PSF SHARPENING & POST-CORONAGRAPHIC FOCAL “SENSING”

Gilles Orban de Xivry 1st international vortex workshop Caltech 08/2016

Introduction & Outline

Outline • PSF sharpening: Principle & Simulation

• Application & progresses on VODCA

• Other techniques: Phase diversity & Fourier analysis

Quasi-static aberrations control (NCPA) from focal plane / post-coronagraph images

Detector

Computer DM

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PSF SHARPENING

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PSF sharpening : Principle 1. Apply modal basis

2. Image quality metric (e.g. Strehl)

3. Optimization algorithm search for next command(s) usually applied as offsets to the reference slopes of the wavefront sensor (closed-loop)

Apply this to post-coronagraph images giving us an improved dynamic range (subtraction of Airy disk) and thus sensitivity

Lamb M., 2015

Before After (on 21 Zernike modes)

E.g. at 655nm with ALPAO DM 97-13.5

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Aberrations and contrast Basic simulations at λ= 3.75 μm:

• Small aberrations hypothesis: 1st order aberration in Lyot plane (Huby et al. 2016)

• Adding suppressed (by rejection ratio) PSF quadratically

• Basic noises

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50nm 150nm

250nm 400nm

• λ= 3.75 μm

• 150nm wf error

• theoretical rejection = 1500

Injecting aberrations on 100“Zernike” modes (random distribution with decreasing weight on higher modes)

Optimizing 21 “Zernike” modes

PSF sharpening : Simulation (1/2)

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PSF sharpening : Simulation (2/2) • λ= 3.75 μm

• 150nm wavefront error rms

• theoretical rejection = 1500

Injecting aberrations on 100“Zernike” modes (random distribution with decreasing weight on higher modes)

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Optimizing 21 modes Optimizing 51 modes

APPLICATION & PROGRESSES ON VODCA

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VODCA bench with DM • ALPAO DM-97 13.5mm aperture; magnification ~ 2.2

• Pupil stop is ~20mm ; Lyot stop at ~90% (using circular pupil)

• Light source: supercontinuum using (L1, L2, L3); or laser IR 1.6 μm

• Using ALPAO calibration: Z2C matrix & influence functions

Best flat obtained by ALPAO in closed-loop with SH 128x128

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VODCA “classic”

DM part

VODCA: Control and Software

Raw contrast curves Fast viewer with basic ROI analysis

DM diag Modes as applied

Python-based device control & VODCA “arbitrator” multi-threads, “real-time”, ipython interface & gui

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VODCA: Pupil registering

Current design uses ~30 actuators with the VODCA stops

Options are:

• Use VODCA stops, and generate Z2C matrix using the pupil registration (to be done)

• Use enlarged Lyot stop & use DM as entrance pupil

• Use higher focal length OAP to reduce magnification (to be done)

Incidence angle initially large is now reduced

DM “pupil” VODCA pupil stop

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VODCA: Beam quality

• VODCA “classic” vs DM path (but with flat mirror)

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With DM path (flat mirror)

VODCA “classic”

Difference basically dominated by defocus

VODCA: Beam quality

The ALPAO flat is definitively not good anymore

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VODCA “classic” DM path with flat mirror

DM flat with normal pupil stop

DM flat full aperture

Post-corono sharpening: raw contrast curves

• Modal (Z2C) control

• Min(flux) within annulus

• Navg= 10frames at each feval

• Conjugated direction method (Powell)

• DM define pupil stop

• Big (and bad) Lyot stop

12 modes –ND=146 30 modes – ND=183 70 modes – ND=296

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Off-axis On-axis

30modes

12modes

70modes

Post-corono sharpening: modal comparison • Reconstructed wavefront using

the influence functions

From mode 21 onwards

From mode 7 onwards

From focus onwards

12 modes 30 modes 70 modes

~250nm WF rms above astigmatism

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Summary & comments so far

A long to do list: • Improve integration & calibration of DM

• change magnification,

• pupil registration & new Z2C & calibration,

• determine a good flat

• Choice & usage of optimizer - Optimizer based on lmfit (non-linear minimization in the leastsq sense)

- Trying other non-sequential minimization: speed up, reduce the number of frames needed, and reduce stress on DM: Nelder-Mead or even “leastsq” (Levenberg-Marquardt) with different metric (min ROI flux)

• Test different metrics

• Inject aberration and compare to the fitted modes

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ALTERNARTIVE TECHNIQUES

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Phase diversity : COFFEE Phase diversity between two (or more) images to avoid degeneracy.

Resolution of inverse problem to find phase aberrations φ:

With the modeled post-coronagraphic PSF:

Maximum a priori metric by minimizing the neg-log-likelihood 𝐽𝑀𝐴𝑃 (and a priori gaussian)

d downstream; “u” upstream; , coronagraph model

B. Paul, 2014; Mugnier L. M. et al, 2016

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Phase diversity : high-order diversity

• Typically diversity: low-order (focus or astigmatism) and high amplitude (125nm – 500nm for λ=1600nm)

Make it unusable for science

• Alternative is high-order, low amplitude diversity, e.g. waffle mode with 20 cycle over aperture (Mugnier L. M., 2016)

• Application to VODCA with ALPAO-97 might be challenging but to be considered: • Max period is 5cycle over aperture

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Fourier analysis of focal-plane images

• Using Fourier plane of the image 𝑂𝑇𝐹 = ℱ 𝑃𝑆𝐹

• Assumption of small aberrations (linear pupil phase) allows a linear model between phase in pupil φ and the phase measured in the Fourier plane Ф

Φ= A φ

• Asymmetry in the pupil plane ensures inversion of the problem.

Application to the vortex:

Pupil phase and Lyot phase can also be expressed as a linear relationship to first order (Huby et al. 2015).

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F. Martinache + 2016

Conclusions

• Focal sharpening on VODCA • In progress

• Requires improvement in integration & calibration, and optimization algorithm

• Other methods: • Phase diversity (e.g. with COFFEE) looks interesting – also implies to

have a well known phase diversity, plate scale, etc.

• Fourier plane (or other dOTF techniques) looks interesting and elegant – also a possibility (although challenging) for DM calibration

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ALPAO DM

FPS on 70 modes start to introduce higher order Zernike modes:

(total difference amount to ~45nm)

Comparing the Zernike “ALPAO” basis with theoretical Zernike basis

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ALPAO DM

• Creep effect

Bitenc U., et al. 2014 (Durham)

Resolution: 120x120

With interferometer (much higher resolution)

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dOTF

• Delta phase diversity allows to recover phase using differential OTF

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Alternative methods using focal plane images

Alternative methods include

• Electric field conjugation: dark holes

• Self-coherent camera : imply hardware modification

• Phase diversity: e.g. COFFEE

• Fourier plane (OTF)

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