THE SUBARU CORONAGRAPHIC EXTREME AO HIGHSENSITIVITY VISIBLE WAVEFRONT SENSORSChristophe Clergeon1a, Olivier Guyon1, Frantz Martinache1, Jean-Pierre Veran3, EricGendron2, Gerard Rousset2, Carlos Correia3, and Vincent Garrel1

1 Subaru Telescope, 650 N A’ohoku place, Hilo Hawaii, USA2 Observatoire de Paris, 5 place Jules Janssen, Meudon, France3 HRC-CNRC, 5971 West Saanich Road, Victora BC, Canada

Abstract. A diffraction-limited 30-meters class telescope theoretically provides a 10 mas resolutionlimit in the near infrared. Modern coronagraphs offer the means to take full advantage of this angularresolution allowing to explore at high contrast, the innermost parts of nearby planetary systems to withina fraction of an astronomical unit: an unprecedented capability that will revolutionize our understandingof planet formation and evolution across the habitable zone. A precursor of such a system is the Sub-aru Coronagraphic Extreme AO project. SCExAO [9] uses advanced coronagraphic technique for highcontrast imaging of exoplanets and disks as close as 1 λ/D from the host star. In addition to unusualoptics, achieving high contrast at this small angular separation requires a wavefront sensing and controlarchitecture which is optimized for exquisite control and calibration of low order aberrations. To com-plement the current near-IR wavefront control system driving a single MEMS type deformable mirrormounted on a tip-tilt mount, two high order and high sensitivity visible wavefront sensors have beenintegrated to SCEXAO: – a non-modulated Pyramid wavefront sensor (CHEOPS) which is a sensitiv-ity improvement over modulated Pyramid systems now used in high performance astronomical AO, –a non-linear wavefront sensor [4] designed in 2012 by Subaru Telescope with the collaboration of theNRC-CNRC which is expected to improve significantly the achieved sensitivity of low order aberationsmeasurements. We will present the CHEOPS last results measured in laboratory and during its first lightdownstream the Subaru AO188 instrument, and then conclude introducing the primary prototype of theSCExAO non-linear curvature wavefront sensor which is planned to be tested on sky in 2014.

1 Introduction

One of the biggest challenge for ground-based telescopes, and especially for future ExtremelyLarge Telescopes (ELTs), is the direct observation of Earth like planets in their host star hab-itable zone. The high contrast required to directly image an Earth-like planet and the actualcoranagraphic performances reached in laboratories lead the astronomers’ s interest toward thesurvey of low flux stars. The direct observation of habitable planets around low flux stars (only0.08 - 0.12 AU for a M type star at 3 to 5 pc, i.e. 2 to 3 λ /D in H band with a thirty metertelescope) is a realistic challenge requiring both high telescope resolution and high contrastimaging. Without an accurate knowledge and control of the low-order aberrations (residualtip-tilt, defocus etc), high contrast imaging or good resolution of objects will be challenging.Nowadays, only diffraction limited wavefront sensors [5] are capable of reaching this degree ofaccuracy. WFSs such as the pyramid wavefront sensor [10] when non-modulated or the non-linear curvature wavefront sensor [4] are both promising in the field of planet direct imaging.

a christophe@naoj.org

Third AO4ELT Conference - Adaptive Optics for Extremely Large TelescopesFlorence, Italy. May 2013ISBN: 978-88-908876-0-4DOI: 10.12839/AO4ELT3.13398

We introduce in this paper the first results of the integration of a non-modulated pyramid wave-front sensor on the Subaru Coronagraphic Extreme AO (SCExAO) project. To conclude, we willbriefly introduce the primary prototype of the SCExAO non-linear wavefront sensor design.

2 A non-modulated Pyramid Wavefront Sensing for High PerformanceAdaptive Optics - Theoretical approach and Simulations

While existing pyramid wavefront sensors use modulation to maintain a linear response overa wide wave-front aberration range, non-modulated pyramid theoretically offers significantlyhigher sensitivity for low order aberrations, achieving nearly optimal conversion of wavefrontphase aberration into intensity signal. We succeed to demonstrate with simulations the abilityof the pyramid to close the loop without modulation first downstream an AO correction andthen on the full atmospheric turbulence. Despite a non-linear response, and in ideal but realisticobservation conditions (perfect deformable mirror, bright source, fast detector), we demonstratethat selecting the right close loop parameters, the correction of the low order aberrations canconverge and reach the pyramid linear response range after only few iterrations, opening newperspectives on high contrast astronomical imaging.

2.1 Pyramid Low order modes measurement:

2.1.1 Pyramid sensitivity illustration with a simple slope measurement

Similar to a 2x2 quad cells, the pyramid determines the local slope measuring the position of thecentroid on its apex. From Tyler & Fried (1981)[8] we know that the slope measurement errorσ is directly proportional to the size of the spot on the sensor (here the pyramid) and the signal-noise ratio of the detector (mostly photon noise for recent detectors). When non-modulated (seefig. 1 a), the slope measurement is estimated with the maximum precision σdi f f proportional tothe diffraction limited sized spot (λ/D).

Fig. 1. PWFS slope measurement sensitivity without (a) and with modulation (b).

When modulated (see fig. 1 b) and with the same number of photons received by the detector, thespot size on the pyramid gets wider, increasing the slope measurement error σmod proportionalto the modulation radius ξo.

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In other words, the modulation breaks down the measurement sensitivity that we would observewith diffraction limited conditions.

2.1.2 Frequency sensitivity analysis

This analysis has been completed by Guyon (2005) [3] , looking at precisely the impact of themodulation as a function of spatial frequency. Creating speckles in the Fourier plane applyingsine waves on the DM, Guyon generalizes to all spatial frequencies the fact that speckles infor-mation is only accessible when the four pupils record signal (fringes in the pyramid pupils, seefig. 2.Thus, the entire wavefront correction is only accessible when no optical saturation occured (seefig. 2 modulation instants 1, 3, 5 & 7). Introducing the sensitivity to photon noise parameter,he highlighted the fact that the pyramid wavefront sensor is more impacted by the photon noiseduring modulation: rotating the PSF and the speckles around the apex, the signal is more oftensaturated (see fig. 2). The modulation pulls down consequently the signal-noise ratio.

Fig. 2. Speckle signal detection evolution for one PWFS modulation period. The figure describes themodulation sequence of the PWFS. Two speckles surround the PSF core (sine wave applied to the DM).When located in two different pyramid quadrants (see Guyon [3]) the speckles interfere with the PSFrings creating fringes (signal) in the pyramid pupils (positions 0, 2, 4 and 6). When located in the samequadrant, no fringes, but one of the pyramid pupil saturates (positions 1, 3, 5 and 7).

Figure 3 shows the correlation between spatial frequencies and photon noise sensitivity. Whenclose to the PSF core (low spatial frequencies), the signal is statistically more often saturated(as explained previously). For higher spatial frequencies (speckles far from the PSF core), thesensitivity to photon noise decreases when the separation angle from the PSF core increases

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Fig. 3. Speckle signal detection vs spatial frequency during modulation.

(more signal acquired during the modulation cycle) . When modulated, low spatial frequenciesare measured with poorer sensitivity.

2.2 Simulation of a non-modulated Pyramid loop convergence in low and highturbulence conditions:

In the previous paragraph we pointed the fact that in our pursuit of low order measurementsensitivity, a small modulation is still a disadvantage in particular for high contrast imaging.Developping a high sensitivity visible wavefront sensor for SCExAO, advanced simulationshave been implemented. The goal of this analysis was to identify the conditions required for thenon-modulated pyramid WFS to close the loop downstream an AO correction (low turbulenceusually encountered in ExAO and especially in SCExAO case) and on the full atmosphereturbulence, understanding the limits of such performance when close to the linearity pyramidresponse domain.

Table 1. Simulation Parameters.Input Wavefront ErrorTurbulence Profile Kolmogorov (seeing 0.5” zenith angle: 0.785 rad, alt.: 4200m).

First AO correction parametersInstrument Subaru Adaptive Optics (AO188)WFS Curvature with 188 elementsDM Bimorph 188 actuatorsCorrection speed 2 KHzOutput wavelength 750nmExpected performances SR 40-60 %

ExAO WFS (SCExAO)WFS Non-modulated pyramid WFSDM MEMS 32x32 actuatorsPupil diameter 28 actuatorsParticularity Full PWFS signal calibrated

The algorithm loads a Kolmogorov based model phasemap partially corrected (or not dependingon the study case) with a first conventional AO system (simulations parameters defined in tables

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1 and 2). The pyramid apex plane image is computed applying a Fourier transform (FT) to thewavefront. The Fourier plane image is divided in four parts. Four pyramid pupil images are thendetermined applying the inverse FT for each PSF quadrants. The control loop follows a con-ventional linear AO control scheme based on a modal (Zernike and sine waves) reconstruction.

Table 2. Simulation hypothesis

Hyp 1 Perfect deformable mirrorHyp 2 Very bright source (high SNR)Hyp 3 Detector and loop faster than the turbulence coherence time

2.2.1 Post ao wavefront correction (SCExAO case)

The next figures present the close loop results (simulations) observed on a dynamic wavefronterror with a non-modulated Pyramid WFS. Figures 4 and 5 (right) show the expected perfor-mances in good AO correction conditions (AO188 SR=60 %). 500 Fourier modes (sine waves)are corrected with an ideal simulated DM. The red curve (see fig. 5) represents the evolutionof the first level AO residual error received at SCExAO input. The blue curve represents theexpected residual after the non-modulated PWFS correction. The aberrations correction (in ab-sence of noise) succeed to converge until the linearity limit (1 rad) after few iterrations (c.f. bluecurve, 0.5 rad rms residual error at 60% SR). The PSF is centered and the bright speckles clouddiminished until forming a diffraction-limited PSF core within the DM correction limits ( seefigure 4, DM correction at ± 12 λ/D).

Fig. 4. Post ao wavefront correction: (left) SCExAO input: Kolmogorov phasemap error corrected withthe AO188 (188 elements curvature WFS), (center) simulated PSF after AO188 correction, (right) cor-rected PSF after SCExAO non-modulated PWFS correction (DM correction at ± 12 λ/D ).

For low AO188 performances conditions (see figure 5 left, 40% SR), the loop is closed un-til reaching the pyramid linear domain in less than 20 iterations (100 Zernike modes sensedand corrected in this simulation). The dashed lines represent, the general, the first100 Zernikemodes, and 6th first Zernike contributions in the wavefront error fluctuations, without pyra-mid correction. Full lines, the associated residual errors after the non-modulated pyramid WFScorrection.

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Fig. 5. Non-modulated Pyramid WFS correction - input: AO188 dynamic wavefront error

2.2.2 Full atmospheric turbulence correction

Results described in the previous section demonstrated the ability of the non-modulated pyramidwavefront sensor to close the loop after a first level AO correction. Thus, pointing that despite anon-linear response, the pyramid correction converges to the linear domain after few iterations,especially for the low order aberrations. Taking the optimal tested loop configuration (Numberof sensed and corrected Zernike modes=100, gain=1, WFS wavelength=750nm), a last simula-tion has been tested on a full atmospheric turbulence error to verify the non-modulated pyramidlimits during general astronomical observations. The phasemap used in this test has been gen-erated with a Kolmogorov profile simulator.

Fig. 6. Non-modulated Pyramid WFS correction - input: Full atmosphere and dynamic turbulence.

Figures above show the full atmospheric wavefront correction expected in ideal conditions witha non-modulated pyramid WFS. On the left, the residual error converges and stays stable at 1.47rad rms (out of pyramid linear range at 750nm) in less than 40 iterations, in dynamic conditions.A Zernike mode decomposition (scalar projection, right figure) completed before (blue curve)

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and after (red curve) closing the loop confirm the good correction of the lower order aberrationsand the contribution of the non-corrected modes on the residual.

3 CHEOPS, the SCExAO visible wavefront sensor first Lab & Skyresults

The goal of the presented analyses was to identify the conditions required for the non-modulatedpyramid WFS to close the loop. Despite a non-linear response and in ideal but realistic obser-vation conditions we demonstrate that selecting the right close loop parameters, the correctionof the low order aberations can converge and reach the pyramid linear response range after fewiterrations. Starting from this encouraging results and taking into account the high speed andlow noise new detector generation, we made the choice to develop a non-modulated pyramidwavefront sensor on the SCExAO visible channel (see figure 7). The table below (3) gathers themain specifications of our new high sensitivity visible wavefront sensor.

Table 3. Optical Design Specifications

WFS wavelength 725 - 850 nmF ratio on the pyramid f / 35Pyramid type Microlens array (SUSS Micro Optic), Pitch 500�, focal length: 15mmDetector Andor, Zyla (Pix 6.5�, Speed 1.7KHz (ROI 120x120px), RN 1e-Pyramid Pupils 50 px/pupil diameter (0.16” on sky per microlens)

Fig. 7. CHEOPS first loop closure in static abberations conditions: (Left) CHEOPS optical design onSCExAO visible channel – (Center) Top: PWFS pupils image, 4 sine waves applied on the 1024 actuatorsMEMS (Boston micromachines) between 1 and 12 λ/D (0.5 rad amplitude at 750 nm) . Gain = 0.01 (May 2013), bottom: associated PSF in the image plan – (Right) Pyramid image and associated PSF afterclosing the loop.

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After closing the loop in static conditions on 10 Zernike modes in January 2013, we recentlyimplemented a modal correction algorithm with sine waves to take advantages of the full spa-tial resolution of our deformable mirror (MEMS type mirror). A successfull test in May 2013permited to close the loop on 10 Fourier modes at 200 Hz in static aberation conditions. InSeptember 2013, the SCExAO non-modulated pyramid wavefront sensor reached a new mile-stone closing the loop in laboratory on 260 Fourier modes on a static AO188-type wavefronterror. Our next challenge will be to close the loop on a dynamic AO188-type wavefront aberra-tion before the SCExAO PWFS engineering nights in december 2013 on Sky.

4 Conclusion

In this analysis, we tried to demonstrate the necessity of non-modulation to take full advantagesof the sensitivity offered by the pyramid wavefront sensor. Convinced with the simulationsresults that it is possible to close the loop after a first level AO correction, we started the inte-gration of the non-modulated PWFS on SCExAO visible channel. Since May 2013, we succeedto achieve encouraging results in laboratory correcting static wavefront errors, and especiallyAO188-type phasemap errors. The next crucial tests to be continued in Fall 2013, before ourengineering night on Sky in December 2013, will be the correction of a dynamic wavefront withthe non-modulated PWFS.In parallel we developed with the collaboration of the NRC-CNRC, a prototype of the actualnon-linear curvature wavefront sensor tested in MMT [6] for SCExAO. The non-linear cur-vature wavefront sensor [4] is a conventional curvature wavefront sensor (Roddier) using anon-linear reconstruction algorithm to retrieve the phase error ( Phase diversity or Gerchberg-Saxton, [7]). From four quasi-monochromatic beams, four pupils plans conjugated with fourdifferent altitudes are reimaged at the same time on the same detector (visible high speed cam-era). The first prototype has been machined and will be implemented in parallel of the non-modulated PWFS in 2014.

Fig. 8. First SCExAO Non-Linear Curvature WFS. The non-linear curvature wavefront sensor is a con-ventional curvature wavefront sensor (Roddier) using a non-linear reconstruction algorithm to retrievethe phase error ( Phase diversity or Gerchberg-Saxton, [7]). The first prototype designed with the collab-oration of the NRC-CNRC (Marc Andre Boucher-INO) will be integrated on SCExAO in 2014.

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References

1. Clergeon, C., Guyon, Verran, Martinache, Gendron, Rousset, Non Modulated PyramidWavefront Sensing For High Performance Adaptive Optics: I - Close Loop Convergence,(expected publication winter 2013)

2. Guyon, O. et al, SPIE, Vol 736-74 (2010)3. Guyon, O., Limits of adaptive Optics for High contrast Imaging, ApJ, 629, 592-614 (2005)4. Guyon, PASP, High Sensitivity Wavefront Sensing with a non-linear Curvature Wavefront

Sensor, 122, (2010)5. Guyon, O., High Contrast Imaging: New Techniques and Scientific Perspectives for ELTs,

Proc. of AO4ELTs3, Paper 16504 (2013)6. Guyon, O., Putting the non-linear Curvature Wavefront Sensor on the 6.5m MMT telescope,

Proc. of AO4ELTs3, Paper 13283 (2013)7. Carlos Correia, Jean-Pierre Veran, Olivier Guyon, Christophe Clergeon, Wave-front recon-

struction for the non-linear curvature wave-front sensor,Proc. of AO4ELTs3, Paper 13290(2013)

8. G.A.Tyler, D.L.Fried. Image-position error associated with a quadrant detector,J.Opt.Soc.Al.,Vol. 72, No.6 (1981).

9. Jovanovic, N., Guyon, O., Martinache, Clergeon, C., Singh, G., Vievard, S., Kudo, T.,Garrel, V., Norris, B., Tuthill, P., Stewart, P., Huby, E., Perrin, G., Lacour, S., Proc. ofAO4ELTs3, Paper 13396 (2013)

10. Roberto Ragazzoni, Pupil plane wavefront sensing with an oscillating prism, Journal ofModern Optics, Vol.43 289-293 (1996).

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