The PSF homogenization problem in large imaging surveys

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The PSF homogenization problem in large imaging
surveys

• Emmanuel BERTIN (TERAPIX)

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PSF Variations

• From exposure to exposure
• Seeing changes
• Defocusing, jittering, tracking errors
• Pupil rotation (alt-az telescopes)
• Within the field
• Optical aberrations
• Charge transfer problems on some CCDs

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Co-adding images with different PSFs

• 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 10RMS.
• The distribution of seeing FWHM has a positive
  skewness

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Seeing FWHM distributions in the optical (I band)
EIS-Wide (NTT)
VIRMOS (CFHT)
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Seeing FWHM variations during the night
2MASS Jarrett et al. 2000
SDSS Yasuda et al. 2001
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Co-adding images with different seeing

• 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. 1999) affected

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Co-adding images with different seeing 2

• 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

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Homogenizing the PSF?

• 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

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

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

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Effects of flat-fielding on flux sensitivity
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Consequences of PSF homogenization the good

• PSF homogenization corrects for PSF anisotropy.
• 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.
• Provides a relative photometric calibration that
  can handle inhomogeneous sensitivity across the
  field.

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Consequences of PSF homogenization the bad

• 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.

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PSF homogenization as seen in Fourier space (1D)
Moffat PSFs with FWHMs 0.6 and 0.9 (pixel
size0.18)
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PSF homogenization as seen in Fourier space (2D)
Example of a 2D kernel MTF to convert 0.9 FWHM
images to 0.75 FWHM
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PSF-homogenization how does it look like?
Originally 0.6
Originally 0.9
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Conclusion

• 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!