1. Instituto de Astrofísica de Andalucía
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
ANALYSIS OF PSF OF WIDE ANGLE CAMERA AND NARROW ANGLE CAMERA OF THE IMAGING INSTRUMENT OSIRIS FOR ROSETTA MISSION
22 February 2007
The IAA-INTA Team

2. Instituto de Astrofísica de Andalucía
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
Main Tasks
Comparison among analytical fits of the Point Spread Function (PSF) using different bidimensional profiles
Best fit for the curve wings (analysis for saturated stars)
Analysis of the residuals of the curve fit
Variation of curve fit parameters in the field of view
Variation of curve fit parameters due to time and temperature

3. Methodology Working on the images taken up today by NAC and WAC
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
Methodology
Working on the images taken up today by NAC and WAC
Assuming stars as point light sources
Plotting pixels values in tridimensional graphics
Operate an analytical fit with five different bidimensional curves: Gaussian, Lorentz, Sersic, Moffat, Waussian

4. Instituto de Astrofísica de Andalucía
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
What images look like
Full frame images (both of NAC and WAC) are 2048 x 2048 pixels size
WAC field of view is
12° x 12°
NAC field of view is
2.4° x 2.4°
WAC_ T Z_ID12_ _F12
Filter: "Empty", "Red“; Exp Time:

5. Plot of a star Tridimensional plot of the same star after processing
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
Plot of a star
a star in a NAC image
NAC_ T Z_ID10_ _F22
Filter: "FFP-Vis", "Orange"
Exp Time:
Tridimensional plot of the same star after processing
Sky background subtraction
Normalization (total volume of solid equal to 1)

6. Plot of a star Tridimensional plot of the same star after processing
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
Plot of a star
a star in a WAC image
WAC_ T Z_ID12_ _F12
Filter: "Empty", "Red“
Exp Time:
Tridimensional plot of the same star after processing
Sky background subtraction
Normalization (total volume of solid equal to 1)

7. Possible analytical fits
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
Possible analytical fits
GAUSSIAN
WAC_ T Z_ID12_ _F12
Filter: "Empty", "Red“; Exp Time:

8. Possible analytical fits
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
Possible analytical fits
LORENTZ
WAC_ T Z_ID12_ _F12
Filter: "Empty", "Red“; Exp Time:

9. Possible analytical fits
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
Possible analytical fits
SERSIC
WAC_ T Z_ID12_ _F12
Filter: "Empty", "Red“; Exp Time:

10. Possible analytical fits
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
Possible analytical fits
MOFFAT
WAC_ T Z_ID12_ _F12
Filter: "Empty", "Red“; Exp Time:

11. Possible analytical fits
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
Possible analytical fits
WAUSSIAN
WAC_ T Z_ID12_ _F12
Filter: "Empty", "Red“; Exp Time:

12. Onedimensional comparison of the fits
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
Onedimensional comparison of the fits 1. 2. 3. 4. 5.
1. Gaussian fit
2. Lorentz fit
3. Sersic fit
4. Moffat fit
5. Waussian fit
NAC_ T Z_ID10_ _F82
Filter: "Neutral", "Orange“; Exp Time: ; Target: Vega

13. Characteristics of the fit
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
Characteristics of the fit
Curves can be affected by asymmetry: the fit performed by our software allows the individuation of two main axes of an elliptic base
The fit allows the elliptic base to be rotated of an arbitrary angle (f) respect to the image coordinates
The fit is done with the values of the bidimensional integral of the curve over a pixel area
gaussian fit with function values
NAC_ T Z_ID10_ _F84
Filter: "Neutral", "Blue“; Exp Time:

14. Characteristics of the fit
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
Characteristics of the fit
Curves can be affected by asymmetry: the fit performed by our software allows the individuation of two main axes of an elliptic base
The fit allows the elliptic base to be rotated of an arbitrary angle (f) respect to the image coordinates
The fit is done with the values of the bidimensional integral of the curve over a pixel area
gaussian fit with values of function integral over the pixel
NAC_ T Z_ID10_ _F84
Filter: "Neutral", "Blue“; Exp Time:

15. Analysis of saturated stars
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
Analysis of saturated stars
Our software allows the analysis of saturated stars. This analysis is possible because during the fit process the contribution by bad (saturated) pixels can be ignored
In this case only the wings of the image of the star contribute to the fit process
gaussian fit affected by saturated pixels
NAC_ T Z_ID10_ _F22
Filter: "FFP-Vis", "Orange“; Exp Time:

16. Analysis of saturated stars
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
Analysis of saturated stars
Our software allows the analysis of saturated stars. This analysis is possible because during the fit process the contribution by bad (saturated) pixels can be ignored
In this case only the wings of the image of the star contribute to the fit process
gaussian fit not affected by saturated pixels
NAC_ T Z_ID10_ _F22
Filter: "FFP-Vis", "Orange“; Exp Time:

17. Best fit and residuals analysis
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
Best fit and residuals analysis
The value of residuals of the different curves gives information on the best fit
We are developing the possibility to make a map of the residuals in order to analyze if each pixel residual is higher than statistical pixel error. In this case a correction map would be useful to make the function fit better
Yellow = image values
Blue = best curve fit integral values
NAC_ T Z_ID10_ _F22
Filter: "FFP-Vis", "Orange“; Exp Time:

18. Instituto de Astrofísica de Andalucía
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
Preliminary Results
By now the software has been tested over a few images of the WAC and NAC
Our preliminary results
NAC PSF FWHM gaussian fit = 1.5 px
WAC PSF FWHM gaussian fit = 1.4 px
are consistent with previous calibration tests (Da Peppo et al., 2004)
Our analysis reveals that not always gaussian fit is the best one, in many cases other curves seemed to fit better. In the following example the comparison between gaussian fit and moffat fit revealed that moffat fit was better

19. Instituto de Astrofísica de Andalucía
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
Preliminary Results
Yellow = image values
Blue = gauss curve fit integral values
Yellow = image values
Red = waussian curve fit integral values
Residuals
Gaussian
Lorentz
Sersic
Moffat
Waussian
NAC_ T Z_ID10_ _F82
Filter: "Neutral", "Orange“
Exp Time
Target Vega

20. Example of image analysis
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
Example of image analysis
Image name: WAC_ T Z_ID10_ _F12
Filter: "Empty", "Red“; Exp Time:
Number of stars examined: 25
Number of sectors examined: 5
Best curve fit:
Moffat fit: 23 cases
Sersic fit: 2 cases (both in the central sector of the image)
Both Gaussian and Moffat fit analysis show:
No rotation dependence on the sector
No asymmetry dependence on the sector
Gaussian FWHM = / px
Mean Moffat fit parameters f = a / (1+ (r/s)4)
a = /
s = /

21. Example of image analysis
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
Example of image analysis
Image name: WAC_ T Z_ID10_ _F12
Filter: "Empty", "Red“; Exp Time:
Number of stars examined: 25
Number of sectors examined: 5
Best curve fit:
Moffat fit: 23 cases
Sersic fit: 2 cases (both in the central sector of the image)
Both Gaussian and Moffat fit analysis show:
No rotation dependence on the sector
No asymmetry dependence on the sector
Gaussian FWHM = / px
Mean Moffat fit parameters f = a / (1+ (r/s)4)
a = /
s = /

22. On work and future development
Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial
On work and future development
The software is being tested to
prove that it is working properly
We will analyze a significant number
of stars (also saturated stars) of WAC
and NAC images to evaluate the fit
parameters of the Point Spread Function
In particular we will check the consistence of fit parameters of PSF all over the field of view and we will look for any variation of them due to time and temperature
If residuals result significant compared with the noise, we will develop a numerical map for a better fit.