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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 This presentation is for the Defense of my PhD Thesis. The laboratory where I have realize my work is the Onera and the university, the University of Nice It will present the “Application of AO to FSOC” The presentation will be in English…

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**Free-Space Optical Communications**

Atmospheric turbulence Telescope Objective: Present typical FSO Free-space optical communication systems = FSO For those no familiar with FSO systems, this a representation of a typical system for the metropolitan area. The communication link is composed of 2 telescopes facing each other and sending information by a laser beam, propagating through free-space (that is without a wave guide) Typical Free-Space Optical (FSO) system

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**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 The reason why we want to use FSOs is the numerous natural advantages they offer compared to traditional communication links (free from interference, no freq regulation, their data throughput is comparable to fiber optics and the fact that they are relatively easy to install compared to conventional systems. FSO system are mainly used in metropolitan area networks, where the use of cabled communication system cannot be easily considered and for temporary network installation, like for disaster recovery… All these clear advantages are to be mitigated by the fact that FSO systems are very sensitive to atmospheric conditions, and mainly fog and atmospheric turbulence. In this presentation, dealing with AO compensation methods, I will only concentrate on turbulence issues.

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**Presentation outline FSO and Atmospheric turbulence**

Comparison of different Adaptive Optics correction strategies wrt FSO performance Implementation of the dual-beam full-wave correction Conclusion and perspectives The general outline of the presentation is the following: I will first present the impact of atmospheric turbulence on FSO systems by introducing typical metrics to quantify link quality and briefly put forward different possible correction strategies by AO in order to precompensate for perturbations. I will then compare these performance with respect to FSO needs. One of the studied correction appears to be the best solution available. The problem is that no implementation has actually be proposed. To try to answer this issue, I will show part III a possible implementation strategy for this particular correction.

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**Presentation outline FSO and Atmospheric turbulence**

Turbulence effects on FSO systems AO Precompensation: existing methods Comparison of different Adaptive Optics correction strategies wrt FSO performance Implementation of the dual-beam full-wave correction Conclusion and perspectives The first part of the presentation is composed of first the study of atmospheric turbulence on FSO systems and then of the presentation of existing methods for AO based precompensation.

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**Laser beam propagation and turbulence**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Laser beam propagation and turbulence Atmospheric turbulence Telescope Laser propagation through turbulence When a laser beam propagates through free-space it suffers from perturbations induced by atmospheric turbulence. The main effects are a random displacement of the beam centroid (also called beam wander), a broadening of the beam (of beam spreading) and spatial and temporal fluctuations (or scintillation). Since the main quantity of interest for FSO systems is the integrated power in the bucket over the pupil aperture, atmospheric turbulence will clearly lead to fluctuations of the collected signal and a degradation of the link Movie is slowed compared to reality (about a hundred times) Cn2: typical of a turbulence strength during the day approx. 30m above the ground. L = 10 km λ = 1.5 µm Dpupil = 30 cm Wind speed = 5 m.s-1 Cn2 = m-2/3

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**Laser beam propagation and turbulence**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Laser beam propagation and turbulence Atmospheric turbulence Telescope Laser propagation through turbulence When a laser beam propagates through free-space it suffers from perturbations induced by atmospheric turbulence. The main effects are a random displacement of the beam centroid (also called beam wander), a broadening of the beam (of beam spreading) and spatial and temporal fluctuations (or scintillation). Since the main quantity of interest for FSO systems is the integrated power in the bucket over the pupil aperture, atmospheric turbulence will clearly lead to fluctuations of the collected signal and a degradation of the link Movie is slowed compared to reality (about a hundred times) Cn2: typical of a turbulence strength during the day approx. 30m above the ground. L = 10 km λ = 1.5 µm Dpupil = 30 cm Wind speed = 5 m.s-1 Cn2 = m-2/3 Power in the Bucket: I

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**Turbulence effects on FSO systems**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Turbulence effects on FSO systems Histogram I Intensity Histogram Temporal evolution I Time [s] (Goal: first order characterization of I evolution) When looking at the temporal evolution of the Power in the Bucket as a function of time; we see that the stronger the turbulence strength (which can be characterized by Cn2), the stronger the fluctuations. For strong turbulence, these fluctuations can even bring a complete extinction of the signal. Equivalently we can look at the intensity histograms for different Cn2. The stronger the turbulence, the lower will be the mean intensity and higher will be intensity fluctuations. To the first order, the optical link can be characterized by the mean intensity and intensity fluctuations. D = 30 cm, L = 10 km, l = 1.5 µm Wind speed = 5 m.s-1 Cn2 = 10-16, 10-15, m-2/3

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**Link quality estimation**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Link quality estimation Estimation of FSO link quality: Detection noise Intensity probability density function (PDF) <BER> Goal pI log-normal for weak perturbations pI for strong perturbations ? Mitigation: decrease fluctuations & increase <I> In order to estimate the quality of the FSO link, we can use the average bit error rate. It is simply the ratio between the mean bit errors to the total of emitted bits. In the presence of atmospheric turbulence, the error should be calculated by averaging over the intensity density probability function. Where \sigma_d is the detection noise and pI the intensity density probability function. If we consider a log-normal probability function for pI (which is a valid consideration for the weak turbulence case); the <BER>, as a function of the average collected intensity, is the following. The black curve represents the BER w/o any turbulence. The green curve for a weak turbulence of 10-16, the orange curve for The red and blue curves represent the <BER> respectively for and The fact that the blue curve is below the red curve despite the fact that the turbulence strength is higher, is due to a saturation effect for intensity fluctuations. We know that log-normal distribution is only valid for weak turbulence. For strong turbulence no analytical solution is available. Log-normal is generally considered to underestimate the tail of the real probability density function, and thus will simply underestimate the real average BER. To a first order approximation <I> will increase the SNR and sI will change the slope of the BER curve. Unfortunately a typical value for sI/<I> is 0.5 (that a typical BER of 10-2), whereas the goal is to reach BER values below 10-9. The goal of any correction or turbulence mitigation system will thus be to increase <I> and reduce sI. A reasonable value for sI/<I> is 0.1, where it is sufficiently close to the BER w/o turbulence and can easily reach desired BER values. Several means of reducing intensity fluctuations are possible: by increasing the aperture diameter, or diversity techniques (aperture averaging and spatial diversity has for example been studied by Khalighi where I am a co-author). Other mitigation methods are possible but only AO seems a true promising solution. That being send, several implementations of the AO system are possible. What are the existing AO correction methods? M.A. Khalighi et al., “Fading Reduction by Aperture Averaging and Spatial Diversity in Optical Wireless Systems”, JOCN, 2009

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**Conventional AO principle**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Conventional AO principle Atmospheric turbulence Telescope 1 Telescope 2 WFS DM RTC Laser Data Beacon Correction: Wavefront (WF) measurement: back-propagating laser beacon Deformable Mirror (DM) controlled by WF measurement The first possible implementation is the conventional OA. It was first proposed for implementation on FSO systems by Primmerman in 1991. A counter-propagating laser beacon is sent from telescope number 2 in order to probe atmospheric turbulence. The wavefront sensor, measures the phase perturbations and the real time calculator applies the opposite deformation to the deformable mirror. Because of propagation reciprocity, the DM shape enables the precompensation of the data-holding forward-propagating laser beam (here in red). The existing implementations are mainly limited to either short distances or advantageous turbulence distribution for perturbation measurements (like in between mountains, where most of the turbulence is located close to emitter). The conventional AO is the main correction strategy used in astronomy C.A. Primmerman et al., “Compensation of atmospheric optical distortion using a synthetic beacon”, Nature,1991 Conventional AO

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**Conventional AO limitation : strong perturbations regime**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Conventional AO limitation : strong perturbations regime Wave amplitude cancellation and phase discontinuity Branch points intensity phase When the propagation configuration is less advantageous, we enter in the strong perturbation regime. And the wave after propagation will suffer from amplitude cancellation and phase discontinuity. Amplitude variability (scintillation) will cause problems during WF measurement This means that geometrical WFS and also that continuous DM are no longer adapted Both these problems can be solved, and we will see what it can provide. Geometrical WFS (scintillation, WF discontinuity) not adapted Correction with continuous DM not adapted Conventional AO

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**Direct phase control Atmospheric turbulence Implementation Limitations**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Direct phase control Atmospheric turbulence Telescope 1 Telescope 2 DM Laser RTC Receiver Feedback Data 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 Due to these limitations, some authors have proposed a direct control of the phase. The implementation consist in controlling the shape of one or 2 DMs by directly maximizing the metric of interest: here the received power in the bucket. This is an iterative process than has the advantage of not utilizing any WFS. The main limitation of this approach is the need for fast converging algorithm and AO loop. Thanks to efficient algorithms (such as the one proposed by Professor Vonrontsov) and technology evolution this approach can be seriously considered. M. A. Vorontsov, et al., ‘Adaptive phase distortion correction based on parallel gradient-descent optimization,” Optics letters, 1997. Direct control

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**Dual-beam Full-wave correction**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Dual-beam Full-wave correction Telescope 1 Telescope 2 Full-wave conjugation Laser Full-wave conjugation Pupil truncation Full-wave conjugation Dual-beam full-wave correction (Barchers1) Only conceptual proposition Weak turbulence study only Proof of correction convergence Proposed a dual-beam phase-only correction A third and different approach consists of a dual-beam full-wave correction It consists in first sending a laser beam from telescope #1 to the #2. At the level of the #2 telescope, a phase and amplitude (or full-wave) conjugation is undertaken. The precompensated beam is then send form #2 to #1. The process is the identically repeated at #1, where a full-wave conjugation is applied. Thus both telescope perform a full-wave correction on a all-ready precompensated beam. It’s the only correction strategy that proposes the correction for both the forward and backward propagating beams. The wave emitted from one telescope is simply the complex conjugated of the received field, time the pupil aperture. The need of propagating back and forth arise from the spatial limitation induced by the aperture. Without any aperture, only one conjugation is sufficient to reach a perfect correction. Barchers was the first to propose such a correction strategy. But he only proposed a theoretical study in the limited case of weak turbulence. He, on the other hand, proved the convergence of the correction. And also proposed a simpler correction strategy where only the phase part of the wave is controlled and not like for the full-wave, both the phase and amplitude. [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. Dual-beam

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**AO: a solution capable of reaching such a requirement?**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion 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 To sum up the introductory part of my presentation: We have seen that the propagation of a laser beam through turbulence crease important intensity fluctuations at the receiver. I’ve introduced the mean BER to quantify the FSO performance and that intensity fluctuations are the main cause of high BER and are incompatible with FSO requirements. In order to reach these requirements, we need to both increase <I> and decrease sI/<I>. To reach a typical value for the <BER> = 10-12, we need to decrease intensity fluctuations below approx. 0.1. Several implementation concepts have been shown, but a question remains: are these systems capable of reaching the desired requirement? to my knowledge, no comparative study has been performed to compare these different strategies in terms of FSO performance. AO: a solution capable of reaching such a requirement?

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**Presentation outline FSO and Atmospheric turbulence**

Comparison of different Adaptive Optics correction strategies wrt FSO performance Implementation of the dual-beam full-wave correction Conclusion and perspectives This part partially presents the personal work accomplished during my PhD thesis. I will first compare the effectiveness of the previously mentioned AO correction strategies with respect to there FSO performance. The third part of my presentation will try to propose an implementation solution for the best studied correction.

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**Presentation outline FSO and Atmospheric turbulence**

Comparison of different Adaptive Optics correction strategies wrt FSO performance Conventional AO Direct phase control Dual-beam full-wave correction Dual-beam phase-only correction Implementation of the dual-beam full-wave correction Conclusion and perspectives Conventional AO Direct control Dual-beam FW Dual-beam PO I will first present conventional AO and direct phase control results I will then show the performance of the phase and amplitude correction based on the dual-beam full-wave correction strategy. Finally I will show results for a degraded version of the dual-beam full-wave correction strategy limited to the control of the phase only.

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**Increasing turbulence strength**

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): Altitude h [m] Cn2 [m-2/3] Turbulence model h-4/3 (day) Increasing turbulence strength Cn2 = m-2/3 Cn2 = m-2/3 Cn2 = m-2/3 h-2/3 (night) Today: 2-3km are easily attainable, from 5km problems linked to turbulence arise but some companies (Aoptix, Shaktiware, and others) have started to answer this issue. We will look at 10km, a more challenging propagation distance. The wavelength selection is set mainly by component maturity and the fact that 1.5microns is a typical wavelength used in telecommunication systems; In terms of total size and thus cost of the system, I will concentrate on a typical value of D=30cm. Nevertheless, I will generally present a broader spectrum for different pupil diameters. The studied turbulence strengths are typical of weak, medium and strong turbulence conditions. If we look at a typical distribution of the Cn2 as a function of the altitude above the ground. Studying these Cn2 can be seen as equivalent to placing the FSO system at different altitudes. This graph show typical values for the mean Cn2, but Cn2 has an important temporal and spatial variability. Studying these limited number of parameters, is nevertheless not restrictive. The actual parameter of interest is generally the product of Cn2 and propagation distance L. Thus L and Cn2 are dual parameters, and studying a 10km propagation distance with a certain turbulence strength can be equivalent to studying a shorter distance with a stronger turbulence… These images show a typical intensity distributions after the propagation of a laser beam for these typical propagation conditions. The impact of turbulence strength is clearly visible

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**Study modeling tool: Pilot**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Study modeling tool: Pilot d d’ Atmospheric propagation turbulence turbulence Simulation code Turbulent phase screen Fresnel propagation In order to model the propagation through turbulence we use a propagation modeling tool called Pilot. It consists in considering that optical propagation through turbulence can be decomposed on one side by turbulent phase screens (concentrating the actual turbulence volume) and on the other side by a propagation in the vacuum between these screens by Fresnel propagation.

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**Conventional AO 7x7 Shack-Hartmann wavefront sensor (WFS)**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Conventional AO σI/<I> Pupil Diameter [m] 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 Lets first start with the conventional AO correction In order to perform these simulation, I’ve used a 7 by 7 SH WFS with a noiseless phase reconstruction of the 38 first Zernike modes. It can be shown that increasing the number of modes is not useful for the strong turbulence case. The figure presents the impact of conventional correction on intensity fluctuations as a function of the pupil diameter, for different turbulence strengths green represents a weak turbulence of 10-16, the orange curves represent a intermediate turbulence of and the curves in red for strong turbulence or Throughout the presentation I will try to stick to this color code that kind of look like the same color code used for traffic lights… Is also shown the results without correction (dashed curves) and with conventional correction (solid curves). By setting the goal in terms of intensity fluctuations to 0.1, we see that: There is no real interest for any correction for the weak turbulence case. That for this type of correction and for strong turbulence, the goal can only be reached for very large apertures (which is contradictory with the fact that we want to limit our self to apertures below D=30cm). The only interest of this solution is for medium turbulence and aperture size between approx. 18cm and 25cm, where it is possible to bring intensity fluctuations below 0. 1. Conventional AO

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**Direct phase control <I> I sI/<I>**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Direct phase control D = 30 cm, DM: 7x7 actuators No further gain by increasing number of actuators SPGD: Sequential Parallel Gradient Descent <I> I Iteration steps Cn2 = m-2/3 Iteration steps For the direct control of the phase, I’ve used a similar configuration with a 30cm pupil diameter and a 7 by 7 DM. It can be observed that increasing the number of actuators does not dramatically increase correction performance. The control law used a simple implementation of SPGD algorithm. Looking at the power in the bucket as a function the number of iteration for a single turbulence distribution, we indeed observe that the algorithm seems capable of increasing the power in the bucket. In terms of short-term exposures we clearly see an energy concentration. For FSO systems, we prefer to look at statistical values: We can see that direct phase control can indeed increase mean intensity and decrease intensity fluctuations (long-term exposure confirm the energy concentration issue) We also see that direct phase control, for D=30cm, is not capable of lowering intensity fluctuations below 0.1 for strong turbulence conditions. Direct phase control and conventional AO seem to give similar results, with a slight advantage for direct phase control in strong turbulence (due to scintillation issues). sI/<I> D = 30 cm, L = 10 km, l = 1.5 µm Cn2 = 10-16, 10-15, m-2/3 Identical correction level to conventional, slightly better for strong turbulence Iteration steps Direct control

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**Full-wave correction – Performance vs. D**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Full-wave correction – Performance vs. D Weak turbulence (Barchers): Cn2 = 10-16, m-2/3 Beam wander speckle Before After Cn2 = m-2/3 σI/<I> I = 99.2% I = 99.8% Cn2 = m-2/3 I = 92.5% I = 98.2% Pupil Diameter [m] The low correction efficiency recorded for classical phase-only correction systems, justifies the study of other methods and in particular the full-wave correction. Firstly, by looking at weak turbulence results we see that. Short-exposure images show a clear increase in the total collected intensity, even if the initial value is already high. These values were obtained for a 30cm aperture and a single turbulence realization, if we look at intensity fluctuations as a function of the pupil diameter (the solids curves being the fluctuations after correction and the dashed curves w/o any correction). 2 different regimes can be observed: the separation between the 2 can be scaled by LF for smaller than 2LF values, the main reason for fluctuations is related to beam wander. Correcting effectively for it is thus very efficient. As seen on the figure, the difference between the uncorrected curves and the corrected curves steeply increases with increasing aperture diameter. After approximately 25cm, the behavior changes. The decrease is due to the fact that more and more speckles are averaged over larger apertures. The difference between correction and uncorrected values seems relatively constant after this point. As observe for the conventional AO: the interest for AO correction for the weak turbulence regimes is very limited. D = 30 cm LF = √λL = 12cm scaling parameter 2LF no FSO interest Dual-beam FW

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**Full-wave correction – Performance vs. D**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Full-wave correction – Performance vs. D Strong turbulence: Cn2 = 10-14m-2/3 σI/<I> Pupil Diameter [m] Before After Cn2 = m-2/3 I = 40.2% I = 80.8% D = 30 cm For strong turbulence conditions, the behavior is slightly different. Again, we observe that the full-wave correction can effectively concentrate energy within the pupil aperture. When looking at intensity fluctuations as a function of the pupil diameter, we see that the decrease is mainly due to beam spreading and is thus inversely proportional to D. The scaling value is replaced by lambdaL/piRho0 (approximately equal to 50cm for cn2=10-14) By setting the fluctuations limit to 0.1: We see that the needed aperture diameter to reach this value is greatly decreased by the correction. Only a 25cm pupil is needed for Cn2=10-14 whereas w/o any correction a pupil diameter of over 60cm is required. The dual-beam full-wave correction seems a very efficient correction strategy whatever D even for strong turbulence. It thus presents a strong interest for FSO systems. Mainly beam spreading: sI proportional to D-1 LF is replaced by = 50cm (Cn2 = 10-14m-2/3) Efficient correction whatever D FSO interest Dual-beam FW

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**Full-wave correction – Performance vs. D**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Full-wave correction – Performance vs. D Strong turbulence: Cn2 = 10-14, m-2/3 Before After σI/<I> Cn2 = m-2/3 I = 40.2% I = 80.8% D = 30 cm For strong turbulence conditions, the behavior is slightly different. Again, we observe that the full-wave correction can effectively concentrate energy within the pupil aperture. When looking at intensity fluctuations as a function of the pupil diameter, we see that the decrease is mainly due to beam spreading and is thus inversely proportional to D. The scaling value is replaced by lambdaL/piRho0 (approximately equal to 50cm for cn2=10-14) By setting the fluctuations limit to 0.1: We see that the needed aperture diameter to reach this value is greatly decreased by the correction. Only a 25cm pupil is needed for Cn2=10-14 whereas w/o any correction a pupil diameter of over 60cm is required. The dual-beam full-wave correction seems a very efficient correction strategy whatever D even for strong turbulence. It thus presents a strong interest for FSO systems. Pupil Diameter [m] Mainly beam spreading: sI proportional to D-1 LF is replaced by = 50cm (Cn2 = 10-14m-2/3) Efficient correction whatever D FSO interest Dual-beam FW

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**Full-wave correction – Intensity Histogram**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Full-wave correction – Intensity Histogram Full-wave correction Histogram I When looking at intensity histograms, we observe that whereas the log-normal distribution is not appropriate to describe strong turbulence regimes, it seems a reasonable assumption for all studied regimes after a full-wave correction, confirming the fact that the correction strongly reduces the impact of turbulence on the optical link. Log-normal approximation with D = 30 cm Not appropriate for strong turbulence regimes without correction Seems reasonable after full-wave correction for all regimes D = 30 cm, L = 10 km, l = 1.5 µm Cn2 = 10-16, 10-15, 10-14, m-2/3 Dual-beam FW

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**Full-wave correction – Average Bit Error Rate**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Full-wave correction – Average Bit Error Rate No correction D = 30 cm, L = 10 km, l = 1.5 µm Cn2 = 10-15, 10-14, m-2/3 <BER> Full-wave correction 3.10-4 <BER> 0.98 0.8 0.33 <I> Full -wave 2.10-2 0.3 0.92 0.06 No Corr. 10-15 10-14 Cn2 Strong turbulence Cn2 = 10-14 ok Very strong Cn2 = ok if I0/sd * 4 In terms of a more FSO related metric, we observe that the average BER is strongly reduced whatever the turbulence strength. Before correction, we go from a BER approximately of 10-2 to under with correction. This table sums up typical values of turbulence and correction efficiency. We see that the need of correction is very limited for medium turbulence But very efficient for strong turbulence. For even stronger turbulence, the desired BER level cannot be easily reached. Nevertheless, it can observed that the average power in the bucket shows a fairly high value, strongly increasing the received flux and the slope of the BER curve is much steeper than without correction. Dual-beam FW

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**Full-wave correction – Iteration influence**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Full-wave correction – Iteration influence σI/<I> <I> Number of iterations Number of iterations Few iterations needed Fluctuations divided by approx. 10 I’ve mentioned in the introduction that the correction is performed on both sides of the FSO link, and that the convergence of the correction is naturally achieved iteratively. It can be seen that only a few iterations are needed what ever the turbulence strength and that again a strong reduction of intensity fluctuations is obtained. These results where published in an SPIE paper earlier this year. D = 30 cm, L = 10 km, l = 1.5 µm Cn2 = 10-16, 10-15, 10-14, m-2/3 N. Schwartz et al., “Mitigation of atmospheric effects by adaptive optics for free-space optical communications,” SPIE 2009 Dual-beam FW

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**Dual-beam phase-only correction**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Dual-beam phase-only correction I = 25% I= 41% Cn2 = 10-16m-2/3 Cn2 = 10-15m-2/3 Cn2 = 10-14m-2/3 Before After D = 30 cm Typical intensity distribution phase-only correction Identical to dual-beam full-wave only-phase is controlled Telescope 2 Telescope 1 Emitted beam (not corrected) Phase-only conjugation Pupil truncation The results obtained with the dual-beam full-wave correction are very promising, but since the control of phase and amplitude is a slightly complicated issue, we decided to look at a simpler version of the correction where only the emitted phase is controlled. The presented diagram recalls the propagation configuration The emitted wave is simply the product of an uncorrected beam U0 times the opposite phase of the received wave and the pupil aperture P. Short-exposure images show the phase-only correction efficiency for different turbulence strength. It seems that whereas the correction efficiency seems similar to full-wave correction for weak turbulence, the strong turbulence case is much less efficient. Dual-beam PO

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**Phase-only VS Full-wave correction**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Phase-only VS Full-wave correction Full-wave Phase-only <BER> <BER> These results are confirmed by BER curves. Where: The global correction effectiveness is clearly below the full-wave correction, in particular for strong turbulence the correction efficiency does not allow to reach desired correction levels. Global effectiveness below full-wave correction sI/<I> < 0.1 for medium turbulence only D = 30 cm, L = 10 km, l = 1.5 µm Cn2 = 10-15, m-2/3 Dual-beam

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**Need for phase and amplitude correction strategy**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion 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 (sI/<I>[D=30 cm] > 0.1) Phase and amplitude: full-wave correction Efficient beyond weak fluctuation regime Few iterations needed to achieve convergence (<10) To conclude this part, 3 different phase-only corrections have been studied. We observe: whereas they all seem efficient in weak and intermediate turbulence level their correction level is not sufficient for strong perturbations and cannot reach the desired correction level (without strongly increasing the pupil diameter). We, in parallel, have studied a phase and amplitude correction strategy, which seems capable of reaching desired correction levels for all studied turbulence levels. Even if it is by nature a iterative correction, a very limited number of iterations are needed to achieve convergence. This tends to prove that a phase-only correction is in general insufficient and one should try to correct for both phase and amplitude. Actually no implementation is proposed. Need for phase and amplitude correction strategy

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**Presentation outline FSO and Atmospheric turbulence**

Comparison of different Adaptive Optics correction strategies wrt FSO performance Implementation of the dual-beam full-wave correction Conclusion and perspectives This conclusion brings us the 3rd part of the presentation where I will try to provide an implementation solution of the best correction studied: the dual-beam full-wave correction.

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**Open issues for wave correction**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion 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? In order to try to control for both phase and amplitude of the wave, we shall first answer some open questions. To obtain a spatial description of the field we will use spatial sampling. A modal analysis is indeed impractical due to phase branch points. To achieve the desired performance level, we have to know what is the number of degrees of freedom should be used. And also how can we control and measure the wave.

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**Presentation outline FSO and Atmospheric turbulence**

Comparison of different Adaptive Optics correction strategies wrt FSO performance Implementation of the dual-beam full-wave correction Wave sampling influence Practical way of wave measurement and control Conclusion and perspectives Whereas I’ve answered to the first question, part 3 will try to answer to the other 2: that is the wave sampling influence and how to control and measure the wave.

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**Wave sampling geometry**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Wave sampling geometry U U is the mean measured field N2 = Number of sampling points N = D/d Square geometry is considered D d The wave sampling geometry is described here, where D is the square pupil side and d is the elementary wave sampling point U is simply the integral of the electromagnetic field over the sampling surface d and measures the mean field. N2 represents the number of sampling points within the aperture And the pupil geometry is from now on considered to be square.

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**D/r0 seems a good parameter to scale system complexity**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Sampling influence Influence of spatial sampling on the corrected field in the pupil plane N <I> σI/<I> N Cn2 10-16 10-15 10-14 D/r0 1.6 6.5 26 Nc = N | (sI/<I> = 0.1) 1 3 10 If we study the influence of the spatial sampling of the pupil plane with first the mean intensity and then intensity fluctuations. We see the correction effectiveness saturates after a certain value that only a few sampling points seems necessary to reach the requirement. The table compares N (or the square root number of actuators) needed in order to reach the requirement and the scaling parameter D/r0. Since the ratio between 2 values is approximately constant, D/r0 seems a good parameter to scale system complexity Nc / (D/r0) ~ 2 D/r0 seems a good parameter to scale system complexity D = 23.5 cm, L = 10 km, l = 1.5 µm Cn2 = 10-16, 10-15, m-2/3

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**Does sampling impact convergence?**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Does sampling impact convergence? σI/<I> <I> Iteration number Iteration number It interesting to note that correcting for fewer sampling points does not dramatically change convergence time, and only approximately 10 iterations are still needed to achieve convergence. Few iterations are needed to achieve convergence (<10)

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**Phase and amplitude control**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion 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 Phase modulation Amplitude modulation z Laser DM Energy loss Laser DM In order to control both phase and amplitude without loss of energy, several possibilities are available. First by the addition of a phase modulator and an amplitude modulator. Obvious energy losses due to the attenuator do not enable a lossless control Another solution is to use 2DMs. When using a single DM in the pupil, a lossless phase-only control is obtained. When using 2DMs separated by a distance z, we observe energy losses due to diffraction by the first mirror. [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

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**Phase and amplitude control**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Phase and amplitude control 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 E2 E1 E0 Mach-Zehnder |E1|2+ |E2|2 = |E0|2 In order to control both for phase and amplitude, w/o energy loss: suppose you want to control only 2 points. The use of a Mach-Zehnder interferometer will make possible the control of both the phase and amplitude of E1 and E2 from a single source E0. The phase shifter phi0 will control for the relative amplitude between the 2 waves and phi1 and phi2 for their phase. If you want to control more points, it is possible to make all beams interfere in a tree structure architecture. Here is presented the control of 4 waves from a single wave. Use in reverse, it is possible to measure phase and amplitude by classical interferometric approaches.

38
**Implementation – Principle**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Implementation – Principle Pupil geometry (diffraction) + fiber optics injection energy loss at reception Basic performance estimate (square geometry) for sI/<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% Cn2 = 10-14m-2/3 Sub-pupils Pupil I = 33.1% In order to perform the dual-beam full-wave correction this is the kind of implementation that can be used. A spatial sampling of the pupil is performed by circular sub-pupils and injected into optical fibers. The short-exposure images show a clear increase in the collected intensity. The dashed square represents pupil diameter. Due to the chosen sub-pupil geometry and the injection into fiber optics used, we observe a lower final power in the bucket value after correction. Nevertheless, the basic performance estimation based on a filled square geometry for intensity fluctuations are not greatly modified by the pupil geometry. We previously observed and we still observe here, that only 100 sampling points are sufficient to achieve the desired performance level.

39
**Conclusion – Part III Spatial sampling**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion Conclusion – Part III Spatial sampling Innovative solution for phase and amplitude correction Only a few actuators are necessary to lower fluctuations sI/<I> = (N2 = 100 actuators, for 20 < D < 30 cm) D/r0 seems a good parameter to scale system complexity The proposed implementation is an innovative solution for phase and amplitude correction. I showed that only a few numbers of sampling points are necessary to achieve performance level. In between for 0.2 < D < 0.3, only 100 actuators are necessary. I showed that D/r0 seems a good parameter to scale system complexity Thus if we want to either achieve more effective correction or for example reach longer propagation distances, the system complexity can easily be scale to reach the desired correction level.

40
**Presentation outline FSO and Atmospheric turbulence**

Comparison of different Adaptive Optics correction strategies wrt FSO performance Implementation of the dual-beam full-wave correction Conclusion and perspectives I will now conclude and present the perspectives for this work

41
**Conclusion Three different phase-only correction strategies studied**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion 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 Conventional AO Direct control Dual-beam PO Dual-beam FW I’ve studied 3 different phase-only correction Whereas phase control seems efficient in weak to intermediate turbulence, it show insufficient for strong turbulence. This study tends to prove that independently from correction strategy, a phase-only correction a generally insufficient. I then studied a phase and amplitude control It proved to be an efficient correction strategy even for strong turbulence conditions that only a limited number of iterations are required to reach convergence; and that only a limited number of sampling points are necessary to reach performance. To my knowledge, no implementation of the full-wave correction is available, I proposed means to simply realized this correction. where the control is eased by the direct relation to wave measurements classical interferometric approaches can be used for wave measurement and an interesting particularity of this implementation is that there is no energy loss by the control of the phase and amplitude.

42
**Perspective FSO with conventional AO: Field tests in 2010**

Context & existing methods – Correction comparison – Full-wave implementation – Conclusion 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 As for the perspectives: A field test will be performed next year it will use a conventional AO correction with a 25cm aperture and a 8by8 SH WFS (reconstructing 50 Zernike modes) it will also use several back-propagating laser beacons in order to mitigate scintillation effects on the WF measurements. A project is currently under study (the scapel project) which has for goal to conduct the development of mid IR components and a long distance FSO link. In parallel there is the lab test planed for next year in order to test full-wave correction The gain obtained by working at longer wavelengths is to be able to reach longer propagation distances (the goal of the scalpel project is to reach 20km or more). Working at longer wavelengths also enables a decrease in the overall AO complexity. In parallel, I am currently preparing an article base on the presented results.

43
**Publications Proceedings Articles Patent: Popular Science**

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) This work led to a short film on FSO systems and Adaptive Optics It was realized by Onera team members for popular science and presenting research to a young public. And it received the Jury prize (jury directed by Axel Kahn) of the ‘Les chercheurs font leur cinéma’ film festival last month.

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