1. Telescope pointing models Telescope & Instrumentation Robotisation on Dome C Puerto Santiago, Tenerife T. Granzer

2. What is it for?  Describes miss-alignments in the two principal telescope axis.  Used to improve pointing ( RMS point  1")  Improves open-loop tracking ( RMS track  1"/h)

3. Classic pointing model 7-parameter model (alt/az mount): A N,A E … tilt of az -axis against N,E N PAE … non-perpendicularity of alt to az axis B NP … non-perpendicularity of opt. axis to alt axis T F …tube flexure

4. Pure harmonic model Use complete set of orthogonal polynomials on the sphere: Y lm … spherical harmonics

5. Mixed models: Classic plus low-order terms of harmonic model

6. Tracking Use open-loop tracking errors instead of pointing offset Will result in a different parameter set. (five parameter classic)

7. Quality requisitions  singular point at E=90° for Alt/az mounts,  =90° for parallactic mounts  Tube flexure: h->0  'Wrap around' Az>360° ? Distribution of stars on hemisphere important

8. Quality limits Parameter correlation in classic model: Will lead to high correlation between N PAE and B NP

9. Quality limits Parameter normalisation: Replace a lm : to avoid correlation with constant terms

10. Deriving Tile the sky in equal-sized tiles, acquire (bright) stars and measure offset, least square fits. From 18 th Feb to 17 th March, we obtained 28 pointing models, each with N  500

11. Results High correlation on B NP and N PAE A N,E (az)  A N,E (alt) A N,E (az)  A N,E (alt)

12. RMS (classic model)  Altitude axis less than azimuth  …but no influence of N

13. Covariance ….but decreasing covariance in N PAE and B NP measures quality of fit

14. Bootstrap From model,  on parameters, RMS Classic bootstrap: Duplication of measures, fit several times, variance of solution

15. Bootstrapping analysis …gives a good hint on quality

16. Bootstrapping vs. N bootstrapping  's better correlated to N then RMS

17. Harmonic model (l=2)  l=2 (9 constants) bad in az, in alt as good as classic  Problem: rapid increase in parameters for high l

18. Higher-order models: An f(3az) correlation visible

19. Mixed model Include f(3az), Y 11, Y 1-1  In az, an f(2az) might still be present  No systematic in alt clearly detectable.

20. RMS extended  Harmonic model good in alt  Extended model down to 1"

21. Temperature Dependency Temperature span limited (10°) Temperature drift in A N,E (tilt of telescope az)

22. Consequences  A stable mount is required for good pointing.  Temperature drifts in some parameters already on rocky grounds.  Drifts of the ice will not be completely plane-parallel and thus introduce drifts in the pointing model with time.  …but use of science observations may introduce bias.