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

Application of adaptive optics to Free-Space Optical

communications

Noah SchwartzUniversité de Nice Sophia-Antipolis

Ecole doctorale Sciences Fondamentales et Appliquées

December 17, 2009PhD Thesis Defense N. Schwartz

2

Free-Space Optical Communications

Atmospheric turbulence

Telescope Telescope

Typical Free-Space Optical (FSO) system


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


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


5


I. FSO and Atmospheric turbulenceI. Turbulence effects on FSO systems

II. AO Precompensation: existing methods





6

Laser beam propagation and turbulence

L = 10 km

λ = 1.5 µm

Dpupil = 30 cm

Wind speed = 5 m.s-1

Cn2 = 2.10-14 m-2/3

Telescope


Laser propagation through turbulence

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion


7

Laser beam propagation and turbulence

L = 10 km

λ = 1.5 µm

Dpupil = 30 cm


Cn2 = 2.10-14 m-2/3

Telescope


Laser propagation through turbulence


Power in the Bucket: I


8

His

tog

ram

I

Intensity Histogram

Turbulence effects on FSO systemsI

D = 30 cm, L = 10 km, = 1.5 µm


Cn2 = 10-16, 10-15, 10-14 m-2/3

Temporal evolution

Time [s]


IIII

I

I


9

Goal

Estimation of FSO link quality:

Link quality estimation

dssps

erfcBER I

dturb

0 22

5.0II

What are the existing AO correction methods?



Detection noise

Intensity probability density function (PDF)

• pI log-normal for weak perturbations

• pI 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

d

I

20


bitssentofNumber

errorsofNumberBER


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


Telescope 1

Laser

WFS

DM

RTC

BeaconData


Conventional AO


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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


Conventional AO


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, 1997.

Telescope 2


Telescope 1

DM

Data

RTC

Laser


Direct control

Feedback

Receiver


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Dual-beam Full-wave correction

• Dual-beam full-wave correction (Barchers1)• Only conceptual proposition

• Weak turbulence study only

• Proof of correction convergence

• Proposed a dual-beam phase-only correction

PUU *

2121Pupil 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, 2002.

Telescope 2Telescope 1

Full-wave conjugation

Full-wave conjugationLaser

21U21U


Dual-beam


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Conclusion – part I

• Laser beam propagation through turbulence• Creates intensity fluctuations at receiver

• Incompatible with FSO requirements in terms of <BER>

• FSO systems needs• Increase mean intensity

• Decrease fluctuations below (<BER> below 10-9)

• 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?

1.0II

I



15







16



II. Comparison of different Adaptive Optics correction strategies wrt FSO performanceI. Conventional AO

II. Direct phase control

III. Dual-beam full-wave correction

IV. Dual-beam phase-only correction



Direct control

Conventional AO

Dual-beam

PO PO

Dual-beam

FW FW


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Altitude h [m]

Cn

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): 3/21415162 10,10,10 mCn

Increasing turbulence strength

Cn2 = 10-16 m-2/3 Cn

2 = 10-15 m-2/3 Cn2 = 10-14 m-2/3h-4/3 (day)

h-2/3 (night)


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Study modeling tool: Pilot

Atmospheric propagation

turbulence turbulence

d d’

Fresnel propagation

Fresnel propagation

Simulation code

Turbulent phase screen

Turbulent phase screen



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Conventional AO

• 7x7 Shack-Hartmann wavefront sensor (WFS)• Noiseless phase reconstruction: 38 Zernike modes• Performance of conventional AO

• Weak turbulence (Cn2 = 10-16m-2/3): No AO interest

• Strong scintillation (Cn2 = 10-14m-2/3): for D > 55 cm

• Medium turbulence (Cn2 = 10-15m-2/3): fluctuations drop below 0.1

σI/

Pupil Diameter [m]

1.0II

1.0II


Conventional AO


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IDirect phase control

• D = 30 cm, DM: 7x7 actuators• No further gain by increasing number of

actuators• SPGD: Sequential Parallel Gradient Descent

Cn2 = 10-14 m-2/3



Iteration steps

Iteration steps

I/

Iteration steps

D = 30 cm, L = 10 km, = 1.5 µm

Cn2 = 10-16, 10-15, 10-14 m-2/3

1.0II

Identical correction level to conventional, slightly better for strong turbulence


Direct control


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Full-wave correction – Performance vs. D

• LF = √λL = 12cm scaling parameter 2LF

• no FSO interest

σI/

Pupil Diameter [m]

I = 99.8%

I = 98.2%I = 92.5%

Cn

2 =

10-1

5 m

-2/3

L2

1.0II

speckleBeam wander

1.0II

I = 99.2%

Cn

2 =

10-1

6 m

-2/3

Weak turbulence (Barchers): Cn2 = 10-16, 10-15 m-2/3

D = 30 cm

Before After

L


Dual-beam

FW FW


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• Mainly beam spreading: I proportional to D-1

• LF is replaced by = 50cm (Cn2 = 10-14m-2/3)

• Efficient correction whatever D FSO interest

σI/

Pupil Diameter [m]

I = 40.2% I = 80.8%

Cn

2 =

10-1

4 m

-2/3

0L

1.0II

Strong turbulence: Cn2 = 10-14m-2/3

Before After

0L


Dual-beam

FW FW

D = 30 cm


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• Mainly beam spreading: I proportional to D-1

• LF is replaced by = 50cm (Cn2 = 10-14m-2/3)

• Efficient correction whatever D FSO interest

σI/

Pupil Diameter [m]

I = 40.2% I = 80.8%

Cn

2 =

10-1

4 m

-2/3

0L

1.0II

Strong turbulence: Cn2 = 10-14, 7.10-14 m-2/3

Before After

0L


Dual-beam

FW FW

D = 30 cm


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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

His

tog

ram

I


Full-wave correction

Dual-beam

FW FW

D = 30 cm, L = 10 km, = 1.5 µm

Cn2 = 10-16, 10-15, 10-14, 7.10-14 m-2/3


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Full-wave correction – Average Bit Error Rate<

BE

R>

• Strong turbulence Cn2 = 10-14

• ok

• Very strong Cn2 = 7.10-14

• ok if I0/d * 43.10-233.10-153.10-4<BER>

0.980.80.33

Fu

ll -

wav

e

4.10-182.10-20.3<BER>

0.920.30.06

No

C

orr

.

10-1510-147.10-14Cn2

Full-wave correction

No correction

D = 30 cm, L = 10 km, = 1.5 µm

Cn2 = 10-15, 10-14, 7.10-14 m-2/3


d

I

20

Dual-beam

FW FW


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Full-wave correction – Iteration influence σI/• Few iterations needed

• Fluctuations divided by approx. 10

D = 30 cm, L = 10 km, = 1.5 µm

Cn2 = 10-16, 10-15, 10-14, 7.10-14 m-2/3

Number of iterations Number of iterations

N. Schwartz et al., “Mitigation of atmospheric effects by adaptive optics for free-space optical communications,” SPIE 2009


Dual-beam

FW FW


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Dual-beam phase-only correction

Identical to dual-beam full-waveonly-phase is controlled

PU

UUU

21

*21

021

I = 25% I= 41%

Cn

2 =

10-1

6 m-2

/3C

n2

= 1

0-15 m

-2/3

Cn

2 =

10-1

4 m-2

/3

Before AfterD = 30 cm

Typical intensity distribution

phase-only correction

Telescope 2Telescope 1

21U21U

Emitted beam (not corrected)

Phase-only conjugation

Pupil truncation


Dual-beam

PO PO


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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

Cn2 = 10-15, 10-14 m-2/3

Full-wave Phase-only


Dual-beam

d

I

20 d

I

20


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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



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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?



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III. Implementation of the dual-beam full-wave correctionI. Wave sampling influence

II. Practical way of wave measurement and control



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Wave sampling geometry

d

fieldneticElectromagU

U

d

D

• U is the mean measured field• N2 = Number of sampling points• N = D/d• Square geometry is considered



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σI/

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

Cn2 = 10-16, 10-15, 10-14 m-2/3

Cn2 10-16 10-15 10-14

D/0 1.6 6.5 26

NcN | I/ = 0.1) 1 3 10Nc / (D/0) ~ 2

D/0 seems a good parameter to scale system complexity


N




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Does sampling impact convergence?

• Few iterations are needed to achieve convergence (<10)

σI/Iteration number



Iteration number



36

z

Laser

DM DMDM

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 concept1

• Looses by diffraction2 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., 1998.

[2] N. Vedrenne, “Propagation optique en forte turbulence,” PhD Thesis, 2008

Phase modulation

Amplitude modulation

Energy loss

Laser

DM



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• Suppose you want to control only 2 points

• interferometer

• To control N2 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

0

2

1

0

2

1

1

0

2

0

2

1

E2

E1

E0

Mach-Zehnder|E1|2+ |E2|2

= |E0|2



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

• N2 = 100 sufficient to achieve desired performance


No Correction Correction

D = 30 cm, d = 1 cm

I = 16.8%

Cn

2 =

10-1

4 m-2

/3

Sub-pupils

Pupil

I = 33.1%


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

(N2 = 100 actuators, for 20 < D < 30 cm)

• D/0 seems a good parameter to scale system complexity



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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 N2 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


Direct control

Conventional AO

Dual-beam

PO PO

Dual-beam

FW FW

0

2

1

0

2

1

1

0

2


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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



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• 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 l’Optique Adaptative”: Prize “from the heart“

• “Panique à Vera Cruz”: Jury prize (Axel Khan)

Publications

Documents

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