Effects of as built mirrors analysis using fft
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Effects of as-built Mirrors - analysis using FFT -. LIGO I mirror phase map FFT tools Thermal lensing Beam splitter curvature. Hiro Yamamoto, Biplab Bhawal, Xiao Xu, Raghu Dodda (SLU). Beam splitter phase map. WA4K BS. x 10 -8. nm. WA4K BS - curvature subtracted. nm.

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Effects of as built mirrors analysis using fft

Effects of as-built Mirrors- analysis using FFT -

  • LIGO I mirror phase map

  • FFT tools

  • Thermal lensing

  • Beam splitter curvature

Hiro Yamamoto, Biplab Bhawal,

Xiao Xu, Raghu Dodda (SLU)


Beam splitter phase map

Beam splitter phase map

WA4K BS

x 10-8

nm

WA4K BS - curvature subtracted

nm

concave ROC > 200km, convex ROC > 720km

LSC - Aug. 18, 2004


Smooth extrapolation from 15cm to 24cm

Smooth extrapolationfrom 15cm to 24cm

WA4k BS after curvature subtracted

Limited case study shows almost no difference

10nm

-7.5cm

7.5cm

LSC - Aug. 18, 2004


Contrast defect ugly but harmless cr from dark port

Contrast Defect- Ugly but harmless CR from dark port -

LSC - Aug. 18, 2004


Ligo i mirror phase maps available

LIGO I Mirror phase maps available

  • All phase maps available from e2e home page

    • LHO4k, LHO2k, LLO4k

    • Smooth extrapolation set and reference set

    • 128 x 128 and 256 x 256

  • Tilt removed

    • Poor mans ASC

  • R.Dodda (2003 SURF from SLU), X.Xu (2004 SURF from Caltech)

LSC - Aug. 18, 2004


Fft tools

FFT tools

  • Beam splitter curvature

    • Explicit support by adding pixel by pixel extra length by √2 x sag

    • Planned to confirm using e2e (modal model)

  • FFT lock vs LSC lock

    • FFT lock uses only CR, LSC lock uses CR and SBs

    • Lock FFT by itself -> Lock using ASQ,REFL,POB

    • DARM,CARM change by 10^-12m, PRC,MICH by 10^-9m

    • Quantitative results affected, most of qualitative results OK

    • Discussed later

  • Propagation with magnification (not in this talk)

    • Virgo Physics Book, Volume 2 “OPTICS and related TOPICS”, 3.1.7

    • FFT pixel size can be scaled - 25 cm mirrors to mm detector

    • Fields can be propagated through telescopes to actual detectors

LSC - Aug. 18, 2004


Thermal lensing in fft phil w calculated based on mit model

Thermal lensing in FFT- Phil W. calculated based on MIT model -

Optical thickness @ 1w

Ropt=1.7km

radius (m)

Sideband recycling gain

Power = 58mW

total heating (mW)

LSC - Aug. 18, 2004


Gaussian and annular

Gaussian and Annular

Piston subtracted

Optical thickness (10-6m)

LSC - Aug. 18, 2004


Beam splitter curvature

Beam splitter curvature

0.23 (cold) ~ 0 (hot)



ref

0.027

tra

-0.005

rayleigh length z0 = 3.6km, distance to waist z = -1km, RITM=-14km, RBS=-200km,

Beam curvature Rf(BS) = -14km, Rf(ITMy)= 1/(1/Rf(BS) -(n(ITMy)-1)/Rm)=-27km

LSC - Aug. 18, 2004


Itm differential heating vs beam splitter curvature

ITM differential heating vs beam splitter curvature

Power on ITMy

hot

hot

hot

U=0.1

L=7.5

U=-1.8

L=2.3

lower SB

E1

lower SB

E2

upper SB

upper SB

curved

hot

 in mrad

hot

cold

U=20

L=13

U=10

L=24

upper SB

lower SB

lower SB

upper SB

cold

flat

hot

LSC - Aug. 18, 2004


Gaussianity of cr sbs

Power only

thermal

Gaussianity of CR & SBs

Power on Symmetric port : log(power) vs x2

hot

hot

CR

x

lower

y

upper

+ +

flat

hot

curved

hot

5cm

hot

cold

flat

cold

flat

hot

LSC - Aug. 18, 2004


Sb gain vs gaussian heating with curved bs

SB gain vs Gaussian heating with curved BS

lower SB

upper SB

common heating

differential heating

ITMy 40mW

ITMy 60mW

Flat BS

(power ITMx, power ITMy)

powerX,Y for common heating

powerX for differential heating

LSC - Aug. 18, 2004


Sb gain vs annular heating

SB gain vs annular heating

Lower SB

Upper SB

Flat BS

60mW

Gaussian

On both

Recycling gain

ITMx annular heating

ITMy annular heating

200km BS

-200 mW

200 mW

LSC - Aug. 18, 2004


Fft vs lsc lock

FFT vs LSC lock

n(ITMx)-n(ITMy)

0.96-0.96

1.10-0.96

lower SB

upper SB

FFT lock

LSC lock

symmetric

SB becomes more

symmetric

differential

LSC - Aug. 18, 2004


Dark port sideband profile after lsc lock

Dark Port sideband profile- after LSC lock -

upper SB

200kBS curvature

With phase map

Symmetric heating

With phase map

Differential heating

No phase map

Symmetric heating

lower SB

LSC - Aug. 18, 2004


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