LIGO-G040043-00-Z 1ST7 Interferometer

The ST7 Interferometer

Andreas KuhnertRobert Spero

Jet Propulsion LaboratoryCalifornia Institute of Technology

LIGO-G040043-00-Z 2ST7 Interferometer

ST7 Concept

• Measure suspended masses within spacecraft

• Test thruster performance in drag-free control

• Hitch ride on LISA Pathfinder

Optical bench

TM1 TM2

• Interferometer optical bench fixed to spacecraft

• x1 and x2 measured separately; x1 + x2 is low-noise

x1x2

LIGO-G040043-00-Z 3ST7 Interferometer

Optical Bench

Beam-splitter

Collimator

Insensitive path

Sensitive path

IntensityMonitor

Optical Fiber

Quadrant photodiode

20 cm

TM1 TM2

LIGO-G040043-00-Z 4ST7 Interferometer

Interferometer Features

Beam diameter 1 mm, Rayleigh range 70 cm, sensitive path lengths 10 cm.

No modulators, phasemeters, intensity stabilization, or frequency stabilization.

Requires test mass to be positioned near mid-fringe.

Intensity monitored, noise removed in data analysis.

Separate measurements of both bench/test-mass distances.

Quadrant photodiodes monitor total fringe signal, and two axes of alignment.

Automatic alignment, autonomous operation.

LIGO-G040043-00-Z 5ST7 Interferometer

Manual Alignment

Thermal Expansion

Homodyne Signal

A

B

A

B

Optical Bench

LIGO-G040043-00-Z 6ST7 Interferometer

Contacted Optics in Vacuum Chamber

LIGO-G040043-00-Z 7ST7 Interferometer

Testbed Drift

LIGO-G040043-00-Z 8ST7 Interferometer

60 pm rms opticalbench modulation

Testbed Noise

1000

100

10

1

mHz

pm

/rtH

z

1 100

Allocated noise

Measured noise

LIGO-G040043-00-Z 9ST7 Interferometer

Measurements Demonstrate:

1. Analog electronics and ADC noise adequately low

2. Thermal sensitivity probably adequately low

3. Bench motion suppression typically x200, without calibration (x1000 needed)

4. Frequency stabilization not needed

5. Intensity noise can be suppressed in data analysis

LIGO-G040043-00-Z 10ST7 Interferometer

Alignment Sensitivity 1:Geometric error

xS= s1

s1

p

xc= p

xS= s1 sin xc= p cos

Errors are correlated, and of same order: s1 ~ p

s1 = 40 ; p = 10 cm; = 400 rad

LIGO-G040043-00-Z 11ST7 Interferometer

Alignment Sensitivity 2:Fringe position error

xx= x (w2 = x 106,w=beam radius

p + x

LIGO-G040043-00-Z 12ST7 Interferometer

Total angle-jitter noise

Test mass jitter, 1 rad/rthz

Displacement noise, 30 pm/rthz

Transverse error, 40 m

Misalignment, 400 rad

Fringe center error, 30 nm

LIGO-G040043-00-Z 13ST7 Interferometer

Initialization

1. Starting state 2. IFO finds bright fringe

3. GRS moves to quarter fringe 4. IFO Aligns

5. GRS to half fringe Position

Inte

nsi

ty

LIGO-G040043-00-Z 14ST7 Interferometer

Dithered alignment -- concept

LIGO-G040043-00-Z 15ST7 Interferometer

Dithered alignment -- Simulink model

LIGO-G040043-00-Z 16ST7 Interferometer

Dithered alignment -- Simulink run

LIGO-G040043-00-Z 17ST7 Interferometer

Bright fringe finder -- Simulink model

LIGO-G040043-00-Z 18ST7 Interferometer

Bright fringe finder -- Simulink run

LIGO-G040043-00-Z 19ST7 Interferometer

QPD difference alignment -- Simulink model

LIGO-G040043-00-Z 20ST7 Interferometer

QPD difference alignment -- Experiment

LIGO-G040043-00-Z 21ST7 Interferometer

QPD difference signal alignment sensitivity

LIGO-G040043-00-Z 22ST7 Interferometer

Sum vs. difference signals at half-fringe

LIGO-G040043-00-Z 23ST7 Interferometer

Backups

LIGO-G040043-00-Z 24ST7 Interferometer

Intensity Pattern with Misalignment

• Horizontal misalignment shown.

• Pattern insensitive to fringe offset near mid-fringe.

• Sample with 4 pixels (quadrant photodiode). Difference/sum response:

dQ/d = sqrt(8kw/3)

LIGO-G040043-00-Z 25ST7 Interferometer

Static Misalignment and Static Longitudinal Error

Fringe Visibility Error Sensitivity

w=0.5 mm

w=1.0 mm

w=2.0 mm

0

1

Misalignment (rad) Bright Mid Dark

Electronicnoise

Alignmentnoise