Telescope pointing models
description
Transcript of Telescope pointing models
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.