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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 Gregor project meeting AIP, 14th/15th 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 (RMSpoint 1") • Improves open-loop tracking (RMStrack 1"/h)
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
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
Quality limits Basis functions in classic model not orthogonal, i.e. , in particular Will lead to high correlation between NPAE and BNP
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.
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
Often used: mixed models Classic plus low-order terms of harmonic model e.g.
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?
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
Classic model An f(3az) correlation visible
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”
Mixed model Include f(3az), Y11, Y1-1 • In az, an f(2az) might still be present • No systematic in alt clearly detectable.
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)
Covariance Decreasing covariance in NPAE and BNP measures quality of fit
RMS comparison • Classic model sufficient, if RMS10” • Harmonic model fit well, but requires many measures • Mixed good compromise
Bootstrap From model, on parameters, RMS Classic bootstrap: Duplication of measures, fit several times, variance of solution
Bootstrapping analysis …gives a good hint on quality
Bootstrapping vs. N bootstrapping 's better correlated to N then RMS
Temperature Dependency Temperature span limited (10°) Temperature drift in AN,E (tilt of telescope az)
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.