Fourier-Based Predictive AO Schemes for Tomographic AO systems

1. 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. Outline A final note on GEMS astrometry – the on detector guide window The mechanics of Fourier predictive control Implementing multi-layer predictive control on Shane AO Extending predictive control to tomographic systems: Simulations Application to GEMS telemetry

3. 1-2 mas Astrometry on Bright Stars (V > 4) with the GEMS On-Detector Guide Window • 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 GEMS On-Detector Guide Windows

4. 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

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.

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

9. ShaneAO instrument characteristics

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

11. Outline A final note on GEMS astrometry – the on detector guide window The mechanics of Fourier predictive control Implementing multi-layer predictive control on Shane AO Extending predictive control to tomographic systems: Simulations Application to GEMS telemetry

12. Simulation Design 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 LGS LGS LGS

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

14. 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 Phase height cannot be constrained in sparsely-sampled regions from tomography alone! Multi-sampled regions

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

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

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

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

19. From Identification to Correction For a tomographic system: Apply a priorthat 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. Summary We will Implement Predictive Control on the Upgraded Shane AO System In simulation, shifting and averaging predictive control provides 3-13% benefits in tomographic wavefront estimation quality at all layers 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. This can be exploited to design filters that reject multiple common detections across layers, which are likely to result from tomographic reconstruction error.