1. Effects of as-built Mirrors - analysis using FFT - Hiro Yamamoto, Biplab Bhawal, Xiao Xu, Raghu Dodda (SLU)  LIGO I mirror phase map  FFT tools  Thermal lensing  Beam splitter curvature

2. LSC - Aug. 18, 20042 Beam splitter phase map WA4K BS WA4K BS - curvature subtracted x 10 -8 nm concave ROC > 200km, convex ROC > 720km

3. LSC - Aug. 18, 20043 Smooth extrapolation from 15cm to 24cm WA4k BS after curvature subtracted 7.5cm -7.5cm Limited case study shows almost no difference 10nm

4. LSC - Aug. 18, 20044 Contrast Defect - Ugly but harmless CR from dark port - Mode matched, identical arms 5.5e-7 + as-built arms6.8e-5 + BS curvature1.2e-4 + Mirror phase maps2.3e-4 + Differential heating2.5e-4

5. LSC - Aug. 18, 20045 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)

6. LSC - Aug. 18, 20046 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

7. LSC - Aug. 18, 20047 Thermal lensing in FFT - Phil W. calculated based on MIT model - Ropt=1.7km Optical thickness @ 1w Sideband recycling gain radius (m) total heating (mW) Power = 58mW

8. LSC - Aug. 18, 20048 Gaussian and Annular Piston subtracted Optical thickness (10 -6 m)

9. LSC - Aug. 18, 20049 Beam splitter curvature    ref  tra 0.23 (cold) ~ 0 (hot) 0.027 -0.005 rayleigh length z 0 = 3.6km, distance to waist z = -1km, R ITM =-14km, R BS =-200km, Beam curvature R f (BS) = -14km, R f (ITMy)= 1/(1/R f (BS) -(n(ITMy)-1)/R m )=-27km

10. LSC - Aug. 18, 200410 ITM differential heating vs beam splitter curvature hot cold hot curved cold hotflat lower SB upper SB lower SB upper SB lower SB upper SB lower SB upper SB Power on ITMy  U =-1.8  L =2.3  U =0.1  L =7.5  U =10  L =24  U =20  L =13 E1 E2  in mrad

11. LSC - Aug. 18, 200411 Gaussianity of CR & SBs hot flat hot coldflat hot curved cold hotflat Power on Symmetric port : log(power) vs x 2 CR lower upper + x y 5cm

12. LSC - Aug. 18, 200412 SB gain vs Gaussian heating with curved BS powerX,Y for common heating powerX for differential heating lower SB upper SB (power ITMx, power ITMy) common heating differential heating ITMy 40mW ITMy 60mW Flat BS

13. LSC - Aug. 18, 200413 SB gain vs annular heating Recycling gain 60mW Gaussian On both Upper SB Lower SB Flat BS 200km BS ITMy annular heatingITMx annular heating 200 mW-200 mW

14. LSC - Aug. 18, 200414 FFT vs LSC lock lower SBupper SB FFT lockLSC lock FFTLSC  CR 0.3-1.9  SB+ -0.6-2.3  SB- 7.25.1 Spob-0.57i  CR 0.2-8  SB+ 4.9-1.2  SB- 11.85.1 Spob-0.48i-0.50i symmetric differential 0.96-0.961.10-0.96 n(ITMx)-n(ITMy) SB becomes more symmetric

15. LSC - Aug. 18, 200415 Dark Port sideband profile - after LSC lock - upper SB lower SB No phase map Symmetric heating With phase map Symmetric heating With phase map Differential heating 200k BS curvature