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

April 2001 OPTICON workshop in Nice 2 PSF Variations From exposure to exposure: From exposure to exposure:  Seeing changes  Defocusing, jittering, tracking errors  Pupil rotation (alt-az telescopes) Within the field Within the field  Optical aberrations  Charge transfer problems on some CCDs From exposure to exposure: From exposure to exposure:  Seeing changes  Defocusing, jittering, tracking errors  Pupil rotation (alt-az telescopes) Within the field Within the field  Optical aberrations  Charge transfer problems on some CCDs

April 2001 OPTICON workshop in Nice 3 Co-adding images with different PSFs For most surveys, PSF variations are dominated by the seeing For most surveys, PSF variations are dominated by the seeing  In the optical domain, “almost unconstrained” seeing FWHM varies typically by 30% RMS (a factor 2 peak-to-peak).  This represents a factor 4 in peak intensity!!  When constraints are set (queue scheduling), this can be reduced to ~10%RMS.  The distribution of seeing FWHM has a positive skewness For most surveys, PSF variations are dominated by the seeing For most surveys, PSF variations are dominated by the seeing  In the optical domain, “almost unconstrained” seeing FWHM varies typically by 30% RMS (a factor 2 peak-to-peak).  This represents a factor 4 in peak intensity!!  When constraints are set (queue scheduling), this can be reduced to ~10%RMS.  The distribution of seeing FWHM has a positive skewness

April 2001 OPTICON workshop in Nice 4 Seeing FWHM distributions in the optical (I band) EIS-Wide (NTT) VIRMOS (CFHT)

April 2001 OPTICON workshop in Nice 5 Seeing FWHM variations during the night 2MASS: Jarrett et al SDSS: Yasuda et al. 2001

April 2001 OPTICON workshop in Nice 6 Co-adding images with different seeing In the case of fully overlapping images: In the case of fully overlapping images:  Non-linear combinations affect the photometry of unresolved sources (e.g. Steidel & Hamilton 1993 )  The core of the PSF can no longer be approximated by a Gaussian (“German helmet”).  May affect shear correction   2 Image combination ( Szalay et al ) affected In the case of fully overlapping images: In the case of fully overlapping images:  Non-linear combinations affect the photometry of unresolved sources (e.g. Steidel & Hamilton 1993 )  The core of the PSF can no longer be approximated by a Gaussian (“German helmet”).  May affect shear correction   2 Image combination ( Szalay et al ) affected

April 2001 OPTICON workshop in Nice 7 Co-adding images with different seeing [2] In the case of partial overlaps: In the case of partial overlaps:  The PSF changes abruptly from place to place  Need for a “PSF-map”  Difficult to implement (cf. context-maps) !!  Minimizing the number of image boundaries puts strong constraints on the survey dithering strategy  Gaps between CCDs almost unusable for scientific use (unequal coverage, not enough stars to define a PSF)  Less dithering yields astrometric and photometric solutions which are less robust In the case of partial overlaps: In the case of partial overlaps:  The PSF changes abruptly from place to place  Need for a “PSF-map”  Difficult to implement (cf. context-maps) !!  Minimizing the number of image boundaries puts strong constraints on the survey dithering strategy  Gaps between CCDs almost unusable for scientific use (unequal coverage, not enough stars to define a PSF)  Less dithering yields astrometric and photometric solutions which are less robust

April 2001 OPTICON workshop in Nice 8 Homogenizing the PSF? Make the PSF everywhere the same Make the PSF everywhere the same  Technique similar to that of image subtraction ( Tomaney & Crotts 1996, Alard & Lupton 1998, Alard 2000 )  Convolution kernel with a restricted number of degrees of freedom.  BUT: no unique reference image available!  One must define one. An isotropic Gaussian/Moffat-like function with the FWHM of the median seeing is a convenient choice Make the PSF everywhere the same Make the PSF everywhere the same  Technique similar to that of image subtraction ( Tomaney & Crotts 1996, Alard & Lupton 1998, Alard 2000 )  Convolution kernel with a restricted number of degrees of freedom.  BUT: no unique reference image available!  One must define one. An isotropic Gaussian/Moffat-like function with the FWHM of the median seeing is a convenient choice

April 2001 OPTICON workshop in Nice 9 At which stage of the pipeline must the PSF be homogenized? Image warping affects the PSF (and its variability). Image warping affects the PSF (and its variability). Re-projection to an equal-area grid corrects for flux distorsions produced by flat-fielding Re-projection to an equal-area grid corrects for flux distorsions produced by flat-fielding  PSF homogenization (adaptive kernel filtering) must be done AFTER image warping. Image warping affects the PSF (and its variability). Image warping affects the PSF (and its variability). Re-projection to an equal-area grid corrects for flux distorsions produced by flat-fielding Re-projection to an equal-area grid corrects for flux distorsions produced by flat-fielding  PSF homogenization (adaptive kernel filtering) must be done AFTER image warping.

April 2001 OPTICON workshop in Nice 10 Effects of flat-fielding on flux sensitivity

April 2001 OPTICON workshop in Nice 11 Consequences of PSF homogenization: the good PSF homogenization corrects for PSF anisotropy. PSF homogenization corrects for PSF anisotropy. PSF Homogenization removes the ambiguity of the definition of a star centroid for asymmetric PSFs : PSF Homogenization removes the ambiguity of the definition of a star centroid for asymmetric PSFs :  Astrometric calibration still needed, but it does not need to be more accurate than, say, a fraction of the stellar FWHM.  Fine “tuning” of astrometric centering is taken care of by the variable PSF-correction. PSF homogenization can include flux rescaling as a free parameter. PSF homogenization can include flux rescaling as a free parameter.  Provides a relative photometric calibration that can handle inhomogeneous sensitivity across the field. PSF homogenization corrects for PSF anisotropy. PSF homogenization corrects for PSF anisotropy. PSF Homogenization removes the ambiguity of the definition of a star centroid for asymmetric PSFs : PSF Homogenization removes the ambiguity of the definition of a star centroid for asymmetric PSFs :  Astrometric calibration still needed, but it does not need to be more accurate than, say, a fraction of the stellar FWHM.  Fine “tuning” of astrometric centering is taken care of by the variable PSF-correction. PSF homogenization can include flux rescaling as a free parameter. PSF homogenization can include flux rescaling as a free parameter.  Provides a relative photometric calibration that can handle inhomogeneous sensitivity across the field.

April 2001 OPTICON workshop in Nice 12 Consequences of PSF homogenization: the bad PSF Homogenization is a linear and (locally) shift- invariant process: PSF Homogenization is a linear and (locally) shift- invariant process:  Image artifacts will spread beyond the masked areas  Prior interpolation of image defects might be necessary  Objects that touch the frame boundaries must be excluded  Correlation at the PSF scale will be introduced in the noise.  Will one have to use “correlation-maps” for optimum detection, or will the variations of the noise correlation function be negligible in “reasonable” cases?  The next generation of source extraction software must be able to measure and make extensive use of the (background) noise correlation function. PSF Homogenization is a linear and (locally) shift- invariant process: PSF Homogenization is a linear and (locally) shift- invariant process:  Image artifacts will spread beyond the masked areas  Prior interpolation of image defects might be necessary  Objects that touch the frame boundaries must be excluded  Correlation at the PSF scale will be introduced in the noise.  Will one have to use “correlation-maps” for optimum detection, or will the variations of the noise correlation function be negligible in “reasonable” cases?  The next generation of source extraction software must be able to measure and make extensive use of the (background) noise correlation function.

April 2001 OPTICON workshop in Nice 13 PSF homogenization as seen in Fourier space (1D) Moffat PSFs with FWHMs 0.6” and 0.9” (pixel size=0.18”)

April 2001 OPTICON workshop in Nice 14 PSF homogenization as seen in Fourier space (2D) Example of a 2D kernel MTF to “convert” 0.9” FWHM images to 0.75” FWHM

April 2001 OPTICON workshop in Nice 15 PSF-homogenization: how does it look like? Originally 0.6” Originally 0.9”

April 2001 OPTICON workshop in Nice 16 ConclusionConclusion Awaits implementation in SWarp Awaits implementation in SWarp  Major undertaking:  Speed issues  Robustness in “empty” regions  Astrometric fine-tuning issue  Photometric “anchors” must be specified  Adequacy for critical scientific analyses like weak gravitational lensing measurements needs to be assessed! Awaits implementation in SWarp Awaits implementation in SWarp  Major undertaking:  Speed issues  Robustness in “empty” regions  Astrometric fine-tuning issue  Photometric “anchors” must be specified  Adequacy for critical scientific analyses like weak gravitational lensing measurements needs to be assessed!