Source of scattered light

Baffles and cryostat : Scattered light noise

Jean-Yves VINET

Main beam

Mirror

Source of scattered light

( ) s x

D

( ) s y

Propagated scattered light = speckle D

Rough mirror

Hypotheses :

Distribution of scattered light vs scattering angle :

( )

p θ κ

≈ θ

0

g

w

θ λ

= π

For angles much larger than

LSD of seismic motion :

2

-8

10 Hz

( ) 10 m/ Hz

x f f

δ ≈ ^  ^ 

 

θ

2 2 2

2 0

1 ' '

2 2 2

(

( , , ') )exp exp

2

x x x x

kw ik

D D

C D x x

D p

θ π

ε

−

     

 

   

 

=

Memory of the stored mode

Distribution of Scattered light : Mirror’s roughness

Integrated Scatt. losses

Emission of SL

Reflexion of SL 2d scattering

TEM00

TEM00

D₁

1( ) s x

3( ) s x

2

( ) s x

4( ) s x

Spurious (noisy) phase modulation caused by the coupling :

00, TEM s

γ =< >

Moving reflecting element

5( ) s x

D₂

emitter

receiver

5 2 2 3 2 2 1 1

, s , M P ( . )m s , M P [ . (m P M )]

γ

M1

M₁

M₂

m D₁

D₂ s₁

s₂ s₃ s₄

s₅ Φ

Φ

1 2

e

m x s ( )

( ) x s

( ) x dx

γ =

∫

1 1 2 2

* m x m x ( ) ( ') * s

( ) x s

( ') * x s

( ) x s

( ') * x dxdx '

γγ = ∫

2

. (

, , ')

* m x ( ) ( ') * m x C D x x . C D ( , , ' x x ) dxd x ' γγ

Γ ≡ = ∫

Coupling coefficient with TEM00 :

Expectation value :

In terms of the speckle autocorrelation :

1/ 2 θ δ x f( )

= Γ

δ x ^≪ λ

( ) δ x t

PSD of SL-noise : If

Reflecting element

θ

( )t 4π cos x t( )

φ θ δ

∆ = λ

Possible cases of coupling

1) Direct reflection from elementary spots IM
IM and EM
EM

1) Transmission EM
IM and IM
EM via inner baffle edge

3) Transmission EM
IM and IM
EM via

spots on the inner edge

D

(α,β)

r_C

Direct reflection

By reflecting element

Relevant parameters : -distance from mirror -Misaligment

(α,β)

D=0.9 m,

∆α

∆α

D=2.2 m,

∆α

∆α

β ^{= 0}

r

= D

S=10

m

Case of input zone baffle
End mirror D=3000 m,

∆α

ROC of the reflecting element

Conclusions for small reflecting defects : -Unsensitive to ROC of the zone

-Sensitive to the distance

-Sensitive to the pointing error

Summary

2

-25 -1/2

2

-25 -1/2

2

-25 -1/2

-24

10 Hz

0.9 m : ( ) 3.65 10 Hz , 0.46°

10 Hz

1.5 m : ( ) 5.96 10 Hz , 0.28°

10 Hz

2.2 m : ( ) 8.53 10 Hz , 0.19°

10 Hz 5 m : ( ) 1.75 10

D h f

f

D h f

f

D h f

f

D h f

α α α

 

= =   ∆ =

 

 

= =   ∆ =

 

 

= =   ∆ =

 

= = 

2

Hz-1/2, α 0.09°

 ∆ =

 

θ

θ

1 2

2 α = θ θ ⁺

1 2

2

µ = θ θ ⁻

α µ

D₁ D₂

Reflexion of scattered light by the inner edge of a baffle

or by a

reflecting element under

grazing incidence

D=0.9 m ^,

∆α

D=5 m,

∆α

D=2.2 m,

∆α