Telescope pointing models Telescope Instrumentation Robotisation on Dome

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

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

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

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

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

Quality requisitions Distribution of stars on hemisphere important Øsingular point at E=90° for Alt/az mounts, =90° for parallactic mounts ØTube flexure: h->0 Ø'Wrap around' Az>360° ?

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

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

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

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

RMS (classic model) ØAltitude axis less than azimuth Ø…but no influence of N

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

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

Harmonic model (l=2) Øl=2 (9 constants) bad in az, in alt as good as classic ØProblem: rapid increase in parameters for high l

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

Mixed model Include f(3 az), Y 11, Y 1 -1 ØIn az, an f(2 az) might still be present ØNo systematic in alt clearly detectable.

RMS extended ØHarmonic model good in alt ØExtended model down to 1"

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

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