1. Vision and Revision Wavefront Sensing from the Image Domain Benjamin Pope @fringetracker

2. Our Group 2 Peter Tuthill Ben Pope (me!) Frantz Martinache Nick Cvetojevic Anthony Cheetham Niranjan Thatte

3. James Webb Space Telescope ›The James Webb Space Telescope is the next- generation NASA major space observatory ›A 6.5 m diameter segmented primary mirror will make it the largest civilian space telescope ›Left: a full scale mockup of the telescope in Munich 3

4. Phasing the JWST ›A major issue with JWST will be in using a segmented mirror in space ›No current robust, cheap approach to making sure the mirrors are aligned with required ~ nm accuracy ›This is where we come in! ›Mirror segments have actuators in tip, tilt, piston and curvature ›We can use these to correct the phasing 4

5. Fourier Amplitudes and Phases 5 V  Amplitudes Phases V  Amplitudes Phases Albert Michelson Pablo Picasso

6. Interferometry: Phase ›The phase delay between two receivers relates to the position of the astrophysical object 6

7. Interferometry: Phase ›The phase delay between two receivers relates to the position of the astrophysical object ›If the atmosphere disrupts the wavefront, this information is corrupted by errors! 7

8. Closure Phase 8

9. Redundant Baselines 9 Duplicate baselines!

10. Non-Redundant Masking ›If we put a mask on the telescope aperture and let through only one copy of each baseline, we overcome this problem ›Non-redundant masking gives us good amplitude measurements – and also lets us recover some phase information 10 Aperture masks used on NIRC2 (image courtesy of Peter Tuthill).

11. Kernel Phase Interferometry ›Kernel phase is a method of image deconvolution for high resolution astronomy ›Works on Nyquist-sampled, space-based or well-corrected (extreme) AO images ›A software-only idea similar to the aperture masking approach ›Delivers contrast ~ hundreds within λ/D ›Can also be used as a wavefront sensor (Martinache sensor) ›Only five papers so far! ›A solution looking for a problem! 11

12. Linear Phase Transfer 12

13. Kernel Phase Interferometry 13

14. Phase Reconstruction ›What about the other way – get phases from their autocorrelation? ›The singular value decomposition also lets us create a pseudoinverse, such that ›This allows for an approximate reconstruction of pupil phases: ›This maps modes in the Fourier plane onto modes in the pupil, i.e. inverting the autocorrelation ›Reconstruct wavefronts using only an image! 14

15. The Asymmetric Pupil ›The Fourier plane (FT of the image) is the autocorrelation of the pupil -Not sensitive to all symmetries! A symmetric pupil can sense only even modes ›A Fourier wavefront sensor needs to have pupil asymmetry to sense asymmetric modes -This could be achieved with thick spider(s), e.g. right. -Alternatively, could mask out subapertures 15

16. Martinache Wavefront Sensor Simulations ›Uses row phases (complement of kernel space) ›Wavefront sensor is your science camera! ›Initial Strehl > 35% required – can iterate to as high as 97% in simulations ›Sensitivity near-optimal for a given flux and wavefront error 16

17. Experimental Setup I ›The microelectromechanical (MEMS) segmented mirror from Dragonfly was used as a JWST analogue ›This has piston, tip and tilt on each segment with ~ few nm precision ›Phasing JWST is hard – no apparatus in space! ›Ideal test case for the new wavefront sensor 17

18. Experimental Setup II ›Laser introduced from single mode fibre ›Passed to MEMS array and through mask ›Imaged onto Xenics IR camera 18

19. First Step - FICSM ›The first step in phasing a segmented mirror like this is the FICSM approach – ‘Fizeau interferometric cophasing of segmented mirrors’ (Cheetham et al) 19

20. How do you Solve a Problem like A Mirror? ›We want a ‘tweeter’ on top of coarse phasing with FICSM ›Martinache (2013) theory says you need an asymmetric pupil › We could do this with bars – or single segments ›That does work – but you still have planes of mirror symmetry for which the sensor is weak ›If you take out the same pattern you included with FICSM, you have no symmetries 20

21. Pupil Modes ›Below: examples of normal modes of the discrete pupil model used in our experiment ›These play the role of the Zernike basis for expanding optical aberrations on a circular pupil 21

22. Degrading the Wavefront 22

23. Wavefront Restoration ›Yes we can! ›Right: reconstructed wavefront ›Don’t let the colourbar scare you – there are a couple of bad points ›Actual RMS piston error reduced < 10nm on all segments ›Strehl > 99%! 23

24. Quick and Dirty ›While we found that the not-at-all symmetric segment tilting worked best, can we get away with doing fewer segments? -Better if moving mirrors is risky, expensive or slow ›Yes we can! A single asymmetry (particularly in the outer ring) was found to work (top) -Has some issues with sensing modes symmetric with respect to the line of reflection symmetry ›A wedge asymmetry (3 in outer ring, one in inner) also works (bottom) 24

25. How well can we Measure a Single Segment? 25 ›Pistoned a single segment (3) in 20 nm steps from -300 to +300 ›Reconstruction is very accurate… within limits ›You lose it when linearity fails ›Phases are also correlated – sensing modes globally is a bad way to reconstruct phases on a single segment ›When phasing the whole mirror in closed loop, this correlated error beats down to zero as you make the whole thing flat

26. Restoring a PSF 26 ›Left: animation of a stretched PSF as our algorithm converges ›This is with a scalene triangle of segments removed

27. Restoring a PSF 27 ›Also works with a wedge removed

28. Restoring a PSF 28 ›Or in fact a single segment!

29. Oxford-SWIFT at Palomar ›Hale 200-inch telescope has the PALM-3000 extreme AO system – the highest order AO currently available for experiments ›Oxford has the Short Wavelength Integral Field specTrograph (SWIFT) on P3K – a high spatial and spectral resolution IFU from 650-1000 nm ›SWIFT has historically had problems with non common path error – never achieves even internal diffraction limit -Hard to correct with conventional methods, because of the optical layout ›Ideal test case for our wavefront sensing method 29

30. HODM Mask ›Right: the mask we placed over the high order DM to get the pupil asymmetry ›This was probably overkill, but we wanted to make sure it worked the first time! 30

31. Results ›Left top: 940nm ; bottom, 970 nm PSF ›You can see two, maybe 3 Airy rings ›This would not ordinarily be especially impressive – but SWIFT has an internally very complicated layout and has never seen Airy rings before! ›This was achieved with only the LODM ›HODM correction should get it to the diffraction limit! 31

32. The Phase Map ›Right: Final phase map subtracted from LODM offsets ›Could maybe have improved – but had to stop to do science observations! 32

33. Next Directions ›Now that we’ve demonstrated this in the lab and on Palomar… -JWST needs phasing! But can we maybe get a ‘spider sense’ from using the spiders as the asymmetric mask? -HARMONI, the first-light IFS for the E-ELT is predicted to suffer from very bad non common path error – ideal case! -Project 1640 – another Palomar IFS for exoplanet studies 33

34. Thanks! Thank you for listening! 34