6/28/02 What causes pitch and Yaw motion of MMT3?
1. Objective
A suspended optic is excited through the suspension point. E2e models coupling of translational motion of
the suspension point into pitch and yaw motion of the suspended optic. To verify the model, measure
coherence between translational motion of the suspension point and mirror’s pitch/yaw motion.
Measurement is made using MMT3 in vacuum (HAM1) with local damping servo on.
2. Method
Fig. 1 illustrates optics arrangement on HAM1 schematically, and defines the orientations of the
four axes. To measure pitch and yaw of MMT3, optical lever signal (L1: ASCMMT3_OPLEV_PITCH/YAW) were used. Motion of the suspension point cannot be measured
directly. So, OSEM sensor signals were used assuming that each sensor signal represents motion
of the supporting point along one axis as shown in Table 1. This assumption seems to be
reasonable for the following reasons. Our previous investigation has shown high coherence
among sensor signals from mutually parallel magnets on the same table (such as MMT1 side and
MMT3 side or MC1 side and SM side, etc) and very low coherence among sensor signals from
mutually perpendicular magnets (such as MMT1 rear and MMT3 side). This indicates that the
OSEM signal represents the table motion in the axes parallel to the magnet. Because of the
rigidity of the suspension structure, the transfer function between the table surface and the
supporting point can be considered to be nearly unity. With Data Test Tool (dtt), coherence
among these DAQ signals was measured.
Table 1 OSEM sensor and axis represented
OSEM
MMT1 lower left (L1:SUS-MMT1_SENSOR_LL)
MMT1 side (L1:SUS-MMT1_SENSOR_SIDE)
MC1 lower left (L1:SUS-MMT1_SENSOR_SIDE)
MC1 side (L1:SUS-MMT1_SENSOR_SIDE)
V/U
axis
U (beam line)
V (horizontal)
U/V (diagonal)
V/U (perpendicular to U/V)
V (horizontal)
MMT1
U/V (diagonal)
U (beam line)
Optical lever
detector
MMT3
Optical lever
laser source
Fig. 1 Optics on HAM1 and optical lever, and definition of four axes.
MC1
3. Results
Fig. 10 shows coherence of MMT3 LL to MC1 LL (U/V) and MC1 SIDE (V/U). The common direction
between U and U/V or V and V/U is obviously +/- U. Thus this figure can be interpreted as representing
table’s U translational motion. High coherence observed near 1.5 Hz, 2.3 Hz and 7.2 Hz can be interpreted
as stack’s U-U transfer resonance frequencies. Low coherence in 1.8 Hz – 6.5 Hz except for these
resonance frequencies indicates that in this frequency range U motion is not the dominant table motion.
Fig.10 Ummt3 vs U/V MC1, V/U MC1 (table's U motion)
1.2
mc1 LL mmt3 LL
coherence
1
mc1 SIDE vs mmt3 LL
0.8
stack U-U transfer
0.6
stack V-V transfer
0.4
stack W-yaw transfer
0.2
stack W-W transfer
0
0
2
4
6
8
10
Hz
Fig. 11 shows coherence of MMT3 SIDE (V) to MC1 LL (U/V) and MC1 SIDE (V/U). The common
direction between V and U/V or V and V/U is obviously +/- V. High coherence is seen from 1.8 Hz – 3.2
Hz with dips at 1.5 Hz and 2.3 Hz. The first peak is near the first stack V-V resonance at 1.8 Hz, and the
second peak is near the second stack V-V resonance at 3.2 Hz. The dip frequencies are stack U-U transfer
resonance. So it can be interpreted that the low coherence at these frequencies is due to U- motion of the
table at resonance (i.e., the table is selectively excited in U motion at these frequencies and therefore the
coherence in the +/-V direction is low). The other large peak near 7 Hz seems to be the third stack V-V
resonance at 7.3 Hz. The low coherence in 3.2 Hz – 6.5 Hz indicates that in this frequency range V motion
is not the dominant motion of the table.
Fig. 11 Vmmt3 vs U/V MC1, V/U MC1 (table's V motion)
1.2
mc1 LL mmt3 side
coherence
1
mc1 SIDE vs mmt3 side
0.8
stack U-U transfer
0.6
stack V-V transfer
0.4
stack W-yaw transfer
stack W-W transfer
0.2
0
0
2
4
6
Hz
8
10
Fig. 12 shows coherence between MMT1 LL (U) and MMT3 LL (U). The common mode between these
signals is either table’s U motion, table’s pitch motion (table’s U motion relative to suspension point or tilt),
or table’s yaw (table’s rotational motion on a horizontal plane) motion. High coherence is observed from
0.2 Hz – 2.9 Hz (see Fig. 16 below). The fact that Fig. 10 (table’s U motion) does not show high coherence
except at 1.5 Hz and 2.3 Hz in this range indicates that pitch and/or yaw motion is the dominant table
motion in this frequency range except for dips. The dip in Fig. 12 seems to be due to MMT1’s optics
motion (mainly pendular motion) at the resonance; i.e., at this frequency MMT1 is selectively excited while
MMT3 is not selectively excited, and therefore the coherence between the two optics is relatively low.
coherence
Fig. 12 Ummt1 vs Ummt3 (table's pitch or yaw)
1.2
mmt1 LL vs mmt3 LL
1
0.8
stack U-U transfer
0.6
stack W-yaw transfer
0.4
stack W-W transfer
0.2
MMT3 resonance
0
MMT1 resonance
stack V-V transfer
0
2
4
6
8
10
Hz
Fig. 13 shows coherence between MMT1 SIDE (V) and MMT3 SIDE (V). The common mode between
these two combination is either table’s V motion, table’s other pitch motion (table’s V motion relative to
suspension point), or table’s yaw (table’s rotational motion on a horizontal plane) motion. High coherence
is observed from 0.2 Hz – 3 Hz (see Fig. 17 below). The fact that Fig. 11 shows low coherence in <1.8 Hz
and >3.2 Hz indicates that yaw motion is the dominant table motion in 0.2 Hz – 1.8 Hz, and V-motion is
dominant in 1.8 Hz – 3.2 Hz. (Ignore table’s pitch motion along V because it simply excites side motion of
MMT3).
Fig. 13 Vmmt1 vs Vmmt3 (table's yaw)
mmt1 SIDE vs mmt3
side
stack U-U transfer
coherence
1.2
1
0.8
stack V-V transfer
0.6
stack W-yaw transfer
0.4
0.2
stack W-W transfer
0
0
2
4
6
Hz
8
10
Fig. 14 shows coherence between MMT3 LL (U) and MMT3 optical lever pitch. High coherence is
observed in 0.2 Hz – 2.5 Hz with dips at 0.8 Hz-1.4 Hz and 1.5 Hz – 1.8 Hz. This pattern resembles Fig. 12
(table pitch/yaw) than Fig. 10. (see Fig. 14-b). This indicates that MMT3 mirror is most likely excited by
tables pitch motion (differential U motion between MMT1 magnet height and MMT3 magnet height).
Fig. 14 Ummt3 vs mmt3 opt lev pitch
1.2
0.8
mmt1 LL vs mmt3
Pitch
stack U-U transfer
0.6
stack V-V transfer
0.4
stack W-yaw transfer
0.2
stack W-W transfer
coherence
1
0
0
2
4
Hz
6
8
10
Fig. 14-b Comparison of Fig. 14 with Fig.10 and Fig. 12
coherence
1.2
mmt1 LL vs mmt3 Pitch
1
stack U-U transfer
0.8
stack V-V transfer
0.6
stack W-yaw transfer
0.4
stack W-W transfer
0.2
mmt1 LL vs mmt3 LL
0
0
2
4
6
Hz
8
10
mc1 LL mmt3 LL
Fig. 15 shows coherence of Optical lever yaw to MC1 U/V and MC1 V/U. Coherence between MC1 SIDE
(V/U) and Optical lever yaw seems to be “Fig. 13 (table yaw/pitch) minus Fig. 11 (table V)”. This indicates
that MMT3 mirror yaw is caused by table yaw but not by table V, which is understandable. Difference
between the two curves in pattern at <1.8 Hz indicates that U/V and V/U motion in this frequency range is
not in phase, though in Fig. 11 the U/V and V/U show high coherence (via MMT3 side) in 1.8 Hz – 3.2 Hz.
The reason for this frequency dependence of U/V vs V/U coherence is not clear.
Fig. 15 U/V MC1, V/U MC1 vs mmt3 opt lev yaw
1.2
mc1 SIDE vs mmt3
Yaw
mc1 LL mmt3 Yaw
coherence
1
0.8
stack U-U transfer
0.6
stack V-V transfer
0.4
stack W-yaw transfer
0.2
stack W-W transfer
0
0
2
4
6
8
10
Hz
Fig. 15-b U/V MC1, V/U MC1 vs mmt3 opt lev yaw
1.2
mc1 SIDE vs mmt3
Yaw
stack U-U transfer
coherence
1
0.8
stack V-V transfer
0.6
stack W-yaw transfer
0.4
stack W-W transfer
0.2
mmt1 LL vs mmt3 LL
0
0
2
4
6
Hz
8
10
mc1 LL mmt3 side
Fig. 16 shows similarity between table pitch (Fig. 12) and optics pitch (Fig. 14) on an expanded frequency
axis.
Fig. 16 table picth and optics pitch
1.2
coherence
1
0.8
mmt1 LL vs mmt3 LL
0.6
stack U-U transfer
0.4
stack V-V transfer
0.2
stack W-yaw transfer
0
stack W-W transfer
0
0.5
1
1.5
2
2.5
Hz
3
3.5
4
MMT3 resonance
MMT1 resonance
Fig. 17-a, b together show similarity between optics yaw (Fig. 15) and “table
yaw
13) minus table V
mmt1
LL(Fig.
vs mmt3
(Fig. 11)” (blue-green=yellow).
Pitch
coherence
Fig. 17-a table yaw (blue) and optics yaw (yellow)
1.2
1
mmt1 SIDE vs mmt3
side
stack U-U transfer
0.8
0.6
stack V-V transfer
stack W-yaw transfer
0.4
0.2
stack W-W transfer
0
0
0.5
1
1.5
2
2.5
3
3.5
4
mc1 SIDE vs mmt3
Yaw
Hz
Fig. 17-b table yaw (blue) and table V (green)
mmt1 SIDE vs mmt3
side
stack U-U transfer
1.2
coherence
1
0.8
stack V-V transfer
0.6
0.4
stack W-yaw transfer
0.2
stack W-W transfer
0
mc1 LL mmt3 side
0
0.5
1
1.5
2
Hz
2.5
3
3.5
4
4. Conclusion
In conclusion, the following can be said.
1. It seems reasonable to use OSEM sensor in U, V and diagonal directions to estimate HAM table
motions.
2. Coherence between “U (V) and U/V” or “U (V) and V/U” can be used to estimate table’s U (V)
translational motion.
3. Coherence between MMT1 rear and MMT3 rear can be used to estimate table’s pitch (relative to
suspension point) motion.
4. Coherence between MMT1 SIDE and MMT3 SIDE can be used to estimate table’s yaw (horizontal
rotation) motion.
5. MMT3 mirror pitch is caused by table’s pitch motion
6. MMT3 mirror yaw is caused by table’s yaw – table’s horizontal (V) motion.
7. From the facts that the optical lever’s laser is not on the HAM table but on the floor indicate and that
the optical lever signal and OSEM sensor signals show high coherence indicate that the table motion is
most likely caused by floor motion.