study of centroiding algorithms to optimize shack-hartmann wfs in the context of elts

AO4ELTs, 25th of June 2009 1

Study of centroiding Study of centroiding algorithms to optimize Shack-algorithms to optimize Shack-Hartmann WFS in the context Hartmann WFS in the context

of ELTsof ELTsSandrine Thomas Sandrine Thomas

Don Gavel, Olivier Don Gavel, Olivier Lardiere, Rodolphe Conan, Lardiere, Rodolphe Conan,

Sean AdkinsSean Adkins(a) LAO, UCO/Lick Observatory, (b) University of Victoria,(c) Keck Obsevatory

AO4ELTs, Paris, 25th of June 2009

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Designing WFS optimized Designing WFS optimized for Next Generation AO for Next Generation AO

and ELTsand ELTs• Use of laser guide Use of laser guide stars stars

• Extremely large Extremely large telescopes (ELT): > 10telescopes (ELT): > 10

Increase of the Increase of the elongation of the spot elongation of the spot to a few arcsec leading to a few arcsec leading to to lower SNR per pixellower SNR per pixel non negligible structure non negligible structure and time variability of and time variability of the sodium profilethe sodium profile

€

El = rΔhH 2

h = 90 km

h=

20km

D = 30 m TMTpupil

~ 7arcseconds

Δh


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Polar Coordinate Polar Coordinate DetectorDetectorCCD optimized for LGS AO wavefront sensing on an ELTCCD optimized for LGS AO wavefront sensing on an ELT

• Rectangular “pixel islands” in each Rectangular “pixel islands” in each subaperturesubaperture• Major axis of each rectangle aligned Major axis of each rectangle aligned with axis of elongation in that with axis of elongation in that subaperturesubaperture• Allows good sampling of a CW LGS image Allows good sampling of a CW LGS image alonalong g the elongation axisthe elongation axis• Allows tracking of a pulsed LGS imageAllows tracking of a pulsed LGS image


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Previous resultsPrevious results

• Simulation and theoretical derivations shown in Simulation and theoretical derivations shown in Thomas et al, 2008 for a Gaussian spot.Thomas et al, 2008 for a Gaussian spot.

• Test of linearity, i.e. sampling and troncature Test of linearity, i.e. sampling and troncature • Added photon and readout noise Added photon and readout noise • Best sampling and size of the array, Best sampling and size of the array, 1.8pix/fwhm, 4x16 for the polar CCD1.8pix/fwhm, 4x16 for the polar CCD

EEtotal total = E = Enoisenoise + E + ELinLin + E + Esodiumsodium + + E Ediff diff + … + …

Readout noise+

Photon noise+

(background noise)

Under Sampling+

Truncation

Time variability +

Structure

Diffraction spike+

Cross talk


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Real profiles are needed to Real profiles are needed to understand the effect of the understand the effect of the

sodium layer variability on the sodium layer variability on the performance of the wavefront performance of the wavefront

sensorsensor

Time resolution: ~ 0.5sTime resolution: ~ 0.5s

600 mNickel, 1m Shane, Shane, 3m3m

90 km

Pixel size=0.36”

26.8 m• 6 nights from November 2005 until March 2008 (Mainly fall and winter)• 97 images -> ~ 3000030000 synthetic profiles

Launch the laser Launch the laser from the Shane from the Shane Telescope and let Telescope and let the Nickel one driftthe Nickel one drift

• Profile evolutionProfile evolution• Time scale of refocusingTime scale of refocusing• Thickness evolution Thickness evolution • Projection on the CCD of a Projection on the CCD of a

SHWFS:SHWFS:• Algorithm comparisonsAlgorithm comparisons• Comparison with other Comparison with other

errors errors


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The night of the February The night of the February 9th 20069th 2006

Altitude

Tim

e

Altitude

Tim

e

Altitude

Tim

e


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Truncation Truncation effect of effect of the sodium the sodium

layer layer

10 km 10 km

October 10th 2006,beginning of the night (left), end of the night (right)

<10 m for a FoV greater than 18km

<10 m for a FoV greater than 20km

October 10th 2006 February 9th 2006

The depth of focus of The depth of focus of the TMT at 90 km is the TMT at 90 km is about 10 metersabout 10 meters


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Time considerationsTime considerations• The depth of focus of the TMT at 90 km is about 10 metersThe depth of focus of the TMT at 90 km is about 10 meters=> Need to refocus at about 1m=> Need to refocus at about 1m• The temporal power spectrum of the variations will The temporal power spectrum of the variations will

determine how often this measurement needs to be made. determine how often this measurement needs to be made.

An average over all samples gives a -1.7 power law An average over all samples gives a -1.7 power law from 0.01 to 1 Hz Similar results from the LIDAR data from 0.01 to 1 Hz Similar results from the LIDAR data presented by Pfrommer et al.presented by Pfrommer et al.Extrapolating this power law to the 1 meter variations Extrapolating this power law to the 1 meter variations gives ~0.2s in average (faster end of the NGS WFS rate gives ~0.2s in average (faster end of the NGS WFS rate for the TMT telescope)for the TMT telescope)


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Projection on the CCD in Projection on the CCD in the context of the TMTthe context of the TMT

• SHWFS: 60x60 subapertures of 0.5mSHWFS: 60x60 subapertures of 0.5m• Detector: 25ms integration time and Detector: 25ms integration time and

500ms readout time.500ms readout time.• Readout noise: 1-5 eReadout noise: 1-5 e--

• Motion = 0.8 FWHMMotion = 0.8 FWHM• Typical seeing condition: 1.19”Typical seeing condition: 1.19”• No up-link correctionNo up-link correction

h = 90 km

h=

20km

D = 30 m TMTpupil

~ 7arcseconds

Δh

2.102.1022 - 10 - 1044 photons photonsat 589nm, arriving at 589nm, arriving on SH on SH


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Projection on the Projection on the CCDCCD

• One line = 1 synthetic profileOne line = 1 synthetic profile• Get the number of pixels from the FOV and the Get the number of pixels from the FOV and the

pixel sizepixel size• => get a 2D image => get a 2D image • Convolution with diffraction of the subaperture Convolution with diffraction of the subaperture

(50 cm) (50 cm) • Convolution with the atmospheric blur (1.19”)Convolution with the atmospheric blur (1.19”)

Profile Diffraction Seeing blur

Altitude

Tim

e


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MethodMethod• Use of different centroiding algorithms to Use of different centroiding algorithms to

calculate the position of the spot: thresholded calculate the position of the spot: thresholded CoG, Correlation (Parabolic fit and CoG), CoG, Correlation (Parabolic fit and CoG), Matched filter.Matched filter.

• Choice of the reference - average over 12/40/160 Choice of the reference - average over 12/40/160 images ie 6, 20 secondsimages ie 6, 20 seconds

• Wavefront reconstruction using Fourier TransformWavefront reconstruction using Fourier Transform• Decomposition in Zernike coefficientsDecomposition in Zernike coefficients

Wavefront reconstruction using Correlation, SNR=18


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Motion of the spot, Oct Motion of the spot, Oct 10th 0610th 06

Number of pixels: 128x128 Resolution: 14.4 pixels per FHWM

Position of the sub-aperture = 14m, 60x60 sub-apertures

Number of pixels: 16x16Resolution: 1.8 pixels per FHWM

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.QuickTime™ and a

YUV420 codec decompressorare needed to see this picture.


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Aberrations due to the sodium Aberrations due to the sodium variationsvariations

(From simulations only)(From simulations only)• No noise, 60x60 subaperturesNo noise, 60x60 subapertures• Using an average of the 10 profiles as a reference, every 10 profiles.Using an average of the 10 profiles as a reference, every 10 profiles.

• Expected radially symetric aberrationsDefocus (Z4), spherical (Z11), second order Spherical (Z22)• Z14 and Z26 are quadrature trefoil aberrations• Defocus = 38nmPrevious results when using a Gaussian elongated spot:9nm rms WF for SNR = 100


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Check simulation with results Check simulation with results from the University of from the University of

Victoria’s benchVictoria’s benchQuickTime™ and a

YUV420 codec decompressorare needed to see this picture.

• 2 sources (LGS+NGS), 1 10x10 DM, 2 SH-WFSs2 sources (LGS+NGS), 1 10x10 DM, 2 SH-WFSs• ““LGS-WFS”: 32x32 elongated spots SH-WFS:LGS-WFS”: 32x32 elongated spots SH-WFS:

• subaperture=15x15px, spot sampling =2x8pxsubaperture=15x15px, spot sampling =2x8px• the DM stretches the spots during the WFS exposure to the DM stretches the spots during the WFS exposure to reproduce elongated spotsreproduce elongated spots• Max. FOV = 20km-thick Na layer for side spotsMax. FOV = 20km-thick Na layer for side spots

• ““NGS-WFS”: 12x12 unelongated spots SH-WFS NGS-WFS”: 12x12 unelongated spots SH-WFS (subap=8x8px, (subap=8x8px, spot=2px)spot=2px)

See Conan et al. talk later


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High SNR, 32x32 High SNR, 32x32 subapertures subapertures SimulationsSimulations

• SNR ~ 140SNR ~ 140 : Nph = 900, nr = 5e-, 16x16 pixels : Nph = 900, nr = 5e-, 16x16 pixels• Reference is an average of 40 profiles calculated every 40 profiles, (~ 20s)Reference is an average of 40 profiles calculated every 40 profiles, (~ 20s)

Noise floor due to photon and readout noise: ~0.5nm rms

All algorithms gives very similar results to less than 1nm rms

Same kind of aberrations as the case with no noise


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High SNR, 32x32 High SNR, 32x32 subaperturessubaperturesLab resultsLab results

• SNR ~ 140SNR ~ 140 , 15x15 pixels , 15x15 pixels• Reference is an average of 40 profiles calculated every 40 profiles, (~ 20s)Reference is an average of 40 profiles calculated every 40 profiles, (~ 20s)

• Same kind of aberrations except for the Zernike 26• More differences between algorithms• The correlation using a parabolic fit as the peak finder is better except for the different high powered Zernike• Noise floor at about 0.5nm rms.


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Low SNR, 32x32 Low SNR, 32x32 subaperturessubaperturesSimulationsSimulations

• SNR ~ 18SNR ~ 18 : Nph = 900, nr = 5e-, 16x16 pixels : Nph = 900, nr = 5e-, 16x16 pixels• Reference is an average of 40 profiles calculated every 40 profiles, (~ 20s)Reference is an average of 40 profiles calculated every 40 profiles, (~ 20s)

• Noise floor due to photon and readout noise increases to 2-4 nm rms

• More asymmetric types of aberrations appear due to the low SNR, more particularly Z6, Z9 and Z20-Z21• The correlation gives best results by 1nm rms


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Low SNR, 32x32 Low SNR, 32x32 subaperturessubaperturesLab resultsLab results• SNR ~ 18SNR ~ 18 , 15x15 pixels , 15x15 pixels

• Reference is an average of 40 profiles calculated every 40 profiles, (~ 20s)Reference is an average of 40 profiles calculated every 40 profiles, (~ 20s)

• Apparition of the same non-symmetric aberrations, Z6, Z9, Z20-Z21• Noise floor increased to 1nm rms for the correlation and 2 for the other two algorithms• The correlation is giving the best results • Those results are lower than simulations: Maybe due to a mismatch in the SNR


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ConclusionsConclusions• Sodium layer analysis:Sodium layer analysis:

• FoV needed to get centroiding accuracy of the FoV needed to get centroiding accuracy of the order of TMT depth of focus is 20kmorder of TMT depth of focus is 20km

• Variations of the mean sodium layer altitude Variations of the mean sodium layer altitude are ~1km on a time scale of a few secondsare ~1km on a time scale of a few seconds

• LGS induced aberrations:LGS induced aberrations:• In the context of the TMT, the error due to the In the context of the TMT, the error due to the sodium layer is 30nm rms. The time scale used sodium layer is 30nm rms. The time scale used was 20s.was 20s.

• At a SNR of 18, the error higher than focus due At a SNR of 18, the error higher than focus due to the sodium layer is comparable to the error to the sodium layer is comparable to the error due to photon and readout noise.due to photon and readout noise.

• The correlation method give better results for The correlation method give better results for such SNRssuch SNRs


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Future work Future work • Simulation of more turbulent profiles Simulation of more turbulent profiles such as the one from Feb 9th 2006 such as the one from Feb 9th 2006

• Understand non-symmetric aberration like Understand non-symmetric aberration like Z6, Z9 Z21Z6, Z9 Z21

• Understand the disagreements between Understand the disagreements between simulations and lab worksimulations and lab work

• Reference update time scaleReference update time scale• Add atmospheric turbulenceAdd atmospheric turbulence• Simulate the polar CCDSimulate the polar CCD• Study the advantage of pulse trackingStudy the advantage of pulse tracking


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AcknowledgmentsAcknowledgments• The authors would like to gratefully acknowledge the

Gordon and Betty Moore Foundation for postdoctoral support of Dr. Thomas via the Laboratory for Adaptive Optics at UC Santa Cruz.We also gratefully acknowledge the support of the National Science Foundation Science and Technology Center for Adaptive Optics, managed by the University of California at Santa Cruz. This material is based in part upon work supported by AURA through the National Science Foundation under AURA Cooperative Agreement AST 0132798, Scientific Program Order No. 6 (AST-0336888) as amended.


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Previous resultsPrevious results

EEtotaltotal = E = Enoisenoise + + EELinLin

€

SNR = NphNph + Npix × Nr^2

• compromise between the sampling and the compromise between the sampling and the truncation for different values of SNRtruncation for different values of SNR

Optimal sampling = Optimal sampling = 1.5 pix1.5 pixOptimal array = Optimal array = 44x16 pix16 pix


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Previous results from Previous results from Elongated Gaussian spotElongated Gaussian spot

• compromise between the sampling and the compromise between the sampling and the truncation for different values of SNRtruncation for different values of SNR• For low SNR : noise dominates, all array For low SNR : noise dominates, all array sizes are equivalent if sizes are equivalent if sampling ~ 1.1 pixsampling ~ 1.1 pix

• For medium SNR : For medium SNR : sampling = 1.5 pixsampling = 1.5 pix and and array array = 4.7 sigma= 4.7 sigma

• For high SNR : For high SNR : sampling = 1.5 pixsampling = 1.5 pix and and array = 4.7 sigmaarray = 4.7 sigma

If el=4 than for medium SNR and for 1.8 pix, optimal array is 4If el=4 than for medium SNR and for 1.8 pix, optimal array is 416 pix16 pixIf el=4 than for high SNR and for 2 pix, optimal array is 6If el=4 than for high SNR and for 2 pix, optimal array is 620 pix20 pix


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Sodium ProfileSodium Profile• Data from Lick Observatory, Don Gavel on Feb 9th 2005Data from Lick Observatory, Don Gavel on Feb 9th 2005

Relative Altitude (km)

Inte

nsity

Tim

e (s)

study of centroiding algorithms to optimize shack-hartmann wfs in the context of elts

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