april 2001 opticon workshop in nice 1 psf-fitting with sextractor emmanuel bertin (terapix)

April 2001April 2001 April 2001April 2001 OPTICON workshop in NiceOPTICON workshop in Nice OPTICON workshop in NiceOPTICON workshop in Nice 11

PSF-fitting with SExtractorPSF-fitting with SExtractorPSF-fitting with SExtractorPSF-fitting with SExtractor

Emmanuel BERTIN (TERAPIX)Emmanuel BERTIN (TERAPIX) Emmanuel BERTIN (TERAPIX)Emmanuel BERTIN (TERAPIX)


Source extraction and the PSFSource extraction and the PSFSource extraction and the PSFSource extraction and the PSF

• Knowledge of the image PSF is useful forKnowledge of the image PSF is useful for Optimum matched filtering and detectionOptimum matched filtering and detection Source deblending in star fieldsSource deblending in star fields Accurate and robust astrometryAccurate and robust astrometry Optimum point-source photometry on Optimum point-source photometry on

background-noise limited imagesbackground-noise limited images Deconvolving the shape parameters of Deconvolving the shape parameters of

extended sourcesextended sources Object classificationObject classification

• Knowledge of the image PSF is useful forKnowledge of the image PSF is useful for Optimum matched filtering and detectionOptimum matched filtering and detection Source deblending in star fieldsSource deblending in star fields Accurate and robust astrometryAccurate and robust astrometry Optimum point-source photometry on Optimum point-source photometry on

background-noise limited imagesbackground-noise limited images Deconvolving the shape parameters of Deconvolving the shape parameters of

extended sourcesextended sources Object classificationObject classification


Building a model of the PSFBuilding a model of the PSFBuilding a model of the PSFBuilding a model of the PSF

• Requirements:Requirements: Model variations across the fieldModel variations across the field Be able to deal with (moderate) Be able to deal with (moderate)

undersamplingundersampling Number of degrees of freedom as small as Number of degrees of freedom as small as

possiblepossible

• Requirements:Requirements: Model variations across the fieldModel variations across the field Be able to deal with (moderate) Be able to deal with (moderate)

undersamplingundersampling Number of degrees of freedom as small as Number of degrees of freedom as small as

possiblepossible


PSF modelsPSF modelsPSF modelsPSF models

• Analytical Analytical vsvs tabulated models tabulated models Analytical models are simpler to implement Analytical models are simpler to implement

and can deal with undersampling “naturally”and can deal with undersampling “naturally” BUT: simple (not instrument-dependent) models BUT: simple (not instrument-dependent) models

have trouble handling PSF features like diffraction have trouble handling PSF features like diffraction effects (spikes and rings)effects (spikes and rings)

Such features can be tabulated provided that the data are Such features can be tabulated provided that the data are correctly sampled, but this is not always the case (ex: correctly sampled, but this is not always the case (ex: WFPC2, NICMOS,…)WFPC2, NICMOS,…)

Tabulated models don’t have these limitationsTabulated models don’t have these limitations BUT: over- and under-sampling are not properly BUT: over- and under-sampling are not properly

handled.handled.

• Analytical Analytical vsvs tabulated models tabulated models Analytical models are simpler to implement Analytical models are simpler to implement

and can deal with undersampling “naturally”and can deal with undersampling “naturally” BUT: simple (not instrument-dependent) models BUT: simple (not instrument-dependent) models

have trouble handling PSF features like diffraction have trouble handling PSF features like diffraction effects (spikes and rings)effects (spikes and rings)

Such features can be tabulated provided that the data are Such features can be tabulated provided that the data are correctly sampled, but this is not always the case (ex: correctly sampled, but this is not always the case (ex: WFPC2, NICMOS,…)WFPC2, NICMOS,…)

Tabulated models don’t have these limitationsTabulated models don’t have these limitations BUT: over- and under-sampling are not properly BUT: over- and under-sampling are not properly

handled.handled.


A solution: “super-tabulation”A solution: “super-tabulation”A solution: “super-tabulation”A solution: “super-tabulation”

• The PSF is tabulated at a resolution The PSF is tabulated at a resolution which depends on the stellar FWHM which depends on the stellar FWHM (typically 3 pixels/FWHM)(typically 3 pixels/FWHM) Minimize redundancy in cases of bad seeingMinimize redundancy in cases of bad seeing Handle undersampled data by building a Handle undersampled data by building a

“super-tabulated” PSF model“super-tabulated” PSF model Find the sample values by solving a system using Find the sample values by solving a system using

stars at different positions on the pixel gridstars at different positions on the pixel grid Intuitive approach: solve in Fourier space. Easy but Intuitive approach: solve in Fourier space. Easy but

suboptimum (no weighting)suboptimum (no weighting) Working in direct space gives much more robust resultsWorking in direct space gives much more robust results

• The PSF is tabulated at a resolution The PSF is tabulated at a resolution which depends on the stellar FWHM which depends on the stellar FWHM (typically 3 pixels/FWHM)(typically 3 pixels/FWHM) Minimize redundancy in cases of bad seeingMinimize redundancy in cases of bad seeing Handle undersampled data by building a Handle undersampled data by building a

“super-tabulated” PSF model“super-tabulated” PSF model Find the sample values by solving a system using Find the sample values by solving a system using

stars at different positions on the pixel gridstars at different positions on the pixel grid Intuitive approach: solve in Fourier space. Easy but Intuitive approach: solve in Fourier space. Easy but

suboptimum (no weighting)suboptimum (no weighting) Working in direct space gives much more robust resultsWorking in direct space gives much more robust results


Solving in Fourier spaceSolving in Fourier spaceSolving in Fourier spaceSolving in Fourier space

Aliased portion of the spectrumAliased portion of the spectrum

Lauer 1999Lauer 1999

Reconstructed NICMOS PSFReconstructed NICMOS PSF


Solving in direct spaceSolving in direct spaceSolving in direct spaceSolving in direct space

• A resampling kernel A resampling kernel hh, based on a compact interpolating , based on a compact interpolating function (function (Lanczos3 Lanczos3 ), links the “super-tabulated” PSF to the ), links the “super-tabulated” PSF to the real data: the pixel real data: the pixel ii of star of star jj can be written as can be written as

• A resampling kernel A resampling kernel hh, based on a compact interpolating , based on a compact interpolating function (function (Lanczos3 Lanczos3 ), links the “super-tabulated” PSF to the ), links the “super-tabulated” PSF to the real data: the pixel real data: the pixel ii of star of star jj can be written as can be written as

kik

kjij hP xx kik

kjij hP xx

• The The k k ’s are derived using a weighted ’s are derived using a weighted 2 2 minimization. minimization. Lots of computations involved:Lots of computations involved:

Sparse matrix processing necessarySparse matrix processing necessary The oversampling of faint peripheral pixels can be dropped.The oversampling of faint peripheral pixels can be dropped.

• The The k k ’s are derived using a weighted ’s are derived using a weighted 2 2 minimization. minimization. Lots of computations involved:Lots of computations involved:

Sparse matrix processing necessarySparse matrix processing necessary The oversampling of faint peripheral pixels can be dropped.The oversampling of faint peripheral pixels can be dropped.


Handling PSF variationsHandling PSF variationsHandling PSF variationsHandling PSF variations

• PSF variations are assumed to be a smooth function PSF variations are assumed to be a smooth function of object coordinatesof object coordinates The variations can be decomposed on a polynomial basis The variations can be decomposed on a polynomial basis XXl l

• PSF variations are assumed to be a smooth function PSF variations are assumed to be a smooth function of object coordinatesof object coordinates The variations can be decomposed on a polynomial basis The variations can be decomposed on a polynomial basis XXl l

klik

kj

llij hXP xx klik

kj

llij hXP xx

• A third order polynomial (A third order polynomial (l l =10) is generally sufficient =10) is generally sufficient to describe the variation of the PSF with position in the to describe the variation of the PSF with position in the fieldfield

• A third order polynomial (A third order polynomial (l l =10) is generally sufficient =10) is generally sufficient to describe the variation of the PSF with position in the to describe the variation of the PSF with position in the fieldfield


Example ofExample of lk lk PSF components PSF components for a UH8k imagefor a UH8k image

Example ofExample of lk lk PSF components PSF components for a UH8k imagefor a UH8k image

Cste x x2 x3 y yx yx2 y2 y2x y3Cste x x2 x3 y yx yx2 y2 y2x y3


Reconstructed UH8k PSFReconstructed UH8k PSFReconstructed UH8k PSFReconstructed UH8k PSF


Finding prototype starsFinding prototype starsFinding prototype starsFinding prototype stars

• Basically we are looking for something we don’t know Basically we are looking for something we don’t know yetyet PSF variability makes the stellar locus “fuzzy” in feature PSF variability makes the stellar locus “fuzzy” in feature

spacespace Problems due to crowding at low galactic latitudeProblems due to crowding at low galactic latitude Confusion with galaxies in cluster areasConfusion with galaxies in cluster areas

• Empirically designed automatic selection based on Empirically designed automatic selection based on magnitude,half-light radius, ellipticity, crowding and magnitude,half-light radius, ellipticity, crowding and saturation flags seems to work finesaturation flags seems to work fine Remaining configuration parameters for selection essentially Remaining configuration parameters for selection essentially

consist of acceptable FWHM range and ellipticityconsist of acceptable FWHM range and ellipticity Iterative rejection procedure based on similarity between Iterative rejection procedure based on similarity between

samples and a rough PSF estimatesamples and a rough PSF estimate

• Basically we are looking for something we don’t know Basically we are looking for something we don’t know yetyet PSF variability makes the stellar locus “fuzzy” in feature PSF variability makes the stellar locus “fuzzy” in feature

spacespace Problems due to crowding at low galactic latitudeProblems due to crowding at low galactic latitude Confusion with galaxies in cluster areasConfusion with galaxies in cluster areas

• Empirically designed automatic selection based on Empirically designed automatic selection based on magnitude,half-light radius, ellipticity, crowding and magnitude,half-light radius, ellipticity, crowding and saturation flags seems to work finesaturation flags seems to work fine Remaining configuration parameters for selection essentially Remaining configuration parameters for selection essentially

consist of acceptable FWHM range and ellipticityconsist of acceptable FWHM range and ellipticity Iterative rejection procedure based on similarity between Iterative rejection procedure based on similarity between

samples and a rough PSF estimatesamples and a rough PSF estimate


Half-light radius/magnitude Half-light radius/magnitude diagramdiagram

Half-light radius/magnitude Half-light radius/magnitude diagramdiagram


Fitting the PSF modelFitting the PSF modelFitting the PSF modelFitting the PSF model

• Identify star “clusters”, like in DAOPhot Identify star “clusters”, like in DAOPhot ((Stetson 1987Stetson 1987) and proceed interatively:) and proceed interatively: First a unique star is fittedFirst a unique star is fitted

The basic centering algorithm is a modified gradient The basic centering algorithm is a modified gradient descentdescent

The star is subtracted from the cluster and a local The star is subtracted from the cluster and a local maximum sufficiently distant from the peak of the maximum sufficiently distant from the peak of the first star is identifiedfirst star is identified

Two stars are fitted and subtracted, and a new Two stars are fitted and subtracted, and a new maximum is foundmaximum is found Iterate up to 11 stars/cluster orIterate up to 11 stars/cluster or Stop if stars coalesce during the centering processStop if stars coalesce during the centering process

• Identify star “clusters”, like in DAOPhot Identify star “clusters”, like in DAOPhot ((Stetson 1987Stetson 1987) and proceed interatively:) and proceed interatively: First a unique star is fittedFirst a unique star is fitted

The basic centering algorithm is a modified gradient The basic centering algorithm is a modified gradient descentdescent

The star is subtracted from the cluster and a local The star is subtracted from the cluster and a local maximum sufficiently distant from the peak of the maximum sufficiently distant from the peak of the first star is identifiedfirst star is identified

Two stars are fitted and subtracted, and a new Two stars are fitted and subtracted, and a new maximum is foundmaximum is found Iterate up to 11 stars/cluster orIterate up to 11 stars/cluster or Stop if stars coalesce during the centering processStop if stars coalesce during the centering process


Current PerformanceCurrent PerformanceCurrent PerformanceCurrent Performance

• Processing speed:Processing speed: For building the PSF model:50-100 stars/second For building the PSF model:50-100 stars/second

(XP1000)(XP1000) For the PSF-fitting: ~50-1000 stars/second (XP1000)For the PSF-fitting: ~50-1000 stars/second (XP1000)

• Measurement accuracy:Measurement accuracy: Slightly better than DAOPhot on properly sampled, Slightly better than DAOPhot on properly sampled,

non-crowded fieldsnon-crowded fields Slightly worse than DAOPhot (one pass) on properly Slightly worse than DAOPhot (one pass) on properly

sampled, crowded fieldssampled, crowded fields Significantly better than DAOPhot on undersampled Significantly better than DAOPhot on undersampled

imagesimages

• Processing speed:Processing speed: For building the PSF model:50-100 stars/second For building the PSF model:50-100 stars/second

(XP1000)(XP1000) For the PSF-fitting: ~50-1000 stars/second (XP1000)For the PSF-fitting: ~50-1000 stars/second (XP1000)

• Measurement accuracy:Measurement accuracy: Slightly better than DAOPhot on properly sampled, Slightly better than DAOPhot on properly sampled,

non-crowded fieldsnon-crowded fields Slightly worse than DAOPhot (one pass) on properly Slightly worse than DAOPhot (one pass) on properly

sampled, crowded fieldssampled, crowded fields Significantly better than DAOPhot on undersampled Significantly better than DAOPhot on undersampled

imagesimages


Application: Comparison with Application: Comparison with DAOPhot on NGC 6819 (CFH12k)DAOPhot on NGC 6819 (CFH12k)

Application: Comparison with Application: Comparison with DAOPhot on NGC 6819 (CFH12k)DAOPhot on NGC 6819 (CFH12k)

Kalirai et al. 2001aKalirai et al. 2001a


Application: Photometric accuracy in Application: Photometric accuracy in NGC 6819 (CFH12k)NGC 6819 (CFH12k)

Application: Photometric accuracy in Application: Photometric accuracy in NGC 6819 (CFH12k)NGC 6819 (CFH12k)

Kalirai et al. 2001bKalirai et al. 2001b


Application: Colour-magnitude Application: Colour-magnitude diagrams in NGC 6819 (CFH12k)diagrams in NGC 6819 (CFH12k)Application: Colour-magnitude Application: Colour-magnitude

diagrams in NGC 6819 (CFH12k)diagrams in NGC 6819 (CFH12k)

Kalirai et al. 2001bKalirai et al. 2001b


ConclusionConclusionConclusionConclusion

• Currently available as an external module: Currently available as an external module: “PSFEx”“PSFEx”

• PSFEx is not, and will not be publicly available PSFEx is not, and will not be publicly available Completeness issuesCompleteness issues The current product can be used in the wrong wayThe current product can be used in the wrong way

• Awaiting final implementation in SExtractor3 Awaiting final implementation in SExtractor3 for public releasefor public release

• Currently available as an external module: Currently available as an external module: “PSFEx”“PSFEx”

• PSFEx is not, and will not be publicly available PSFEx is not, and will not be publicly available Completeness issuesCompleteness issues The current product can be used in the wrong wayThe current product can be used in the wrong way

• Awaiting final implementation in SExtractor3 Awaiting final implementation in SExtractor3 for public releasefor public release

april 2001 opticon workshop in nice 1 psf-fitting with sextractor emmanuel bertin (terapix)

Documents

image psf

supertabulated psf modelfind

supertabulationthe psf

trouble handling psf

tabulated models dont

star fieldsaccurate

unique star

pixel i of star j