A study of Pyramid WFS behavior under imperfect illumination

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

2. “Not-perfect” illumination conditions • Chromatism • Re-imaging optics distortion • Re-imaging optics MTF • Partial correction (SR<1) • Non linearity issue • Modulation effect Other error sources Pyramid peculiarities …in the framework of GMCAO concept optimization…

3. PWFS Internal Closed Loop NGS Dichroic Mirror Collimator Deformable Mirror Objective Monochr. Optical Fiber Open Loop Without DM YAW 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. Rigaut&Gendron SH noise model (1992) Ragazzoni&Farinato PWFS Sensitivity (1999) Last 2 polynomials SHWFS PWFS First n-1 polynomials TNG LBT E-ELT OWL Pyramid WFS gain in limiting magnitude: theory Any measurement aimed to identify the location on the pupil of a photon approaching the focal plane will destroy to some extent the /Dresolving power capability. DD/q • Same sampling • Geometrical approximation • Closed loop • Same reconstructor

5. PYRAMIR experiment, Peter et al. (2010) On-sky results Ragazzoni&Farinato,1999 prediction Spatial sampling Measurements PWFS PWFS gain SHWFS Pyramid WFS gain in limiting magnitude: data 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. N * S photons ~/r0 ~/D Pyramid Tip-Tilt N * (1-S) photons SHWFS ~/D ~/r0 Heisenberg uncertainty principle Pyramid WFS gain in limiting magnitude: a generalization for SR<1

7. ~0.07 ~0.5 Esposito et al. 2010 Pyramid WFS gain in limiting magnitude: a generalization for SR<1 • Black curve: • 40m-class telescope • Typical Paranal atmosphere • R-band sensing wavelength

8. Pyramid linearity: range estimation Aberration Z3-1 propagation through pyramid simulation steps: PSF obtained from the electric field, used as a feedback Re-imaged pupils Pyramid faces simulation Aberrated WF 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. Pyramid linearity: range estimation Linearity range for each Zernike radial order:

10. Paranal 40-layers CN2 profile model Pyramid linearity: single order error estimation Assumed atmospheric parameters: Output: Data • r0,500nm=0.14m • Von Karman Spectrum • L=25m • D=40m (E-ELT-like) • typical value for each input aberration mode Non-linearity error: linearity deviation of each mode for that given amplitude, obtained linearly extrapolating from the curves

11. Aberration on a single mode (Von Karman spectrum) Pyramid linearity: cumulative error estimation

12. Aberration on a single mode (Von Karman spectrum) single-mode non-linearity error Pyramid linearity: cumulative error estimation

13. Aberration on a single mode (Von Karman spectrum) single-order non-linearity error single-mode non-linearity error Pyramid linearity: cumulative error estimation

14. Aberration on a single mode (Von Karman spectrum) Residual global non-linearity error single-order non-linearity error single-mode non-linearity error Pyramid linearity: cumulative error estimation

15. Pyramid linearity: Modulation effect Aberration Z31 • Circular modulation • r = 3/D • …preliminary results to be double-checked

16. Aberration on a single mode (Von Karman spectrum) single-mode non-linearity error (3/D modulation) Pyramid linearity: Modulation effect

17. Aberration on a single mode (Von Karman spectrum) single-order non-linearity error (3/D modulation) single-mode non-linearity error (3/D modulation) Pyramid linearity: Modulation effect

18. Aberration on a single mode (Von Karman spectrum) Residual global non-linearity error (3/D modulation) single-order non-linearity error (3/D modulation) single-mode non-linearity error (3/D modulation) Pyramid linearity: Modulation effect

19. PWFS Internal Closed Loop NGS Dichroic Mirror Collimator Deformable Mirror Objective Monochr. Optical Fiber Open Loop Without DM YAW • Fine tuning of parameters: • Maximum residual non-linearity error • Number of corrected modes • Sensitivity Number of actuators Modulation amplitude Next steps: iteration of the work…

20. Conclusions (well… first results..) • We evaluated a model to approximate the PWFS gain in sensitivity with respect to a SHWFS in partial correction conditions (SR<1) under geometrical approximation • 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 correction (in terms of number of modes) • We studied the behaviour of a PWFS under partial correction (in terms of modes), if modulation is introduced.

21. Thank you

23. Zernike Z2-2 term 4 “pure” pupils 4 “barreled” pupils Retrieved WF Re-imaging optics error sources: field distortion

24. MAD Pupil Re-Imager: Re-imaging optics error sources: MTF High-spatial frequencies  smaller gain than Low-frequencies

25. GWS FoV: 2’- 6’ MHWS FoV: 2’ NIRVANA-GWS Pupil Re-imager: Other error sources: Re-imaging optics MTF High-spatial frequencies  smaller gain than Low-frequencies

26. Apochromatic Achromatic Chromatic 1 2 3  1 2    n3 n1 n1 n2 n n2 n3 n1 n n2 n1 n2 wavelength wavelength wavelength focus focus focus Other error sources: Chromatism