An Optical Readout System for the LISA Gravitational Reference Sensor

Fausto Acernese, Rosario De Rosa, Luciano Di Fiore, Fabio Garufi, Adele La Rana and Leopoldo Milano

INFNsezione di Napoli

Università degli Studi di Napoli "Federico II"

Università degli studi di Salerno

LISA(Laser Interferometer Space Antenna)

ESA-NASA collaboration:

•Three spacecrafts in a equilateral triangle formation 5 milion km sidelength

•Heliocentric orbit, following the Earth

•Each spacecraft contains 2 test masses in geodesic motion

LISA Sensitivity Curve

LISA sensitivity depends on the ability to set the test masses in free fall!

100 10-1

10-20

10-21

10-4

Detection threshold (S/N = 5)

for a 1-year observation

10-3 10-2

10-23

10-22

10-19

10-18

Frequency (Hz)

Binary confusion limit

h Frequency range: 0.1 mHz < f < 0.1 HzRXJ1914.4+2456

401820-30

BHs M102 Θ6

BHs M102 Θ4

BH M1010 Θ6

Lisa spacecraft layout

Because of the 60° angle between the test masses, to rectify the relative position of test masses and spacecraft we need:

•Microthrusters driven by capacitve sensor to move the spacecraft along the main axis of the interferometer

•Electrostatic actuation to move the test masses along the direction ortogonal to the main axis

Test masses

Some Fundamental issues:

•Free fall of test masses

•Spacecraft stationary around test masses

Gravitational Reference Sensor (GRS) control

loop. A capacitive sensor drives

microthrusters.

Lisa spacecraft layout

Because of the 60° angle between the test masses, to rectify the relative position of test masses and spacecraft we need:

•Microthrusters driven by capacitve sensor to move the spacecraft along the main axis of the interferometer

•Electrostatic actuation to move the test masses along the direction ortogonal to the main axis

Some Fundamental issues:

•Free fall of test masses

•Spacecraft stationary around test masses

Gravitational Reference Sensor (GRS) control

loop. A capacitive sensor drives microthrusters.

Electrode housing + test mass

•First Plate: surface of the test mass. Second Plate: connected to the spacecraft.

•Sensitivity requirements

Reference solution: Capacitive Sensor

Translational DOFs

Hznm/ 2

•Sensitivity requirements

•It will be tested in the technology demonstration mission LISA Pathfinder.

Reference solution: Capacitive Sensor

Rotational DOFs

Hznrad/ 200

Is there a possible alternative solution for the GRS?

Goal: Integration of the optical readout in the present design of the GRS.

Why an optical readout?

•Risk reduction: back-up readout in case the capacitive one fails after the launch.

•Redundancy: an independent readout provides extra information on couplings etc..

•Sensitivity: an optical readout is potentially more sensitive for some DOF.A smaller noise level can relax the requirements on the cross couplings of noise in the other DOFs along the main axis!

Optical readout system for the GRS of LISA

Optical readout system for the inertial sensor of LISA

•The drag free control loop should not spoil the position noise on the main interferometer axis X (410-11 m/Hz 1/2).

•In the present LISA baseline, the position of the test mass along the main interferometer axis X is read interferometrically, while the transverse DOFs (Y and Z) are read by the capacitive sensor.

•Assuming the sensitivity of the capacitive sensor (210-9 m/Hz1/2) for the Y and Z axes, taking into account that there are two proof masses per arm and putting some safety factor, we get a very strict requirement (~ 10-3) for the maximum coupling of noise in the transverse DOFs to the main axis.

•Any improvement in sensitivity for the transverse DOFs turns out in a corresponding relaxation of the requirements on cross couplings.

Optical lever:

•laser beam sent to the test mass through a SM optical fiber

•position of the reflected beam measured by a position sensor (QPD or PSD).

Advantages: simplicity, robustness.The sensitivity depends on input power and measurement range (beam size for QPD or detector size for PSD).

With a suitable combination of three beams and sensors we can recover the six DOF of the test mass.

Our proposal for the optical read-out

Laser

Test massQPD

Optical fiber

Potential sensitivity for the ORO

Shot noise ORO

Electronic noise ORO

El.+Sh. noise ORO

Translational DOFs

Capacitive sensor requirement

Total Power: 0.2 mW

Spot size:

0.4 mm

Wavelength:=633 nm

• Back action, due to the radiation pressure of the light beam hitting the test mass:

F = radiation pressureP = power of the laser beam

• Compatibility with the present LISA design

Requirements for the ORO

HzN106

c

P2F 16

~~

HzW10P 7~

Work in progress in Napoli

•Characterization of the sensitivity of our ORO

Many different setups to improve the sensitivity and reduce the position sensor noise.

•Integration of the ORO in LISA

Real scale prototype.

•Test of the ORO on Trento Torsion pendulum

Test of the sensitivity and of the back action in conditions as near as possible to the free fall.

Rigid set up for the study of the sensitivity

•Bench: single block of stainless-steel with interfaces for fiber couplers and sensors.•The system is symmetric for differential measurements.•The "test mass" can be moved for calibration.•The whole set-up is closed in a box to prevent effects due to air flows etc.

Total Power = 0.18 mW Spot size = 0.4 mm = 633 nm beam path = 110 mm

Sensitivity to the translational DOFs

1/f1/2

1/f

The electrode housing and the ORO prototype

•LISA Test-flight Package (LTP) model for the electrode housing

•Small spaces for ORO and light ray trajectories

•ORO realization has to take into account the overall dimensions of the electrode housing and the caging mechanism

3 Fiber couplers

3 Position sensors

The electrode housing and the ORO prototype

In the z and x trajectories of the beam the electrodes work as mirrors, reflecting light back to the test mass.

Electrode Mirrors

Electrode Mirrors

Simplified figure

Z

YX

Szz

Lz

Protoype design compatible with LTP electrode housing project

Top View

Lxproj

Ly

Sx

d

x

y

Goals:

•Experimental test of the correct passing of the light beams through the overall dimensions of the electrode housing. Not a test of sensitivity.

•Study of the optical matrix.

Front View

Our real scale prototype

Note: here we are using psd and not qpd

PSD X Signals: Xh , Xv

PSD Y Signals: Yh , Yv

y

x

z

PSD Z Signals: Zh , Zv

Fiber couplers

Portrait of a prototype (during the assembling phase)

A detail of the prototype: angled connections of the

ferrulae of the optical fibers

Front view of the prototype

•The light beams come out correctly, after making few adjustments with thin steel layers ( 100 m).

•We calculated the analytical matrix of the system and we compared it with the measured experimental one.

Z

Y

X

Degrees of freedom of the test mass

φ

η

θ

Z

Y

X

C

v

h

v

h

v

h

Z

Z

Y

Y

X

X

FVector of the photodiode signals

Working on the prototype

• B allows to calculate the position of the test mass once you know the signals from the photodiodes.

• We can measure the matrix elements of the inverse matrix of B:

•We can calculate A analitically, the matrix elements depending only on the geometry of the system.

v

h

v

h

v

h

6661

161514131211

Z

Z

Y

Y

X

X

B........B

............

............

............

...............

BBBBBB

φ

η

θ

Z

Y

X

Matrix of the system

1BA CAF

The measured matrix AEx

The analytical matrix ATh

φ

η

θ

Z

Y

X

00.01200.10201.922500

00.02810000

000.0266000

0.05400000.34730

00.02330000

0.090000001.9318

Z

Z

Y

Y

X

X

v

h

v

h

v

h

φ

η

θ

Z

Y

X

?....1.83-0.02-0.03

......0.11-0.03-0.06

......0.06-0.01-0.01

......0.04-0.340.04-

......0.030.002-0.012

???0.170.013-1.94-

Z

Z

Y

Y

X

X

v

h

v

h

v

h

Noise level in the reconstruction of the test mass motion in 6 DOFs

•The noise level measured using the rigid set up considered so far refers to the displacement noise of a single beam on the detector.

•In order to evaluate the noise level in the reconstruction of the test mass motion in 6 DOF, we must take into account:

the geometry of the ORO

the linear combination of the signals read by the photodiodes.

Matrix ATH

Noise level in the reconstruction of the test mass motion in 6 DOFs

n

1/26

1m

1m2

1/22v16

2h15

2v14

2h13

2v12

2h11

δXBδX(f)

)δZ(B)δZ(B)δY(B)δY(B)δX(B)δX(BδX

Expected noise for each degree of freedom:

Assuming the three QPDs being affected by the same noise level δXn:

By using the measurement of the lowest noise level obtained with the rigid set up, we get the expected noise for each degree of freedom of our prototype.

Note:

We assume that the X, and are read interferometrically with negligible noise, while Y, Z and are given by the ORO with the geometry of our prototype.

The noise on Y is higher than the other two because of the small angle of the Y beam.

Sensitivity curves of the translational DOFs of the test mass related to the protoype’s geometry

Zmeas

Ymeas

Ymodel

Zmodel

Capacitive sensor

Sensitivity curves of the rotational DOFs of the test mass related to the protoype’s geometry

The measured noise level is already good enough.

Capacitive sensor

x

y

z

Capacitive sensor

Optical sensor

1

2

3

4

Next steps: testing the prototype on the torsion pendulum in Trento

•Four masses pendulum

•Single “soft” DOF: rotations xb translations, free fall

•Capacitive sensor on mass 1

•Optical sensor on mass 2

Images kindly granted by the LISA team in Trento.

Mass 2 Side view

QPD

QPD

Next steps: testing the prototype on the torsion pendulum in Trento

In this configuration the ORO is sensitive to x translations and to rotations and around z and

y axis.

z

xy

Shaft

Fiber coupler

Fiber coupler

Conclusions :

Next steps:

About the sensitivity…

The measured ORO sensitivity for the single beam is better than the capacitive sensor sensitivity for f > 1mHz.

The measured noise level is a factor 3-5 higher than the model noise (shot + electronic noise). Further improvements looks feasible.

About the integration in LISA…

The integration of a 6 DOF system in the present design of the GRS (the one on LTP) looks feasible and has been verified in a real scale bench top prototype.

Usage of an optical readout would relax considerably the specifications on cross couplings.

Angular noise level is already good enough.

For the LISA GRS we should be able to find a beam geometry enabling to extract the Z and Y DOFs of the test mass with a sensitivity between 1 and 0.1 nm/Hz1/2.

Thank you for your attention!

Any questions?