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

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

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

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_2004-09-23T07.16.06.570Z_ID12_3610002002_F12 Filter: "Empty", "Red“; Exp Time: 600.0000

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_2004-09-23T08.11.06.598Z_ID10_3610005002_F22 Filter: "FFP-Vis", "Orange" Exp Time: 600.0000 Tridimensional plot of the same star after processing Sky background subtraction Normalization (total volume of solid equal to 1)

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_2004-09-23T07.16.06.570Z_ID12_3610002002_F12 Filter: "Empty", "Red“ Exp Time: 600.0000 Tridimensional plot of the same star after processing Sky background subtraction Normalization (total volume of solid equal to 1)

Possible analytical fits Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial Possible analytical fits GAUSSIAN WAC_2004-09-23T07.16.06.570Z_ID12_3610002002_F12 Filter: "Empty", "Red“; Exp Time: 600.0000

Possible analytical fits Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial Possible analytical fits LORENTZ WAC_2004-09-23T07.16.06.570Z_ID12_3610002002_F12 Filter: "Empty", "Red“; Exp Time: 600.0000

Possible analytical fits Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial Possible analytical fits SERSIC WAC_2004-09-23T07.16.06.570Z_ID12_3610002002_F12 Filter: "Empty", "Red“; Exp Time: 600.0000

Possible analytical fits Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial Possible analytical fits MOFFAT WAC_2004-09-23T07.16.06.570Z_ID12_3610002002_F12 Filter: "Empty", "Red“; Exp Time: 600.0000

Possible analytical fits Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial Possible analytical fits WAUSSIAN WAC_2004-09-23T07.16.06.570Z_ID12_3610002002_F12 Filter: "Empty", "Red“; Exp Time: 600.0000

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_2004-09-24T13.33.23.893Z_ID10_3610001002_F82 Filter: "Neutral", "Orange“; Exp Time: 0.0500; Target: Vega

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_2004-09-24T13.34.03.715Z_ID10_3610003002_F84 Filter: "Neutral", "Blue“; Exp Time: 0.0700

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_2004-09-24T13.34.03.715Z_ID10_3610003002_F84 Filter: "Neutral", "Blue“; Exp Time: 0.0700

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_2004-09-23T08.11.06.598Z_ID10_3610005002_F22 Filter: "FFP-Vis", "Orange“; Exp Time: 600.0000

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_2004-09-23T08.11.06.598Z_ID10_3610005002_F22 Filter: "FFP-Vis", "Orange“; Exp Time: 600.0000

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_2004-09-23T08.11.06.598Z_ID10_3610005002_F22 Filter: "FFP-Vis", "Orange“; Exp Time: 600.0000

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

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 0.00323331 Lorentz 0.00705940 Sersic 0.00778817 Moffat 0.00256934 Waussian 0.00705920 NAC_2004-09-24T13.33.23.893Z_ID10_3610001002_F82 Filter: "Neutral", "Orange“ Exp Time 0.0500 Target Vega

Example of image analysis Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial Example of image analysis Image name: WAC_2004-09-15T21.26.33.613Z_ID10_3610017002_F12 Filter: "Empty", "Red“; Exp Time: 60.0000 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 = 1.39 +/- 0.21 px Mean Moffat fit parameters f = a / (1+ (r/s)4) a = 0.397 +/- 0.082 s = 0.729 +/- 0.123

Example of image analysis Instituto de Astrofísica de Andalucía Instituto Nacional de Técnica Aerospacial Example of image analysis Image name: WAC_2004-09-15T21.26.33.613Z_ID10_3610017002_F12 Filter: "Empty", "Red“; Exp Time: 60.0000 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 = 1.39 +/- 0.21 px Mean Moffat fit parameters f = a / (1+ (r/s)4) a = 0.397 +/- 0.082 s = 0.729 +/- 0.123

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.