April 2001 OPTICON workshop in Nice 1 PSF-fitting with SExtractor Emmanuel BERTIN (TERAPIX)

April 2001 OPTICON workshop in Nice 2 Source extraction and the PSF Knowledge of the image PSF is useful for Knowledge of the image PSF is useful for  Optimum matched filtering and detection  Source deblending in star fields  Accurate and robust astrometry  Optimum point-source photometry on background-noise limited images  Deconvolving the shape parameters of extended sources  Object classification Knowledge of the image PSF is useful for Knowledge of the image PSF is useful for  Optimum matched filtering and detection  Source deblending in star fields  Accurate and robust astrometry  Optimum point-source photometry on background-noise limited images  Deconvolving the shape parameters of extended sources  Object classification

April 2001 OPTICON workshop in Nice 3 Building a model of the PSF Requirements: Requirements:  Model variations across the field  Be able to deal with (moderate) undersampling  Number of degrees of freedom as small as possible Requirements: Requirements:  Model variations across the field  Be able to deal with (moderate) undersampling  Number of degrees of freedom as small as possible

April 2001 OPTICON workshop in Nice 4 PSF models Analytical vs tabulated models Analytical vs tabulated models  Analytical models are simpler to implement and can deal with undersampling “naturally”  BUT: simple (not instrument-dependent) models have trouble handling PSF features like diffraction effects (spikes and rings)  Such features can be tabulated provided that the data are correctly sampled, but this is not always the case (ex: WFPC2, NICMOS,…)  Tabulated models don’t have these limitations  BUT: over- and under-sampling are not properly handled. Analytical vs tabulated models Analytical vs tabulated models  Analytical models are simpler to implement and can deal with undersampling “naturally”  BUT: simple (not instrument-dependent) models have trouble handling PSF features like diffraction effects (spikes and rings)  Such features can be tabulated provided that the data are correctly sampled, but this is not always the case (ex: WFPC2, NICMOS,…)  Tabulated models don’t have these limitations  BUT: over- and under-sampling are not properly handled.

April 2001 OPTICON workshop in Nice 5 A solution: “super-tabulation” The PSF is tabulated at a resolution which depends on the stellar FWHM (typically 3 pixels/FWHM) The PSF is tabulated at a resolution which depends on the stellar FWHM (typically 3 pixels/FWHM)  Minimize redundancy in cases of bad seeing  Handle undersampled data by building a “super- tabulated” PSF model  Find the sample values by solving a system using stars at different positions on the pixel grid  Intuitive approach: solve in Fourier space. Easy but suboptimum (no weighting)  Working in direct space gives much more robust results The PSF is tabulated at a resolution which depends on the stellar FWHM (typically 3 pixels/FWHM) The PSF is tabulated at a resolution which depends on the stellar FWHM (typically 3 pixels/FWHM)  Minimize redundancy in cases of bad seeing  Handle undersampled data by building a “super- tabulated” PSF model  Find the sample values by solving a system using stars at different positions on the pixel grid  Intuitive approach: solve in Fourier space. Easy but suboptimum (no weighting)  Working in direct space gives much more robust results

April 2001 OPTICON workshop in Nice 6 Solving in Fourier space Aliased portion of the spectrum Lauer 1999 Reconstructed NICMOS PSF

April 2001 OPTICON workshop in Nice 7 Solving in direct space A resampling kernel h, based on a compact interpolating function (Lanczos3 ), links the “super-tabulated” PSF to the real data: the pixel i of star j can be written as A resampling kernel h, based on a compact interpolating function (Lanczos3 ), links the “super-tabulated” PSF to the real data: the pixel i of star j can be written as The  k ’s are derived using a weighted  2 minimization. The  k ’s are derived using a weighted  2 minimization.  Lots of computations involved:  Sparse matrix processing necessary  The oversampling of faint peripheral pixels can be dropped. The  k ’s are derived using a weighted  2 minimization. The  k ’s are derived using a weighted  2 minimization.  Lots of computations involved:  Sparse matrix processing necessary  The oversampling of faint peripheral pixels can be dropped.

April 2001 OPTICON workshop in Nice 8 Handling PSF variations PSF variations are assumed to be a smooth function of object coordinates PSF variations are assumed to be a smooth function of object coordinates  The variations can be decomposed on a polynomial basis X l PSF variations are assumed to be a smooth function of object coordinates PSF variations are assumed to be a smooth function of object coordinates  The variations can be decomposed on a polynomial basis X l A third order polynomial (l =10) is generally sufficient to describe the variation of the PSF with position in the field A third order polynomial (l =10) is generally sufficient to describe the variation of the PSF with position in the field

April 2001 OPTICON workshop in Nice 9 Example of  lk PSF components for a UH8k image Cste x x 2 x 3 y yx yx 2 y 2 y 2 x y 3

April 2001 OPTICON workshop in Nice 10 Reconstructed UH8k PSF

April 2001 OPTICON workshop in Nice 11 Finding prototype stars Basically we are looking for something we don’t know yet Basically we are looking for something we don’t know yet  PSF variability makes the stellar locus “fuzzy” in feature space  Problems due to crowding at low galactic latitude  Confusion with galaxies in cluster areas Empirically designed automatic selection based on magnitude,half-light radius, ellipticity, crowding and saturation flags seems to work fine Empirically designed automatic selection based on magnitude,half-light radius, ellipticity, crowding and saturation flags seems to work fine  Remaining configuration parameters for selection essentially consist of acceptable FWHM range and ellipticity  Iterative rejection procedure based on similarity between samples and a rough PSF estimate Basically we are looking for something we don’t know yet Basically we are looking for something we don’t know yet  PSF variability makes the stellar locus “fuzzy” in feature space  Problems due to crowding at low galactic latitude  Confusion with galaxies in cluster areas Empirically designed automatic selection based on magnitude,half-light radius, ellipticity, crowding and saturation flags seems to work fine Empirically designed automatic selection based on magnitude,half-light radius, ellipticity, crowding and saturation flags seems to work fine  Remaining configuration parameters for selection essentially consist of acceptable FWHM range and ellipticity  Iterative rejection procedure based on similarity between samples and a rough PSF estimate

April 2001 OPTICON workshop in Nice 12 Half-light radius/magnitude diagram

April 2001 OPTICON workshop in Nice 13 Fitting the PSF model Identify star “clusters”, like in DAOPhot ( Stetson 1987 ) and proceed interatively: Identify star “clusters”, like in DAOPhot ( Stetson 1987 ) and proceed interatively:  First a unique star is fitted  The basic centering algorithm is a modified gradient descent  The star is subtracted from the cluster and a local maximum sufficiently distant from the peak of the first star is identified  Two stars are fitted and subtracted, and a new maximum is found  Iterate up to 11 stars/cluster or  Stop if stars coalesce during the centering process Identify star “clusters”, like in DAOPhot ( Stetson 1987 ) and proceed interatively: Identify star “clusters”, like in DAOPhot ( Stetson 1987 ) and proceed interatively:  First a unique star is fitted  The basic centering algorithm is a modified gradient descent  The star is subtracted from the cluster and a local maximum sufficiently distant from the peak of the first star is identified  Two stars are fitted and subtracted, and a new maximum is found  Iterate up to 11 stars/cluster or  Stop if stars coalesce during the centering process

April 2001 OPTICON workshop in Nice 14 Current Performance Processing speed: Processing speed:  For building the PSF model: stars/second (XP1000)  For the PSF-fitting: ~ stars/second (XP1000) Measurement accuracy: Measurement accuracy:  Slightly better than DAOPhot on properly sampled, non- crowded fields  Slightly worse than DAOPhot (one pass) on properly sampled, crowded fields  Significantly better than DAOPhot on undersampled images Processing speed: Processing speed:  For building the PSF model: stars/second (XP1000)  For the PSF-fitting: ~ stars/second (XP1000) Measurement accuracy: Measurement accuracy:  Slightly better than DAOPhot on properly sampled, non- crowded fields  Slightly worse than DAOPhot (one pass) on properly sampled, crowded fields  Significantly better than DAOPhot on undersampled images

April 2001 OPTICON workshop in Nice 15 Application: Comparison with DAOPhot on NGC 6819 (CFH12k) Kalirai et al. 2001a

April 2001 OPTICON workshop in Nice 16 Application: Photometric accuracy in NGC 6819 (CFH12k) Kalirai et al. 2001b

April 2001 OPTICON workshop in Nice 17 Application: Colour-magnitude diagrams in NGC 6819 (CFH12k) Kalirai et al. 2001b

April 2001 OPTICON workshop in Nice 18 ConclusionConclusion Currently available as an external module: “PSFEx” Currently available as an external module: “PSFEx” PSFEx is not, and will not be publicly available PSFEx is not, and will not be publicly available  Completeness issues  The current product can be used in the wrong way Awaiting final implementation in SExtractor3 for public release Awaiting final implementation in SExtractor3 for public release Currently available as an external module: “PSFEx” Currently available as an external module: “PSFEx” PSFEx is not, and will not be publicly available PSFEx is not, and will not be publicly available  Completeness issues  The current product can be used in the wrong way Awaiting final implementation in SExtractor3 for public release Awaiting final implementation in SExtractor3 for public release