1. AO4ELT3 May 31, 2013 Fourier-Based Predictive AO Schemes for Tomographic AO systems S. Mark Ammons Lawrence Livermore National Laboratory May 31, 2013 Thanks to: Lisa Poyneer Alex Rudy Don Gavel Claire Max Luke Johnson Benoit Neichel Andrés Guesalaga Angela Cortes

2. AO4ELT3 May 31, 2013 1.A final note on GEMS astrometry – the on detector guide window 1.The mechanics of Fourier predictive control 2.Implementing multi-layer predictive control on Shane AO 3.Extending predictive control to tomographic systems: Simulations 4.Application to GEMS telemetryOutline

3. AO4ELT3 May 31, 2013 1-2 mas Astrometry on Bright Stars (V > 4) with the GEMS On-Detector Guide Window GEMS On-Detector Guide Windows  GSAOI on-detector guide windows can be read out quickly and saved to prevent target star saturation  1-2 mas stability on central star position (over short term) for V > 4 stars  Performance limited by flat-fielding and detector artifacts on ODGW

4. AO4ELT3 May 31, 2013 We will Implement Predictive Control on the Upgraded Shane AO System  Project funded by the University of California Office of the President  Goals:  Develop 4-dimensional LQG tomographic predictive control for MCAO and MOAO systems  Implement single-conjugate predictive control on the upgraded Shane LGS AO system at Lick Observatory Optimal control schemes use a model: We need a model of both the control system and the operating conditions (e.g. noise level and atmosphere) Many methods assign parameters MVU/Keck Bayesian - assign star brightness and r0 estimate For best performance, we need to be “data-driven” and use actual measurements to populate our model Getting wind velocity a little wrong is OK Getting wind direction a lot wrong is very bad

5. AO4ELT3 May 31, 2013

7. ShaneAO: Adaptive Optics System at the Shane 3-meter Telescope (LGS mode, new fiber laser) ShaneAO is a diffraction- limited imager, spectrograph, and polarimeter for the visible and near-infrared science bands. 7

8. AO4ELT3 May 31, 2013 Shane AO will Deliver Improved Strehl over Existing Lick System 8 Airy core forming LGS mode, new fiber laser

9. AO4ELT3 May 31, 2013 ShaneAO instrument characteristics 9 Detector sampling 0.035arcsec/pixel Field of view 20arcsec square Science detector: Hawaii2RG Hawaii2RG Science wavelength coverage: 0.7 to 2.2 microns 0.7 to 2.2microns Spectral resolution R = 500 Slit width: 0.1 arcseconds 0.1arcsec Slit decker: 10 arcseconds (?) 10arcsec Slit angle on sky adjustable 0-360° Long-exposure stabilityhold to the diffraction-limit for one hour hold to ½ slit width for 4 hours Polarimitry mode: polarization analyzer and variable angle waveplate Delta magnitude within seeing disk Dm K =10 Minimum brightness tip/tilt star: m V =18 Tip/tilt star selection field 120arcsec Sky coverage ~90%LGS mode Minimum brightness natural guide star m V =13 Camera readout modesCorrelated double-sampling (CDS) up the ramp (UTR) sub-frame region of interest (ROI) quick take Exposure support:Multiple frame co-added automated nod and expose coordinated with telescope (snap-i- diff, box-4, box-5) automated darks sequence based of history of science exposures Observations supportautomatic data logging automatic data archiving

10. AO4ELT3 May 31, 2013 ShaneAO is being Asssembled with First Light in Fall 2013 10 Deformable Mirror Wavefront Sensor Science Detector

11. AO4ELT3 May 31, 2013 1.A final note on GEMS astrometry – the on detector guide window 1.The mechanics of Fourier predictive control 2.Implementing multi-layer predictive control on Shane AO 3.Extending predictive control to tomographic systems: Simulations 4.Application to GEMS telemetryOutline

12. AO4ELT3 May 31, 2013 Simulation Design LGS Three-Layer Atmosphere We simulate an 8-m MOAO system with tomography:  3 LGSs over 120” diameter  3-layer Taylor frozen-flow atmospheric model assumed at 0, 5, 10 km (55%, 30%, 15%)  Wind velocities randomized, 0-15 m/s  200 realizations of 1 second length, 1 kHz operation  To isolate the effect of prediction on tomographic error, we add no WFS noise

13. AO4ELT3 May 31, 2013 Back-Projection Tomography 25 iterations per time step, alternating pre- conditioned conjugate gradient / linear steps Minimum Variance Back-Projection Tomography (Gavel 2004)

14. AO4ELT3 May 31, 2013 Correction Scheme – Shift & Average Multi-sampled Voxels Wind Identification and Estimation not simulated For each layer, replace voxels in downwind direction with shifted and averaged voxels from tomographic time history Only shift voxels originating in multi-sampled region, where height can be effectively determined Wind vectors assumed to be known perfectly Multi-sampled regions Phase height cannot be constrained in sparsely- sampled regions from tomography alone!

15. AO4ELT3 May 31, 2013 Prediction Improves RMS Errors on Layer Estimates After 1 second, on average, the layer estimates improve 3-13% Downwind regions improve 10- 30%, especially for high altitude layers Fractional Improvement in Layer Estimates Ground layer 5 km layer 10 km layer

16. AO4ELT3 May 31, 2013 Prediction Improves RMS Errors on Layer Estimates With downwind layers better determined, the tomographic error improves beyond the radius of the guide stars Tomographic Error vs. Field Radius Maps of Improvement in Layer Estimates LGS radius With shift & average Without shift & average

17. AO4ELT3 May 31, 2013 Application to GEMS Telemetry Method #1: Apply wind identification step to pseudo open loop slopes provided by A. Guesalaga and B. Neichel Method #2: 1.Perform tomographic reconstruction on pseudo open- loop slopes to estimate true volumetric phase 2.Apply wind identification step to layers of different atmospheric heights We expect that wind layers separated by height will have different temporal properties.

18. AO4ELT3 May 31, 2013 Tomographic Reconstruction + Wind Identification Cleanly Separates Layers Pseudo Open-Loop slopes Tomographically- reconstructed ground layer Tomographically- reconstructed 4.5 km layer The temporal properties of layers are cleanly distinguished by a tomographic reconstruction (using only geometric information!)

19. AO4ELT3 May 31, 2013 From Identification to Correction For a tomographic system: Apply a prior that wind vectors in layers separated by geometric tomography should be uncorrelated. If a wind peak is seen with a certain vector that corresponds to a stronger detection in another layer, reject those frequencies. For faster tomography for on-line use: Use Guesalaga & Cortes autocorrelation technique

20. AO4ELT3 May 31, 2013Summary 1. We will Implement Predictive Control on the Upgraded Shane AO System 2.In simulation, shifting and averaging predictive control provides 3-13% benefits in tomographic wavefront estimation quality at all layers 1.From GEMS telemetry: Adding a tomographic reconstruction to pseudo-open loop slopes, using geometric information only, cleanly separates the temporal properties of the wind flow. 2.This can be exploited to design filters that reject multiple common detections across layers, which are likely to result from tomographic reconstruction error.