psf reconstruction: a review of the quests d. le mignant & r. flicker

PSF reconstruction: a review of the quests

D. Le Mignant & R. Flicker

PSF reconstruction: a review 2/25

Outline

• The challenge of PSF variability

• Science requirements

• Approaches to reconstructing the PSF

• Telemetry based PSF reconstruction

• The many challenges yet ahead


The challenge of PSF variability

Atmospheric variations during observations of the Galactic Center.

The red points indicate measurements at zenith while the green data points are from Galactic Center images (courtesy M. Britton, Caltech).



• Atmospheric turbulence profile and wind profile vary with time.

1. Temporal variation of wf phase: r0, t0, 0, L0, d0 2. Temporal variation of wf amplitude: scintillation

• E.g., Kenyon 2006

• Na profile vary with time as well1. E.g., Drummond 2004, d’Orgeville 2003, Chueca 2004

1. AO correction is only partial1. AO PSF displays a core/halo structure 2. Energy fraction in core/halo vary with time, field

location and wavelength



QuickTime™ and a decompressor

are needed to see this picture.

Keck AO

PSF SR=1

SR=0.65

Kp, NGS, R mag. = 7



SR=0.15

Kp, NGS, R mag. = 15.3

Gemini/Hokupa’a GC data 4 nights - 30sec itime - 4.8”x4.8” fov(from Christou et al. 2004)


Science-based requirements:towards quantitative AO science

The astronomers define:1. Photometry precision (and accuracy)2. Astrometry precision (and accuracy)3. Sensitivity for high-contrast and low-brightness regimes4. Morphology (spatially resolved 1 & 2)5. Completeness fraction (need to observe x objects)

The instrument team derive requirements for the AO facility:

1. Residual wavefront error over the science field (OPD, SR, EE)

2. Residual tip-tilt error, differential atmospheric refraction residual, non-common path calibrations

3. Efficiency: acquisition time, duty cycle during observing sequence

4. Etc..

5. PSF calibrations requirements


The science requirementse.g., TMT

• Differential photometric precision– Systematic errors in differential photometry should

under 2% (10 mn integ. @ 1m over the 30” FOV).

– Absolute photometry accuracy should be of 2%

• Differential astrometry– Residual time dependent distortions should be

less than 10 arcsec or limited by the intrinsic variations caused byt the atmosphere (over 30” FOV).


The challenge of calibrating the PSF• In many cases, the science field

does not include a “good” PSF calibrator– SNR, distance from GS,

background object/emission, occulting mask, etc

• Dedicated PSF observations is unlikely to match the science observations– Atmospheric turbulence variations,

GS flux, centroid gain, pupil angle, etc

– Setup & SNR on the science instrument

– Difficulty to reproduce the GS / science field geometry (anisoplanatism)

– Time consuming



Melbourne et al. 2007




The wavefront error residuals• The wavefront error residuals on each sensor (TT, LOWFS, HOWFS): – Fitting error– Detection noise, spatial aliasing, DM/WFS calibrations

– Centroid gain (spot size), loop delay, non-linearity for DM and WFS

• The atmospheric dependent aberrations:– Isokinetic, isoplanatic effects – Focal anisoplanatism

• The telescope, AO and science instrument optics:– The telescope optics wavefront error

– Static and varying non-common path aberrations


The knowledge of the PSF Science

Method

Isoplanatic (NGS) Field dependent LGS-assisted

Auto-calibration Differential imaging

Image selection?

PSF per iso. field PSF per iso. field

PSF observations On-axis GS

Field stars or cluster

GS

Field stars or cluster

Ancillary data WFC data WFC data

Cn2

PSF cam monitoring

WFC data

Cn2

Na profile?

PSF monitoring

Model-based PSF Fitting error

Speckle density

Aniso. TF

Aniso. FWHM kernel

Aniso. TF

Aniso. FWHM kernel

Numerical (Myopic) deconvolution

Adaptive kernel Adaptive kernel

Methodology used depends on science field, science requirements, observing facility, skills, etc.


Designing the observations for the PSF

• On-axis: simultaneous (or a-posteriori) differential techniques used primarily for detection of stellar companion or disk in high-contrast regimes – In imaging mode, different flavor of the roll

subtraction techniques: e.g, Liu 2004, Marois et al. 2006, Biller et al. 2007, Fitzgerald et al. 2007

– In imaging spectroscopy: e.g, McElwain et al. 2007, Janson et al. 2008

– IFS in preparation for the extreme-AO: Mugnier et al. 2008, Fitzgerald et al. 2008 (see S aturday’s session)

AU Mic observations and roll subtraction technique - Fitzgerald et al. 2007


• Voitsetkhovich et al. 1998, computed the structure function due to residual phase aberrations resulting from anisoplanatism, and predicted SR as a function of distance from guide star.

• Fusco et al. 2000: analytical expression for the off-axis OTF as the product of the on-axis OTF x an anisoplanatic transfer function (ATF). Demonstrated method using Cn2 data.

• Weiss et al. 2002, demonstrated similar method with ALFA + Cn2 data

• Britton (PASP, 2006) uses similar principles to predict and reconstruct field dependent PSF, based on DIMM/MASS Cn2 data at Palomar.

Field-dependent PSF estimation methods

Anisoplanatic structure function estimated from Cn2 data


Field-dependent PSF estimation methodsin the absence of Cn2

• Simultaneous (or a-posteriori) observations of a calibration field to estimate and parameterize anisoplanatism effect from “wide” field PSF s(e.g., Larkin et al. 2000, Steinbring et al. 2005, Minowa et al. 2005, Cresci et al. 2006)

• Cresci et al. 2006, 2007 in study of Survey of Wide Area with Naco (SWAN - 15 sq. arcmin) described the PSF as convolution between on-axis and a spatially varying kernel (an elliptical Gaussian elongated towards the AO guide star).

26.8” off-axis star in NGC 6752

PSF, model PSF and residuals


Isoplanatic PSF calibration methodsOn-axis and isoplanatic PSF:Extract PSF from data over an isoplanatic field (PSF is

field independent) and use estimated PSF with (myopic) deconvolution or PSF fitting techniques

• Direct model fitting or blind deconvolution techniques (e.g., Jefferies et al. 1993, Fusco et al. 1999, Diolaiti et al. 2000, Barnaby et al. 2000, Christou et al. 2004, Marchis et al. 2006)– See Christou et al. 2004 for a comparison of photometry and

astrometry on crowded fields (and low SR) with IDAC, StarFinder and parametric deconvolution.

• Modeling the modulation transfer function, combined with OTF of the AO system to derive the corrections for the photometry (e.g., Sheehy et al. 2006) . Photometry accuracy within a few % compared to HST.

• PSF reconstruction from wavefront controller data at the CFHT using the Veran method (e.g., Beuzit et al. 2004)


WFC telemetry-based PSF reconstructionVeran et al. 1997, JOSA A, v14, 11

• PSF related to other quantities “easier” to model and reconstruct:

• Total OTF as the product of component OTFs


WFC telemetry-based PSF reconstruction

Reconstructed long exposure OTF

Diffraction limited static OTF

High-order component ofthe turbulent phase OTF

Corrected mirror modes residual OTF

Assuming:1. No scintillation2. Gaussian statistics for the residual phase error3. Parallel and orthogonal phase components are statistically uncorrelated 4. Structure function of the residual phase is homogeneous5. “infinite bandwidth” approximation

Veran et al. 1997, JOSA A, v14, 11

Estimate phase structure function

from WFC data / model

Measured PSF(high SNR or artificial source)

Atmospheric turbulencemodel scaled by D/r0

(Kolmogorov, van Karman)


WFC telemetry-based PSF reconstructionVeran et al. 1997, JOSA A, v14, 11

• The parallel component can be estimated from the mean residual phase structure function

• Uij functions computed for mirror modes M over the aperture P

<T>: residual mode covariance matrix measured by averaging cross-products of modal coordinates during an exposure.

Nx(N+1)/2 Uij functions that are computed once



• Uij functions with 100-1000 actuators (and corrected modes) produces Gb of data to store and load for each calculations (heavy and slow).

• Two new algorithms which take advantage of the eigen decomposition of the residual parallel phase covariance matrix :

Gendron et al. 2006, A&A, 457, 359

N mirror modes that needs to be computed on-the-fly

Vii algorithm:The residual parallel phase covariance matrix is diagonal in this new basis



• Instantaneous PSF: the eigen decomposition is used to compute phase screens

• The phase screens follow the same statistics as the residual parallel phase covariance matrix.

• Instantaneous OTF averaged out to produce long exposure of the mirror space PSF.

• Does not include the uncorrected part of the phase! • Useful to assess variability of the AO PSF

Gendron et al. 2006, A&A, 457, 359



• Uij and Vij methods provide identical results in simulation

• Vii implementation show faster computation time (~ 20x gain for N =160)

Gendron et al. 2006, A&A, 457, 359

Radial average of PSF for 3 stars: 7.3, 12.3 and 13.6 (bottom to top)

Residual phase only (no fitting error)


Components of the PSF reconstruction

• Residual mode covariance matrix

– Temporal modeling required – DM control law– r, spatial aliasing simulated or

modeled– n, noise covariance matrix– u, y and s from telemetry (Keck)– Separable TT structure function

• Fitting error (orthogonal phase)– Turbulence PSD based on Kolmogorov or van

Karman models (e.g. Flicker 2008)– Model for the atmosphere (measured or

reference Cn2) – Binary mask (spatial high-pass filter) on

the turbulence PSD (e.g., Veran, Jolissaint) – Monte-Carlo simulation to estimate ratio of

the PSD (e.g., Flicker 2008)– Scaled by D/r0 with r0 (and L0) estimated from

the modal variance based on the DM commands


Estimating the PSF from the AO-system• Veran 1997 for CFHT-PUEO

– designed, integrated and commissioned with AO system, PSF reconstruction data delivered with science data, used for routine operations since 1998.

• Weiss et al. 2003 for ALFA on-axis– Demonstrated principle in NGS AO. Some quantities not readily available from telemetry.

Not (fully) implemented for science operations.

• Egner et al. 2004 for ALFA off-axis– Uses on-axis principle, plus an anisoplanatism term. Requires simultaneous Cn2 data.

Principle demonstrated. The effort is not currently being pursued for routine operations.

• Jolissaint et al. 2005 for Gemini-Altair– Demonstrated principle in NGS AO, developed OPERA software, awaiting more engineering

data and integration for routine operations. The effort is not pursued in the short term.

• Fitzgerald et al. 2004 for Lick AO– Demonstrated principle in NGS AO. Needed to improve calibrations and spot size

estimation, then include TT sensor for LGS. The effort is not pursued in the short term.

• Clenet et al. 2006 &2008 for VLT/NACO– Developed Vii method. Demonstrated in simulation and test bench. Changes to NACO RTC

done. Awaiting more engineering data and full integration. More tests being performed on Sesame AO bench. See Talk on Saturday.

• Marino et al. 2006 for the Dunn Solar Telescope– Demonstrated principle for solar AO. Integrated for routine operations? Effort pursued?

• Flicker et al. 2008 for the Keck II AO– Started in Nov 07. Goal; NGSAO demonstrated by end of year. Development of system

components.


Addendum by Ralf (7/24/2008)


Future challenges for PSF reconstruction

• Only one telemetry-based system in operation– Designed-in and built-in for PUEO, integrated with AO – Performance for different science areas?

• What is the required accuracy for the reconstructed PSF with current systems?– Jolissaint’s poster this evening

• Difficult integration with current AO systems?– Significant effort that requires AO scientists,

development phases, test time on bench, changes to existing systems, integration, eng. time, observatory and users’ support!


Future challenges for PSF reconstruction• Ancillary data such as Cn2 are critical to AO integration and

performance monitoring. – Britton and others also demonstrated it provides an accurate solution for the

anisoplanatic PSF reconstruction.

• Missing from this review are the tomography-based algorithm and demonstration for PSF reconstruction. – MCAO should provide more PSF uniformity

• If telemetry-based PSF reconstruction techniques critical for AO quantitative science with future systems, then it is important to learn more about PSF reconstruction using current AO systems. If so, – Requires collaboration between astronomers and AO scientists.– Develop an observing scenario for the PSF knowledge and calibration

for the science cases

• “Developing PSF knowledge benefit the science"

Thank you!

psf reconstruction: a review of the quests d. le mignant & r. flicker

Documents

partialao psf

psf methodology

psf reconstructionthe

science instrumentdifficulty

science field opd

sciencebased requirements

science instrument optics

etcdedicated psf observations