Telescope pointing models

Telescope & Instrumentation Robotisation on Dome C

Puerto Santiago, Tenerife

T. Granzer

Classic pointing model

7-parameter model (alt/az mount):

ETAAAAEE

EBENEAAEAAAA

cossincos

sectantancostansin

FENoff

NPPAEENoff

AN,AE… tilt of az-axis against N,ENPAE… non-perpendicularity of alt to az axisBNP…non-perpendicularity of opt. axis to alt axisTF… tube flexure

Pure harmonic model

Use complete set of orthogonal polynomials on the sphere:

)EA,(

)EA,(

,lm

mllm

l,mlmlm

YEE

YAA

Ylm… spherical harmonics

Mixed models:

Classic plus low-order terms of harmonic model

0,0

,class

0,0

,class

)EA,(

)EA,(

ml

mllmlm

ml

mllmlm

YEEE

YAAA

Tracking

Use open-loop tracking errors instead of pointing offset

Will result in a different parameter set.

EE

EA

A

EE

EE

AA

A

AA

(five parameter classic)

Quality requisitions

singular point at E=90° for Alt/az mounts, =90° for parallactic mounts

Tube flexure: h->0

'Wrap around' Az>360° ?

Distribution of stars on hemisphere important

Quality limits

Parameter correlation in classic model:

2/fortantan1sec 2 EEEE

Will lead to high correlation between NPAE and BNP

Quality limits

Parameter normalisation:

Replace alm:

dEAfaa lmlmlm

2/

),(~

to avoid correlation with constant terms

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

Results

High correlation on BNP and NPAE

High correlation on BNP and NPAE

AN,E (az)

AN,E (alt)

AN,E (az)

AN,E (alt)

RMS (classic model)

Altitude axis less than azimuth

…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)

l=2 (9 constants) bad in az, in alt as good as classic

Problem: rapid increase in parameters for high l

Higher-order models:

An f(3az) correlation visible

Mixed model

Include f(3az), Y11, Y1-1

In az, an f(2az) might still be present

No systematic in alt clearly detectable.

RMS extended

Harmonic model good in alt

Extended model down to 1"

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 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.