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Telescope pointing models

Telescope pointing models. Gregor project meeting AIP, 14 th /15 th Oct, 2010. T. Granzer. What is it for?. Describes miss-alignments in the two principal telescope axis, alt-az or ra-de etc.. Used to improve initial pointing ( RMS point  1")

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Telescope pointing models

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  1. Telescope pointing models Gregor project meeting AIP, 14th/15th Oct, 2010 T. Granzer

  2. What is it for? • Describes miss-alignments in the two principal telescope axis, alt-az or ra-de etc.. • Used to improve initial pointing (RMSpoint 1") • Improves open-loop tracking (RMStrack 1"/h)

  3. Classic pointing model 7-parameter model, follows from pure spherical trigonometry of an imperfectly aligned telescope: (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

  4. Tracking relevance Differentiate with respect to time: (five parameter classic, only two parallactic: ) Use open-loop tracking errors instead of pointing offset, will of course result in different values for the parameters

  5. Quality limits Basis functions in classic model not orthogonal, i.e. , in particular Will lead to high correlation between NPAE and BNP

  6. Quality limits (cont’d) Reach orthogonality with constant terms by parameter normalisation: Replace ai: e.g. Allows for quality assessment of the PM solution by calculating the correlation coefficients and the condition number.

  7. Or: pure harmonic model Use complete set of orthogonal polynomials on the sphere (better hemisphere): Ylm… spherical harmonics Guarantees orthonormality (+quality assessment!): … but may require lots of parameters

  8. Often used: mixed models Classic plus low-order terms of harmonic model e.g.

  9. 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° ? • Hysteresis?

  10. Deriving Tile the sky in equal-sized tiles, acquire (bright) stars and measure offset, least square fits. From 18th Feb to 17th March 2007, we obtained 28 pointing models, each with N 500

  11. Classic model An f(3az) correlation visible

  12. Harmonic model (h>20°) • l=2 (9 constants) bad in az, in alt as good as classic • Problem: rapid increase in parameters for high l • l=6(az), l=5(alt), 22 constants RMS<2”

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

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

  15. Covariance Decreasing covariance in NPAE and BNP measures quality of fit

  16. RMS comparison • Classic model sufficient, if RMS10” • Harmonic model fit well, but requires many measures • Mixed good compromise

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

  18. Bootstrapping analysis …gives a good hint on quality

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

  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 possible, but may be a simple time drift (sagging of telescope). • Pointing model can be checked during normal observations. • …but use of science observations may introduce bias.

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