1. Fast & Furious: a potential wavefront reconstructor for extreme adaptive optics at ELTs Visa Korkiakoski and Christoph U. Keller Leiden Observatory Niek Doelman TNO Science and Industry Raluca Marinica and Michel Verhaegen Delft Center for Systems and Control

2. Outline Scope: real-time WF sensing for XAO at ELTs Why to investigate new wavefront sensing methods? – Issues with roof sensor Fast & Furious – A new focal plane wavefront sensing algorithm – Brief introduction & current status

3. Issues with roof sensor Requirements for EPICS XAO WFS driven by the need for very high contrast A possible option is a roof-sensor Detailed simulations: see (Korkiakoski et al 2010)

4. Issues with roof sensor Fulfills the requirements, but has some challenges: – Nonlinearity – Fast WF reconstruction still to be solved Should we fix the nonlinearity by modulation? Residual WF (6 λ/D mod) RS measurement (modulation 6 λ/D) NO!

5. Issues with roof sensor The performance does not scale as you expect – Spiders & windshake at E-ELT + nonlinear sensor can cause unexpected results Residual WF (6 λ/D mod) RS measurement (modulation 6 λ/D)

6. Issues with roof sensor Traditional WF reconstruction requires a command matrix having a size of 55000 x 30000 Fast reconstruction requires approximations – So far, no detailed performance comparisons have been shown Zonal interaction matrix: 3% non-zero elements Command matrix: 0% non-zero elements

7. Fast & Furious We have been studying an alternative wavefront sensing option: no WFS at all AO residual < 1 rad rms DM Focal plane Science camera Focal plane Science camera Fast & Furious algorithm Control & DM fitting Corrected WF Images WF estimates DM commands

8. Fast & Furious How does F&F differ from other focal plane methods? – Linear approximation Cut down the complexity – Use of pupil symmetries & phase diversity Extremely fast + smaller role for the diversity – Iterative WF correction Applicable to systems with a deformable mirror

9. Fast & Furious All the needed pieces have been around, we combine earlier results – Small-phase solution (Gonsalves 2002) Approximate complex amplitudes linear function of WF Use the symmetry properties of pupil Much of the WF information can be obtained from a single PSF measurement, use diversity for the rest – Iterative phase-diversity Use the adaptive optics DM change as a diversity (Gonsalves 2010)

10. Fast & Furious: principle An example: consider a sinusoidal wavefront An example: consider a sinusoidal wavefront Wavefront (rad) See the math at (Keller et al 2012), (Korkiakoski et al 2012)

11. Fast & Furious: principle Measured PSF An example: consider a sinusoidal wavefront An example: consider a sinusoidal wavefront Wavefront (rad) See the math at (Keller et al 2012), (Korkiakoski et al 2012)

12. Fast & Furious: principle Measured PSF An example: consider a sinusoidal wavefront An example: consider a sinusoidal wavefront Wavefront (rad) See the math at (Keller et al 2012), (Korkiakoski et al 2012) ??

13. See the math at (Keller et al 2012), (Korkiakoski et al 2012) Fast & Furious: principle Measured PSF The main lobe and 1 st side lobes are accurately modeled by a linear approximation

14. Linear approximation

15. Measured PSF The lobes further have a negligible contribution to the PSF

16. See the math at (Keller et al 2012), (Korkiakoski et al 2012) Fast & Furious: principle Measured PSF The main lobe and 1 st side lobes are accurately modeled by a linear approximation Pay attention to the conservation of the energy! The lobes further have a negligible contribution to the PSF

17. See the math at (Keller et al 2012), (Korkiakoski et al 2012) Fast & Furious: principle The next idea: use symmetry The next idea: use symmetry Measured PSF The pupil function is symmetric. Can use make use of that?

18. See the math at (Keller et al 2012), (Korkiakoski et al 2012) Fast & Furious: principle Even PSF component Odd PSF component Measured PSF The next idea: use symmetry The next idea: use symmetry

19. Also the wavefront can be broken to odd and even parts: Even PSF component Odd PSF component Fast & Furious: principle How do the odd/even PSF parts relate to odd/even WF parts?

20. Fast & Furious: principle The odd WF part can be reconstructed by a single FFT using the odd PSF Odd PSF component See the math at (Keller et al 2012), (Korkiakoski et al 2012) 1 FFT

21. Fast & Furious: principle Even WF is more tricky: using even PSF, we get only absolute values of the even WF in Fourier space. For the sign, use phase diversity. Even WF is more tricky: using even PSF, we get only absolute values of the even WF in Fourier space. For the sign, use phase diversity. Even PSF, Previous New odd PSF New even PSF Applied DM correction 2 FFTs

22. Fast & Furious: principle The real FFTs can be combined. In total, we need 2 complex FFTs. The other can be replaced by a small-kernel convolution. The real FFTs can be combined. In total, we need 2 complex FFTs. The other can be replaced by a small-kernel convolution. Even PSF, Previous New odd PSF New even PSF Applied DM correction 2 FFTs

23. Fast & Furious: computation Conventional reconstruction: O(N 2 ), depends on the actuator & subaperture count Fast & Furious: O(N log N), depends on valid detector area Can be implemented at an EPICS scale with current technology

24. Fast & Furious: results The algorithm has been experimentally verified – Low order correction (DM 37 actuators) – Static phase: correct only non-common path aberrations – See (Korkiakoski et al 2012), (Keller et al 2012) SR: 0.66 SR: 0.36 SR: 0.79 SR: 0.80SR: 0.3 The recorded PSF with F&F

25. Fast & Furious: results The performance exactly matches the simulations SR: 0.66 SR: 0.36 SR: 0.79 SR: 0.80SR: 0.3 Required convergence time as a function of noise

26. Fast & Furious: summary Challenges – Cannot deal with WF errors > 1 rad rms – Atmospheric evolution can cause problems – Works only with monochromatic light Future developments – Dealing with coronagraphs / camera saturation – Experimental validation with high-order modes (SLM tests at Leiden Observatory, HOT at ESO, FFREE at IPAG)

27. Thank you for your time!

28. Issues with roof sensor Are there simple ways for fast WF reconstruction for non-modulated roof sensor? Signal measured when an actuator pushed