April 2001 OPTICON workshop in Nice 1 The PSF homogenization problem in large imaging surveys Emmanuel BERTIN (TERAPIX)

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

The PSF homogenization The PSF homogenization problem in large imaging problem in large imaging

surveyssurveys

The PSF homogenization The PSF homogenization problem in large imaging problem in large imaging

surveyssurveys

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


PSF VariationsPSF VariationsPSF VariationsPSF Variations

• From exposure to exposure:From exposure to exposure: Seeing changesSeeing changes Defocusing, jittering, tracking errorsDefocusing, jittering, tracking errors Pupil rotation (alt-az telescopes)Pupil rotation (alt-az telescopes)

• Within the fieldWithin the field Optical aberrationsOptical aberrations Charge transfer problems on some CCDsCharge transfer problems on some CCDs

• From exposure to exposure:From exposure to exposure: Seeing changesSeeing changes Defocusing, jittering, tracking errorsDefocusing, jittering, tracking errors Pupil rotation (alt-az telescopes)Pupil rotation (alt-az telescopes)

• Within the fieldWithin the field Optical aberrationsOptical aberrations Charge transfer problems on some CCDsCharge transfer problems on some CCDs


Co-adding images with different Co-adding images with different PSFsPSFs

Co-adding images with different Co-adding images with different PSFsPSFs

• For most surveys, PSF variations are For most surveys, PSF variations are dominated by the seeingdominated by the seeing In the optical domain, “almost In the optical domain, “almost

unconstrained” seeing FWHM varies typically unconstrained” seeing FWHM varies typically by 30% RMS (a factor 2 peak-to-peak).by 30% RMS (a factor 2 peak-to-peak).This represents a factor 4 in peak intensity!!This represents a factor 4 in peak intensity!!

When constraints are set (queue When constraints are set (queue scheduling), this can be reduced to scheduling), this can be reduced to ~10%RMS.~10%RMS.

The distribution of seeing FWHM has a The distribution of seeing FWHM has a positive skewnesspositive skewness

• For most surveys, PSF variations are For most surveys, PSF variations are dominated by the seeingdominated by the seeing In the optical domain, “almost In the optical domain, “almost

unconstrained” seeing FWHM varies typically unconstrained” seeing FWHM varies typically by 30% RMS (a factor 2 peak-to-peak).by 30% RMS (a factor 2 peak-to-peak).This represents a factor 4 in peak intensity!!This represents a factor 4 in peak intensity!!

When constraints are set (queue When constraints are set (queue scheduling), this can be reduced to scheduling), this can be reduced to ~10%RMS.~10%RMS.

The distribution of seeing FWHM has a The distribution of seeing FWHM has a positive skewnesspositive skewness


Seeing FWHM distributions in the Seeing FWHM distributions in the optical (I band)optical (I band)

Seeing FWHM distributions in the Seeing FWHM distributions in the optical (I band)optical (I band)

EIS-Wide (NTT)EIS-Wide (NTT) VIRMOS VIRMOS (CFHT)(CFHT)


Seeing FWHM variations during Seeing FWHM variations during the nightthe night

Seeing FWHM variations during Seeing FWHM variations during the nightthe night

2MASS: Jarrett 2MASS: Jarrett et al. 2000et al. 20002MASS: Jarrett 2MASS: Jarrett et al. 2000et al. 2000

SDSS: Yasuda SDSS: Yasuda et al. 2001et al. 2001SDSS: Yasuda SDSS: Yasuda et al. 2001et al. 2001


Co-adding images with different Co-adding images with different seeingseeing

Co-adding images with different Co-adding images with different seeingseeing

• In the case of fully overlapping images:In the case of fully overlapping images: Non-linear combinations affect the Non-linear combinations affect the

photometry of unresolved sources (e.g. photometry of unresolved sources (e.g. Steidel & Hamilton 1993Steidel & Hamilton 1993))

The core of the PSF can no longer be The core of the PSF can no longer be approximated by a Gaussian (“German approximated by a Gaussian (“German helmet”).helmet”).May affect shear correctionMay affect shear correction

22 Image combination ( Image combination (Szalay et al. 1999Szalay et al. 1999) ) affectedaffected

• In the case of fully overlapping images:In the case of fully overlapping images: Non-linear combinations affect the Non-linear combinations affect the

photometry of unresolved sources (e.g. photometry of unresolved sources (e.g. Steidel & Hamilton 1993Steidel & Hamilton 1993))

The core of the PSF can no longer be The core of the PSF can no longer be approximated by a Gaussian (“German approximated by a Gaussian (“German helmet”).helmet”).May affect shear correctionMay affect shear correction

22 Image combination ( Image combination (Szalay et al. 1999Szalay et al. 1999) ) affectedaffected


Co-adding images with different Co-adding images with different seeing [2]seeing [2]

Co-adding images with different Co-adding images with different seeing [2]seeing [2]

• In the case of partial overlaps:In the case of partial overlaps: The PSF changes abruptly from place to placeThe PSF changes abruptly from place to place

Need for a “PSF-map”Need for a “PSF-map” Difficult to implement (cf. Difficult to implement (cf. context-mapscontext-maps) !!) !!

Minimizing the number of image boundaries puts Minimizing the number of image boundaries puts strong constraints on the survey dithering strategystrong constraints on the survey dithering strategy Gaps between CCDs almost unusable for scientific use Gaps between CCDs almost unusable for scientific use

(unequal coverage, not enough stars to define a PSF)(unequal coverage, not enough stars to define a PSF) Less dithering yields astrometric and photometric Less dithering yields astrometric and photometric

solutions which are less robustsolutions which are less robust

• In the case of partial overlaps:In the case of partial overlaps: The PSF changes abruptly from place to placeThe PSF changes abruptly from place to place

Need for a “PSF-map”Need for a “PSF-map” Difficult to implement (cf. Difficult to implement (cf. context-mapscontext-maps) !!) !!

Minimizing the number of image boundaries puts Minimizing the number of image boundaries puts strong constraints on the survey dithering strategystrong constraints on the survey dithering strategy Gaps between CCDs almost unusable for scientific use Gaps between CCDs almost unusable for scientific use

(unequal coverage, not enough stars to define a PSF)(unequal coverage, not enough stars to define a PSF) Less dithering yields astrometric and photometric Less dithering yields astrometric and photometric

solutions which are less robustsolutions which are less robust


Homogenizing the PSF?Homogenizing the PSF?Homogenizing the PSF?Homogenizing the PSF?

• Make the PSF everywhere the sameMake the PSF everywhere the same Technique similar to that of image Technique similar to that of image

subtraction (subtraction (Tomaney & Crotts 1996Tomaney & Crotts 1996, , Alard & Lupton 1998Alard & Lupton 1998, , Alard 2000Alard 2000))

Convolution kernel with a restricted number Convolution kernel with a restricted number of degrees of freedom.of degrees of freedom.

BUT: no unique reference image available!BUT: no unique reference image available! One must One must definedefine one. An isotropic one. An isotropic

Gaussian/Moffat-like function with the FWHM of Gaussian/Moffat-like function with the FWHM of the median seeing is a convenient choicethe median seeing is a convenient choice

• Make the PSF everywhere the sameMake the PSF everywhere the same Technique similar to that of image Technique similar to that of image

subtraction (subtraction (Tomaney & Crotts 1996Tomaney & Crotts 1996, , Alard & Lupton 1998Alard & Lupton 1998, , Alard 2000Alard 2000))

Convolution kernel with a restricted number Convolution kernel with a restricted number of degrees of freedom.of degrees of freedom.

BUT: no unique reference image available!BUT: no unique reference image available! One must One must definedefine one. An isotropic one. An isotropic

Gaussian/Moffat-like function with the FWHM of Gaussian/Moffat-like function with the FWHM of the median seeing is a convenient choicethe median seeing is a convenient choice


At which stage of the pipeline At which stage of the pipeline must the PSF be homogenized?must the PSF be homogenized?At which stage of the pipeline At which stage of the pipeline

must the PSF be homogenized?must the PSF be homogenized?

• Image warping affects the PSF (and its Image warping affects the PSF (and its variability).variability).

• Re-projection to an equal-area grid Re-projection to an equal-area grid corrects for flux distorsions produced by corrects for flux distorsions produced by flat-fieldingflat-fielding PSF homogenization (adaptive kernel PSF homogenization (adaptive kernel

filtering) must be done AFTER image filtering) must be done AFTER image warping.warping.

• Image warping affects the PSF (and its Image warping affects the PSF (and its variability).variability).

• Re-projection to an equal-area grid Re-projection to an equal-area grid corrects for flux distorsions produced by corrects for flux distorsions produced by flat-fieldingflat-fielding PSF homogenization (adaptive kernel PSF homogenization (adaptive kernel

filtering) must be done AFTER image filtering) must be done AFTER image warping.warping.


Effects of flat-fielding on flux Effects of flat-fielding on flux sensitivitysensitivity

Effects of flat-fielding on flux Effects of flat-fielding on flux sensitivitysensitivity


Consequences of PSF Consequences of PSF homogenization: the goodhomogenization: the good

Consequences of PSF Consequences of PSF homogenization: the goodhomogenization: the good

• PSF homogenization corrects for PSF anisotropy.PSF homogenization corrects for PSF anisotropy.• PSF Homogenization removes the ambiguity of PSF Homogenization removes the ambiguity of

the definition of a star centroid for asymmetric the definition of a star centroid for asymmetric PSFs :PSFs : Astrometric calibration still needed, but it does not Astrometric calibration still needed, but it does not

need to be more accurate than, say, a fraction of the need to be more accurate than, say, a fraction of the stellar FWHM.stellar FWHM.

Fine “tuning” of astrometric centering is taken care Fine “tuning” of astrometric centering is taken care of by the variable PSF-correction.of by the variable PSF-correction.

• PSF homogenization can include flux rescaling PSF homogenization can include flux rescaling as a free parameter.as a free parameter. Provides a relative photometric calibration that can Provides a relative photometric calibration that can

handle inhomogeneous sensitivity across the field.handle inhomogeneous sensitivity across the field.

• PSF homogenization corrects for PSF anisotropy.PSF homogenization corrects for PSF anisotropy.• PSF Homogenization removes the ambiguity of PSF Homogenization removes the ambiguity of

the definition of a star centroid for asymmetric the definition of a star centroid for asymmetric PSFs :PSFs : Astrometric calibration still needed, but it does not Astrometric calibration still needed, but it does not

need to be more accurate than, say, a fraction of the need to be more accurate than, say, a fraction of the stellar FWHM.stellar FWHM.

Fine “tuning” of astrometric centering is taken care Fine “tuning” of astrometric centering is taken care of by the variable PSF-correction.of by the variable PSF-correction.

• PSF homogenization can include flux rescaling PSF homogenization can include flux rescaling as a free parameter.as a free parameter. Provides a relative photometric calibration that can Provides a relative photometric calibration that can

handle inhomogeneous sensitivity across the field.handle inhomogeneous sensitivity across the field.


Consequences of PSF Consequences of PSF homogenization: the badhomogenization: the bad

Consequences of PSF Consequences of PSF homogenization: the badhomogenization: the bad

• PSF Homogenization is a linear and (locally) PSF Homogenization is a linear and (locally) shift-invariant process:shift-invariant process: Image artifacts will spread beyond the masked Image artifacts will spread beyond the masked

areasareas Prior interpolation of image defects might be necessaryPrior interpolation of image defects might be necessary

Objects that touch the frame boundaries must be Objects that touch the frame boundaries must be excludedexcluded

Correlation at the PSF scale will be introduced in Correlation at the PSF scale will be introduced in the noise.the noise. Will one have to use “correlation-maps” for optimum Will one have to use “correlation-maps” for optimum

detection, or will the variations of the noise correlation detection, or will the variations of the noise correlation function be negligible in “reasonable” cases?function be negligible in “reasonable” cases?

The next generation of source extraction software must The next generation of source extraction software must be able to measure and make extensive use of the be able to measure and make extensive use of the (background) noise correlation function.(background) noise correlation function.

• PSF Homogenization is a linear and (locally) PSF Homogenization is a linear and (locally) shift-invariant process:shift-invariant process: Image artifacts will spread beyond the masked Image artifacts will spread beyond the masked

areasareas Prior interpolation of image defects might be necessaryPrior interpolation of image defects might be necessary

Objects that touch the frame boundaries must be Objects that touch the frame boundaries must be excludedexcluded

Correlation at the PSF scale will be introduced in Correlation at the PSF scale will be introduced in the noise.the noise. Will one have to use “correlation-maps” for optimum Will one have to use “correlation-maps” for optimum

detection, or will the variations of the noise correlation detection, or will the variations of the noise correlation function be negligible in “reasonable” cases?function be negligible in “reasonable” cases?

The next generation of source extraction software must The next generation of source extraction software must be able to measure and make extensive use of the be able to measure and make extensive use of the (background) noise correlation function.(background) noise correlation function.


PSF homogenization as seen in PSF homogenization as seen in Fourier space (1D)Fourier space (1D)


Moffat PSFs with Moffat PSFs with FWHMsFWHMs 0.6”0.6” andand 0.9” 0.9”

(pixel size=0.18”)(pixel size=0.18”)

Moffat PSFs with Moffat PSFs with FWHMsFWHMs 0.6”0.6” andand 0.9” 0.9”

(pixel size=0.18”)(pixel size=0.18”)




Example of a 2D kernel Example of a 2D kernel MTF to “convert” 0.9” MTF to “convert” 0.9”

FWHM images to 0.75” FWHM images to 0.75” FWHMFWHM

Example of a 2D kernel Example of a 2D kernel MTF to “convert” 0.9” MTF to “convert” 0.9”

FWHM images to 0.75” FWHM images to 0.75” FWHMFWHM


PSF-homogenization: how does it PSF-homogenization: how does it look like?look like?

PSF-homogenization: how does it PSF-homogenization: how does it look like?look like?

Originally 0.6”Originally 0.6”Originally 0.6”Originally 0.6” Originally 0.9”Originally 0.9”Originally 0.9”Originally 0.9”


ConclusionConclusionConclusionConclusion

• Awaits implementation in SWarpAwaits implementation in SWarp Major undertaking:Major undertaking:

Speed issuesSpeed issues Robustness in “empty” regionsRobustness in “empty” regions Astrometric fine-tuning issueAstrometric fine-tuning issue Photometric “anchors” must be specifiedPhotometric “anchors” must be specified

Adequacy for critical scientific analyses like Adequacy for critical scientific analyses like weak gravitational lensing measurements weak gravitational lensing measurements needs to be assessed!needs to be assessed!

• Awaits implementation in SWarpAwaits implementation in SWarp Major undertaking:Major undertaking:

Speed issuesSpeed issues Robustness in “empty” regionsRobustness in “empty” regions Astrometric fine-tuning issueAstrometric fine-tuning issue Photometric “anchors” must be specifiedPhotometric “anchors” must be specified

Adequacy for critical scientific analyses like Adequacy for critical scientific analyses like weak gravitational lensing measurements weak gravitational lensing measurements needs to be assessed!needs to be assessed!

Documents

April 2001 OPTICON workshop in Nice 1 The PSF homogenization problem in large imaging surveys Emmanuel BERTIN (TERAPIX)