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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
Telescope pointing models

Telescope & Instrumentation Robotisation on Dome C

Puerto Santiago, Tenerife

T. Granzer

classic pointing model
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

pure harmonic model
Pure harmonic model

Use complete set of orthogonal polynomials on the sphere:

Ylm… spherical harmonics

mixed models
Mixed models:

Classic plus low-order terms of harmonic model


Use open-loop tracking errors instead of pointing offset

(five parameter classic)

Will result in a different parameter set.

quality requisitions
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° ?
quality limits
Quality limits

Parameter correlation in classic model:

Will lead to high correlation between NPAE and BNP

quality limits1
Quality limits

Parameter normalisation:

Replace alm:

to avoid correlation with constant terms


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


High correlation on BNP and NPAE

AN,E (az) 

AN,E (alt)


High correlation on BNP and NPAE

AN,E (az) 

AN,E (alt)

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

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


From model,  on parameters, RMS

Classic bootstrap: Duplication of measures, fit several times, variance of solution

bootstrapping analysis
Bootstrapping analysis

…gives a good hint on quality

bootstrapping vs n
Bootstrapping vs. N

bootstrapping 's better correlated to N then RMS

harmonic model l 2
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
higher order models
Higher-order models:

An f(3az) correlation visible

mixed model
Mixed model


f(3az), Y11, Y1-1

  • In az, an f(2az) might still be present
  • No systematic in alt clearly detectable.
rms extended
RMS extended
  • Harmonic model good in alt
  • Extended model down to 1"
temperature dependency
Temperature Dependency

Temperature span limited (10°)

Temperature drift in AN,E (tilt of telescope az)

  • 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.