Tomography and calibration for Raven: from simulations to laboratory results

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1 Tomography and calibration for Raven: from simulations to laboratory results Kate Jackson a, Carlos Correia b, Olivier Lardière a, Dave Andersen c, Colin Bradley a, Laurie Pham a, Celia Blain a, Reston Nash a, Darryl Gamroth a, Jean-Pierre Veran c a University of Victoria, 3800 Finnerty Rd., Victoria, BC, Canada; b Centre for Astrophysics, University of Porto, Rua das Estrelas Porto, Portugal; c NRC/Herzberg Institute of Astrophysics, 507 West Saanich Rd.,Victoria, BC, Canada ABSTRACT This paper discusses static and dynamic tomographic wave-front (WF) reconstructors tailored to Multi-Object Adaptive Optics (MOAO) for Raven, the first MOAO science and technology demonstrator recently installed on an 8m telescope. We show the results of a new minimummean-square error (MMSE) solution based on spatio-angular (SA) correlation functions, which extends previous work in Correia et al, JOSA-A 203 to adopt a zonal representation of the wave-front and its associated signals. This solution is outlined for the static reconstruction and then extended for the use of stand-alone temporal prediction and as a prediction model in a pupilplane based Linear Quadratic Gaussian (LQG) algorithm. We have fully tested our algorithms in the lab and compared the results to simulations of the Raven system. These simulations have shown that an increase in limiting magnitude of up to one magnitude can be expected when prediction is implemented and up to two magnitudes when the LQG is used.. THE RAVEN PROJECT A considerable amount of work both theoretical and practical with respect to Wide-field Adaptive Optics (WFAO) and tomography has been undertaken in the past two decades. 2 Multi-Object AO (MOAO) is an instance of WFAO (parallel to multi-conjugate AO) that promises to increase the corrected field to 5-0 arcmin 3 albeit in a discrete number of directions and not in the whole field. More recently, dedicated efforts toward proofing the concepts and mitigating the risks of MOAO have been made on multiple fronts, starting from open-loop (OL)-AO demonstrators 4, 5 and working up to a single science channel MOAO testbed. 6 Work has been done in both the MOAO and MCAO context on improving tomographic reconstruction techniques, specifically: In low SNR regimes to improve performance on dim natural guide stars (NGSs), thus increasing sky coverage, and in computational efficiency in anticipation of 30-40m class Extremely Large Telescopes (ELT) WFAO instruments which will see orders of magnitude increases in the sizes of the matrices which will need to be manipulated within the data processing pipeline. While the risks associated with MOAO have kept proposed VLT and ELT instruments on the drawing board, the scientific promise is so great that multiple on-sky demonstrators have been developed. The Visible Light Laser Guidestar Experiments (ViLLaGEs) 5 is a MEMS deformable Further author information: (Send correspondence to K. Jackson) K. Jackson: katjac@uvic.ca, Telephone: Adaptive Optics Systems IV, edited by Enrico Marchetti, Laird M. Close, Jean-Pierre Véran, Proc. of SPIE Vol. 948, 9482K 204 SPIE CCC code: X/4/$8 doi: 0.7/ Proc. of SPIE Vol K-

2 Calibration Unit i Off -axis sources Lscreens) OL OL OL WFS WFS WFS Ai.--A- (DM figure source BS DM CL WFS A VRI BS JHK Rot Telescope Flip mirror N Z a m u en a Acq. Cam era WFS Beam combiner > IRCS BS BS DM JHK VRI Rot DM figure source Figure : Functional optical block diagram of Raven. Dashed blocks are deployable. Raven consists of 8 main subsystems: the deployable Calibration Unit, the Open-Loop NGS WFSs, the Science Pick-offs, the Science Relays, the Closed-Loop NGS Truth/Figure WFSs, the Beam Combiner, the LGS WFS and the Acquisition Camera. CL WFS mirror (DM)-based AO testbed on the Nickel -meter telescope at Lick Observatory. It was the first on-sky experiment to successfully demonstrate open loop control. The Victoria Open Loop Test-bed (VOLT) 4 was an experiment aimed at distilling the problems of open loop control into a simple experiment. 7 Canary is the first MOAO demonstrator instrument to go on-sky it is installed at the 4 meter William Herschel Telescope 6, 8 and is considered a pathfinder for Eagle on the European Extremely Large Telescope (E-ELT). Raven has many of the same technical aims as Canary, but also has some significant differences; for example Raven will be the first MOAO instrument on an 8 m class telescope feeding an AO-optimized science instrument, the Subaru InfraRed Camera and Spectrograph (IRCS). 9 As it is both a science and technology demonstrator, the design has been more strictly constrained by science requirements such as sky coverage and minimum performance requirements. Much effort has been invested in establishing the baseline parameters of Raven, 3, 0 the optomechanical design, and estimating the type of performance that can be expected with a variety, 2 of tomographic WF reconstruction algorithms. A functional block diagram of the Raven system is shown in Fig. ; some of the main optical subsystems include the calibration unit (CU)/telescope simulator, 3 NGS OL WFSs paths and science pick off arms. 0 Some of the main technical specifications are provided in Table. The science gain achievable by Raven, in comparison to classical AO systems such as Subaru AO88, 4 will be modest, because Raven will only have two science channels. Nevertheless, the 8 m aperture of the Subaru telescope enables science that is not achievable on smaller telescopes, and Raven will be capable of delivering high ensquared energy into the IRCS slit with a goal of 30% in H-band. 3 Proc. of SPIE Vol K-2

3 Table : Raven specifications. Calibration Unit Telescope D 8 m r cm L 0 40 m Fractional r 0 [0.596; 0.224; 0.80] Altitudes [0, 5, 0] km Wavefront Sensor RON 0.2 e N NGS 3 Order 0 0 θ pix 0.4 arcsec N pix 2 framerate up to 500Hz Hz Centroiding algorithm thresholded Centre-of-Gravity DM Order 3 3 Number of valid actuators IMPROVING SKY COVERAGE WITH DYNAMIC TOMOGRAPHIC ALGORITHMS FOR MOAO MOAO systems achieve their scientific potential by taking advantage of their multiplexing observing capabilities. As is well known for any AO system, the availability of sufficiently bright guide-stars overshadows the utility of AO, even more so when the main scientific goals involve resolving photometric and kinematic science observations concentrating the light sufficiently to obtain spectra for several targets in a reasonable amount of time. Since such targets are usually very faint and not suitable for guiding the AO system, other natural guide-stars must be found that are sufficiently close. Therefore the sky-coverage, i.e. the percentage of available sky for observing, imposes a strong constraint on the observable targets. As a pathfinder instrument intended to perform scientific observations, it is of key importance that interesting science targets are available to Raven. With a static tomographic reconstructor, Raven s limiting magnitude will approach 4.5 (for 30%ensquared-energy) using a reduced frame rate of 80Hz. As stated in Andersen et al, PASP 202, 3 sky coverage for Raven will be low. The probability that there are three stars with R < 4.5 in a 2 arcmin diameter FOR has been estimated to be about 3%. Star densities are increasing as a power law at these magnitudes, so going magnitude deeper can increase the density of available stars by.8. There are several ways to approach the challenge of increasing the limiting magnitude; these include longer integration periods on the WFSs to increase SNR, better centroiding algorithms to obtain more accurate slope measurements in low signal regimes, and better noise rejection in the tomographic reconstructor itself. Ideally, an optimal combination of these ideas can be achieved. The modelling and testing of prediction models and potential improvement in terms of Raven s limiting magnitude are the subject of this work. More sophisticated centroiding algorithms can (and will) be used in parallel with the methods developed here, but their development and analysis is outside the scope of this paper. Proc. of SPIE Vol K-3

4 2. Minimization Criterion This section follows closely the presentation in Correia et al, JOSA-A, 204. MOAO systems require an open-loop estimate of the atmosphere over a large field in a discrete number of correction directions. Under the hypothesis that the turbulent atmosphere is a sum of N l thin layers located at a discrete number of different altitudes h l, the aperture-plane WF φ(ρ, θ, t) indexed by the bi-dimensional spatial coordinate vector ρ = (ρ x, ρ y ) in direction θ = (θ x, θ y ) at time t is defined as N l φ(ρ, θ, t) = W l (ρ + h l θ, t) () l= where W l (ρ, t) is the l th -layer wave-front. The aperture-plane WF phase is not measured directly in most AO systems and the WF phase is reconstructed from a set of discrete measurements using a measurement model. In this case, the Shack-Hartmann (SH)-WFS linear measurement model: s = Γφ + η, (2) with Γ a linear transformation from discrete phase points representing a specific spatial location to SH-WFS slopes with a spatial sampling twice as dense as the number of sub-apertures. The discrete stencil is composed of 9 weights per sub-aperture; it is computed from the expansion of the WF onto a basis of linear splines. The noise, η, is assumed to be a gaussian, zero mean random process with known variance. In MOAO, the objective cost function is the minimization of the aperture-plane residual phase variance in selected science directions, β = [β... β Nβ ], an estimate is made for each direction, β i, φ(βi R = arg min ) φ(β i ) 2 R L 2(Ω) where φ is the actual phase (represented in an arbitrary basis), L 2 is the Euclidean norm over the aperture Ω and is the ensemble average over time for an individual optimization direction. φ(β i ) Rs α, is the estimated phase (estimated quantities are indicated by the hat symbol) for that optimization direction, and s α are noisy measurements made in specific GS directions, (3) α = [α... α Nα ] T. (4) A well established solution to this minimization criterion is the Minimum Mean Square Error (MMSE) solution. 5 8 It states that for two jointly Gaussian, zero mean, random variables (in this case s α and φ β )with covariances, Σ = [ ] Σφβ,φ β Σ φβ,s α, (5) Σ sα,φ β Σ sα,s α the estimate, ˆφ β, of the value taken by φ β for a given s α which minimizes the Mean Square Error of Eq. 3 can be written, φ β = Σ (φβ,s α)σ s α s α (6) where, in general, β α for practical reasons, and where φ β is the pupil-plane phase estimate representing the decomposition of the WF in all the m-β science directions. This paper focuses strictly on the so-called spatio-angular (SA) approach. Tests have been carried out in a zonal basis; an extensive examination of layer-based prediction in a Zernike basis Proc. of SPIE Vol K-4

5 for Raven tomography can be found in. In this zonal approach, to compute the SA covariance matrix, the separation vector, r is defined as a function of the altitude of the layer, h l, and the coordinates of the subappertures, ρ. Computing the covariance between lenslets on different WFSs requires the position in the pupil of subapperture i on WFS n: (ρ i,n ), projected into layer l at h l in the direction of that WFS, (θ n ). The coordinates of the the subapperture in any layer are, (ρ xi,n + θ xn h l ), (ρ yi,n + θ yn h l ), (7) and the separation vector between subapperture i on WFS n and subapperture j on WFS m at layer l is, r i,j,l = (ρ i,n ρ j,m ) + h l (θ n θ m ), (8) where the first term of the right hand side of the equation is the particular separation between the subappertures in the pupil and the second term is the global WFS separation vector. From the covariance function for finite outer scale, C φ (r) = ( L0 r 0 ) 5/3 Γ(/6) 2 5/6 π 8/3 ( ) 5/6 ( 2πr 2πr J k L 0 L 0 ) ( ) 5/ Γ(6/5) (9) the SA covariance matrix between WFSs n and m can be computed for a given C 2 n profile with N l layers for every baseline, r, Σ(r, r 0, L 0 ) n,m φ = N l l= fr 0l Σ φ (r l, r 0, L 0 ), (0) where fr 0l is the factional Fried parameter r 0, l fr 0 l =, L 0 is the outer scale and r l is a concatenation of all the baselines i, j. To simplify notation, this expression is referred to as Σ n,m. To be able to use the phase covariance matrices with the input slope measurements, use the phase to slopes model, Γ, φ β = Σ β,α Γ T (ΓΣ α,α Γ T + Σ η ) s α, () which is equivalent to Eq. 6. For practical reasons, the phase is mapped back onto slopes in the β directions; this is due to the DM calibration available from the system. In Raven, the science DMs (SDMs) are calibrated via an interaction matrix between them and the CL-WFS on each science channel (see Sec. 2.2). The easiest DM fitting step therefore goes from slopes to commands, so it is convenient to estimate ŝ β, 2.2 Calibration ŝ β = Γ φ β = ΓΣ β,α Γ T (ΓΣ α,α Γ T + Σ η ) s α. (2) MOAO systems stress the need for accurate calibration since there is no feedback loop. In any OL system, there may be misalignments between the OL-WFSs, and in Raven in particular the OL- WFSs are rotated with respect to each other and the CL-WFSs which makes the tomographic step more challenging. To cope with the latter, several different approaches have been explored. The easiest way is to assume all WF measurements are in a regular and aligned reference coordinate system so it is important to note the reference basis of the slopes and slope estimates. We start by building a transformation matrix that relates measured open-loop slopes from all the WFSs through, Proc. of SPIE Vol K-5

6 s α = Σ (s α,s α)σ s α s α. (3) In Raven, the reference coordinate system, s α is chosen to be the CL-WFS; note that Eq. 3 does not transform the OL slopes to CL slopes. It changes the basis onto which the slopes are projected in an optimal way using an MMSE approach. The output of this step is open-loop slopes expressed in the CL-WFS space, which can be rotated, translated and magnified with respect to the OL-WFS space. This matrix is built on Raven by applying a large set of Hadamard commands to the calibration DM (CDM) to fully span the measurement space. The open-loop slopes from all WFSs are then collected and the covariance matrices assembled. The same could be successfully done with synthetic matrices using the actuator-mapping method 9 which identifies a set of metaparameters from the system: rotation, translation, differential magnification, etc. that are used in two ways: ) fine calibration of the system and 2) generate a set of theoretical or synthetic transformation matrices from these parameters. In real-time operation, the OL-WFS slopes are pre-transformed to CL-WFS space and then fed to the tomographic reconstructor. Using Eq. (2) the slopes in the science direction are estimated and finally projected onto the DM influence-functions using a calibrated command matrix computed from the inverse closed-loop interaction matrix between CL-WFS and SDM using truncated singular value decomposition. In a single equation we have u β = C }{{} Command mat. ΓΣ β,α Γ T (ΓΣ α,α Γ T + Σ η ) }{{} Tomographic reconstructor 2.3 Predictive Tomographic Reconstructor Σ (s α,s α)σ s α }{{} Transformation s α (4) Applying the Taylor frozen flow hypothesis allows us to equate spatial displacement within the pupil to temporal delay at a fixed position in the pupil. A single step pupil-plane predictor can be developed by leading out the computation in the direction of the wind profile. As a result, the reconstructor given in Eq. (2) is computed with a modified direction vector. To compute the predictive covariance between the OL-WFS directions, α n and the science object directions, β m, shift the global separation vector in each layer according to the wind velocity, v, and the sample time, T s, δ = vt s (5) r i,j = (ρ i,n ρ j,m ) + h l [α n (β m + δ)]. (6) Following Eq. () above, the predictive SA reconstructor can be expressed as R = Σ β+δ,α (Σ α,α + Σ η ). (7) One of the appealing aspects of this algorithm is that it will have the same dimensions as the static reconstructor and adds no computational complexity to the real-time path. The benefit of using the SA reconstructor is that it decouples the real-time path complexity from the number of atmospheric layers used in the model, this means that many layers may be used provided the computational resources are available to carry out the background task of updating the reconstructor in a timely manner. Additionally, in the zonal representation of the explicit layered reconstructor, grid points must be traced into atmospheric layers and interpolation must be carried out to obtain their values in any arbitrary direction which can lead to errors. This interpolation is not required in the SA case. For these reasons, the SA formulation was extended to the LQG algorithm presented next. Proc. of SPIE Vol K-6

7 2.4 Spatio-Angular Linear Quadratic Gaussian Controller The SA formulation can easily be extended to state-space modeling providing a full dynamic WF reconstruction using the LQG framework. Unlike previous work 20 we resort to a full-sa LQG which has several computational advantages to add up to those stated above, in particular a reduced number of states, admitting a minimal representation with a single WF instance at a given time-step. We provide here a top-level description of the LQG algorithm and refer the reader to standard textbooks in the literature for further information 8, 2 and earlier papers on the subject 20, 22 The standard steps of the LQG algorithm are as follows ŝ k k = Γˆx k k (8) ˆx k k = ˆx k k + M (s α ŝ k k ) (9) ˆx k+ k = Aˆx k k. (20) where x is the state vector, (k k p) means mathematical conditioning of the state at time-step k on information at time-step k p, Γ is still the measurement model, M is computed from the solution of the Riccati Equation and A is the prediction model. In the explicit layer algorithm, the state vector may contain several instances of the phase vector which itself contains a vector for each layer in the atmosphere model, ϕ = [ϕ, ϕ 2,..., ϕ Nl ] T. The dimensions of various matrices therefore scale with the number of layers. Additional matrix multiplications which propagate the phase between the layers and the pupil (H α ) must also be carried out at each time step. The prediction model, A ϕ, is a block-diagonal matrix to predict the phase in each layer at time-step k +. In the pupil-plane LQG, the spatio-temporally optimal estimate of the phase in the pupil at time k + in the direction of the GSs is made, ŝ k k = Γ φ (α) k k (2) φ (α) (α) k k = φ k k + M (s α ŝ k k ) (22) φ (α) k+ k = A φ φ(α) k k. (23) The Riccati equation is solved using the doubling algorithm and converges within 0 iterations, which translates into several seconds of computing time. The predictive model, A φ is the SA algorithm as described in Sec. 2.3, except that instead of leading off the position vector in the science direction, Eq. 6 is rewritten as, r = (ρ i,n ρ j,m ) + h l [α n (α m + δ)], (24) for n, m = : N GS including the cases where n = m, with N GS the total number of GSs. From this lenslet position vector, the prediction matrix, A can be defined as, A φ = Σ α+δ,α Σ α,α. (25) It can be seen in Eq. 23 that the result of the controller is the estimate of the predicted phase in the GS directions. The predicted phase in the science directions are then computed from using the static SA reconstructor, φ (α) k+ k Proc. of SPIE Vol K-7

8 φ (β) k+ k = Σ β,α Σ (α) α,α φ k+ k. (26) This algorithm is expressed assuming integer frame delays; these delays are due to the amount of time taken for camera readout, data processing, DM command application, etc. In Raven (or in any instrument), this may not be equal to a multiple of frames. A fixed system delay of 3ms has been allocated for camera read-out, wavefront reconstruction and DM actuation (the minimum delay in readout from the cameras is 2ms). The maximum frame rate of Raven will be 500 Hz (integration time of 2ms) but can and will be reduced by up to a factor of 0 according to the magnitude of the GSs being used. There are therefore two delay scenarios: The integration time is less than the system delay, in which case there are two frames of delay, and the integration time is greater than (or equal to) the system delay, in which case there is one frame plus a fraction of a frame of delay. Both scenarios are outlined in Figs. 2a and 2b. Exposure begins New DM Exposure CMOs applied ends Exposure begins Exposure ends New DM MO applied v <J I- V V I I I I Integrate (pg -0 ms) I ->i > Readout and process (3 ms) -> Integrate (2ms) I Readout a d process (3 ms) I (a) Long exposure timing (b) Short exposure timing Figure 2: Timing cases. It will be shown in the following sections that more benefit can be derived from carrying out temporal prediction when the total system lag (processing plus WFS integration time) is large. With this in mind, it is likely that the system will be operated in the scenario of Fig. 2a when prediction or LQG control is being carried out. Because of the OL nature of MOAO, asynchronous cases can be easily handled by an additional temporal prediction step which is outside of the state feedback loop. This means that a single frame delay can be assumed in generating the (α) estimated phase, φ k+ k and, subsequently, the extrapolation to the science direction given in Eq. 26 can be replaced by, φ (β) k++t lag k = Σ β+δ,α Σ (α) α,α φ k+ k. (27) In order to estimate the phase corresponding to the time at-which the commands will actually be applied to the DM, the value of δ must be vt lag where T lag = 3ms. Because the exposure is long, for example 0ms, the phase estimate could potentially be made for.5 frames of delay, which corresponds to the middle of the exposure and would require, in this example δ = v 5ms. 3. RAVEN SIMULATION System modelling of Raven was carried out in two separate parts. The first part involved the study of a broad swath of parameter space using two independent simulation tools. The parameter space was explored in order to establish and/or verify design parameters, as well as determine if Raven can realistically meet the proposed performance requirements and deliver useful MOAO-corrected images to the Subaru IRCS spectrograph. 3 The second part focussed Proc. of SPIE Vol K-8

9 specifically on implementing tomographic reconstructor algorithms with the intention of improving on the baseline performance case. 3. Model Parameters The figure-of-merit used to establish the quality of the wavefront correction is the ensquared energy; this is computed as the ratio of the amount of light falling on a simulated science camera within an area corresponding to the width of the slit in IRCS (40 milliarcseconds) to the total amount of light reaching the detector. Strehl ratios are also computed, as it is a value of interest to the astronomical community. Model parameters were set to those identified in Tab as those representing the Raven system and telescope simulator. Some additional model-specific parameters are given in Tab. 2. Table 2: Raven Baseline Configuration Parameters used in all simulation cases presented below. wind speeds [5.68; 6; 7] m/s wind direction [90; 80;80] deg NGS radii 45 arcsec Valid Subaps 80 f sample Hz λ W F S 0.64 µm DM stroke infinite DM influence cubic DM cross-coupling 30% DM valid actuators 97 Sci Channels 2 pure delay = 3ms λ eval.65 µm 3.2 Results There is a trade-off to consider in AO when selecting the framerate of the system: Increased integration time on the detectors leads to a better SNR which can improve AO performance, but also introduces more temporal lag error which degrades AO performance. The quality of the image will increase with SNR to a point and then begin to decrease as the lag error exceeds the SNR gain. The reconstructors in Eqs. 2 (static), 7 (predictive) and Sec. 2.4 (LQG) were implemented in simulation and the framerate at-which the peak performance was achieved for each reconstructor at increasing GS magnitudes was determined; the results are summarized in Table. 3. In passing, let us note that the theoretical estimate of the Full Width Half Max (FWHM) of the long exposure PSF for the baseline atmosphere in J band (.2 µm) can be computed for a finite outer scale using the expression developed in 23 for the ratio, L 0 /r 0 > 20. With r 0 = 0.56cm at 0.5µm and L 0 = 30m (chosen from median conditions on Mauna Kea), this computation yields an expected FWHM of arc seconds in J-band. The FWHM of a simulated long exposure science image was computed to be arc seconds, confirming good agreement between theory and simulation. The results show that the framerate at-which peak performance occurs for both the predictive and LQG algorithms is slower than that of the static algorithm for each magnitude; not only that, Proc. of SPIE Vol K-9

10 Table 3: Raven End-to-End simulation results. The optimal performance ( % ensquared energy) for each GS magnitude is shown for the zonal static SA, and compared to stand-alone SA Prediction and the full SA LQG algorithm. GS mags static SA SA Prediction SA LQG EE lag Strehl lag EE lag Strehl lag EE lag Strehl lag Maximum Strehl Ratio for a give Magnitude and System Lag Static Prediction LQG 70 Maximum Ensquared Energy for a given Magnitude and System Lag Static Prediction 52 LQG Strehl Ratio [%] Sample Rate [Hz] Ensquared Energy [%] Sample Rate [Hz] Guide Star Magnitude Guide Star Magnitude Figure 3: Static reconstructor vs Stand-alone Prediction and LQG: Strehl ratios (left) and ensquared energy (right) as a function of NGS magnitude. Left axis shows best achieved performance with a static reconstructor compared to the predictive and LQG reconstructors; right axis shows the OL-WFS sample rate at which that performance is obtained. but the overall performance at each GS magnitude is improved with the predictive algorithm and again with the LQG. The data is plotted in Fig. 3; here it can be seen that by using temporal prediction equivalent performance can be achieved with higher magnitude GSs when using a lower framerate. The results indicate that the gain in limiting magnitude is approximately one magnitude for simple prediction and two magnitudes for the LQG algorithm. 4. LABORATORY TEST RESULTS The telescope simulator is equipped with a broad spectrum source, an array of pinholes and a series of filters which allow incremental changes in the magnitudes of all asterism stars at once. A cross section of measurements across NGS WFS frame rates were taken for two different filters to show the improvement in performance using prediction and LQG control over the static reconstructor as well as compare the performance executing the predictive algorithms on fainter stars to that using the static algorithm using brighter stars. A plot of the results of these measurements is shown in Fig. 4. The diameter of the asterism used is approximately 2 arminutes. Proc. of SPIE Vol K-0

11 44 Laboratory Test results Ensquared Energy [%] Static Mag 3 Pred Mag 3 LQG Mag 3 Static Mag 5 Pred Mag 5 LQG Mag Frame Rate [Hz] Figure 4: Measured ensquared energy in a 40 milliarcsecond slit of science images taken while running the NGS WFSs at varying frame rates and executing static, predictive and LQG algorithms at two different magnitude settings. The science images in Fig. 5 represent the best performance achieved for each reconstruction method for a fixed magnitude, they clearly show that the EE is increased and the spot image becomes smaller for both predictive and LQG algorithms over the static reconstructor EE= !RCS slit á Figure 5: Performance comparison for Static, Predictive and LQG tomographic reconstruction algorithms. The performance achieved in lab tests is lower than that predicted by simulations in all reconstructor cases, but the trend of increasing peak performance by between 2 and 3 % with each increase in reconstructor complexity can be seen to be reflected in both the simulation data and the measured data. The exception is the static reconstructor at magnitude 5 in the laboratory results; at this point, the signal on the WFSs becomes quite low and the thresholded centre of gravity (CoG) begins to fail in the lab setting. The overall decrease in performance can be attributed to any number of sources; these include imperfect calibration, underestimation of noise sources in the simulation compared to reality, effects of the rotated WFSs, DM fitting, OL go-to errors, and non-common path aberrations (NCPA) between the OL and science paths, as Proc. of SPIE Vol K-

12 well as between the CL WFSs and the science camera. An investigation into the effects of these errors on simulation results is under way. A trend noted in the laboratory measurements for brighter GSs is that the peak performance of the static and LQG reconstructors occur at rates slightly slower than the frequencies predicted by simulation, but the simple prediction performance peaks at a much slower frequency than expected. We speculate that this may be due to the total amount of turbulence generated by the CU being a bit lower than expected; there may also be more noise than anticipated in the real system. As a result, the predictive algorithm would need to go to lower frequencies (greater temporal lag) to see the most gains. The increased noise may also push the peak performance of the static reconstructor toward lower frequencies, although not as much. Because the LQG handles noise and temporal lag, the decrease in turbulence will still push the peak to slower frame rates, but an increase in noise will have less effect on the LQG than on the simple predictor. This trend is not reflected in the measurements using dimmer GSs, however the shifting of the peaks toward lower frequencies may mean that the system cannot be run slow enough to spot the new peaks in the data. 5. CONCLUSIONS AND FUTURE WORK Simulation results for an MOAO system using static and dynamic tomographic reconstructors have shown that a gain in limiting magnitude of one magnitude can be expected from the use of a simple prediction within the tomographic step and reducing the overall framerate of the system. This can be achieved with no increase in the computational complexity of the real time pipeline. A gain of up to two magnitudes can be expected if the SA LQG algorithm presented in this paper is used, increasing the number of computations, but in a much more conservative way compared to the explicit layered LQG algorithm. The simulation results are supported by laboratory measurements taken on Raven with the telescope simulator. Some aspects of reality are not yet captured by the simulation, but the trend of the LQG improving over the simple prediction and over the static reconstructor holds. A more thorough analysis of the effects of different errors within the system on the overall performance in simulation is underway. Looking to the future, Raven has successfully carried out static MOAO on-sky on the Subaru telescope, and an atmospheric wind profiler is to be implemented for the next set of Engineering nights, to occur in August 204, whereby the dynamic algorithms presented here can be tested on-sky. Acknowledgements C. Correia acknowledges the support of the European Research Council through the Marie Curie Intra-European Fellowship with reference FP7-PEOPLE-20-IEF, number All the simulations and analysis done with the object- oriented MALTAB-based AO simulator (OOMAO) 24 freely available from REFERENCES [] Correia, C. et al., Static and predictive tomographic reconstruction for wide-field multiobject adaptive optics systems, J. Opt. Soc. Am. A 3 (203). [2] J.W.Hardy, [Adaptive Optics for Astronomical Telescopes], Oxford, New York (998). [3] Andersen, D. R. et al., Performance modeling for the raven multi-object adaptive optics demonstrator, PASP 24 (202). Proc. of SPIE Vol K-2

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