Osservatorio Astronomico di Padova A study of Pyramid WFS behavior under imperfect illumination...

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


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…



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”



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



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)



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



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



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.



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



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:



Aberration on a single mode (Von Karman spectrum)

Pyramid linearity: cumulative error estimationPyramid linearity: cumulative error estimation




single-mode non-linearity error






single-order non-linearity error






single-order non-linearity error

Residual global non-linearity error




Pyramid linearity: Modulation effectPyramid linearity: Modulation effect

• Circular modulation

• r = 3/D

• …preliminary results to be double-checked

Aberration Aberration ZZ3311




single-mode non-linearity error (3/D modulation)






single-order non-linearity error (3/D modulation)






single-order non-linearity error (3/D modulation)

Residual global non-linearity error (3/D modulation)




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



• 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.



Thank you





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



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



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’



Other error sources: ChromatismOther error sources: Chromatism

31 2

n1 n2 n3

11 3332211 nnnn

Apochromatic

n1 n2 n3

focusfocus

wav

elen

gth

wav

elen

gth

11 2211 nn

1 2

n1 n2

Achromatic

n1 n2

focusfocus

wav

elen

gth

wav

elen

gth

1 n

n

Chromatic

n

focusfocus

wav

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Osservatorio Astronomico di Padova A study of Pyramid WFS behavior under imperfect illumination...

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