Calibration of coalignment in FESTIVAL

Updated 4 August 2007 - Frédéric Auchère

Stars are used to investigate the accuracy of the mapping engine of FESTIVAL and the coalignment of the coronagraphs on board SOHO and STEREO.

Each visualization GUIs in FESTIVAL provides a reference frame that can be used to calibrate the accuracy of the absolute positioning of the images on the sky. Once the mapping engine of FESTIVAL is validated, the software can be used as a tool for investigating the alignment and/or co-alignment of instruments. The visualization GUIs are designed to display projected views of the sky. These view can contain both imaging data (e.g. SECCHI images) and vectorial overlays (e.g. lines, polygons). A vectorial overlay can be used to display a set of polygons representing stars. FESTIVAL uses two possible frames of reference called Heliocentric Ecliptic North Up (HENU) and Heliocentric Solar North Up (HSNU). The Z axis is Sun centered, the X axis is pointing towards either ecliptic north or solar north, and the Y axis is completing a right handed orthogonal coordinate system. Knowing the position of the stars, the orientation of the ecliptic plane, the orientation of the solar equator and the position of the spacecraft in a common system of coordinates, it is possible to compute the position of the stars in the two frames of reference used by FESTIVAL and to display them on top of SECCHI or SOHO data for comparison. We have done this for SOHO/C2 and C3, and for SECCHI/COR2, HI1 and HI2 (A & B spacecraft).

Stars

For the position of stars, we used the Hipparcos catalogue (Turon et al., 1993). The Hipparcos catalogue contains 118218 entries, is complete down to visual magnitude 7 (15405 stars) and includes stars down to magnitude 14. The position of stars are given in the International Celestial Reference System (ICRS) for epoch J1991.25. The axes of the ICRS are consistent within 0.1 arcsecond with the J2000.0 equatorial celestial coordinates. For our application, we do not distinguish between the two systems. The proper motion of stars in right ascension and declination is used to compute their position at epoch J2000.0. The position of the spacecraft (SOHO or STEREO) are known in the J2000.0 Heliocentric Aries Ecliptic system. For STEREO, this information is listed in the FITS header, while for SOHO it is read in the orbit files via the GET_ORBIT IDL function. In J2000.0, the solar rotation axis has equatorial celestial coordinates (a = +286.11°, d =+63.85°) and the inclination of the ecliptic is 23.4392911°. With these parameters, the positions of the stars are computed in one of the two possible frames of reference (HENU or HSNU). Note that annual aberration is not taken into account. However, this effect is small (30 arcseconds at most for an observer on the Earth), and since the frames of reference of FESTIVAL are Sun centered, the aberration of the Sun should be subtracted. The final correction should be minute.

Data calibration

The data are calibrated using SECCHI_PREP for SECCHI data, and LASCO_PREP (a FESTIVAL routine) for LASCO data. LASCO_PREP calls GET_SUN_CENTER to get the position of the Sun in the images and the roll angle. The optical distortion in LASCO is taken into account using the distortion parameters listed in the DISTORTION_COEFFS program. The optical distortion in HI1 and HI2 is taken into account using the distortion parameters listed in the FITS headers. For SECCHI data, FESTIVAL uses the nominal pointing and roll angle information contained in the CRVAL1, CRVAL2 and CROTA fields of the FITS headers.

Results

We presents preliminary results for the comparison between the theoretical and observed position of stars. We used stars down to visual magnitude 6. The alignment of LASCO data was checked for about 20 dates between December 2006 and January 2007 (date of last available non-quicklook data). Figures 1a and b shows representative images for January 2007. The images are displayed in the HSNU coordinate system. Figure 1a shows the composite image created by FESTIVAL. We superimposed a Carrington grid to materialize the position of the Sun. Figure 1b is the same with red stars overlayed (click on the small image to open he full size images). Overall, the match between computed and observed stars is within one pixel in both C2 and C3. C3 may be positioned systematically about one pixel southward. There seems also to be a systematic radial error at the very edge of the C3 field of view, the observed stars being about two pixels outwards compared to the computed position. This could be due to an error in the C3 distortion parameters. This has to be investigated.

This series of test shows that, except at the outer edge of C3 where there may be some residual optical distortion, the absolute positioning of LASCO C2 and C3 data is accurate to within about 1 pixel, i.e. 11.9 arcseconds for C2 and 56.0 arcseconds for C3. The origin of this possible discrepancy has to be investigated.

We performed similar tests on SECCHI COR2, HI1 and HI2 data taken between 15 March 2007 and 15 august 2007. According to the previous results, we could expect FESTIVAL to be able to position SECCHI data to within a pixel of the theoretical star positions. As can be seen in Figures 2a, 3a, 4a and 5a, the nominal positioning of SECCHI data is off by several arcminutes in all telescopes (HI1A, HI2A, HI1B and HI2B respectively), and the amplitude and direction of the roll/shift varies through the mission. We will discuss the case of COR2 later. We tried to visually match the theoretical star fields by applying correction angles in a system of coordinates fixed to the instrument's detectors. The Z axis of this system is along the optical axis, the X axis points towards the top of the detector, and the Y axis completes a right handed orthogonal coordinate system. We found that we could match the theoretical star fields to within about 1 or 2 pixels for most data taken between 15 March and 15 August 2007 by applying the following rotations to the images:

Corrected images for mid-august 2007 are shown Figure 2b, 3b, 4b and 5b for HI1A, HI2A, HI1B and HI2B respectively. Sorry, the date do not correspond exactly to those of the uncorrected images of Figures 2a, 3a, 4a and 5a. We estimate the accuracy of this visual method to be around 0.05° in roll (around Z) and 0.02° for the two other angles. Of course, considering the size of stars in HI2B, the estimate is very crude. We tried to match the brightest area of the spots. The correction angles are constant for the data that we analyzed, except for some data (mostly HI2A) that seem to present erratic displacements.

We could not find a set of angles to match the star fields in the COR2 A & B images. We could find a roll angle around Z so that two triangles formed by observed and computed stars have their edges parallel, but then no rotation around X or Y could make the vertex match. We list in table 1 the roll angles estimated for COR2 A & B.

We did not perform similar tests for COR1.

Figure 1a. C2/C3. No stars overlayed. SOHO/C2 : 1-Jan-2007 00:06:05 SOHO/C3 : 1-Jan-2007 00:18:05	Figure 1b. Same as 1a with stars. SOHO/C2 : 1-Jan-2007 00:06:05 SOHO/C3 : 1-Jan-2007 00:18:05
Figure 2a. SECCHI HI1A 16-Aug-2007 21:47:59	Figure 2b. SECCHI HI1A 16-Aug-2007 21:48:59
Figure 3a. SECCHI HI2A 16-Aug-2007 22:19:00	Figure 3b. SECCHI HI2A 16-Aug-2007 22:21:00
Figure 4a. SECCHI HI1B 14-Aug-2007 00:08:04	Figure 4b. SECCHI HI1B 14-Aug-2007 14:53:04
Figure 5a. SECCHI HI2B 16-Aug-2007 00:09:03	Figure 5b. SECCHI HI2B 15-Aug-2007 00:09:03

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