Investigation of the influence of suspended optic’s motion on

LIGO detector sensitivity

Sanichiro Yoshida

Southeastern Louisiana University

The beginning..

LIGO E2E (H. Yamamoto)

(1) Interested in comparing mechanical simulation of e2e and

measurement (stack motion, mirror motion).

(2) Need good seismic motion data, including correlation.

SLU (Students)

(1) Interested in studying dynamics of LIGO suspended optics.

(2) Measurement and modeling at site - Good for undergraduates.

SLU (S. Yoshida)

(1) Background- Input optics implementation.

(2) Interested in effect of input optics to LIGO performance.

Suspended optics on HAM table

Suspension point

Shadow sensor

Suspension wire

Shadow sensorWire standoff

Shadow sensor Safety stop

Stiffener plateSuspension tower

HAM (Horizontally Accessible Module) table

(1) field and optics(2) mechanical motions(3) electronics(4) input data (seismic motion, frequency noise, etc)

Table top motion (displacement 3, rotation 3) = ground motion (6) x stack transfer function (6x6)

=(x1 - x2)/L?

E2e simulation:

HAM table

x1

x2

Vibration isolation stacks

Model of transfer of the floor motion to optic

Optic motion (Output)

Floor motion (Input)

TG->Ht

HAM table motion

THt->Sp1

Suspension point motion

TSp->Op

Measurement 1 Measurement 2 Measurement 3

E2e simulation

LIGO research group at SLU

Undergraduate students• Raghuveer Dodda (Physics/Computer Science major)• Tiffany Findley (Physics major)

Physics Faculty• David P. Norwood (Optics)• Sanichiro Yoshida (LLO, UF LIGO)

Contents

• MMT3 motion - dark port signal coherence

• HAM1 table YAW motion measurement

• Floor motion measurement

• E2e boxes for MMT3

• Model suspension analysis at SLU

* MMT3 (Mode Matching Telescope on HAM1)

MMT3 motion - dark port signal coherence

MMT3 on HAM1

Input optics. Different color represents different subsystems. Optical lever is outside vacuum on a pier.

Mode Cleaner

Mode Matching Telescope

To IFO

MC2MC1

MC3MMT2

MMT1

MMT3

From PSL HAM1 HAM2

Optical lever

MMT3 motion and correlation to dark port signal

• Power Spectrum of MMT3 – peaks seen ~ 1.5Hz, where MMT 3 has no resonance

• Coherence between MMT3 motion and ASC_Q beam – peaks seen ~ 1.5Hz

MMT3/BS coherence to dark port signal @ ~1.5 Hz

Both data taken at the same time when arms are fully locked.

BS

MMT3

1.5 Hz

MMT3/BS to AS_I/AS_Q coherence base line data

Arms not locked due to train

Resonant frequencies

• MMT3 resonance

pendular: 0.762 Hz

pitch: 0.627

yaw: 0.506

side: 0.732

vertical: 12.32

• HAM resonance

U - U: 1.5, 2.3 Hz

V - V: 1.6, 2.8

Vert - Yaw: 7.2, 8.0

U: beam lineV: transverse

HAM1 table YAW motion measurement

HAM table motion measurement by shadow sensors

Measured HAM1 YAW

HAM1 yaw (measured)

0.E+00

1.E-06

2.E-06

3.E-06

4.E-06

5.E-06

0 0.5 1 1.5 2 2.5 3f (Hz)

power spectrum

7/26/02

Floor motion measurement

Corner station seismometer spectra (LLO)

X (U)

Y (V)

HAM1 accelerometer spectra

X (U)

Y (V)

Floor motion correlation measurement

P1 P2 P3

P4

P5

X arm

Y armPortable seismometer location

Beam splitter

LLO

Phase delay in y component along x arm

8/19/02 seis y vs position x

20

40

60

80

100

120

1 1.2 1.4 1.6 1.8 2

f (Hz)

phase (deg)

position 1

2

3x

Standing wave due to reflectionat HAM resonance? ~1.5 Hz

HAM

Phase delay in seismometer signal

8/19/02 seis x vs position y

20

40

60

80

100

120

1 1.2 1.4 1.6 1.8 2

f (Hz)

phase (deg)

position 1

4

5

y

8/19/02 seis y vs position x

20

40

60

80

100

120

1 1.2 1.4 1.6 1.8 2

f (Hz)

phase (deg)

position 1

2

3

x

seis x vs position x

20

40

60

80

100

120

1 1.2 1.4 1.6 1.8 2

f (Hz)

delta phase (deg)

position 1

2

3

8/19/02 seis y vs position y

20

40

60

80

100

120

1 1.2 1.4 1.6 1.8 2

f (Hz)

phase (deg)

position 1

4

5

x

y

E2e boxes for MMT3

Free hanging mirror model (SUS3D.box)

• iput = motion of HAM1 at the location of MMT3 as calculated by the OSEM-method

• oput = x,y,z,xtheta,ytheta,ztheta of MMT3 (as a function of time)

• The PS of the output reveals peaks at:

MMT3 Yaw: 0.5 Hz (MMT3 yaw peaks) , 1.4 -1.6 (HAM1 peaks)

[ m(mmt3,sun) = m(mmt3,ham1) + m(ham1,grd) + m(grd,sun). Since, there is no m(grd,sun) in the iput, we should not see any m(grd,sun) peaks in oput. ]

Results of SUS3D.box – the free hanging mirror

MMT3 YAW (output) HAM 1 YAW (input)

Floor to optic model (MMT3.box )

This box takes floor motion as input and outputs table motion (=suspension point motion) and optics motion

xOp(t)

xG (t)

THt->Op

TG->Htp

xHt(t)

Model suspension at SLU

SLU model suspension (1)

Mechanical Oscillator

L

m

SLU model suspension (1)

mass

Mechanical Oscillator

Ring-down measurement (1)

1D Ringdown

y = -0.0201x + 1.0187

y = -0.0095x + 0.9918

y = -0.0139x + 1.0353

0

0.2

0.4

0.6

0.8

1

1.2

0 25 50 75 100 125Time (s)

Amplitude ln(cm)

without tape

with tape

with tape and oil

Damping coefficient estimated for three conditions.

Frequency response (1)

Frequency Response

0

2

4

6

8

10

12

5.5 6 6.5 7

Angular frequency (rad/s)

Amplitude (cm)

Measured Data

Theoretical Values

Damping coefficient from ring-down measurement used for theory.

SLU model suspension (2)

Mechanical Oscillator

Suspension Block

Mirror

Block

Front View Side View

SLU model suspension (2)

Mechanical OscillatorSuspension block

Optical lever beamCCD camera

Setup for yaw/pitch motion measurement

Optical lever

Mechanical oscillatorSuspended mass

wire

Yaw/pitch motion measurement

x

y

Optical lever beam spot

Sample optical lever signal

run 2 and 3 (0.99 Hz)

0

50

100

150

0 100 200 300

x

y Run 2

Run 3

Ring-down measurement (2)

3D Ringdown (Yaw Motion)

y = -0.0166x + 1.0066

y = -0.0085x + 0.9902

0

0.2

0.4

0.6

0.8

1

1.2

0 50 100 150

Time (seconds)

Optical lever reading

ln (cm)

without tape

with tape

Frequency dependence (2)

Frequency Response with tape

-0.1

0

0.1

0.2

0.3

0.4

0 0.5 1 1.5 2 2.5

Frequency (Hz)

Angle (rad)

Measured Data

Theoretical Values

Summary

• E2e simulation of suspended optics

– Influence on IFO

• Floor to table top modeling

– Supporting data taking

• Table top to optic modeling

– Model suspension

• Measurement of seismic motions with correlation is very important.