Stefan Hild For the GEO-team

March 2008, ILIAS WG1, Pisa

Projection of small angle scattering

Stefan Hild ILIAS WG1 meeting, March 2008, Pisa Slide 2

Overview

Intro: small angle scattering

Measurement of the small angle scattering function of a GEO600 core optic

Potential coupling paths of small angle scattering

Projection of the scattered light noise of one of the GEO600 catchers

Stefan Hild ILIAS WG1 meeting, March 2008, Pisa Slide 3

How much scattered light is necessary to limit the sensitivity of GEO600 ?

102

103

10-19

10-18

10-17

Frequency [Hz]

Displacement [m/sqrt(Hz)]

GEO600, May 06

102

103

10-19

10-18

10-17

Frequency [Hz]

Displacement [m/sqrt(Hz)]

GEO600, May 06

1.5e-19 m/sqrt(Hz)

Achieved displacement sensitivity

Accurary of the phase readout

Frequency [Hz]

sen

sitiv

ity [

m/s

qrt

(Hz)

]

Stefan Hild ILIAS WG1 meeting, March 2008, Pisa Slide 4

How much scattered light is necessary to limit the sensitivity of GEO600 ?

ECAssuming angle between EC and to be 90 deg.

With EC = sqrt(2.7kW) we get

tiny amount of light

Stefan Hild ILIAS WG1 meeting, March 2008, Pisa Slide 5

Small angle scattering in general The amount of scattered light varies with the mirror.

We are interested in very small angles, for instance = 0.1m/600m = 1.7mrad

Often the scattering funktion is assumed to be cosine-like

scattering angle

ampl

itude

Sandblasted metal works

Super polished mirror

Stefan Hild ILIAS WG1 meeting, March 2008, Pisa Slide 6

Photographs of the north end mirror

Stefan Hild ILIAS WG1 meeting, March 2008, Pisa Slide 7

Measurement of the small angle scattering of a GEO test mass

Can measure the light passes next to the mirror (red circle).

We get:

Since the modulation depth is similar to main beam:

Using:

We end up at:

Stefan Hild ILIAS WG1 meeting, March 2008, Pisa Slide 8

Two different scattering scenarios

A: Light on the mirror scattered directly into the incoming beam (instead of following the folded arm).

B: Scattered light hitting the metal works around the mirror is scattered back into the interferometer mode.

Stefan Hild ILIAS WG1 meeting, March 2008, Pisa Slide 9

Scenario A: Direct back scattering in the folded arms

Direct back scattering from MFn and MFe causes 1200m pathlength difference => increased frequency noise coupling (be covered by noise projection)

The position of MFn and MFe is only controlled with low bandwidth (0.1 Hz). MFe and MFn movement in combination with small angle scattering can cause noise in detection band.

Stefan Hild ILIAS WG1 meeting, March 2008, Pisa Slide 10

Slide stolen from Haralds talk at the LSC meeting Oct 2008

Stefan Hild ILIAS WG1 meeting, March 2008, Pisa Slide 11

Scenario B: Light scattered back from the catchers.

Catchers are not isolated from ground motion.

If we know: Scattering function of

the mirror and catcher The movement of the

catcher We can do a simple

projection.

Stefan Hild ILIAS WG1 meeting, March 2008, Pisa Slide 12

The scattering processes required

All together 3 scattering processes are required:

• light needs to be scattered onto the catcher.

• light at the catcher needs to be scattered back onto a mirror (MCn).

• at MCn the light needs to be scattered back into the interferometer mode

Stefan Hild ILIAS WG1 meeting, March 2008, Pisa Slide 13

Projection: Step 1

Light power at catcher (90mW)

Effective mode diameter (from W. Winkler PhD thesis)

Stefan Hild ILIAS WG1 meeting, March 2008, Pisa Slide 14

Projection: Step 2

EC

Transforming light power into effective scattering amplitude:

Stefan Hild ILIAS WG1 meeting, March 2008, Pisa Slide 15

Projection: Step 3

ASD of catcher movement

ASD of displacement causedby scattered light from MFn catcher

Stefan Hild ILIAS WG1 meeting, March 2008, Pisa Slide 16

Projection: Step 3

Stefan Hild ILIAS WG1 meeting, March 2008, Pisa Slide 17

More Details can be found in:

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