Exploitation of Corot images

Leonardo Pinheiro3/Nov/05, Ubatuba

Scientific data (overview)

Sismology 5 stars per CCD aperture photometry evaluated on-board

(every second)

35x35 imagesaccumulated on-board(every 8, 16 or 32s) E2

CCD A1 CCD E1

CCD E2CCD A2

Left

Left

Right

Right

E1

A1

A2

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) E2

CCD A1 CCD E1

CCD E2CCD A2

Left

Left

Right

Right

E1

A1

A2

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..

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

Candidate PSF models for fitting

Analytical functions Gaussian Moffat

Empirical PSFs Simulated PSFs

sismology exoplanets

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

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

mv= 6

?

Image formation (sismo side)

projected image How to derive anempirical PSF for

fitting photometry?

attitudejitter

spatialsampling

.

.

.

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)

geometric transformati

on

spatialdownsamplin

g

continuous image

acquiredimage

PSF, in this case

opticaldeformati

on

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 – DkWkX]T [Yk – DkWkX] } ,

whose solution by gradient-descent, after regularization, is:

Xj+1 = Xj + μ [WkTDT ] Yk – [Wk

TDTDWk+ß CTC] Xj

- C is any operator designed to penalize high-fequencies in Xj

- μ, ß are the convergence step and a regularization parameter

Reconstruction results

projected image rebuild image

attitudejitter

spatialsampling

(+ attitude data)

.

.

.

Fitting results w/ reconstructed PSFs

1x

2x

4x

(mv=6)

Fitting results w/ reconstructed PSFs

White noise for 4 different models:

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

Thank you!