Imager reference frame flexure measurements

Using Polaris at an elevation of ~32°, the pixel location of TARF’s origin in the three imagers and their transformations to each of the other reference frames were determined and documented [Meyer 2005]. For measuring elevation dependencies, six different stars were brought successively in the field of view of the FPI and were located at the TARF origin. These six stars have large angular separations covering nearly the entire operational elevation range of the telescope. The telescope was moved several times between these six stars, mostly between stars with a large elevation difference. In total, sixteen motions between these stars were commanded, which cover the CD elevation range from approximately 23° to 60°. Figure 6.2 provides an overview of the test series showing the time dependent actual CD position in degrees, as an approximate measure of the elevation angle, and the identifier of the observed stars at this elevation. In addition, the star observations are numbered consecutively. Star chart sections with the six observed stars at begin and at the end of the test are shown in Figure 6.3 along with the horizontal coordinates Azimuth and Altitude (Appendix C.4.2). The altitude is the angle of the star above the horizon at the observatory location and at the observation time and corresponds approximately to the CD elevation angle of the telescope.

More details on the observatory location in Waco, TX and the conditions during the tests are described in [Harms 2005c].

Figure 6.2. Telescope elevation (CD angle) during star observations over observation time (local time in Waco: CDT) in the night from 02.-03.09.2004.

During the test, the observed stars are imaged in two of the three cameras: FPI and FFI, as well as in HIPO. The exposure time of HIPO was set to 0.5 seconds for Polaris, Beta Cephei, Alpha Cephei and Eta Cephei, and to 2 seconds for HIP47193 and Xi Cephei. The exposure times of the FPI and FFI were set to 2 seconds for the entire test series.

The HIPO centroid data was obtained using the center of mass algorithm described in section 4.3.1. Synchronizing the HIPO centroid data and the imager centroid data requires knowing the exact timing between the two systems. This can be done using the UTC timestamp which is recorded with the HIPO images and the TA housekeeping data using the EGSE (Electrical Ground Support Equipment). However, the UTC timestamp could not be extracted with the data recorded with the EGSE and the time difference to the local computer system time had to be read out manually causing imperfect correlation [Harms 2005b]. In addition, different sampling rates of HIPO and the imager centroid data required interpolation of the imager data to match the according HIPO timestamps.

Figure 6.3. Observed stars along with horizontal coordinates Azimuth and Altitude at start and end time of the test run. The Sky chart is produced using [Cartes du Ciel 2004].

The centroids obtained from the FPI and FFI are compared to those from HIPO by building their differences in EL and XEL, see Figure 6.4. The standard deviations are indicated as error bars at the mean values. It is measured that the boresight position in the FPI relative to that in HIPO changes about 1.1 arcsec in XEL for an elevation change from 23° to about 60°. The effect in elevation is less than 0.27 arcsec. The internal flexure of the HIPO focal plane and the SI flange assembly focal plane itself is measured to be about 0.3 arcsec each in EL and XEL [Haas 2005]. Finite element calculations predict much less flexure (about 0.1 arcsec) for the FPI [Herdt 1998b]. Over the same elevation range, the boresight of the FFI changes relative to that in HIPO by about 9 arcsec in XEL and about 8 arcsec in EL. The differential flexure measured in the FFI is significantly larger due to the fact that the FFI (like the WFI) is mounted on the metering structure and the FPI at the instrument flange. The FEM model predictions for the FFI (see section 3.4.1) are compared to the measurement data in Figure 6.4 and agree reasonably well. These results are very similar to the differential flexures measured between the FFI and the FPI, analyzed in [Meyer 2005]. Temperature effects were not considered during this first experiment series.

While the measurement was performed, the imager boresights were not aligned by means of alignment matrices. The alignment was performed manually by setting the SI boresight definition in the imagers to the measured TARF origin values in [Meyer 2005]. The TARF origin values were measured using Polaris at ~32° and differential flexure is assumed to be

2-Sep-2004 23:00:00 CDT 3-Sep-2004 01:00:00 CDT Polaris (Alpha UMi) Beta Cephei

Alpha Cephei Xi Cephei Eta Cephei

zero at that elevation. The data in Figure 6.4 suggests that there is still a small offset remaining between the measured TARF origin and the data used for the boresight definition.

-2.5 -2 -1.5 -1 -0.5 0 -0.5 0 0.5 1 1.5 2

ΔXELFPI-HIPO [arcsec]

Δ EL FP I-H IPO [ a rcse c] -4 -2 0 2 4 6 8 -14 -12 -10 -8 -6 -4 -2 0 ΔXELFFI-HIPO [arcsec]

Δ EL FF I- HIP O [a rcse c] Model FFI HIP47193 23° Polaris 32° Beta Cep 51° Xi Cep 57°

Alpha and Eta Cep 60°

20° 40°

60°

FPI Differential Flexure FFI Differential Flexure

Figure 6.4. Boresight changes of imagers relative to HIPO at the focal plane depending on the telescope’s elevation angle. The differential flexure for the FPI is shown in the left plot and for the FFI in the right plot.