Effects of as-built Mirrors - analysis using FFT -

1. 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)

2. 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

3. 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

4. Contrast Defect- Ugly but harmless CR from dark port - LSC - Aug. 18, 2004

5. 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

6. 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

7. 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

8. Gaussian and Annular Piston subtracted Optical thickness (10-6m) LSC - Aug. 18, 2004

9. 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

10. 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

11. 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

12. 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

13. 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

14. 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

15. 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