Post on 21-Jan-2016
OsservatorioAstronomicodi Padova
A study of A study of Pyramid WFSPyramid WFS behavior behavior under imperfect illuminationunder imperfect illuminationA study of A study of Pyramid WFSPyramid WFS behavior behavior under imperfect illuminationunder imperfect illumination
Valentina ViottoValentina Viotto
Demetrio Magrin Demetrio Magrin
Maria BergomiMaria Bergomi
Marco DimaMarco Dima
Jacopo FarinatoJacopo Farinato
Luca MarafattoLuca Marafatto
Roberto RagazzoniRoberto Ragazzoni
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Pyramid peculiarities Other error sources
• Partial correction (SR<1)
• Non linearity issue
• Modulation effect
• Chromatism
• Re-imaging optics distortion
• Re-imaging optics MTF
““Not-perfect” illumination conditionsNot-perfect” illumination conditions
…in the framework of GMCAO concept optimization…
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
NGS
Monochr.Optical Fiber
CollimatorDeformable
MirrorObjective
DichroicMirror
PWFS
YAW
InternalClosed Loop
Open LoopWithout DM
Pyramid linearity: VL-WFS conceptPyramid linearity: VL-WFS concept
See POSTER (this conference):Demetrio Magrin et al.“Avoiding to trade sensitivity for linearity in a real world WFS”
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Pyramid WFS gain in limiting magnitude: theoryPyramid WFS gain in limiting magnitude: theory
First n-1 polynomials
Last 2 polynomials
Rigaut&Gendron SH noise model (1992)
Any measurement aimed to identify the location on the pupil of a photon approaching the focal plane will destroy to some extent the /D resolvingpower capability. DD/q
Ragazzoni&Farinato PWFS Sensitivity (1999)
SHWFSSHWFS
PWFSPWFS
M
iiphSH p
1
22 2)(
2
2)( qZSHqZP Q
q
2
2
10log5.2SH
Pm
TNG LBT E-ELT OWL
0rDQ
-Same samplingSame sampling-Geometrical approximationGeometrical approximation-Closed loopClosed loop-Same reconstructorSame reconstructor
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
PYRAMIR experiment, Peter et al. (2010)
Ragazzoni&Farinato,1999 Ragazzoni&Farinato,1999
predictionprediction
MeasurementsMeasurements
On-sky results
Pyramid WFS gain in limiting magnitude: dataPyramid WFS gain in limiting magnitude: data
PWFSPWFS
SHWFSSHWFS
Spatial sampling
PWFS gain
The prediction from RR and JF (1999) can describe, in geometrical approximation, the actual pyramid gain in bright-end
(no assumptions on a SR<1 are done)
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Pyramid WFS gain in limiting magnitude: Pyramid WFS gain in limiting magnitude: a generalization for SR<1a generalization for SR<1
~~/D/D
~~/r/r00
N N ** (1-S) (1-S) photonsphotons
N N ** S S photonsphotons
Pyramid Tip-Tilt
~/D~/r0
2
2
0
2 11 TTSHTTPyr r
DS
2
)(
2
2)( 11 qZSHqZPyr q
QS
Heisenberg uncertainty principle
SHWFSSHWFS
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Pyramid WFS gain in limiting magnitude: Pyramid WFS gain in limiting magnitude: a generalization for SR<1a generalization for SR<1
~0.07~0.07 ~0.5~0.5
Black curve:Black curve:-40m-class telescope-Typical Paranal atmosphere-R-band sensing wavelength
Esposito et al. 2010
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Pyramid linearity: range estimationPyramid linearity: range estimation
Aberrated WF
Aberration Z3-1 propagation through pyramid simulation steps:
PSF obtained from the electric field, used
as a feedback
Re-imaged pupils
Pyramid faces simulation
Linearity range of the sensorLinearity range of the sensor: range in which the retrieved aberration deviates from the actually introduced one less than a certain threshold, in terms of RMS wavefront error.
Reference: linear fit of the results in a non-linearity-negligible regime.
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Linearity range for each Linearity range for each Zernike radial order:Zernike radial order:
Pyramid linearity: range estimationPyramid linearity: range estimation
)]([
)()(
JAPP
JAPJNLE
input
input
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Pyramid linearity: single order error estimationPyramid linearity: single order error estimation
Paranal 40-layers CN2 profile model
• r0,500nm=0.14m• Von Karman Spectrum• L=25m• D=40m (E-ELT-like)
Non-linearity error:Non-linearity error: linearity deviation of each mode for that given amplitude, obtained linearly extrapolating from the curves
• typical value for each input aberration mode
DataData Output:Output:
Assumed atmospheric parameters:Assumed atmospheric parameters:
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Aberration on a single mode (Von Karman spectrum)
Pyramid linearity: cumulative error estimationPyramid linearity: cumulative error estimation
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Aberration on a single mode (Von Karman spectrum)
single-mode non-linearity error
Pyramid linearity: cumulative error estimationPyramid linearity: cumulative error estimation
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Aberration on a single mode (Von Karman spectrum)
single-mode non-linearity error
single-order non-linearity error
Pyramid linearity: cumulative error estimationPyramid linearity: cumulative error estimation
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Aberration on a single mode (Von Karman spectrum)
single-mode non-linearity error
single-order non-linearity error
Residual global non-linearity error
Pyramid linearity: cumulative error estimationPyramid linearity: cumulative error estimation
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Pyramid linearity: Modulation effectPyramid linearity: Modulation effect
• Circular modulation
• r = 3/D
• …preliminary results to be double-checked
Aberration Aberration ZZ3311
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Aberration on a single mode (Von Karman spectrum)
single-mode non-linearity error (3/D modulation)
Pyramid linearity: Modulation effectPyramid linearity: Modulation effect
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Aberration on a single mode (Von Karman spectrum)
single-mode non-linearity error (3/D modulation)
single-order non-linearity error (3/D modulation)
Pyramid linearity: Modulation effectPyramid linearity: Modulation effect
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Aberration on a single mode (Von Karman spectrum)
single-mode non-linearity error (3/D modulation)
single-order non-linearity error (3/D modulation)
Residual global non-linearity error (3/D modulation)
Pyramid linearity: Modulation effectPyramid linearity: Modulation effect
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
NGS
Monochr.Optical Fiber
CollimatorDeformable
MirrorObjective
DichroicMirror
PWFS
YAW
InternalClosed Loop
Open LoopWithout DM
Next steps: iteration of the work…Next steps: iteration of the work…
Fine tuning of parameters:Fine tuning of parameters:-Maximum residual non-linearity errorMaximum residual non-linearity error-Number of corrected modesNumber of corrected modes-SensitivitySensitivity
Number of actuatorsNumber of actuators
Modulation amplitudeModulation amplitude
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
• We evaluated a model to approximate the PWFS gain in sensitivity with respect to a SHWFS in partial partial correctioncorrection conditions (SR<1) under geometrical approximation
ConclusionsConclusions (well… first results..)(well… first results..)
• We retrieved a non-linearity error model based on Fourier wave-optics propagation for PWFS which translates into a residual global error due to non-linearity, after a partial correctionpartial correction (in terms of number of modes)
• We studied the behaviour of a PWFS under partial partial correctioncorrection (in terms of modes), if modulation is introduced.
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Thank you
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Re-imaging optics error sources: field distortionRe-imaging optics error sources: field distortion
4 “pure” pupils4 “pure” pupils 4 “barreled” pupils4 “barreled” pupils Retrieved WFRetrieved WF
Zernike Zernike ZZ22
-2-2 term term
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Re-imaging optics error sources: MTFRe-imaging optics error sources: MTF
High-spatial frequencies smaller gain than Low-frequencies
MAD Pupil Re-Imager:
mmcycles
f
NFfreq
21
300
7.1158
max
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
NIRVANA-GWS Pupil Re-imager:
Other error sources: Re-imaging optics MTFOther error sources: Re-imaging optics MTF
High-spatial frequencies smaller gain than Low-frequencies
mmcycles
f
NFfreq
5.20
220
5.18724
max
GWS FoV: 2’- 6’
MHWSFoV: 2’
Valentina Viotto – A study of Pyramid WFS behavior under imperfect illuminationA study of Pyramid WFS behavior under imperfect illuminationMay 30th, 2013 – AO4ELT3 conference – Florence
OsservatorioAstronomicodi Padova
Other error sources: ChromatismOther error sources: Chromatism
31 2
n1 n2 n3
11 3332211 nnnn
Apochromatic
n1 n2 n3
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11 2211 nn
1 2
n1 n2
Achromatic
n1 n2
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1 n
n
Chromatic
n
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