1. General Features of Fitting Methods
Systematics in shape measurement: the PSF calibration
Paulin-Henriksson Stéphane, Voigt Lisa, Amara Adam, Bridle Sarah, Réfrégier Alexandre
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA

2. Systematics in shape measurement Several sources of systematics
non gaussianity of shape estimators
finite accuracy of the PSF estimation
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA

3. Systematics in shape measurement non gaussianity of shape estimators
Example with the ellipticity of horizontal exponential galaxies: a b
Set-up of this simulation:
a=2 pixels ; b=1 pixel
==> =1/3, rg   2.4 pixels
signal-to-noise ratio of PSF-convolved galaxies constant  60 (gaussian background noise)
centroid uniformly distributed inside the central pixel
fit (2 minimisation) with the true model
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA

4. (way too small for final conclusions)
Ntot  500
(way too small for final conclusions)
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA

5. skewness, likelihood < 5%
<1>=0.3244
true value: =1/3
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA
skewness, likelihood < 5%

6. Systematics in shape measurement non gaussianity of shape estimators
To be done:
increase the statistics
go through the preliminary conclusion: non-gaussianity increases with the SNR
. what are the effects of pixelisation ?
--> Preliminary conclusions: pixelisation makes the deconvolution noisier (obvious) AND increases the non-gaussianity.
--> Will probably lead to a lower limit on the pixel size.
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA

7. Systematics in shape measurement Several sources of systematics
non gaussianity of shape estimators
finite accuracy of the PSF estimation
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA

8. Systematics in shape measurement accuracy of the PSF estimation
The PSF is estimated at the position of the galaxy with a limited accuracy
stars *
galaxy to be deconvolved
area on which the PSF is interpolated
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA
Dilution factor

9. Systematics in shape measurement accuracy of the PSF estimation
The accuracy of the PSF estimation is limited by:
1. limited accuracy of the star shape measurements:
each star is a noisy and pixelised realisation of the PSF
2. PSF variations with the position:
necessary to introduce an interpolation scheme
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA

10. Systematics in shape measurement accuracy of the PSF estimation
The accuracy of the PSF estimation is limited by:
1. limited accuracy of the star shape measurements:
each star is a noisy and pixelised realisation of the PSF
2. PSF variations with the position:
necessary to introduce an interpolation scheme
In the following I am always in the ideal case where the PSF is perfectly stable. Then I study the accuracy of the PSF calibration according to: the SNR of stars, the PSF model and the number of stars. Then I address the issue of pixelisation effects
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA

11. Accuracy of the PSF estimation fitting a gaussian with a gaussian
Very simple case with a gaussian PSF: a b
Shape parameters are analytically predicted (in the case of infinitely small pixels) and verified by a simulation:
a is variable and rule the size
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA

12. ||< est. > -  10-2 10-3 10-4 SNR 10-120
SNR 50
100
150
10-1
(<est. R2> - R2)/R2
10-3
10-5
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA

13. []/0.70 10-1 10-2 SNR [R2]/(2.58a2) 10-1 10-2 10 50 100 500 1000
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA

14. Accuracy of the PSF estimation: the choice of the PSF model
Intuitively, we see that the PSF modeling is a compromise:
a too poor model is unrealistic. It is unable to mimic the real PSF ==> the estimated PSF shape is biased
a too rich model is noisy ==> the estimated PSF shape is noisy
==> necessary to use a model complex enough to mimic the PSF but as simple as possible
The optimal compromise depends on the data set. But we can look for arguments leading to this compromise.
The following is an answer to point 2: we study what are the errors on PSF shape parameters according to the PSF model
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA

15. To look through this, shapelets are very convenient
Truncation of high
spatial frequencies 8 6 4 2 -2 -4 -6 -8
What are the errors on PSF shape parameters according to the PSF model ?
To look through this, shapelets are very convenient M
M=+-2 functions rule the ellipticity
M=0 functions rule the total flux
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA N

16. M simulation: N A given basis has an
Truncation of high
spatial frequencies 8 6 4 2 -2 -4 -6 -8
A given basis has an
effective number of coefficients Np for each shape parameter. The question is in fact: How does a shape parameter measurement depend on Np ? M
simulation:
of stars from SpaceSTEP in various bases
with various SNR (gaussian backg.)
in each basis, stars are simulated and then fitted (2 minimisation)
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA N

17. [R] [] Np[] Np[R] SNR = 50 SNR = 200 SNR = 800
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA

18. Systematics in shape measurement accuracy of the PSF fitting
for<0.1 and SNR>50
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA

19. Systematics in shape measurement accuracy of the PSF fitting
Accuracy of the PSF calibration according to the number of stars (used to compute the calibration)
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA

20. Systematics in shape measurement accuracy of the PSF fitting
For bright stars (SNR typically > 50) and good conditions,
it is possible to invert the previous equations and give the minimum number of stars required to achieve a given precision
Nb of efficient coefficients in the PSF model
dilution factor
SNR of *
scientific requirement
Power (of 3 to 6) depending on the shape parameter
Stéphane Paulin-Henriksson / CEA-Paris --- STEP meeting 20/08/07 / JPL-LA
[Paulin-Henriksson et al., en préparation]