Exploitation of Corot images

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Exploitation of Corot images

• Leonardo Pinheiro
• 3/Nov/05, Ubatuba

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Scientific data (overview)

• Sismology
• 5 stars per CCD
• aperture photometry evaluated on-board(every
  second)
• 35x35 imagesaccumulated on-board(every 8, 16 or
  32s)

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Scientific data (overview)

• Exoplanets
• 6000 stars per CCD
• aperture photometry evaluated on-board(every 32s
  or accumulated over 512s)
• 10x15 imagesfor a few targets(every 32 seconds)

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Interest of Corot star images

• More sophisticated photometry algorithms
• lower sensitivity to periodic perturbations
  (stray light, defocus, etc..)
• robustness to radiation (mainly p)
• robustness to degraded performances (depointing,
  etc..)
• better random noise level, if possible
• Much more data, much more possibilities of
  reduction..

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Exploitation of star images

• Classic algorithms after image processing
• pre-processing aperture photometry
• pre-processing threshold photometry
• PSF fitting photometry
• Combined photometry
• fitting aperture
• fitting threshold

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Candidate PSF models for fitting

• Analytical functions
• Gaussian
• Moffat
• Empirical PSFs
• Simulated PSFs

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Image acquisition

• Corot PSFs are aliased when sampled at the pixel
  size
• acquired images are thus dependent on their
  relative position with respect to the pixel
  lattice
• images are not directly exploitable on PSF
  fitting

acquired data
projected image
cubic interpolation
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Fitting results according to PSF model
Ideal PSF fits perfectly no matter the
start-point
photon noise for mv 6
Aliased PSF leads to fluctuations in response to
attitude jitter
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Image formation (sismo side)
attitude jitter
spatial sampling
How to derive anempirical PSF forfitting
photometry?
projected image
. . .
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Image formation model

• For K acquisitions Yk of an image X, we have
• Yk D.Wk.X nk k 1, 2, .. K
• - D is the spatial sampling operator (CCD
  characteristics)
• - Wk represents the geometric transformations
  (satellite attitude)
• - n is the acquisition noise (Poisson
  readout)

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Model inversion

• Yk D.Wk.X nk k 1, 2, .. K
• The best estimate in a least-square basis can be
  expressed by
• Xest argminX ? Yk DkWkXT Yk DkWkX
  ,

• whose solution by gradient-descent, after
  regularization, is
• Xj1 Xj µ ? WkTDT Yk WkTDTDWkß CTC
  Xj
• - C is any operator designed to penalize
  high-fequencies in Xj
• - µ, ß are the convergence step and a
  regularization parameter

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Reconstruction results
( attitude data)
attitude jitter
spatial sampling
projected image
rebuild image
. . .
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Fitting results w/ reconstructed PSFs
(mv6)
1x
2x
4x
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Fitting results w/ reconstructed PSFs

• White noise for 4 different models

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Conclusions

• PSF reconstruction from seems possible
• enabling the use of fitting algorithms
• and many other applications
• Reconstruction and fitting algorithms have been
  validated on a complete data set from Most space
  telescope

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Thank you!