Vision and Revision

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

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

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

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

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

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

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!

8. Closure Phase • True phases are encoded on baselines, , but errors are on the wavefront and hit each detector separately • If we add up measured phases around a loop, errors cancel out: • If , then the closure phase is immune to error: !

9. Redundant Baselines • Multiple pairs of points sample each baseline. • Random walk in the phasor space corrupts image • Closure phase no longer works! 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 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!

12. Linear Phase Transfer • Martinache (2010) considered a generalisation of closure phase when phase errors are smallenough to be linear • For measured phases are , ‘true’ baseline phases and errors in the pupil plane are • In this case, the phases on each baseline will be where is a transfer matrix relating pupil and image plane phases and the redundancy of each baseline.

13. Kernel Phase Interferometry • Use singular value decomposition: express • Find an operator K such that • This kernel operator maps measured phases to kernel phases which are immune to small errors: • Can recover a large fraction of phase information • Even for a redundant aperture, we still have robust observables – with no need of a mask!

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!

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

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

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

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

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

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

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

22. Degrading the Wavefront • Wavelength: 1600 nm • MEMS settings disturbed by random tips, tilts and pistons nm • Right: Wavefront reconstruction • Can we fix this?

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%!

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)

25. How well can we Measure a Single Segment? • 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 • Left: animation of a stretched PSF as our algorithm converges • This is with a scalene triangle of segments removed

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

28. Restoring a PSF • 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

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!

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!

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

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

34. Thanks! Thank you for listening!