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TRANSCRIPT
Field and Pupil Rotationsfor the VLT
8m unit Telescopes
VLT Report No. 63
Contents
G. Avila K. Wirenstrand
May 2, 1991
1 Definitions and conventions 3
2 Field Rotation 42.1 At the Cassegrain and Nasmyth Foci . . . . . . . . . . . . . . .. 42.2 At the Coude and Combined Foci . . . . . . . . . . . . . . . . ., 5
3 Field Orientation at the Incoherent Combined Focus 8
4 Pupil rotation 94.1 At the Cassegrain and Nasmyth Foci . . . . . . . . . . . . . . .. 94.2 At the Coude and Combined Foci . . . . . . . . . . . . . . . . .. 9
VLT HBFüHT No 63
1 Definitions and conventions
The following definitions are assumed:
• a = altitude (measured zenithwards from the horizon)
• A = azimuth (measured westwards from the southpoint)
• h = hour angle
• </> = Paranallatitude = - 24° 37'
• 8 = deelination
• Wo = h= 15°/hr = sideral rate
• p = parallactie angle
3
• Figure 1 shows the eoordinate system eonvention for an altitude-azimuthteleseope mounting in the south hemisphere.
• Fea, FN and Fe = Field rotation at the Cassegrain, Nasmyth and Coude(Combined) foei respeetively.
• PN and Pe = Pupil Rotation at the Nasmyth and Coude (Combined) foeirespectively.
• DCa, DN and De = Pupil Rotation with respect to the Adapter at theCassegrain, Nasmyth and Coude (Combined) foei respeetively.
• Like the NTT, when the Teleseope Tube is pointing elose to the horizonand one stands up behind the mirror eell, the Platform A (Nasmyth foeusA) is to the left side and the Platform B (Nasmyth foeus B) to the right.
• Sign convention: angles are positives in the standard eountereloekwisedireetion and the observer is in front of the ineoming beam. The eonventionfor the zero angle for both the field and pupil is represented in the Figure 2,where A = 0° and a = 90°.
4 FfELD AND PUPfL ROTATIONS
2 Field Rotation
2.1 At the Cassegrain and Nasmyth Foci
The field rotation at the Cassegrain focus and on the Nasmyth platform as afunction of the hour angle and the declination is given by:
FCa - -pFCa - -pFCa - -pFN - p±aFN - p±äFN - p±ä
where the sign + corresponds to the Nasmyth B Platform and
tanpsin h
-tan 4J cos 6 - sin 6cos h
p cos 4JcosA-
Wo cosap sin Asin 24J sin a sin 2A cos2 4J
w2 - cos2 a2cosa0
sma - sin 6 sin 4J +cos 6 cos h cos 4Ja
- sin Acos 4J-Wo
a Aw2 - -- cos A cos 4J
0 Wo
tanAsinh
-cos h sin 4J - tan 6 cos 4J
Asin 4J + tan a cos A cos 4J-
Wo
These equations are valid for a telescope situated in the South Hemisphere according to the coordinates fixed in the Figure 1. Note that A is measured clockwisedirection.
I
There is also a sign change with respect to the equations for the North hemi-,sphere in the terms containing the azimuth coordinates. At North laltitudes, theazimuth angle is defined with respect to the Nort,h direction.
According to the mechanical limitations of the movement of the telescopetube, the computed values for the aItitude angle (a) were alwa~s s~aÜer' ~,han
• ~ l ~
, "
VLT BEFOBT No 63 5
90°. Also the inverse trigonometrie functions (p and A) were eomputed taking intoeonsideration the sign of quotients in order to find the right quadrant. In someeases, the angles in the seeond and third quadrants were defined with negativevalues in order to be eoherent with the field or pupil orientations illustrated onFigure 2.
A plot of sueh rotations are given in Figures 3 and 4. All the results wereobtained for Paranallatitude (where the VLT will be buHt). The blind point atthe zenith was speeified to be less than one degree. The curves with declinations8 = -24° 7' and -25° 7' show the two elosest values.
The sideral rate and its square are given by
Wo - 15 arcsec/s
w; - 1.091 X 10-3 arcsec/s2
The zero rotation reference point for the field and pupil is fully arbritrarYi thezero can be defined everywhere, only the set of curves have to be shifted upor down aeeordingly. The curves plotted here are defined in agreement to thereferenees shown in the Figure 2. The sky and pupil orientations are representedby the marks in the upper eases. The pupil is defined direetly by the M2 mirror.
When the teleseope is pointing to the zenith (a = 90°) and A = 0°, an observer(looking at the Cassegrain foeus with his head pointing to the North) will perceivethe field and pupil orientations as showed in the figure. The sky south directionas appears on the foeal plane is direeted to the upper point. This position definesthen the zero degrees. Finally the arrow on the drele shows the rotation positivedireetion.
At the Nasmyth platform B, the same observer will note that the sky's southdireetion points to his left. In this ease and by eonvention, the field is alreadyrotated of 90° respeet to the upper point. The pupil is also rotated and invertedas is represented in the same figure.
Table 1 shows the maximal velodties and aeeeierations of the field and pupilat the different fod.
2.2 At the Coude and Combined Foci
Figure 5 shows the Coude Beam set up. The mirror train from M4 to M8 doesnot modify the Nasmyth field rotation provided that all the mirrors lie on thesame plane. Indeed, this plane moves together with the telescope structure. Thelateral magnifieation between the Nasmyth foeus (after M4) and the Coude is+3.33. Therefore the rotation and orientation of the field at the Coude foeus inthe telescope structure frame is the same as for the folded Nasmyth one. On the
6 FIELD AND PupIL ROTATIONS
Table 1: Maximal velocitie5 and acceleration5
FIELD
Cassegrain Nasmyth Coude
Velocity ON 26.03 '/5 -26.03 '/5 -23.21 "/5HA = 0 HA = 0 HA = -6 hr
Os -26.08 '/5 26.08 '/5 -23.27 "/5HA = 0 HA = 0 HA = -6 hr
Acceleration ON 7.70 "/82 -7.77 "/8'J, 0.104 "/82
HA = -0.02 hr HA = -0.02 hr HA = 0Os 7.65 "/82 -7.72" /82 0.103 "/82
HA = 0.02 hr HA = 0.02 hr HA = 0
PUPIL
Velocity ON - 13.64 " /5 -26.15 '/5HA = -1.2 hr HA = -1.3x-4 hr
Os - 13.58 " /5 25.98 '/5HA = -1.2 hr HA = 2x-4 hr
Acceleration ON - -0.104 "/82 7.77 "/82
HA = 0 HA = 0.02 hrOs - -0.103 "/8'J, 7.72 "/8'J,
HA = 0 HA = -0.02 hrON = -24°7'Os = -25°7'HA = Hour Angle in hour5
VLT BEfOßT No 63 7
Earth frame (looking the image coming from M8 as is represented in the lowercase of the Figure 2), the rotation of the field is consequently given by:
Fe - -FN +A +90° = -P T a +A +90°
Fe - -PTä+ AFe - -PTä+ÄÄ 1 1w2 - - sin 2A cos2 </>(tan2 a + 2') - 2' tan a sin A sin 2</>
o
The sign - corresponds to the rotation generated by the coude train issued fromthe B Nasmyth focus.
Figure 6 gives some curves for different declinations. The two coude imagesgenerated by the two coude trains will out of phase of 2a.
At the Incoherent Combined Focus the field rotation velocity is the same asfor the Coude Focus. Indeed, all the mirrors composing the combined train arefixed on the Earth frame. However, the field orientation may be different fromone telescope to the other depending of the optical combined configuration.
8 FIELD AND PUPIL ROTATIONS
3 Field Orientation at the Incoherent Combined Focus
The main restrictions concerning the superposition of the fields generated by thefoUf telescopes are the field orientation and the scale factor which have to be thesame for the all beams. Therefore, in any Telescope array (linear or trapezoidal),the mirror train of each telescope must obey a number of logicallimitations:
1. All the Nasmyth foci must be the same.
2. The magnification factor of all mirror trains must be the same.
3. The design configuration of each train has to be the same for all Telescopes.
4. The mirror Mg that deflects the coude beam towards the combiner train andthe last mirror that send the exit beam to the combiner mirror must havethe same orientation. In other words, the normals to these two mirrors haveto be nearly parallel and lie in a vertical plane passing by the centers of themirrors. This restriction is illustrated in Figure 7 (the mirror configurationat the combined room is not fully defined yet).
Figure 8 shows the field orientation for an individual combined train. Theorientation at both the coude and the combined fod are represented by the crossarrow. In order to keep the same field orientation for any telescope configuration,the final image must stay fixed when the complete telescope moves along a circlecentered at the combined focus.
VLT REPORT No 63
4 Pupil rotation
9
4.1 At the Cassegrain and Nasmyth Fo~i
The seeondary mirror (M2) defines the entranee pupilj the zero referenee is definedas shown in Figure 2, in this ease, the teleseope points to the zenith, the azimuthangle is zero and the observer is looking the ineoming light. In the Cassegrainfoeus frame, the pupil of course does not rotate. However if an instrument ismounted on the Cassegrain adapter and this one is loeked to the field rotation,then the instrument will see the pupil rotate aeeording to:
DCa =p
On the Nasmyth platform frame, the pupil rotates following the altitude angle:
where the sign + eorresponds to the B adapter. Now, the field rotates followingthe equation FN , therefore the rotation of the pupil with respect to the adapteris given by:
DN=-p
It is the same relative rotation as for the Cassegrain adapter but in oppositedireetion (Figure 3).
4.2 At the Conde and Combined Foci
The pupil image at the folded Nasmyth foeus (below M4) has the same orientationas M2. Sinee the eoude train is a positive magnifieation projeetor, the pupilimage orientation at M8 remains the same. At this loeation, the pupil rotateswith respect to the Earth frame as
Pc = =Fa +A +90°
Onee again, the eonstant term is arbitrary and here is used to match the refereneezero point given in Figure 2. The sign - eorresponds to the direetion generatedby the B eoude train.
Finally, the differential rotation between the pupil and the image (eoudeadapter frame) is given again by:
Dc =p
In other words, beeause the azimuth angle is added to both the image and pupil,the differential rotation between them remains the same.
10 ......F..uIE....L.....D.....A~N~D.....P.....U"'_'"P.....L.u.L.....R....Q~T.....(\......T......I""'_Q.........NB
Table 2: Field and Pupil rotations for the VLT
Focus Field. Rotation Pupil Rotation P-F Rotation
Cassegrain -p 0 pNasmyth p±a ±a -pCoude -p =f a +A +90° =fa +A +90° pCombined l-p=fa+A+9001 l=f a +A +9ool Ipl
Figures 9 and 10 show the pupil rotations at the Nasmyth B platform and atthe Coude or Combined focus respectively.
Table 2 shows a summary of the different rotations.
References
1. K. Wirenstrand. ESO Technical Note, February 9, 1984.
2. J. Nelson. Geometrical Relations for an Altitude-Azimuth Telescope. UCTMT Report No. 49. December 1981.
3. The Astronomical Almanac.
z
N 5
Figure 1. Coordinate system convention for an altitude-azimuth mounting atthe South Hemisphere. 6 and <p are negatives in this schema.
Referel1ces
FIELD
Sky orientation
N
s
w
PUPIL
M2 mirror
Cassegrail1 view
A=Oa = 90°
N
1+
Nasmyth view(platform B)
A=Oa = 90°
N-+
Coude view*
A=Oa = 90°
N
1ö
+
* Same at combined focus but the orientation depel1ds of thecombined optical lay-out
Figure 2. Zero reference point for the field and pupil rotations at the differentfod.
-100 r- I -I I I I I , I I I I I
-3 -2 -1 0 1 2 3Hour angle (b)
I i I i I ( I ' I i I '[!]. I i I I I i I i I I I2
1........
0
3......... 03'-"
~..,.J.... -100......Q)
> -2
-3
t, I I I I I I I i I ,'bi. I i I I I i I i I ,~-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Hour angle
345 6
(a)
4 -250
5 -400
6 -850
1 300
2 00
3 -240
-6 -5 -4 -3 -2 -1 0 1 2Hour angle
-100
Figure 3. Field rotation at the Cassegrain Focus
a) Rotation.
b) Velocity. Wo = 15 arcsec/s.
c) Acceleration. w~ = 1.091 X 10-3 arcsec/S2.
300. I I • I 1 I • I • I • I I I I I I I I I I I I
100l
I I I I I I I I . I3 I -
r (200
50~ 11 31 -................0tlD 3Q)
.........-a 3'-"'-"s:: 100~ 00 ..,.J.- ......,.J 4 0ctl0..,.J ......0 Q)
-50 I- 11 4Q:: 0 > -
6I nn I
6000I
3 44- -NO NO
3 3000 3........... ........... 2- .-....,J .,J- -"3 3- -s:: 0 s:: 00 0.- .-.,J .,JltS ltSL.. L..cu ~-2-cu cu0-3000 00 0< <
-4
-6000-6
-1 -.8 -.6 -.4 -.2 0 .2 .4 .6 .8Hour angle
1
(e)
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6Hour angle
(b)4
-
-
-
-
I
3I
2
I -.- 1--'-'
I
I
I
4
3
I
1
-1 0 1Hour angle
I
I
-2
I
oI ( ~ I
-4 -3
. ,
3
f-
50~
100 I-
-100~
_ 2o
3
'- E ~ \ \ 6 d3 1 ~-
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~...,J
·ö 0o......(I)
> -1
~'öo......(I)
> -50 t-
o3'3-
(a)
5 6
4 -250
5 -400
6 -850
1 300
2 00
3 -240
-100I , I , I , I , I I I , I I I , I , I I I I I , I
-6 -5 -4 -3 -2 -1 0 1 2 3 4Hour angle
o
300
Figure 4. Field rotation at the Nasmyth Focus
on platform B.
a) Rotation.
b) Velocity. Wo = 15 arcsec/s.
c)Acceleration. w~ = 1.091 X 10-3 arcsec/s2•
~o:;:; 100«S
...,J
~
bD 200(I)
-a........
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6Hour angle
-1 -.8 -.6 -.4 -.2 0 .2 .4 .6 .8 1Hour angle
-6
4
s::0-2.-~
as....(IJ......(IJ -4oo<
_ 2N
-3..........
~ O~ c{6\/ >- 32 2 4.........
(c)-8
I I I I I I I I I I I I I I I I I I I I I I I I I
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6Hour angle
(c)
34
-6000
s:: 0 I E:::"'" I :;;. Io.-~
as....(IJ......(IJ
0-3000o<
3.........
6000
-~ 3000~.........
M3 1\llIlht====~=F==ff\'M4
Nasmythfocus
M6
Pupil foradaptive optics
M7 I~
Coude focus F/49.9
M5
f--2m--t
Figure 5. Optical Coude Beam setup
150~ 1 120
120 .. - 90........ ........bD bDQ) 90 Q)
"0 "0-.....; -.....;
s:: s:: 600 60 0.- .-+I +IctI Cd+I +I0
300 30~ ,\~2 ~ ~ (a)
~ ~
0 0
r3
~ I-30
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6Hour angle Hour angle
(a) 1 300
4 -250
12 0
05 -400
3 _2406 -850
.51 3 & 4
........0
;).......... 0;)-.....;
Figure 6. Field rotation at the Coude or Combined ~+I
-.5~1I -i (b)Foeus by way of B Nasmyth foeus. .-e>0..... 6a) Rotation. Q)
>b) Veloeity. Wo = 15 arcsec/s.
-1
e) Aeeeieration. w~ = 1.091 X 10-3 arcsec/s2•-1.5
b, I I I I I , , , I , I I , , I I I I I I I ,J-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Hour angle
co
UJ
~
M
N
Cl)
..... -tlOI::
o a:s
r........ =I~
NI
MI
~
I
UJI
CO
UJ N ~..... UJ 0 ~
J
N - I(
2°r?/(1),r?) u0!1tualaooy
..-0-
CX?
CO
~
~ Cl)-tlOI::
o a:s
r...=0~
~::x:I
.:dM ~
I
CL:!I
CX?0 UJ 0 UJ 0 I0 r- UJ N- (
2°r?/(1),r?) u0!1tl.Ialaooy
Mll
From M8
M9 M10
Same orientation ofmirrors M9 and M12
.. \r \
Ml2 Ml3
Coude room Combined room
Figure 7. Mirror train for the Combined Focus
Input fieldorientation
LM9
MII
MIO
W-E
MII
.! I, I, '
I
~AxiSbeam
Input fieldorientation
LM9
MIO
Cf)
IZ
~Output fieldorientation
of combined
Figure 8: Field Orientation for any Telescope Array
(b)
-1I I I I I I I I I I I , I , I I I , I I I I , I I
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6Hour angle
0-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Hour angle
(a)1 30
04 _250
2 00
5 -400
3 -2406 -850
80I / \
1
I
,
/A\I t""
I1::.---......2
\ 3 & 4
-bD60Q,)
.5
-02
'-"
s::
-0
0
3
.-.........
+.J
I
S40
3'-"
6
0~
1
~ 0+.J.....
~
()0-
I /1
Q,)
20, 6
:>-
/'\. ~ -.5
Figure 9. Pupil Rotation at the Nasmyth B platform.
a) Rotation, (b) Velocity (wo = 15 arcsec/s) and c) Acceleration.w~ = 1.091 x 10-3 arc8ec/82.
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6Hour angle
oc- <::::::::: --
.8(e)
.6.4
o
-IOD' « I , I I I I I I f I I I I I I
-.8 -.6 -.4 -.2 0 .2Hour angle
-20-.5,-" ,-"N
NO03 3
"'- "'-........ ........~ ~-- -- -13 -40 3-- --r:: r::0 0:;:; :;:;(lj (lj -1.5r.. -60 3 & 4 r..(I) (I)- -(I) (I)(J (J(J (J~ «
-80
I,
I,
I,
I,
I
100 I- I -300~~~ J
sol4
- - 11 -tIO 0
3Cl)200 ""t1- 3-s::
~ 00.- ~
~ .-cd 100 ()
~ 6 00 .....
Cl)D:: > -501- l! -J
0 5
-lOGt3
I ~
-IOD' I I I [ , f I I , t , I , f • I I [ I I , I , f , r , I , r . I I I
-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -3 -2 -1 0 1 2 3(b)Hour angle Hour angle
(a)
1 300 4 -250 3
2 00 5 -400
3 -240 6 -850 2
-03 1"Figure 10. Pupil Rotation at the Coude or Combined 3--
Focus by way of the Nasmyth B focus. ~ 0~.-(,)a) Rotation. 0.....
Cl)
(b) Velocity. Wo = 15 a·rcsec/s. > -1
c) Acceleration. w; = 1.091 X 10-3 arcsec/s2•
-2
t, I I I I I I ,~ ,';:tj', I I I , I , I , I I j-6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
Hour angle
co
tD
~
M
N
Q)...-1-
QDr::
0~
~
...-I ~0
I :x=NI
MI
~
I
U)
I
CO~
,I
-(,)......,
.....
cq
tq
~
N Q), -QD
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~
~
~N 0
" :x=~,tqI
cq,.....
oooCO,
o NI
(2°M/(1),M) u0!l'9.1alaoov
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