III. Dual-beam full-wave correction IV. Dual-beam phase-only correction III. Implementation of the dual-beam full-wave correction IV. Conclusion and perspectives Direct control Conventional AO Dual-beam PO Dual-beam FW

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December 17, 2009 PhD Thesis Defense N. Schwartz 17 Altitude h [m] C n 2 [m -2/3 ] Turbulence model Study Framework Propagation distance: L = 10 km Wavelength: λ = 1.5 µm (atmospheric window, technology availability) Pupil Diameter: D 30 cm (minimize bulk) Studied Turbulence Strengths (constant): Increasing turbulence strength C n 2 = m -2/3 C n 2 = m -2/3 C n 2 = m -2/3 h -4/3 (day) h -2/3 (night)

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December 17, 2009 PhD Thesis Defense N. Schwartz 18 Study modeling tool: Pilot Atmospheric propagation turbulence dd Fresnel propagation Simulation code Turbulent phase screen Context & existing methods – Correction comparison – Full-wave implementation – Conclusion

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December 17, 2009 PhD Thesis Defense N. Schwartz 19 Conventional AO 7x7 Shack-Hartmann wavefront sensor (WFS) Noiseless phase reconstruction: 38 Zernike modes Performance of conventional AO Weak turbulence (C n 2 = m -2/3 ): No AO interest Strong scintillation (C n 2 = m -2/3 ): for D > 55 cm Medium turbulence (C n 2 = m -2/3 ): fluctuations drop below 0.1 σ I / Pupil Diameter [m] Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Conventional AO

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December 17, 2009 PhD Thesis Defense N. Schwartz 20 I Direct phase control D = 30 cm, DM: 7x7 actuators No further gain by increasing number of actuators SPGD: Sequential Parallel Gradient Descent C n 2 = m -2/3 Iteration steps I / Iteration steps D = 30 cm, L = 10 km, = 1.5 µm C n 2 = , , m -2/3 Identical correction level to conventional, slightly better for strong turbulence Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Direct control

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December 17, 2009 PhD Thesis Defense N. Schwartz 21 Full-wave correction – Performance vs. D L F = λL = 12cm scaling parameter 2L F no FSO interest σ I / Pupil Diameter [m] I = 99.8% I = 98.2% I = 92.5% C n 2 = m - 2/3 speckle Beam wander I = 99.2% C n 2 = m - 2/3 Weak turbulence (Barchers): C n 2 = , m -2/3 D = 30 cm BeforeAfter Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Dual-beam FW

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December 17, 2009 PhD Thesis Defense N. Schwartz 22 Full-wave correction – Performance vs. D Mainly beam spreading: I proportional to D -1 L F is replaced by = 50cm (C n 2 = m -2/3 ) Efficient correction whatever D FSO interest σ I / Pupil Diameter [m] I = 40.2% I = 80.8% C n 2 = m -2/3 Strong turbulence: C n 2 = m -2/3 BeforeAfter Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Dual-beam FW D = 30 cm

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December 17, 2009 PhD Thesis Defense N. Schwartz 23 Full-wave correction – Performance vs. D Mainly beam spreading: I proportional to D -1 L F is replaced by = 50cm (C n 2 = m -2/3 ) Efficient correction whatever D FSO interest σ I / Pupil Diameter [m] I = 40.2% I = 80.8% C n 2 = m -2/3 Strong turbulence: C n 2 = , m -2/3 BeforeAfter Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Dual-beam FW D = 30 cm

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December 17, 2009 PhD Thesis Defense N. Schwartz 24 Full-wave correction – Intensity Histogram Log-normal approximation with D = 30 cm Not appropriate for strong turbulence regimes without correction Seems reasonable after full-wave correction for all regimes Histogram I Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Full-wave correction Dual-beam FW D = 30 cm, L = 10 km, = 1.5 µm C n 2 = , , , m -2/3

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December 17, 2009 PhD Thesis Defense N. Schwartz 25 Full-wave correction – Average Bit Error Rate Strong turbulence C n 2 = ok Very strong C n 2 = ok if I 0 / d * Full - wave No Corr Cn2Cn2 Full-wave correction No correction D = 30 cm, L = 10 km, = 1.5 µm C n 2 = , , m -2/3 Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Dual-beam FW

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December 17, 2009 PhD Thesis Defense N. Schwartz 26 Full-wave correction – Iteration influence σ I / Few iterations needed Fluctuations divided by approx. 10 D = 30 cm, L = 10 km, = 1.5 µm C n 2 = , , , m -2/3 Number of iterations N. Schwartz et al., Mitigation of atmospheric effects by adaptive optics for free-space optical communications, SPIE 2009 Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Dual-beam FW

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December 17, 2009 PhD Thesis Defense N. Schwartz 27 Dual-beam phase-only correction Identical to dual-beam full-wave only-phase is controlled I = 25% I= 41% C n 2 = m -2/3 C n 2 = m -2/3 C n 2 = m -2/3 Before After D = 30 cm Typical intensity distribution phase-only correction Telescope 2Telescope 1 Emitted beam (not corrected) Phase-only conjugation Pupil truncation Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Dual-beam PO

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December 17, 2009 PhD Thesis Defense N. Schwartz 28 Phase-only VS Full-wave correction Global effectiveness below full-wave correction I / < 0.1 for medium turbulence only D = 30 cm, L = 10 km, = 1.5 µm C n 2 = , m -2/3 Full-wavePhase-only Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Dual-beam

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December 17, 2009 PhD Thesis Defense N. Schwartz 29 Conclusion – Part II Phase-only correction 3 different phase-only corrections studied: equivalent performance Efficient correction in weak to intermediate turbulence Not sufficient in strong perturbation regime ( I / [D=30 cm] > 0.1) Phase and amplitude: full-wave correction Efficient beyond weak fluctuation regime Few iterations needed to achieve convergence (<10) Need for phase and amplitude correction strategy Context & existing methods – Correction comparison – Full-wave implementation – Conclusion

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December 17, 2009 PhD Thesis Defense N. Schwartz 30 Presentation outline I. FSO and Atmospheric turbulence II. Comparison of different Adaptive Optics correction strategies wrt FSO performance III. Implementation of the dual-beam full-wave correction IV. Conclusion and perspectives

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December 17, 2009 PhD Thesis Defense N. Schwartz 31 Open issues for wave correction Wave spatial description? Impractical modal analysis of phase (branch points) spatial sampling Number of degrees of freedom? Wave measurement? Wave correction? Context & existing methods – Correction comparison – Full-wave implementation – Conclusion

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December 17, 2009 PhD Thesis Defense N. Schwartz 32 Presentation outline I. FSO and Atmospheric turbulence II. Comparison of different Adaptive Optics correction strategies wrt FSO performance III. Implementation of the dual-beam full-wave correction I. Wave sampling influence II. Practical way of wave measurement and control IV. Conclusion and perspectives

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December 17, 2009 PhD Thesis Defense N. Schwartz 33 Wave sampling geometry U d D U is the mean measured field N 2 = Number of sampling points N = D/d Square geometry is considered Context & existing methods – Correction comparison – Full-wave implementation – Conclusion

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December 17, 2009 PhD Thesis Defense N. Schwartz 34 σ I / N Sampling influence Influence of spatial sampling on the corrected field in the pupil plane D = 23.5 cm, L = 10 km, = 1.5 µm C n 2 = , , m -2/3 Cn2Cn D/ N c N | I / = 0.1)1310 N c / (D/ 0 ) ~ 2 D/ 0 seems a good parameter to scale system complexity Context & existing methods – Correction comparison – Full-wave implementation – Conclusion N

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December 17, 2009 PhD Thesis Defense N. Schwartz 35 Does sampling impact convergence? Few iterations are needed to achieve convergence (<10) σ I / Iteration number Iteration number Context & existing methods – Correction comparison – Full-wave implementation – Conclusion

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December 17, 2009 PhD Thesis Defense N. Schwartz 36 z Laser DM Phase and amplitude control How to control both phase and amplitude without loss of energy? Addition of a phase and a amplitude modulator Obvious energy loss due to attenuation 2 deformable mirrors concept 1 Looses by diffraction 2 in the pupil [1] M.C. Roggeman et al., 2-DM concept for correcting scintillation effects in laser beam projection through turbulent atmosphere, Appl. Opt., [2] N. Vedrenne, Propagation optique en forte turbulence, PhD Thesis, 2008 Phase modulation Amplitude modulation Energy loss Laser DM Context & existing methods – Correction comparison – Full-wave implementation – Conclusion

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December 17, 2009 PhD Thesis Defense N. Schwartz 37 Suppose you want to control only 2 points interferometer To control N 2 points Tree-structure architecture where all beams interfere In reverse (reception) we can measure phase and amplitude with classical interferometric approaches Phase and amplitude control E2E2 E1E1 E0E0 Mach-Zehnder |E 1 | 2 + |E 2 | 2 = |E 0 | 2 Context & existing methods – Correction comparison – Full-wave implementation – Conclusion

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December 17, 2009 PhD Thesis Defense N. Schwartz 38 Implementation – Principle Pupil geometry (diffraction) + fiber optics injection energy loss at reception Basic performance estimate (square geometry) for I / not modified by pupil geometry N 2 = 100 sufficient to achieve desired performance Context & existing methods – Correction comparison – Full-wave implementation – Conclusion No CorrectionCorrection D = 30 cm, d = 1 cm I = 16.8% C n 2 = m -2/3 Sub-pupils Pupil I = 33.1%

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December 17, 2009 PhD Thesis Defense N. Schwartz 39 Conclusion – Part III Spatial sampling Innovative solution for phase and amplitude correction Only a few actuators are necessary to lower fluctuations I / = 0.1 (N 2 = 100 actuators, for 20 < D < 30 cm) D/ 0 seems a good parameter to scale system complexity Context & existing methods – Correction comparison – Full-wave implementation – Conclusion

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December 17, 2009 PhD Thesis Defense N. Schwartz 40 Presentation outline I. FSO and Atmospheric turbulence II. Comparison of different Adaptive Optics correction strategies wrt FSO performance III. Implementation of the dual-beam full-wave correction IV. Conclusion and perspectives

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December 17, 2009 PhD Thesis Defense N. Schwartz 41 Conclusion Three different phase-only correction strategies studied Efficient for weak and medium turbulence Insufficient in strong turbulence phase-only: not implementation issues but conceptual limitation Phase and amplitude control Efficient correction strategy even in strong turbulence Limited number of iterations A few number of actuators N 2 required to achieve performance Novel implementation solution for phase and amplitude control Control directly function of wave measurements Easy wave measurements (classical interferometry approach) Lossless phase and amplitude control Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Direct control Conventional AO Dual-beam PO Dual-beam FW

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December 17, 2009 PhD Thesis Defense N. Schwartz 42 Perspective FSO with conventional AO: Field tests in 2010 Pupil diameter D = 25 cm 8x8 Shack-Hartman WSF (50 Zernike modes) Multi-laser beacon FSO in the mid IR: Scalpel project Development of components Optical test bench for full-wave correction Gain: Increased distance (L = 20 km and more) Decreased AO complexity (number of actuators) Fortune43G Context & existing methods – Correction comparison – Full-wave implementation – Conclusion

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December 17, 2009 PhD Thesis Defense N. Schwartz 43 Proceedings N. Schwartz, N. Védrenne, V. Michau, M.-T. Velluet and F. Chazallet, Mitigation of atmospheric effects by adaptive optics for FSO communications, SPIE, 2009 A. Khalighi, N. Aitamer, N. Schwartz, S. Bournnane, Turbulence Mitigation by Spatial Diversity in Optical Systems, ConTel09, 2009 Articles A. Khalighi, N. Schwartz, N. Aitamer, S. Bournanne, Fading Reduction by Aperture Averaging and Spatial Diversity in Optical Wireless Systems, J. Opt, Commun. Netw. N. Schwartz, V. Michau, N. Védrenne, M.-T. Velluet, Adaptive Optics strategies for free-space optical communications, In preparation Patent: In preparation Popular Science 2 shorts movies presented to film festival in 2008 and 2009 Super-photon et le jeu de lOptique Adaptative: Prize from the heart Panique à Vera Cruz: Jury prize (Axel Khan) Publications

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