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

PSF reconstruction: a review 3/25 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).

PSF reconstruction: a review 4/25 The challenge of PSF variability Atmospheric turbulence profile and wind profile vary with time. 1.Temporal variation of wf phase: r 0, t 0,  0, L 0, d 0 2.Temporal variation of wf amplitude: scintillation E.g., Kenyon 2006 Na profile vary with time as well E.g., Drummond 2004, d’Orgeville 2003, Chueca 2004 AO correction is only partial AO PSF displays a core/halo structure Energy fraction in core/halo vary with time, field location and wavelength

PSF reconstruction: a review 5/25 The challenge of PSF variability 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)

PSF reconstruction: a review 6/25 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 regimes 4.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

PSF reconstruction: a review 7/25 The science requirements e.g., TMT Differential photometric precision –Systematic errors in differential photometry should under 2% (10 mn 1  m 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).

PSF reconstruction: a review 8/25 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

PSF reconstruction: a review 9/25 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

PSF reconstruction: a review 10/25 The knowledge of the PSF Science Method Isoplanatic (NGS) Field dependentLGS-assisted Auto-calibrationDifferential imaging Image selection? PSF per iso. field PSF observationsOn-axisGS Field stars or cluster GS Field stars or cluster Ancillary dataWFC data Cn2 PSF cam monitoring WFC data Cn2 Na profile? PSF monitoring Model-based PSFFitting error Speckle density Aniso. TF Aniso. FWHM kernel Aniso. TF Aniso. FWHM kernel Numerical(Myopic) deconvolution Adaptive kernel Methodology used depends on science field, science requirements, observing facility, skills, etc.

PSF reconstruction: a review 11/25 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 –In imaging spectroscopy: e.g, McElwain et al. 2007, Janson et al –IFS in preparation for the extreme-AO: Mugnier et al. 2008, Fitzgerald et al (see Saturday ’ s session) AU Mic observations and roll subtraction technique - Fitzgerald et al. 2007

PSF reconstruction: a review 12/25 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 Cn 2 data. Weiss et al. 2002, demonstrated similar method with ALFA + Cn 2 data Britton (PASP, 2006) uses similar principles to predict and reconstruct field dependent PSF, based on DIMM/MASS Cn 2 data at Palomar. Field-dependent PSF estimation methods Anisoplanatic structure function estimated from Cn 2 data

PSF reconstruction: a review 13/25 Field-dependent PSF estimation methods in the absence of Cn 2 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

PSF reconstruction: a review 14/25 Isoplanatic PSF calibration methods On-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 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)

PSF reconstruction: a review 15/25 WFC telemetry-based PSF reconstruction Veran 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

PSF reconstruction: a review 16/25 WFC telemetry-based PSF reconstruction Reconstructed long exposure OTF Diffraction limited static OTF High-order component of the turbulent phase OTF Corrected mirror modes residual OTF Assuming: 1.No scintillation 2.Gaussian statistics for the residual phase error 3.Parallel and orthogonal phase components are statistically uncorrelated 4.Structure function of the residual phase is homogeneous 5.“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 turbulence model scaled by D/r 0 (Kolmogorov, van Karman)

PSF reconstruction: a review 17/25 WFC telemetry-based PSF reconstruction Veran et al. 1997, JOSA A, v14, 11 The parallel component can be estimated from the mean residual phase structure function U ij functions computed for mirror modes M over the aperture P : residual mode covariance matrix measured by averaging cross-products of modal coordinates during an exposure. Nx(N+1)/2 U ij functions that are computed once

PSF reconstruction: a review 18/25 WFC telemetry-based PSF reconstruction U ij functions with 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 V ii algorithm: The residual parallel phase covariance matrix is diagonal in this new basis

PSF reconstruction: a review 19/25 WFC telemetry-based PSF reconstruction 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

PSF reconstruction: a review 20/25 WFC telemetry-based PSF reconstruction U ij and V ij methods provide identical results in simulation V ii 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)

PSF reconstruction: a review 21/25 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 Cn 2 ) –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/r 0 with r 0 (and L 0 ) estimated from the modal variance based on the DM commands

PSF reconstruction: a review 22/25 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 Weiss et al 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 for ALFA off-axis –Uses on-axis principle, plus an anisoplanatism term. Requires simultaneous Cn 2 data. Principle demonstrated. The effort is not currently being pursued for routine operations. Jolissaint et al 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 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 &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 for the Dunn Solar Telescope –Demonstrated principle for solar AO. Integrated for routine operations? Effort pursued? Flicker et al for the Keck II AO –Started in Nov 07. Goal; NGSAO demonstrated by end of year. Development of system components.

PSF reconstruction: a review 23/25 Addendum by Ralf (7/24/2008)

PSF reconstruction: a review 24/25 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!

PSF reconstruction: a review 25/25 Future challenges for PSF reconstruction Ancillary data such as Cn 2 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!