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PSF estimation and parametric modelling from scientific data

FP7-OPTICON PSF reconstruction meeting, Marseille 29-30 January 14. PSF estimation and parametric modelling from scientific data. Laura Schreiber Istituto Nazionale di Astrofisica – Osservatorio Astronomico di Bologna. Context.

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PSF estimation and parametric modelling from scientific data

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  1. FP7-OPTICON PSF reconstruction meeting, Marseille 29-30 January 14 PSF estimation and parametric modelling from scientific data Laura Schreiber Istituto Nazionale di Astrofisica – Osservatorio Astronomico di Bologna

  2. Context • Adaptive Optics has become a key technology for all the main existing telescopes (VLT, Keck, Gemini, Subaru, LBT..) and is considered a kind of enabling technology for future giant telescopes (E-ELT, TMT, GMT). • AO systems increase the energy concentration of the Point Spread Function (PSF), but the PSF itself is also characterized by complex shape and spatial variation. • the exceptional advancement in AO technology and observational capability has not been followed by a comparable advancement in the development of data analysis methods.

  3. Science with AO Main science targets: • Crowded stellar fields  resolved stellar populations in GCs and Galaxies (MCAO) • Close binary systems improved angular resolution / dynamical mass estimation (SCAO) • Exoplanets (XAO, SCAO) • Our Galaxy’s central black hole  Mass estimation through stars proper motions measurements (SCAO, MCAO) • Distant galaxies morphology, spectroscopy (MCAO, MOAO)

  4. Imaging techniques • Astrometry:precise measurements of the positions and movements of objects (parallax and proper motion) • Dynamical masses of brown dwarfs [Dupuy et al 2009] • Our Galaxy’s supermassive black hole [Ghez et al 2005] • Formation and evolution of young star clusters [Stolte et al 2008] … • Photometry:is the process of obtaining accurate numerical values for the brightness of objects (aperture phot./ PSF fitting). • Time variability of individual sources • Flux ratios or luminosity functions of multiple systems [Harayama et al. 2008] • Color Magnitude Diagrams of resolved stars (GC age, stellar population, stellar evolution, SFH) […]

  5. How do the AO data look like? • Single Conjugate AO  Highly structuredPSF, small FoV 13 arcsec Galactic center, PUEO@ CFHT, K band Courtesy of F. Rigaut

  6. How do the AO data look like? • Single Conjugate AO  Highly structured and variable PSF M15 Core, @ Keck, K band Courtesy of L. Origlia

  7. How do the AO data look like? • Single Conjugate AO Highly structured and variable PSF AO science demostrationrun 21 arcsec GS M92, FLAO @ LBT, Pisces, J band 1 pixel = 0.021 arcsec ExposureTime = 6 s

  8. How do the AO data look like? • Multi Conjugate AO Improved PSF uniformityacross a largerFoV [Bono et Al 2009] 1 arcmin ωCen, MAD @ VLT, Kband

  9. How do the AO data look like? Grabbed from F. Rigautpresentationat AO4ELT3, Florence 2013

  10. AO results and limitations • SCAO small corrected FoV, PSF spatial variation • Crowded-field AO astrometry appears to be limited by the inaccurate modeling of the Point Spread Function (PSF) [Shoedel 2010] • astrometry of faint sources is biased by residuals due to the incorrect subtraction of the PSF of brighter stars [Fritz 2009] • photometricaccuracyislimited by the SNR and by the knowledge of the PSF [Shoedel2010] • detectionof elongatedsources • Many ‘exotic’ solutionshavebeenfoundto reduce data… Astrometric and photometric measurements with AO systems are mainly limited by errors in the PSF modeling and fitting.

  11. AO results and limitations • SCAO small corrected FoV, PSF spatial variation • Galactic center (NACO): Image is first Wiener-filter-deconvolvedusing a suitable PSF (GS psf) . Local variations in PSF kernels and ringingistaken care with locallyextracted PSF fitting. [Schoedel 2010] • M92 GC (FLAO): ModiefiedRomafot software. PSFfitting with variablemoffat (no parametersfixed). [Bono 2013 Ao4ELT3] • NGC6440 GC (NACO):PSFfitting with starfinderusing an analitical model composed by 3 gaussiancomponents. [Origlia 2008] • Usage of calibration images [Steinbringet al. (2002)] • Usage of calibration HST fields • GalaxySurvey (NACO): Estimate local PSF around guide star image and model the PSF in the fieldas the convolution of the GS PSF and a blurringkernel. [Diolaiti 2000, Cresci 2006] =  off-axis PSF guide star blurring kernel(e.g. Gaussian)

  12. AO results and limitations • MCAO  To improve the PSF uniformityacross the FoV • Suitable to study dense stellar field, galaxymorphology • MAD: Manypapershavebeenpubblished[Melnick SPIE 2012 for a review] • GeMs: First papers are coming out • Alreadyavailablesofwarehavebeenused The presence of tworedclumpsimplies the presens of twodifferent stellar populations. [Ferraro et Al, Nature, 2009] Terzan5, MAD @ VLT, Kband

  13. SF: Exercise of variable PSF FWHM ≈ 3.4 px SR ≈ 0.01 ÷ 0.37 Magnituderange≈ 10 mag High SNR

  14. SF: Exerciseof variable PSF • PSF fittingphotometryusing the true PSF model Photometricerror in the faintermagnitude bin ≈ 0.11

  15. SF: Exercise of variable PSF • PSF fittingphotometryusing the guide star When the PSF variesacross the FoV, the photometricerrordependsmainly on the goodness of the PSF model adoped 1 0 -1 -2 -3 -4 -5 25 21 Photometricerror in the faintermagnitude bin ≈ 0.7

  16. SF: Exercise of variable PSF • PSF fittingphotometryusing the local PSF More subdomains 9 X 9 subdomains 3 X 3 subdomains Photometricerror in the faintermagnitude bin ≈ 0.26 Photometricerror in the faintermagnitude bin ≈ 0.11 Photometricerror in the faintermagnitude bin ≈ 0.14 To be compated with the errorwhenperfect PSF isused ≈ 0.11

  17. PSF estimation I • PSF reconstruction: • the long exposure PSF within the isoplanatic angle from the reference source can be expressed in terms of second-order statistics of the phase of the residual wavefrontthat can be computed from the AO loop data (i.e. WFS measurements, DM commands…) [Veran 1997] • by knowing the Cn2 profile, it is possible to ‘generalize’ the method and model the PFS degradation in the FoV. It is therefore possible to compute (a posteriori) the PSF in any α direction within the FoV[Fusco 2000] • Pros: No need of isolatedbrightstars for modeling the PSF, no extra observation time, availablecronology of PSF variation in time • Critical aspects: determination of the system’sstaticaberrationsand of the opticalturbulenceparamenters; complexity (MCAO?)

  18. PSF estimation II • PSF estimation from data: • Analytical PSF (constant or variable) • Numerical PSF (constant over the entire frame or in subdomains) • Hybrid PSF (analytical model + numerical residual map) • Product of the Blind deconvolution • Implemented in image analysis softwares: • DAOPHOT (analytical/hybrid/smoothly variable) [Stetson 1987] • Romafot(Purely analytic) [Buonanno 1983] • DoPHOT(Analytical) [Schecter 1993] • PSFex (analytical, linear combination of basis vectors) [Bertin 2010] • STARFINDER (numerical/analytical/hybrid, possible hacking) [Diolaiti 2000] • Dolphot (HSTPhot), …

  19. Starfinder • Code for identification and analysis of point-likesources • Designedand developed (1997-2000) for images with structured PSF butuniformacrossfield of view • Numerical PSF • Written in IDL  easy to hack • Graphical User Interface • Available on the Web • Target: to extend the usage of Starfinder to AO images with complex and spatiallyvariablePSFs • Numericallocal PSF by dividing the image in subdomains (MCAO) • Analitical model of the PSF and of itsparametersvatiationacross the Fov by a multi-component parametric model (Gaussian, Moffat, Lorentzian) + map of residualsusing information about AO (GS position, seeing, .. NGS SCAO)

  20. PSF analytical model 3 2 1 1 Narrow Moffat core 2 External torus 3 Broad Gaussian/ Moffat halo

  21. SF variable PSF: analytical model • PSF fittingphotometryusing the estimated PSF model: method Choose the PSF stars(bright, distributed in the FoV) Choose of componentsfor PSF modeling (first iterationone) Fit of parametersvariationwith respect to the GS distance Residualmap= stars – model STARFINDER Photometry and stars positions A priori knowledge of the rotationangle Stack, combine and normalizeresiduals PSF refining

  22. SF variable PSF: analytical model • PSF fittingphotometryusing the estimatedPSF model: results Photometricerror in the faintermagnitude bin ≈ 0.13 To be compated with the errorwhenperfect PSF isused ≈ 0.11

  23. SF variable PSF: analytical model • PSF fittingphotometryusing the estimated PSF model: real data 1 - PSF starsselection: possiblybright and isolated M15, FLAO @ LBT, Pisces, J band

  24. SF variable PSF: analytical model • 2 – Definition of the analytical model: 2D Moffat • 3 – Estimation of the Moffatparametersvariationacross the FoV • Product: PSF model + residual Moffatmajioraxisvariation model Moffat minor axisvariation model Fluxvariation model

  25. SF variable PSF: analytical model Image SyntheticImagemodel

  26. SF variable PSF: Local PSF • PSF extraction from MAORY + MICADO simulatedcrowded stellar fields in distantellipticals (Virgo cluster) [Schreiber 2013] • Map of MaoryPhase A PSF • Differentcrowdingconditions • Differentregions of the FoV Micado FoV MaoryFoV

  27. SF variable PSF: Local PSS • The scope of the work was to explore the [effect of the] photometricerror [on stellar metallicitydistribution] as a function of the crowding and of the PSF variationacross the FoV • Differentcrowding, central (best SR) PSF  telescopere-pointing • Samecrowding, differentPSFs(best and worst SR)  subdomains Comparablephotometricerror, butdifferent zero points (fractions of magnitude) amongdifferentsubdomains Micado FoV

  28. Results • Simulated image: 2 moffat component • easy to model • promisingphotometricaccuracy • Local PSF estimation: ideal for MCAO • Numeric robust • Tested on highlycrowdedsimulated images (with typical MAORY PSF variation)  no effects on photometricaccuracy • Possibledrawback: different zero points • Ideal model for SCAO PSF: hybrid (analytical + residual) • Lessanalyticalcomponentsimplies more robustness (fitalgorithmseasely converge on a small number of pixels) • The case of M15  the estimatedresiduals look indistinguishablewithin 1σ  assuming a constantresidualmapseems to be approprated

  29. Future work • Implement in Starfinder a toolable to model the PSF • Add more complex model of PSF parametersvariationacross the FoV (maybepolynomials)  application to MCAO images • Small variation of the PSF parametersduring the fitting of the fieldstars; residualmap look-up table • Test it on real data and map the photometricerrorvarying SNR and PSF variationmagnitude • Put it on the web ‘My dreamis to receive the data and the associated PSF for the data reduction’ [an astronomerusing AO data]

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