PYRAMID WAVEFRONT SENSOR
PERFORMANCE WITH LASER GUIDE
STARS
F. Quirós-Pacheco1, E. Pinna1, A. Puglisi1, G. Agapito 1
L Busoni1, S. Rabien2, S. Esposito1
1 INAF
– Arcetri
2 MPE – Garching
INTRODUCTION
• Wave-front sensing with extended sources is characterized
by lower sensitivities (w.r.t point sources).
• Larger spots in a focal plane WFS (e.g. Shack-Hartmann)
increase noise propagation: 𝜎 2 ∝ 𝜃/ 𝑁
• What is the effect of extended sources on the pyramid WFS?
• Pyramid sensitivity with 2D extended sources
• Pyramid sensitivity with 3D extended sources
• LGS treated as a 3D extended source
• Why pyramid with LGS on an ELT?
AO4ELT3, FIRENZE, 30 MAY 2013
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PRELIMINARY EXPERIMENTS WITH FLAO
• Laboratory tests @ Arcetri with LBT’s FLAO#2 system in 2011 (E. Pinna et al. AO4ELT2).
• Use of fiber cores (from 0.2 to 1.6 arcsec in diameter) to emulate 2D extended sources.
• One Interaction Matrix done with diff. limited source → modal gain optimization required.
SR(H)~60%
FLAO lab test 2011
E2E
simulations
2013
Estimated
SR@H ~ 60%
AO4ELT3, FIRENZE, 30 MAY 2013
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SENSITIVITY WITH 2D EXTENDED SOURCES
• LBT (8m) telescope
• 30x30 subaps
• 500 KL modes
• 2D extended sources:
• Uniform illumination
• Diam: 0.4” to 1.6”
• IM calibrations done with
extended sources 𝑫 .
• Noise Propagation Coeffs:
𝑝𝑖2 = 𝐷𝑇 𝐷
Noise prop. coeff. [nm / slope rms]
• FLAO system config:
−1
𝑖𝑖
AO4ELT3, FIRENZE, 30 MAY 2013
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2D EXTENSION VS. TILT MODULATION
Is the NGS 2D extension somehow equivalent to a tip-tilt modulation?
Round source (top-hat)
Tip-tilt round modulation
REO
RM
extended object radius
modulation radius
S = C / RM
PYRAMID
EDGES
Slicing the round source
in rings of different RM
FT = total source flux
S = ∫0REO (C /r) [2p r / (p REO2)] dr = 2C / REO
AO4ELT3, FIRENZE, 30 MAY 2013
Ring sensitivity
Ring relative intensity
Same sensitivity when
RM = REO / 2
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2D EXTENSION VS. TILT MODULATION
RM = REO / 2
2D
extension
(2REO)
TT
modulation
(±RM)
0.4”
±5.3 /D
0.8”
±10.6 /D
1.6”
±21.3 /D
FLAO@LBT typical
modulations:
±3.0 < RM <±6.0 (/D)
AO4ELT3, FIRENZE, 30 MAY 2013
Noise prop. coeff. [nm / slope rms]
• LBT (8m) telescope
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HIGH ORDER SENSITIVITY DIFFERENCE
Same sensitivity when
RM = REO / 2
?
The light projected at a distance
d > RM
does not cross the pyramid edge
during the tilt modulation
d
PYRAMID
EDGES
RM
AO4ELT3, FIRENZE, 30 MAY 2013
For modes projecting energy at a distance
d > RM from the PSF center,
the sensitivity is not affected by the modulation
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2D EXTENSION VS. TILT MODULATION
RM = REO / 2
REO
extended object radius
The external rings of the extended
source affect higher modes more than
RM does
RM
modulation
radius
AO4ELT3, FIRENZE, 30 MAY 2013
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3D EXTENDED SOURCES
AO4ELT3, FIRENZE, 30 MAY 2013
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SODIUM VERTICAL DISTRIBUTION EFFECTS
• Study case:
• Telescope: 39m diameter (obs. 28%)
• LGS: launched from center of the pupil
• Pyramid WFS: 78x78 subapertures
• Sampling of 0.5m/subap.
• Pyramid conjugated to 90km layer..
100km
90km
80km
Na Layer
Vertical extension of the Na layer
generates defocused images
𝑎𝑍4 =
100km
Δℎ
2 3 8
h0 +Δℎ 2
𝐷
h0=90km
80km
AO4ELT3, FIRENZE, 30 MAY 2013
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SODIUM VERTICAL DISTRIBUTION EFFECTS
𝚫𝒉
Z4 rms
+3 km
+1.5 km
0 km
-1.5 km
-3 km
+19 m
+9.8 m
0 m
-11 m
-22 m
• Extended object: 2D Gaussian with 0.8arcsec FWHM;
Vertical Intensity Gaussian profile with 3.1km FWHM.
• Pyramid WFS: 78x78 subaps; =589nm; FoV=3.6”
CCD image
from all layers
AO4ELT3, FIRENZE, 30 MAY 2013
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VERTICAL DISTRIB. EFFECTS ON SENSITIVITY
• Vertical distribution introduces a “radial tilt modulation” increasing in
amplitude with the distance from the pupil center
• The pyramid sensitivity decreases in the radial direction with the distance
form the pupil center as the SH does (spot elongation)
Focus = increasing tilt amplitude
Tip
Sx
SIGNAL CUT
AO4ELT3, FIRENZE, 30 MAY 2013
Sy
Tilt
Wavefront Pyramid signals
Linear decreasing of sensitivity
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MODAL SENSITIVITY VS. VERTICAL EXTENSION
• AO system: pyramid WFS 78x78 and DM correction ~4000 KL modes
• IM calibration with 3D extended source → noise propagation coefficients
± 3.0 km
± 0.5 km
• Vertical extension: a) 90±3km b) 90±0.5km (aka LGS with refocusing)
0.8arcsec
FWHM
AO4ELT3, FIRENZE, 30 MAY 2013
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WHY PYRAMID FOR LGS ON ELTS?
• 2D extension: losing the “classical” pyramid advantage in sensitivity (/D vs. /r0)
• Vertical extension: same radial reduction of sensitivity as the SH
BUT
Is the sensitivity the main SH limitation working on ELT LGS?
Na Layer
WFS people are worried about other killers:
• # of pixels required: 100 pix/SA, 800x800
WFS CCD not yet available
SH sub-ap.
• spot truncation: compromise between # of
pixels and allowed WFS FoV
• Na layer variable profiles: multi-peak Na
profiles may create spurious signals on the
WFS
SH WFS: detection on the focal plane
recover X-Y slopes (2 numbers) from ~100 pixels
AO4ELT3, FIRENZE, 30 MAY 2013
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WHY PYRAMID FOR LGS ON A ELT?
Na Layer
and the killers…
• # of pixels required: 4 pixels per SA
(80x80SAs existing 240x240 OCAM2)
• spot truncation: no more truncation
(FoV independent on pixel size and number)
WFS FoV
(adjustable)
Information on
WF slopes
optically
recollected in
the pupil plane
AO4ELT3, FIRENZE, 30 MAY 2013
• Na layer variable profiles: just a variable focus
off-set (slopes information averaged optically,
TBC by simulation)
PYR WFS: detection in the pupil plane
recover X-Y slopes from 4 pixels
(same algorythm as NGS case)
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FUTURE WORK
• Concept: pupil edge lunch of the LGS
• Simulations:
• Closed loop performance with 3D (more GPUs!)
• Multi peak distribution impact (focus offset only?)
• Lab experiment: PEACE bench (Arcetri - ESO - GMT) already
equipped with pyramid WFS and Na lamp
• Vertical extension simulated by defocus on ALPAO DM
• Phasing segmented mirror with Na source
... then on-sky experiment?
AO4ELT3, FIRENZE, 30 MAY 2013
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