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Telescope pointing models

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

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Telescope pointing models

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

  2. Classic pointing model 7-parameter model (alt/az mount): AN,AE… tilt of az-axis against N,E NPAE… non-perpendicularity of alt to az axis BNP… non-perpendicularity of opt. axis to alt axis TF… tube flexure

  3. Pure harmonic model Use complete set of orthogonal polynomials on the sphere: Ylm… spherical harmonics

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

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

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

  7. Quality limits Parameter correlation in classic model: Will lead to high correlation between NPAE and BNP

  8. Quality limits Parameter normalisation: Replace alm: to avoid correlation with constant terms

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

  10. High correlation on BNP and NPAE AN,E (az)  AN,E (alt) Results High correlation on BNP and NPAE AN,E (az)  AN,E (alt)

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

  12. Covariance ….but decreasing covariance in NPAE and BNP measures quality of fit

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

  14. Bootstrapping analysis …gives a good hint on quality

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

  16. 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

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

  18. Mixed model Include f(3az), Y11, Y1-1 • In az, an f(2az) might still be present • No systematic in alt clearly detectable.

  19. RMS extended • Harmonic model good in alt • Extended model down to 1"

  20. Temperature Dependency Temperature span limited (10°) Temperature drift in AN,E (tilt of telescope az)

  21. 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.

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