1. Osservatorio Astronomico di Padova A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto Demetrio Magrin Maria Bergomi Marco Dima Jacopo Farinato Luca Marafatto Roberto Ragazzoni

2. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di 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 conditions …in the framework of GMCAO concept optimization…

3. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova NGS Monochr. Optical Fiber Collimator Deformable Mirror Objective Dichroic Mirror PWFS YAW Internal Closed Loop Open Loop Without DM Pyramid linearity: VL-WFS concept See POSTER (this conference): Demetrio Magrin et al. “Avoiding to trade sensitivity for linearity in a real world WFS”

4. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova Pyramid 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 resolving power capability. D  D/q Ragazzoni&Farinato PWFS Sensitivity (1999) SHWFS PWFS TNG LBT E-ELT OWL -Same sampling -Geometrical approximation -Closed loop -Same reconstructor

5. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova PYRAMIR experiment, Peter et al. (2010) Ragazzoni&Farinato,1999 prediction Measurements On-sky results Pyramid WFS gain in limiting magnitude: data PWFS SHWFS 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)

6. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova Pyramid WFS gain in limiting magnitude: a generalization for SR<1 ~ /D ~ /r 0 N *  (1-S) photons N *  S photons Pyramid Tip-Tilt ~ /D ~ /r 0 Heisenberg uncertainty principle SHWFS

7. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova Pyramid WFS gain in limiting magnitude: a generalization for SR<1 ~0.07 ~0.5 Black curve: -40m-class telescope -Typical Paranal atmosphere -R-band sensing wavelength Esposito et al. 2010

8. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova Pyramid linearity: range estimation Aberrated WF Aberration Z 3 -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 sensor Linearity 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.

9. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova Linearity range for each Zernike radial order: Pyramid linearity: range estimation

10. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova Pyramid linearity: single order error estimation Paranal 40-layers CN 2 profile model r 0,500nm =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 Data Output: Assumed atmospheric parameters:

11. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova Aberration on a single mode (Von Karman spectrum) Pyramid linearity: cumulative error estimation

12. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova Aberration on a single mode (Von Karman spectrum) single-mode non-linearity error Pyramid linearity: cumulative error estimation

13. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova Aberration on a single mode (Von Karman spectrum) single-mode non-linearity error single-order non-linearity error Pyramid linearity: cumulative error estimation

14. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di 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 estimation

15. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova Pyramid linearity: Modulation effect Circular modulation r = 3 /D …preliminary results to be double-checked Aberration Z 3 1

16. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova Aberration on a single mode (Von Karman spectrum) single-mode non-linearity error (3 /D modulation) Pyramid linearity: Modulation effect

17. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di 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 effect

18. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di 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 effect

19. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova NGS Monochr. Optical Fiber Collimator Deformable Mirror Objective Dichroic Mirror PWFS YAW Internal Closed Loop Open Loop Without DM Next steps: iteration of the work… Fine tuning of parameters: -Maximum residual non-linearity error -Number of corrected modes -Sensitivity Number of actuators Modulation amplitude

20. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova partial correctionWe evaluated a model to approximate the PWFS gain in sensitivity with respect to a SHWFS in partial correction conditions (SR<1) under geometrical approximation Conclusions (well… first results..) partial correctionWe 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 correction (in terms of number of modes) partial correctionWe studied the behaviour of a PWFS under partial correction (in terms of modes), if modulation is introduced.

21. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova Thank you

22. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova

23. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova Re-imaging optics error sources: field distortion 4 “pure” pupils 4 “barreled” pupils Retrieved WF Zernike Z 2 -2 term

24. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova Re-imaging optics error sources: MTF High-spatial frequencies  smaller gain than Low-frequencies MAD Pupil Re-Imager:

25. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova NIRVANA-GWS Pupil Re-imager: Other error sources: Re-imaging optics MTF High-spatial frequencies  smaller gain than Low-frequencies GWS FoV: 2’- 6’ MHWS FoV: 2’

26. A study of Pyramid WFS behavior under imperfect illumination Valentina Viotto – A study of Pyramid WFS behavior under imperfect illumination May 30 th, 2013 – AO4ELT3 conference – Florence Osservatorio Astronomico di Padova Other error sources: Chromatism 33 11 22  n1n1 n2n2 n3n3 Apochromatic n1n1 n2n2 n3n3  focus wavelength 11 22  n1n1 n2n2 Achromatic n1n1 n2n2  focus wavelength   n Chromatic n  focus wavelength