PSF estimation and parametric modelling from scientific data Laura Schreiber Istituto Nazionale di Astrofisica – Osservatorio Astronomico di Bologna FP7-OPTICON

PSF estimation and parametric modelling from scientific data

Laura SchreiberIstituto Nazionale di Astrofisica – Osservatorio Astronomico di Bologna

FP7-OPTICON PSF reconstruction meeting, Marseille 29-30 January 14

FP7-OPTICON PSF reconstruction meeting, Marseille 29-30 January 14 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.


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)


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) […]


How do the AO data look like?

Single Conjugate AO Highly structured PSF, small FoV

Galactic center, PUEO@ CFHT, K band

13 a

rcse

c

Courtesy of F. Rigaut



Single Conjugate AO Highly structured and variable PSF

M15 Core, @ Keck, K band Courtesy of L. Origlia



Single Conjugate AO Highly structured and variable PSF

21 a

rcse

c

1 pixel = 0.021 arcsecExposure Time = 6 s

M92, FLAO @ LBT, Pisces, J band GS

AO science demostration run



Multi Conjugate AO Improved PSF uniformity across a larger FoV

ωCen, MAD @ VLT, K band

1 ar

cmin

[Bono et Al 2009]


How do the AO data look like?Grabbed from F. Rigaut presentation at AO4ELT3, Florence 2013


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]– photometric accuracy is limited by the SNR and by the knowledge

of the PSF [Shoedel 2010]– detection of elongated sources

– Many ‘exotic’ solutions have been found to reduce data…

Astrometric and photometric measurements with AO systems are mainly limited by errors in the PSF modeling and fitting.



SCAO small corrected FoV, PSF spatial variation– Galactic center (NACO): Image is first Wiener-filter-deconvolved

using a suitable PSF (GS psf) . Local variations in PSF kernels and ringing is taken care with locally extracted PSF fitting. [Schoedel 2010]

– M92 GC (FLAO): Modiefied Romafot software. PSFfitting with variable moffat (no parameters fixed). [Bono 2013 Ao4ELT3]

– NGC6440 GC (NACO): PSFfitting with starfinder using an analitical model composed by 3 gaussian components. [Origlia 2008]

– Usage of calibration images [Steinbring et al. (2002)] – Usage of calibration HST fields – Galaxy Survey (NACO): Estimate local PSF around guide star image

and model the PSF in the field as the convolution of the GS PSF and a blurring kernel. [Diolaiti 2000, Cresci 2006]

guide staroff-axis PSF blurring kernel(e.g. Gaussian)

=



MCAO To improve the PSF uniformity across the FoV– Suitable to study dense stellar field, galaxy morphology– MAD: Many papers have been pubblished [Melnick SPIE 2012 for a

review]– GeMs: First papers are coming out– Already available sofware have been used

Terzan5, MAD @ VLT, K band

The presence of two red clumps implies the presens of two different stellar populations. [Ferraro et Al, Nature, 2009]


SF: Exercise of variable PSF

FWHM ≈ 3.4 pxSR ≈ 0.01 ÷ 0.37Magnitude range ≈ 10 magHigh SNR



PSF fitting photometry using the true PSF model

Photometric error in the fainter magnitude bin ≈ 0.11



∆𝑚𝑎𝑔≅ 0.172521∆𝑚𝑎𝑔≅ 0.18

When the PSF varies across the FoV, the photometric error depends mainly on the goodness of the PSF model adoped

PSF fitting photometry using the guide star

1

0

-1

-2

-3

-4

-5




PSF fitting photometry using the local PSF

Photometric error in the fainter magnitude bin ≈ 0.26 Photometric error in the fainter magnitude bin ≈ 0.14

To be compated with the error when perfect PSF is used ≈ 0.11


3 X 3 subdomains9 X 9 subdomainsMore subdomains


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 wavefront that 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 isolated bright stars for modeling the PSF, no extra observation time, available cronology of PSF variation in time

– Critical aspects: determination of the system’s static aberrations and of the optical turbulence paramenters; complexity (MCAO?)


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), …


Starfinder

Code for identification and analysis of point-like sources– Designed and developed (1997-2000) for images with structured

PSF but uniform across field 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 spatially variable PSFs – Numerical local PSF by dividing the image in subdomains (MCAO)– Analitical model of the PSF and of its parameters vatiation

across the Fov by a multi-component parametric model (Gaussian, Moffat, Lorentzian) + map of residuals using information about AO (GS position, seeing, .. NGS SCAO)


PSF analytical model

3 Broad Gaussian/ Moffat halo

1 Narrow Moffat core2 External torus

3

1

2


SF variable PSF: analytical model

PSF fitting photometry using the estimated PSF model: method

Choose the PSF stars (bright, distributed in the FoV)

Choose of components for PSF modeling (first iteration one)

Fit of parameters variation with respect to the GS distance

Residual map = stars – model

STARFINDER

Photometry and stars positions

A priori knowledge of the rotation angle

Stack, combine and normalize residuals

PS

F r

efin

ing



PSF fitting photometry using the estimated PSF model: results


To be compated with the error when perfect PSF is used ≈ 0.11



PSF fitting photometry using the estimated PSF model: real data

M15, FLAO @ LBT, Pisces, J band

1 - PSF stars selection: possibly bright and isolated



2 – Definition of the analytical model: 2D Moffat 3 – Estimation of the Moffat parameters variation across the FoV

Product: PSF model + residual

Moffat majior axis variation model Moffat minor axis variation model

Flux variation model


SF variable PSF: analytical modelImage Synthetic Image model


SF variable PSF: Local PSF

PSF extraction from MAORY + MICADO simulated crowded stellar fields in distant ellipticals (Virgo cluster) [Schreiber 2013]– Map of Maory Phase A PSF – Different crowding conditions– Different regions of the FoV

Maory FoV

Micado FoV


SF variable PSF: Local PSS

The scope of the work was to explore the [effect of the] photometric error [on stellar metallicity distribution] as a function of the crowding and of the PSF variation across the FoV– Different crowding, central (best SR)

PSF telescope re-pointing– Same crowding, different PSFs (best and

worst SR) subdomains

Micado FoV

Comparable photometric error, but different zero points (fractions of magnitude) among different subdomains


Results

Simulated image: 2 moffat component– easy to model– promising photometric accuracy

Local PSF estimation: ideal for MCAO– Numeric robust– Tested on highly crowded simulated images (with typical MAORY

PSF variation) no effects on photometric accuracy– Possible drawback: different zero points

Ideal model for SCAO PSF: hybrid (analytical + residual)– Less analytical components implies more robustness (fit algorithms

easely converge on a small number of pixels)– The case of M15 the estimated residuals look indistinguishable

within 1σ assuming a constant residual map seems to be approprated


Future work

Implement in Starfinder a tool able to model the PSF Add more complex model of PSF parameters variation across the

FoV (maybe polynomials) application to MCAO images Small variation of the PSF parameters during the fitting of the field

stars; residual map look-up table Test it on real data and map the photometric error varying SNR

and PSF variation magnitude Put it on the web

‘My dream is to receive the data and the associated PSF for the data reduction’

[an astronomer using AO data]

Documents

PSF estimation and parametric modelling from scientific data Laura Schreiber Istituto Nazionale di Astrofisica – Osservatorio Astronomico di Bologna FP7-OPTICON