1. Exploitation of Corot images Leonardo Pinheiro 3/Nov/05, Ubatuba

2. Scientific data (overview) Sismology 5 stars per CCD aperture photometry evaluated on-board (every second) 35x35 images accumulated on-board (every 8, 16 or 32s) E2 CCD A1CCD E1 CCD E2 CCD A2 Left Right E1 A1 A2

3. Scientific data (overview) Exoplanets ~6000 stars per CCD aperture photometry evaluated on-board (every 32s or accumulated over 512s) 10x15 images for a few targets (every 32 seconds) E2 CCD A1CCD E1 CCD E2 CCD A2 Left Right E1 A1 A2

4. 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..

5. 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 A rather accurate PSF model is required

6. Candidate PSF models for fitting Analytical functions Gaussian Moffat Empirical PSFs Simulated PSFs sismologyexoplanets

7. 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 dataprojected imagecubic interpolation

8. Fitting results according to PSF model Ideal PSF fits ‘perfectly’ no matter the start-point Aliased PSF leads to fluctuations in response to attitude jitter photon noise for m v = 6

9. ? Image formation (sismo side) projected image How to derive an empirical PSF for fitting photometry? attitude jitter spatial sampling......

10. Image formation model For K acquisitions Y k of an image X, we have: Y k = D.W k.X + n k k = {1, 2,.. K} - D is the spatial sampling operator (CCD characteristics) - W k represents the geometric transformations (satellite attitude) - n is the acquisition noise (Poisson + readout) geometric transformation spatial downsampling continuous image acquired image PSF, in this case optical deformation

11. Model inversion Y k = D.W k.X + n k k = {1, 2,.. K} The best estimate in a least-square basis can be expressed by: X est = argmin X {  [Y k – D k W k X] T [Y k – D k W k X] }, whose solution by gradient-descent, after regularization, is: X j+1 = X j + μ  [W k T D T ] Y k – [W k T D T DW k +ß C T C] X j - C is any operator designed to penalize high-fequencies in X j - μ, ß are the convergence step and a regularization parameter

12. Reconstruction results projected imagerebuild image attitude jitter spatial sampling (+ attitude data)......

13. Fitting results w/ reconstructed PSFs 1x 2x 4x (m v =6)

14. Fitting results w/ reconstructed PSFs White noise for 4 different models:

15. 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

16. Thank you!